Equations

221 Practice MCQs available for CA Foundation

Paper

Paper 3: Quantitative Aptitude

Exam Weightage

4-6 Marks

Key Topics

Linear, Quadratic and Cubic Equations

This chapter covers Linear, Quadratic and Cubic Equations and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

Exam Strategy Tip

This topic carries 4-6 Marks weightage. Focus on understanding core concepts rather than memorizing.

Key Terms

Integration

The reverse process of differentiation, used to find the area under a curve, accumulation of quantities, or to solve differential equations. Definite integration gives a numerical value; indefinite integration gives a function + constant C.

All 221 Questions

985
If 3x+y+2x−y=−1\displaystyle \frac{3}{x+y} + \frac{2}{x-y} = -1 and 1x+y−1x−y=43\displaystyle \frac{1}{x+y} - \frac{1}{x-y} = \frac{4}{3} then (x,y)\displaystyle (x, y) is:
MCQ
986
2x+510+3x+1015=5\displaystyle \frac{2x+5}{10} + \frac{3x+10}{15} = 5, find x\displaystyle x
MCQ
987
Find value of x2−10x+1\displaystyle x^2 - 10x + 1 if x=15−26\displaystyle x = \frac{1}{5-2\sqrt{6}}
MCQ
988
The cost of 2\displaystyle 2 oranges and 3\displaystyle 3 apples is 28\displaystyle 28. If the cost of an apple is doubled then the cost of 3\displaystyle 3 oranges and 5\displaystyle 5 apples is 75\displaystyle 75. The original cost of 7\displaystyle 7 oranges and 4\displaystyle 4 apples (in Rs) is:
MCQ
989
In a multiple choice question paper consisting of 100\displaystyle 100 questions of 1\displaystyle 1 mark each, a candidate gets 60%\displaystyle 60\% marks. If the candidate attempted all questions and there was a penalty of 0.25\displaystyle 0.25 marks for wrong answers is:
MCQ
990
The values of x\displaystyle x and y\displaystyle y satisfying the equations 3x+y+2x−y=3\displaystyle \frac{3}{x+y} + \frac{2}{x-y} = 3 and 2x+y+3x−y=233\displaystyle \frac{2}{x+y} + \frac{3}{x-y} = \frac{23}{3} given by
MCQ
991
A plumber can be paid either 600\displaystyle 600 and 50\displaystyle 50 per hour or 170\displaystyle 170 per hour. If the job takes 'n\displaystyle n' hour, for what value of 'n\displaystyle n' the second method earns better wages for the plumber?
MCQ
992
The solution of the following system of linear eqs. 2x−5y+4=0\displaystyle 2x - 5y + 4 = 0 and 2x+y−8=0\displaystyle 2x + y - 8 = 0 will be:
MCQ
993
The solution of the linear simultaneous equations 2x−y=4\displaystyle 2x - y = 4 and 3x+4y=17\displaystyle 3x + 4y = 17 is
MCQ
994
A person purchased 2\displaystyle 2 apples and 5\displaystyle 5 bananas at the cost of 90\displaystyle 90. Later he visited to another shop where shopkeeper told him that if you give me 50\displaystyle 50 and one banana, I can give you 3\displaystyle 3 apples. He agreed to the deal. What is the cost of one apple and one banana?
MCQ
995
In the above table corresponding values of two variable x\displaystyle x and y\displaystyle y have been given. Which of the following equations establishes the relationship between the two variables?x5678y11131517\displaystyle \begin{array}{|c|c|c|c|c|}\hline x & 5 & 6 & 7 & 8 \\ \hline y & 11 & 13 & 15 & 17 \\ \hline \end{array}
MCQ
996
If 2x−3y=1\displaystyle 2x - 3y = 1 and 5x+2y=50\displaystyle 5x + 2y = 50, then what is the value of (x−2y)\displaystyle (x-2y)?
MCQ
997
If xy+yz+zx=−1\displaystyle xy + yz + zx = -1, then the value of x+y1+xy+y+z1+yz+z+x1+zx\displaystyle \frac{x+y}{1+xy} + \frac{y+z}{1+yz} + \frac{z+x}{1+zx} is
MCQ
998
The value of 'k' for system of equations kx+2y=5\displaystyle kx+2y = 5 and 3x+y=1\displaystyle 3x+y = 1 has no solution is
MCQ
999
The cab bill is partly fixed and partly varies on the distance covered. For 456\displaystyle 456 km the bill is 8252\displaystyle 8252, for 484\displaystyle 484 km the bill is Rs. 8728\displaystyle 8728. What will the bill be for 500\displaystyle 500km?
MCQ
1000
The point of intersection between the lines 3x+4y=7\displaystyle 3x+4y = 7 and 4x−y=3\displaystyle 4x-y = 3 lie in the
MCQ
1001
If 125=1+x144\displaystyle \sqrt{\frac{1}{25}} = 1 + \frac{x}{144}, then x\displaystyle x is
MCQ
1002
2x+5+3x+1015=5\displaystyle 2x + 5 + \frac{3x+10}{15} = 5, then the value of x\displaystyle x
MCQ
1003
Solve for x,y\displaystyle x, y and z\displaystyle z.xyx+y=210\displaystyle \frac{xy}{x+y} = 210, yzy+z=140\displaystyle \frac{yz}{y+z} = 140, xzx+z=120\displaystyle \frac{xz}{x+z} = 120
MCQ
1004
If x+5+x−16=7x+5−x−16\displaystyle \sqrt{x+5} + \sqrt{x-16} = \frac{7}{\sqrt{x+5} - \sqrt{x-16}} then x\displaystyle x equals
MCQ
1005
If 2x+y=2x−y=8\displaystyle 2^{x+y} = 2^{x-y} = \sqrt{8}, then the value of x\displaystyle x and y\displaystyle y is
MCQ
1006
If the sides of an equilateral triangle are shortened by 3 units, 4 units and 5 units respectively and a right triangle is formed then the side of an equilateral triangle is:

Chapter 2 Diagram
MCQ
1007
A number consist of two digits such that the digit in one's place in thrice the digit in ten's place. If 36 be added then the digits are reversed. Find the number ____.

Chapter 2 Diagram
MCQ
1008
If a person has cloth of total 91 cm. If he divides it into 3 parts then longest part is twice the shortest one and another part is 3 cm more than shortest one. What is the shortest one?

Chapter 2 Diagram
MCQ
1009
If the cost of 3 bags and 4 pens is 257\displaystyle 257 whereas the cost of 4 bags and 3 pens is 324\displaystyle 324, then the cost of one bag is:

Chapter 2 Diagram
MCQ
1010
The largest side of a triangle is 3 times the shortest side and third side is 4 cm shorter then largest side. If the perimeter of the triangle is at least 59 cm, what is the length of shortest side?

Chapter 2 Diagram
MCQ
1011
The age of a man is four times the sum of the ages of his two sons and after 10 years, his age will be double the sum of their ages. The present age of the man must be

Chapter 2 Diagram
MCQ
1012
Divide 27 into two parts, so that 5 times the first and 11 times the second together equal to 195, then the ratio of first and second part is:

Chapter 2 Diagram
MCQ
1013
A number consist of two digits. The digits in the ten's place is 3 times the digit in the unit's place. If 54 is subtracted from the number, then the digits are reversed. The number is:

Chapter 2 Diagram
MCQ
1014
A number consist of two digits. The digits in tens place is 3 times the digit in the unit's place. If 54 is subtracted from the digits are reversed. The number is

Chapter 2 Diagram
MCQ
1015
A number consist of three digit of which the middle one is zero and the sum of other digits is 9. The number formed by interchanging the first and third digits is more than the original number by 297 find the number?

Chapter 2 Diagram
MCQ
1016
The age of a person is twice the sum of the ages of his two sons and 5 years ago his age was thrice the sum of their ages. Find present age.

Chapter 2 Diagram
MCQ
1017
Ten years ago the age of a father was four times his son. Ten years hence the age of the father will be twice that of his son. The present age of the father and the son are

Chapter 2 Diagram
MCQ
1018
3 Chairs and 3 tables cost 370\displaystyle 370. What is the cost of the table and two chairs?

Chapter 2 Diagram
MCQ
1019
If thrice of A's age 6 years ago be subtracted from twice his present age, the result would be equal to his present age. Find A's Age

Chapter 2 Diagram
MCQ
1020
The sum of two numbers is 62 and their product is 960. The sum of their reciprocals is

Chapter 2 Diagram
MCQ
1021
Three persons Mr. Roy, Mr. Paul and Mr. Singh together have 51\displaystyle 51. Mr. Paul has 4\displaystyle 4 less than Mr. Roy and Mr. Singh has 5\displaystyle 5 less than Mr. Roy. They have the money as:

Chapter 2 Diagram
MCQ
1022
The wages of 8 men and 6 boys amount to 33\displaystyle 33. If 4 men earn 4.50\displaystyle 4.50 more than 5 boys determine the wages of each man and boy

Chapter 2 Diagram
MCQ
1023
The cost of 5 mangoes is equal to the cost of 20 oranges. If the total cost 2 mangoes and 10 oranges is 22.50\displaystyle 22.50, find the cost of two oranges.

Chapter 2 Diagram
MCQ
1024
A man sells 6 radios and 4 televisions for 18,480\displaystyle 18,480. If 14 radios and 2 televisions are sold for the same. What is the price of radio?

Chapter 2 Diagram
MCQ
1025
On the average an experienced person does 7 units of work while a fresh one work 5 units of work daily but the employer has to maintain an output of atleast 35 units of work per day. The situation can be expressed as:

Chapter 2 Diagram
MCQ
1026
X and Y have their present ages in the ratio 6:7\displaystyle 6:7. 14 years ago, the ratio of the ages of the two was 1:5\displaystyle 1:5. What will be the ratio of their ages 21 years from now?

Chapter 2 Diagram
MCQ
1027
A man wants to cut three lengths from a single piece of board of length 91 cm. The second length is to be 3 cm longer than the shortest and third length is to be twice as the shortest. What is the possible length for the shortest piece?

Chapter 2 Diagram
MCQ
1028
If thrice of A's age 6 years ago be subtracted from twice his present age, the result would be equal to his present age. Find A's present age.

Chapter 2 Diagram
MCQ
1029
The cost prices of 3 pens and 4 bags is 324\displaystyle 324, and 4 pens and 3 bags is 257\displaystyle 257, then cost price of 1 pen is equal to

Chapter 2 Diagram
MCQ
1030
In a hostel ration stocked for 400 students upto 31 days. After 28 days 280 students were vacated the hostel. Find the number of days for which the remaining ration will be sufficient for the remaining students.
MCQ
1031
The sum of the two numbers is 80 and the sum of their squares is 34. Taking one number as x\displaystyle x from an equation in x\displaystyle x and hence find the numbers. The numbers are:
MCQ
1032
The value of y\displaystyle y of fraction xy\displaystyle \frac{x}{y} exceeds with x\displaystyle x by 5 and if 3 be added to both the fraction becomes 32\displaystyle \frac{3}{2}. Find the fraction.
MCQ
1033
If difference between a number and its positive square root is 12, the numbers are
MCQ
1034
4 tables and 3 chairs together cost 2,250\displaystyle 2,250 and 3 tables and 4 chairs cost 1,950\displaystyle 1,950. Find the cost of 2 chairs and 1 table.
MCQ
1035
The ages of two persons are in the ratio 5:7\displaystyle 5:7. Eighteen years ago their ages were in the ratio of 8:13\displaystyle 8:13, their present ages (in years) are:
MCQ
1036
A box contains 56\displaystyle 56 in the form of coins of one rupee, 50 paise and 25 paise. The number of 50 paise coin is double the number of 25 paise coins and four times the numbers of one rupee coins. The numbers of 50 paise coins in the box is
MCQ
1037
Find the positive value of k\displaystyle k for which the equations: x2+kx+64=0\displaystyle x^2 + kx + 64 = 0 & x2−8x+k=0\displaystyle x^2 - 8x + k = 0 will have real roots:
MCQ
1038
The sum of two numbers is 75 and their difference is 20. Find the difference of their squares.
MCQ
1039
A number consists of two digits. The digits in tens place is 3 times the digit in the unit's place. If 54 is subtracted from the digits are reversed. The number is
MCQ
1040
4 tables and 3 chairs, together, cost 2,250\displaystyle 2,250 and 3 tables and 4 chairs cost 1,950\displaystyle 1,950. Find the cost of 2 chairs and 1 table.
MCQ
1041
Aman walks a certain distance with certain speed. If he walks 12\displaystyle \frac{1}{2} km an hour faster, he takes 1 hour less. But, if he walks 1 km an hour slower, he takes 3 more hours. Find the distance covered by the man and his original rate of walking:
MCQ
1042
If 2x2−(a+6)x+12a=0\displaystyle 2x^2 - (a+6)x + 12a = 0, then the roots are:
MCQ
1043
Solving equation m+1m=625\displaystyle m + \frac{1}{m} = \frac{6}{25}, the value of m\displaystyle m works out to:
MCQ
1044
The value of p\displaystyle p for which the difference between the root of equation x2+px+8=0\displaystyle x^2 + px + 8 = 0 is 2
MCQ
1045
If the quadratic equation x2+px+q=0\displaystyle x^2 + px + q = 0 and x2+p′x+q′=0\displaystyle x^2 + p'x + q' = 0 have a common root then p+q′\displaystyle p + q'?
MCQ
1046
The harmonic mean of the roots of the equation (5+2)x2−(4+5)x+8+25=0\displaystyle (5 + \sqrt{2})x^2 - (4 + \sqrt{5})x + 8 + 2\sqrt{5} = 0 is
MCQ
1048
The sum of square of any real positive quantity and its reciprocal is never less than:
MCQ
1049
If one root is half of the other of a quadratic equation and the difference in roots is a\displaystyle a, then the equation is
MCQ
1050
If α+β=−2\displaystyle \alpha + \beta = -2 and αβ=−3\displaystyle \alpha\beta = -3, then α,β\displaystyle \alpha, \beta are the roots of the equation, which is:
MCQ
1051
If α,β\displaystyle \alpha, \beta are the roots of the equation x2+x+5=0\displaystyle x^2 + x + 5 = 0 then αβ+βα\displaystyle \frac{\alpha}{\beta} + \frac{\beta}{\alpha} is equal to
MCQ
1052
Let α\displaystyle \alpha and β\displaystyle \beta be the roots of x2+7x+12=0\displaystyle x^2 + 7x + 12 = 0. Then the value of (αβ+βα)\displaystyle (\frac{\alpha}{\beta} + \frac{\beta}{\alpha}) will be:
MCQ
1053
When two roots of QE are a,1a\displaystyle a, \frac{1}{a} then what will be the quadratic equation?
MCQ
1054
Find the condition that one roots is double the other of ax2+bx+c=0\displaystyle ax^2 + bx + c = 0
MCQ
1055
Find the value of K\displaystyle K in 3x2−2kx+5=0\displaystyle 3x^2 - 2kx + 5 = 0 if x=2\displaystyle x = 2
MCQ
1056
The rational root of the equation 0=2p3−p2−4p+2\displaystyle 0 = 2p^3 - p^2 - 4p + 2 is:
MCQ
1057
If the square of a number exceeds twice of the number by 15\displaystyle 15, then number that satisfies the condition is
MCQ
1058
If the second root of the given equation is reciprocal of first root then value of 'K' in the equation 5x2−13x+K=0\displaystyle 5x^2 - 13x + K = 0
MCQ
1059
If the roots of the equation x2−px+q=0\displaystyle x^2 - px + q = 0 are in the ratio 2:3\displaystyle 2:3, then:
MCQ
1060
What will be the value of k\displaystyle k, if the roots of the equation (k−4)x2−2kx+(k+5)=0\displaystyle (k-4)x^2 - 2kx + (k+5) = 0 are equal?
MCQ
1061
If α\displaystyle \alpha and β\displaystyle \beta are roots of the quadratic equation x2−2x−3=0\displaystyle x^2 - 2x - 3 = 0 then the equation whose roots are α+β\displaystyle \alpha + \beta and α−β\displaystyle \alpha - \beta is:
MCQ
1062
If α\displaystyle \alpha and β\displaystyle \beta are roots of the equation x2−(n2+1)x+12(n2+n4+1)=0\displaystyle x^2 - (n^2+1)x + \frac{1}{2}(n^2+n^4+1) = 0 then the value of α2+β2\displaystyle \alpha^2 + \beta^2 is:
MCQ
1063
If α,β\displaystyle \alpha, \beta are the roots of the equation x2−4x+1=0\displaystyle x^2 - 4x + 1 = 0, then value of α3+β3\displaystyle \alpha^3 + \beta^3 will be
MCQ
1064
If α\displaystyle \alpha and β\displaystyle \beta are roots of the equation ax2+bx+c=0\displaystyle ax^2 + bx + c = 0 then the equation whose roots are 1\displaystyle 1 and 1β\displaystyle \frac{1}{\beta} is:
MCQ
1065
If α\displaystyle \alpha and β\displaystyle \beta are roots of the equation x2−8x+12=0\displaystyle x^2 - 8x + 12 = 0 then 1α+1β=\displaystyle \frac{1}{\alpha} + \frac{1}{\beta} =
MCQ
1066
The roots of the equation x2−7x+10=0\displaystyle x^2 - 7x + 10 = 0 are:
MCQ
1067
If one of the root of the equation x2−3x+k=0\displaystyle x^2 - 3x + k = 0 is 1\displaystyle 1 then the value of k\displaystyle k is
MCQ
1068
When two roots of quadratic equations are α\displaystyle \alpha and 1α\displaystyle \frac{1}{\alpha} then what will be quadratic equation.
MCQ
1069
If α\displaystyle \alpha and β\displaystyle \beta be the roots of the equation 2x2−4x−3=0\displaystyle 2x^2 - 4x - 3 = 0 the value of α2+β2\displaystyle \alpha^2 + \beta^2 is
MCQ
1070
If one of the root of the equation x2+7x+p=0\displaystyle x^2 + 7x + p = 0 be reciprocal of the other, then the value of p\displaystyle p is_
MCQ
1071
If one root of the quadratic equation is 2+3\displaystyle 2 + \sqrt{3}, the equation is _____.
MCQ
1072
The roots of the quadratic equation x2−4x+k=0\displaystyle x^2 - 4x + k = 0 are coincident if
MCQ
1073
The roots of the equation x2+(2p−1)x+p2=0\displaystyle x^2 + (2p-1)x + p^2 = 0 are real if
MCQ
1074
The roots of the quadratic equation 9x2+3kx+4=0\displaystyle 9x^2 + 3kx + 4 = 0 are equal if
MCQ
1075
If one root of a equation is 2+5\displaystyle 2 + \sqrt{5}, then the quadratic equation is
MCQ
1076
If one root of the equation x2−3x+k=0\displaystyle x^2 - 3x + k = 0 is 2\displaystyle 2, then the value of k\displaystyle k will be
MCQ
1077
If arithmetic mean between roots of a quadratic equation is 8\displaystyle 8 and the geometric mean between them is 5\displaystyle 5, the equation is
MCQ
1078
Roots of the equation 3x2−14x+k=0\displaystyle 3x^2 - 14x + k = 0 will be reciprocal of each other if:
MCQ
1079
The equation 3x2+mx+n=0\displaystyle 3x^2 + mx + n = 0 has roots that are double that of equation x2+10x+12=0\displaystyle x^2 + 10x + 12 = 0. What is the value of m+n\displaystyle m + n?
MCQ
1080
If α,β\displaystyle \alpha, \beta are the roots of equation x2+7x+12=0\displaystyle x^2 + 7x + 12 = 0 then the equation whose roots (α+β)2\displaystyle (\alpha + \beta)^2 and (α−β)2\displaystyle (\alpha - \beta)^2 will be
MCQ
1081
The equation x2−(p+4)x+2p+5=0\displaystyle x^2 - (p+4)x + 2p + 5 = 0 has equal roots. The value of p\displaystyle p is
MCQ
1082
Let α,β\displaystyle \alpha, \beta be the roots of equation x2+7x+12=0\displaystyle x^2 + 7x + 12 = 0 then the value of (α2β+β2α)\displaystyle \left(\frac{\alpha^2}{\beta} + \frac{\beta^2}{\alpha}\right) will be
MCQ
1083
Given the Quadratic Equation x+1x−1+x−2x+2=31\displaystyle \frac{x+1}{x-1} + \frac{x-2}{x+2} = \frac{3}{1}.
MCQ
1084
The roots of equation 9x2−6.3x+1=0\displaystyle 9x^2 - 6.3x + 1 = 0 are
MCQ
1085
The roots of the equation x2−x+1=0\displaystyle x^2 - x + 1 = 0 are
MCQ
1086
If one root of the QE is 2+3\displaystyle 2 + \sqrt{3}, the equation is
MCQ
1087
If α\displaystyle \alpha and β\displaystyle \beta are the roots of the equation x2+7x+12=0\displaystyle x^2 + 7x + 12 = 0, then the equation whose roots are (α+β)2\displaystyle (\alpha + \beta)^2 and (α−β)2\displaystyle (\alpha - \beta)^2 will be:
MCQ
1088
Roots of the equation 2x2+3x+7=0\displaystyle 2x^2 + 3x + 7 = 0 are α\displaystyle \alpha and β\displaystyle \beta then the value of α−1+β−1\displaystyle \alpha^{-1} + \beta^{-1} is
MCQ
1089
If the ratio of the roots of the equation 4x2−6x+p=0\displaystyle 4x^2 - 6x + p = 0 is 1:2\displaystyle 1:2, then the value of p\displaystyle p is:
MCQ
1090
If roots of equation x2+x+r=0\displaystyle x^2 + x + r = 0 are α\displaystyle \alpha and β\displaystyle \beta and α3+β3=−6\displaystyle \alpha^3 + \beta^3 = -6. Find the value of 'r'
MCQ
1091
If one root is 5z2+13z+y=0\displaystyle 5z^2 + 13z + y = 0 is reciprocal of the other, then the value of y\displaystyle y is
MCQ
1092
Find value of x2−10x+1\displaystyle x^2 - 10x + 1, if x=15−26\displaystyle x = \frac{1}{5 - 2\sqrt{6}}
MCQ
1093
Find the value of k\displaystyle k in 3x2−2kx+5=0\displaystyle 3x^2 - 2kx + 5 = 0 if x=2\displaystyle x = 2.
MCQ
1094
If one root of the quadratic equation is 2−3\displaystyle 2 - \sqrt{3} from the equation, except that the roots are irrational. Then find the Quadratic equation.
MCQ
1095
If the roots of (K−4)x2−2Kx+(K+5)=0\displaystyle (K-4)x^2 - 2Kx + (K+5) = 0 are coincident. Then the value of K\displaystyle K?
MCQ
1096
If x=31/3+3−1/3\displaystyle x = 3^{1/3} + 3^{-1/3} and y=31/3−3−1/3\displaystyle y = 3^{1/3} - 3^{-1/3} then the value (3x2+y2)2\displaystyle (3x^2 + y^2)^2 will be
MCQ
1098
If arithmetic mean between roots of a quadratic equation is 8\displaystyle 8 and the geometric mean between them is 5\displaystyle 5, the equation is _______.
MCQ
1099
The value of 6+6+6+......∞\displaystyle \sqrt{6 + \sqrt{6 + \sqrt{6 + ...... \infty}}}
MCQ
1100
One root of the eq. x2−(2+5m)x+3(7+m)=0\displaystyle x^2 - (2 + 5m)x + 3(7 + m) = 0 is reciprocal of the other. Find the value of m\displaystyle m.
MCQ
1101
The equation x2−(p+4)x+2p+5=0\displaystyle x^2 - (p + 4)x + 2p + 5 = 0 has equal roots. The value of p\displaystyle p is
MCQ
1102
If α\displaystyle \alpha and β\displaystyle \beta are roots of the equation x2−8x+12=0\displaystyle x^2 - 8x + 12 = 0 then 1/α+1/β=\displaystyle 1/\alpha + 1/\beta =
MCQ
1104
If α\displaystyle \alpha and β\displaystyle \beta are the roots of the equation x2+7x+12=0\displaystyle x^2 + 7x + 12 = 0, then the equation whose roots (α+β)2\displaystyle (\alpha + \beta)^2 and (α−β)2\displaystyle (\alpha - \beta)^2 will be:
MCQ
1105
Roots of the quadratic equation x3+9x2−x−9=0\displaystyle x^3 + 9x^2 - x - 9 = 0.
MCQ
1106
The value of 'k' is ______, if 2\displaystyle 2 is the root of the following cubic equation: x3−(k+1)x+k=0\displaystyle x^3 - (k+1)x + k = 0
MCQ
1107
Solve x3−7x+6=0\displaystyle x^3 - 7x + 6 = 0
MCQ
1108
The sol. of cubic eq. x3−23x2+142x−120=0\displaystyle x^3 - 23x^2 + 142x - 120 = 0 is given by the triplet:
MCQ
1109
The roots of the equation x3+x2−x−1=0\displaystyle x^3 + x^2 - x - 1 = 0 are
MCQ
1110
The equation x3−3x2−4x+12=0\displaystyle x^3 - 3x^2 - 4x + 12 = 0 has three real roots. They are:
MCQ
1111
If one of the root of the cubic equation 3x3−5x2−11x−3=0\displaystyle 3x^3 - 5x^2 - 11x - 3 = 0 is 13\displaystyle \frac{1}{3}, then other two roots are:
MCQ
1112
The equation x3−3x2−4x+12=0\displaystyle x^3 - 3x^2 - 4x + 12 = 0 has three real roots, they are:
MCQ
1114
If x=51/3+5−1/3\displaystyle x = 5^{1/3} + 5^{-1/3}, then 5x3−15x\displaystyle 5x^3 - 15x is given by
MCQ
1115
(x+4)\displaystyle (x+4) is a factor of x3+4x2−x−bx+24\displaystyle x^3 + 4x^2 - x - bx + 24. Also, a+b=29\displaystyle a+b = 29. Find the value of b\displaystyle b.
MCQ
1116
Roots of the equation x3+2x2−x−2=0\displaystyle x^3 + 2x^2 - x - 2 = 0:
MCQ
1117
The roots of the cubic eq. x3−7x+6=0\displaystyle x^3 - 7x + 6 = 0 are:
MCQ
4004
If ₹ 58 is divided among 150 children such that each girl and each boy gets 25 p and 50 p respectively. Then how many girls are there?
MCQ
4005
Puru gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Ishu gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross?
MCQ
4006
The quadratic equation 2x2−5x+1=0\displaystyle 2x^2 - \sqrt{5}x + 1 = 0 has
MCQ
4007
For equation x3−6x2+5x+12=0\displaystyle x^3 - 6x^2 + 5x + 12 = 0, the product of two roots is 12. Which of the following is correct set of roots of the equation?
MCQ
4104
If α\displaystyle \alpha and β\displaystyle \beta are the roots of the equation x2−x−6=0\displaystyle x^2-x-6=0, then the value of α3+β3+α2+β2+α+β\displaystyle \alpha^3+\beta^3+\alpha^2+\beta^2+\alpha+\beta is equal to
MCQ
4105
The roots of the equation (xx−1)2−5(xx−1)+6=0\displaystyle \left(\frac{x}{x-1}\right)^2 - 5\left(\frac{x}{x-1}\right) + 6 = 0 are:
MCQ
4106
If α\displaystyle \alpha and β\displaystyle \beta are the roots of the equation 2x2−6x+3=0\displaystyle 2x^2-6x+3=0, then the equation with the roots αβ\displaystyle \frac{\alpha}{\beta} and βα\displaystyle \frac{\beta}{\alpha} is
MCQ
4200
If 2x+3y=34\displaystyle 2x + 3y = 34 and x+yy=138\displaystyle \frac{x+y}{y} = \frac{13}{8}, find the value of 7x+5y\displaystyle 7x + 5y.
MCQ
4202
The value of is 5+5+5+…∞\displaystyle \sqrt{5+\sqrt{5+\sqrt{5+\dots\infty}}} is
MCQ
4250
If α\displaystyle \alpha and β\displaystyle \beta are the roots of the equation 2x2−3x+1=0\displaystyle 2x^2 -3x + 1 = 0 then the equation whose roots are 1/α\displaystyle 1/\alpha and 1/β\displaystyle 1/\beta is:
MCQ
4251
One year ago, the ratio of ages (in years) of A and B was 5:4. The ratio of their ages, 4 years from now, will be 6:5. What will be the age of A (in years) after 10 years from now?
MCQ
1113
If α,β\displaystyle \alpha, \beta are the roots of equation x2−4x+5=0\displaystyle x^2 - 4x + 5 = 0 then the equation having roots 1α\displaystyle \frac{1}{\alpha} & 1β\displaystyle \frac{1}{\beta} is
MCQ
1047
If α\displaystyle \alpha and β\displaystyle \beta are the roots of the equation 2x2+5x+k=0\displaystyle 2x^2 + 5x + k = 0, and 4(α2+β2)+αβ=23\displaystyle 4(\alpha^2 + \beta^2) + \alpha\beta = 23, then which of the following is true?
MCQ
1097
If the ratio of the roots of the Equation 4x2−6x+p=0\displaystyle 4x^2 - 6x + p = 0 is 1:2\displaystyle 1:2. Then the value of p\displaystyle p is:
MCQ
1103
If α,β\displaystyle \alpha, \beta are the roots of the QE 3x2−4x+1=0\displaystyle 3x^2 - 4x + 1 = 0, the eq. having roots α2β\displaystyle \frac{\alpha^2}{\beta} and β2α\displaystyle \frac{\beta^2}{\alpha} is:
MCQ
4304
If ₹ 58 is divided among 150 children such that each girl and each boy gets 25 p and 50 p respectively. Then how many girls are there?
MCQ
4305
Puru gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Ishu gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross?
MCQ
4306
The quadratic equation 2x2−5x+1=0\displaystyle 2x^2 - \sqrt{5}x + 1 = 0 has
MCQ
4307
For equation x3−6x2+5x+12=0\displaystyle x^3 - 6x^2 + 5x + 12 = 0, the product of two roots is 12. Which of the following is correct set of roots of the equation?
MCQ
4404
If α\displaystyle \alpha and β\displaystyle \beta are the roots of the equation x2−x−6=0\displaystyle x^2-x-6=0, then the value of α3+β3+α2+β2+α+β\displaystyle \alpha^3+\beta^3+\alpha^2+\beta^2+\alpha+\beta is equal to
MCQ
4405
The roots of the equation (xx−1)2−5(xx−1)+6=0\displaystyle \left(\frac{x}{x-1}\right)^2 - 5\left(\frac{x}{x-1}\right) + 6 = 0 are:
MCQ
4406
If α\displaystyle \alpha and β\displaystyle \beta are the roots of the equation 2x2−6x+3=0\displaystyle 2x^2-6x+3=0, then the equation with the roots αβ\displaystyle \frac{\alpha}{\beta} and βα\displaystyle \frac{\beta}{\alpha} is
MCQ
4500
If 2x+3y=34\displaystyle 2x + 3y = 34 and x+yy=138\displaystyle \frac{x+y}{y} = \frac{13}{8}, find the value of 7x+5y\displaystyle 7x + 5y.
MCQ
4502
The value of is 5+5+5+…∞\displaystyle \sqrt{5+\sqrt{5+\sqrt{5+\dots\infty}}} is
MCQ
4550
If α\displaystyle \alpha and β\displaystyle \beta are the roots of the equation 2x2−3x+1=0\displaystyle 2x^2 -3x + 1 = 0 then the equation whose roots are 1/α\displaystyle 1/\alpha and 1/β\displaystyle 1/\beta is:
MCQ
4551
One year ago, the ratio of ages (in years) of A and B was 5:4. The ratio of their ages, 4 years from now, will be 6:5. What will be the age of A (in years) after 10 years from now?
MCQ
5352
1. To whom should have Mr. Rohan informed about his resignation? What could be the possible consequence for his non-compliance?
MCQ
5353
2. Based on the shareholding pattern of JK Logistics Ltd. and RK Logistics Ltd., select the correct answer as to the classification of these companies:
MCQ
5354
3. With respect to the act carried out by Mr. Avinash, the partner of the new audit firm, what can you infer about the appointment of AG & Associates, as auditors of JK Logistics Ltd.?
MCQ
5355
4. What is the course of action that XYZ Limited should take for filing of the financial statements with the Registrar with respect to the annual general meeting which could not be held on 5th September, 2024?
MCQ
5356
5. What is the course of action that XYZ Limited should take for filing of the financial statements with the Registrar with respect to the adjourned annual general meeting held on 12thSeptember, 2024?
MCQ
5357
6. What is the course of action that XYZ Limited should take for filing of the financial statements with the Registrar with respect to the extra ordinary general meeting held on 2nd December, 2024?
MCQ
5358
7. In the above case scenario, in case XYZ Limited could not convene the annual general meeting till 2nd December, 2024 and the meeting held on that date was the annual general meeting, what will be the obligation of the company with regard to filing of the financial statements with the Registrar, before conducting the said meeting?
MCQ
5359
8. The Board of Directors of NCL wants to understand from Nirad the implications of 5% holding of BCPL.
MCQ
5360
9. Yogesh, one of the shareholders deposits in advance the remaining amount due on his shares without any calls made by NCL. NCL declared dividend during the year.
MCQ
5361
10. With reference to the Board identified select group of 50 persons and issued private placement offer and applications duly following the required procedure under the corporate laws.
MCQ
5362
11. Considering the provisions of the FEMA, 1999 decide upon the maximum amount of commission that can be paid to Mr. Cooper as well as Consultancy charges to Accurate Consultants Ltd. for which approval of RBI would not be required under the above Act.
MCQ
5363
12. Considering the provisions of the FEMA, 1999 decide upon the process of releasing the containers from Italian ports by the Indian company.
MCQ
5364
13. Considering the provisions of the FEMA, 1999 the possible suggestion that can be given by the legal team regarding investment of USD 260,000 by Mr. Tony in the Rishikesh farmhouse project.
MCQ
5365
14. Where after a partner's death the business is continued in the same Limited Liability Partnership name, the continued use of that name or of the deceased partner's name as a part thereof:
MCQ
5366
15. The General Clauses Act, 1897 is applicable to:
MCQ
5367
2022. The prospectus specified that the amount received from the issue will be exclusively used for manufacturing and distributing some life-saving drugs. In August 2024, the company after proper market survey found that there is ample demand for Artificial Intelligence based software and therefore decided to go forward for development of such type of software. They also wanted to divert a small amount for investment in the equity shares of a large successful company. Since there was surplus money from the above issue of equity shares, the Board of Directors passed two resolutions for the above purpose; the first for investing ` 60,00,000 for development of Artificial Intelligence based software and the second for investing ` 5,00,000 in the Equity Shares in X Limited, which is a listed company. In order to avoid any unwarranted situation from the shareholders, the Directors called for an extra ordinary general meeting in which votes cast in favour of the proposal was in excess of the votes cast against it. Some shareholders objected to the above action of the Board on the following grounds: (i) that the resolution passed in the extra-ordinary general meeting was not proper since the required majority did not approve the same; (ii) that the prescribed details of the notice which was given to the shareholders should also have been published in newspapers (one in English and one in vernacular language), circulating in the city where the registered office of the company is situated indicating clearly the justification for such variation in the use of the funds; and (iii) that the resolution passed for investing 5,00,000 in the Equity Shares in X Limited is illegal. CORPORATE AND OTHER LAWS Referring to the applicable provisions of the Companies Act, 2013, decide, whether the contentions of the shareholders are tenable.
MCQ
5368
2. For the purpose of, or in connection with, a purchase or subscription made or to be made, by any person of or for any shares in the company or in its holding company. As per section 67(3) of the Act, a company may provide the financial assistance, in case of lending money by a company to its employees (other than its directors or key managerial personnel), not exceeding six-month salary of the employees to enable them to buy or subscribe fully paid shares in the company or its holding company and to hold them by way of beneficial ownership. In the given question, Silk Segment Private Ltd. (SSPL) is a wholly owned subsidiary of Silk Block Ltd. (SBL). Thus, SSPL will also be deemed as a public company [by virtue of Section 2(71)]. Hence, considering the above provisions we can answer the following to the questions asked: (i) Mr. Sohan is the Deputy Marketing Manager of SSPL; hence loan may be provided to him upto the limit of his 6 months’ salary i.e. ` 6,00,000. Thus, proposal to grant loan of ` 15,00,000 to Mr. Sohan for purchase of shares in SBL is not valid. Ms. Subarna is a KMP (being the Chief Financial Officer of SSPL), hence, proposal to grant loan to her for purchase of shares in SBL is not valid. (ii) Section 67 of the Act shall not apply to private companies in whose share capital no other body corporate has invested any money. In case where Silk Block Ltd. (SBL) held only 25% shares of Silk Segment Private Ltd. (SSPL), the latter would not be termed as a subsidiary of the former and hence would not be a deemed public company. It will still be regarded as a private limited company. Further, SBL is holding shares in SSPL, thus SSPL will not fall in the exempted class of private companies and accordingly, the provision of section 67(3) of the Companies Act, 2013 shall apply. In view of the above provisions, the answer would remain the same in case only 25% shares of SSPL are held by SBL. (b) Exemption to certain Private Companies: Notification No. GSR 464 (E) dated 5th June 2015, provided certain exemptions to Private Limited Companies relaxing the provisions of the Companies Act 2013 with respect to certain restrictions for acceptance of deposits. The restrictions specified in the clauses (a) to (e) of sub-section (2) of section 73 with respect to certain restrictions for acceptance of deposits like issue of circular, filing the copy of such circular with the Registrar, CORPORATE AND OTHER LAWS depositing of certain amount and certification as to no default committed shall not apply to a private company. They are as follows:
MCQ
5369
Question 1 (a) 1,00,000 Equity shares of ` 100 each were issued at a premium of ` 2 per share by PQR Limited after offer for the same was received from the shareholders in terms of the prospectus issued by the company on 1st April, 2022. The prospectus specified that the amount received from the issue will be exclusively used for manufacturing and distributing some life-saving drugs. In August 2024, the company after proper market survey found that there is ample demand for Artificial Intelligence based software and therefore decided to go forward for development of such type of software. They also wanted to divert a small amount for investment in the equity shares of a large successful company. Since there was surplus money from the above issue of equity shares, the Board of Directors passed two resolutions for the above purpose; the first for investing ` 60,00,000 for development of Artificial Intelligence based software and the second for investing ` 5,00,000 in the Equity Shares in X Limited, which is a listed company. In order to avoid any unwarranted situation from the shareholders, the Directors called for an extra ordinary general meeting in which votes cast in favour of the proposal was in excess of the votes cast against it. Some shareholders objected to the above action of the Board on the following grounds: (i) that the resolution passed in the extra-ordinary general meeting was not proper since the required majority did not approve the same; (ii) that the prescribed details of the notice which was given to the shareholders should also have been published in newspapers (one in English and one in vernacular language), circulating in the city where the registered office of the company is situated indicating clearly the justification for such variation in the use of the funds; and (iii) that the resolution passed for investing 5,00,000 in the Equity Shares in X Limited is illegal. CORPORATE AND OTHER LAWS Referring to the applicable provisions of the Companies Act, 2013, decide, whether the contentions of the shareholders are tenable. (b) Sohan Lal was appointed as the statutory auditor of RST Ltd., a non- government company at the Annual General Meeting held on 30th September, 2023. He has resigned after two months as he wanted to discontinue the practice and surrendered his Certificate of Practice and joined a multinational company. Explain how the new auditor will be appointed by RST Ltd. and the conditions to be complied with in this regard. (c) Murari Lal, a person resident outside India, has invested in four residential immovable properties under construction in Kolkata. Each property is negotiated at ` 2 crore, with the companies owned by builders. This amount is to be paid in two instalments as 60% on immediate basis on booking and the balance on possession of the properties. The above transaction is done by the companies owned by builders through two brokers from USA on commission basis. Mr. Murari Lal as per the terms and conditions remitted 60% of the amount of all four immovable properties directly to the company.
Subjective
5370
Question 2 (a) Silk Segment Private Ltd. (SSPL) is a wholly owned subsidiary of Silk Block Ltd. (SBL) a listed public limited company. The Board of Directors of Silk Segment Private Ltd. have collectively decided upon the proposal to grant loans of ` 15,00,000 and ` 20,00,000 to Mr. Sohan and Ms. Subarna respectively for the purchase of fully paid-up shares in Silk Segment Private Ltd. Mr. Sohan is the Deputy Marketing Manager of Silk Segment Private Ltd. with a monthly salary of ` 1,00,000; whereas Ms. Subarna, a qualified Chartered Accountant, is the Chief Financial Officer of Silk Segment Private Ltd. with a monthly salary of ` 2,00,000. In view of provisions of the Companies Act, 2013, decide: (i) Whether the proposed loans to Mr. Sohan as well as Ms. Subarna can be disbursed by the company keeping in view that Silk Segment is a private limited company? (ii) Whether the answer would be different in case only 25% shares of SSPL are held by SBL? (b) The following are the extracts from the financial statements of BUI Private Limited, which is neither a start-up nor it is an associate or subsidiary company of any other company. Particulars Amount ` Authorised Capital: 10,00,000 Equity Shares of ` 100 each 10,00,00,000 Paid-up Share Capital: 8,00,000 Equity Shares of ` 100 each 8,00,00,000 Securities Premium Reserve Account 2,00,00,000 General Reserves 5,00,00,000 Term Loan from LMR Bank Limited 12,00,00,000 Cash Credit Loan (For Working Capital) 5,00,00,000 The company has never failed to file the Annual Return and Financial Statements with the Registrar. The company has already successfully repaid all the monies which were accepted earlier in the form of deposits along with due interest. Since the company was successful in implementation of its housing project by utilizing the money accepted in the form of deposits, the Board was interested to accepting deposits once more and take up another housing project in NOIDA since the members of the company were having sufficient surplus money which they wanted to invest in the company to start the project. However, their condition was that the same will be provided by them if the company accepts them in the form of deposits and the applicable provisions of the Companies Act, 2013 and Rules made thereunder are strictly complied with. But, the Board of Directors of BUI Private Limited were not in support of depositing any amount in any Deposit Repayment Reserve Account for the purpose of repayment of the said deposits, since the repayment was to be made out of the amount received from the customers who were going to book for the flats in the housing project. Two proposals came for review to the Board, out of which only one proposal was to be selected. The Board wanted you to advise them in choosing the appropriate deposit scheme. Proposal 1 - Acceptance of Deposits of ` 20,00,00,000, to be repaid with interest @ 7% per annum; CORPORATE AND OTHER LAWS Proposal 2 - Acceptance of Deposits of ` 14,00,00,000, to be repaid with interest @ 8% per annum. Referring to the applicable provisions of the Companies Act, 2013, the Rules made thereunder and the notifications issued in this respect, advise the Board stating the justification in support of your advice. (c) State what do you understand by the term 'document' as per the General Clauses Act, 1897? Discuss which of the following will be treated as a document: (i) Power of Attorney (ii) Cheque
Subjective
5371
Question 3 (a) UINA Infra Projects Private Limited was incorporated on 1st June, 2022. Mr. X had already registered the trade name of "UINA Infra projects" on 1st April, 2018 under the Trade Marks Act, 1999. Mr. X was suffering from a pro-longed disease since 1st April, 2021. When Mr. X recovered from illness on 20th May, 2024 and joined his own office on 5th July, 2024, he came to know from his staff members that a company has been incorporated with the name UINA Infra Projects Private Limited. He lodged a complaint with CORPORATE AND OTHER LAWS the Regional Director on 10th July, 2024 requesting him to order the company to change its name. The Regional Director examined the application of Mr. X and on 11th July, 2024, issued a direction to UINA Infra Projects Private Limited to change its name. Mr. D, a director of UINA Infra Projects Private Limited contended that the above direction of the Regional Director was bad in law and therefore not proper on the following grounds: A. That the name of the company is not too identical with or too nearly resembles to the name of any other company; and B. That the stipulated time period of two years of making any complaint with respect to the name in the above ground was already over on 31st May, 2024. Referring to the applicable provisions of the Companies Act, 2013, decide, whether the contention of Mr. D is tenable. Also advise UINA Infra Projects Private Limited the time period within which the company will be required to change its name in case the direction of the Regional Director was valid. (b) (i) Members of World One Limited, holding more than 2% of the total voting power wants the company to give a special notice to move a resolution for appointment of an auditor other than retiring auditor. Explain whether members can do so as per the provisions of the Companies Act, 2013. (ii) If a member of a listed company who has casted his vote through electronic voting, can attend general meeting of the company and change his vote subsequently? (c) Explain the Latin term "Absoluta sententia expositore non indiget" and how would the same help in correctly interpreting a definition given in a legislation or statute?
Subjective
5372
Question 4 (a) Based on the applicable provisions of the Companies Act, 2013, define the term "foreign company" and identify which among the following companies can be categorized as a foreign company: SI. No. Place of Incorporation Registered Additional information 1 Singapore Singapore Developed patient's database for a hospital in Mumbai, India, server in Singapore. 2 UAE UAE No place of business in India but employs agents in India. 3 Cape Town Cape Town Board Meeting held in Leh, India. 4 Germany Germany 49% of the shares held by an Indian company. (b) NS & Associates LLP was formed in the year 2020 and it was engaged in the business of manufacturing of plastic parts for automobiles. It constituted of Mr. Naveen and Mr. Suresh as designated partners who were responsible for obtaining contracts from various automobile manufacturers across the country for supply of spare parts for vehicles. In the year 2021 an investigation was ordered by the Tribunal against the LLP in connection with a financial fraud worth ` 50,25,000. Mr. J one the Accounts Manager and employee of the LLP was accused by the complainant, as one of the perpetrators to the fraud. The Tribunal levied a penalty of ` 1,25,000 to be paid by Mr. J on his conviction. Mr. J approached the Tribunal and provided vital information about the other black sheep involved in the fraud thus aiding in the investigation process. The Tribunal is considering of providing some relief in the penal action taken against him, while the LLP is planning to suspend Mr. J from service for this act. Considering the provisions of Limited Liability Partnership Act, 2008: (i) Decide whether the Tribunal can waive off or reduce the penalty imposed by it on Mr. J? (ii) Can the LLP suspend Mr. J from service for commission of the act, of revealing the name of the other accused involved in the fraud? (b) What do you mean by the rule "Ejusdem Generis"? State any three situations when the Rule of "Ejusdem Generis" is not applied by the courts.
Subjective
5373
Question 5 (a) Quick Money Limited attracts the provisions of section 135 of the Companies Act, 2013 and it has minimum average obligation to spend Corporate Social Responsibility (CSR) amount of ` 15 crore during each of the preceding five years. In this connection, the Board of Directors of the company needs your expert views on the following matters: (i) What is the meaning of "impact assessment"? (ii) Whether impact assessment is required to be taken by all the companies? (iii) Who can conduct impact assessment? (b) State the circumstances under which the winding up of an LLP may be ordered by the Tribunal. (c) Define the term 'person' as per the General Clauses Act, 1897. Discuss which of the following will be treated as a person: (i) An idol (ii) A public body (iii) A company
Subjective
5374
Question 6 (a) Top Spinners Foundation is a company registered under section 8 of the Companies Act, 2013 with a view to promote young and talented people towards becoming of world class cricketers. The foundation selects young boys and girls from different parts of the country via talent hunt competitions and other references from its members, thereby giving them proper training with residential facilities at the designated clubs opened for the purpose. The Foundation had been incorporated as a charitable institution in 2016. Currently it is having 1200 members. The Annual General meeting of the company is usually held at the club cum registered office of the company at Jaipur. The members in one of the general meetings have strongly suggested that the next Annual general meeting of the company be held at a hotel in near vicinity of the Registered office at Jaipur instead of the Club as the same has a congested sitting area. It was also decided by the foundation itself that a 15 days’ notice prior to the Annual General Meeting be given with facility of only physical voting and no E-Voting to be provided to the members. Referring to the relevant rules and provisions of the Companies Act, 2013 decide on the following: (i) Whether it is compelling upon the board to consider the directions regarding shift of the venue for the meeting? (ii) Whether a 15 days' prior notice is valid and as per the law? (iii) Whether the decision to provide the facility of only physical voting and not E-Voting valid? OR (a) Srinivas Iron and Steel Ltd. is a public sector listed company engaged in the manufacture of high-end steel sheets to be supplied to various other entities country-wide. M/s CVB & Associates, Chartered Accountants, had been appointed as the statutory auditors of the company for the term F.Y. 2023-24. Later in the year a financial fraud has come to the fore, not reported by the current auditors in their report, leading to dissatisfaction amongst a group of learned members of the company. The next Annual General Meeting is scheduled on 28.09.2024. The members comprising of Mr. H, Mr. J, Mr. K holding paid up share capital ` 1,50,000; ` 1,00,000; ` 2,50,000 respectively have collectively decided to send a special notice to the company regarding passing of the resolution at CORPORATE AND OTHER LAWS the next Annual General Meeting for appointment of an auditor other than M/S CVB & Associates as the auditor for the next term. Referring to the provisions of the Companies Act, 2013 elaborate: (i) Whether the above members can validly issue such Special Notice to the company? (ii) What will be the last date for issue of such Special Notice by the members to the company? (iii) Whether the company would have to communicate about the above Special Notice to other members after receiving the same? (b) Manish, a shareholder of a company has not claimed his dividends from the company for the last 10 years due to different reasons. He wants to know whether he will be able to recover the dividends declared by the company for all these years. Explain to him, the relevant legal provisions. (c) Referring to the provisions of the Foreign Exchange Management Act, 1999, state the meaning of the term "current account transaction".
Subjective
5375
1. Mr. Praveen has approached you to seek guidance that for how many members he can accord his confirmation to act as proxy as per the provisions of Section 105 of the Companies Act, 2013?
MCQ
5376
2. Mr. Rajan, a member of the company, entitled to vote at a meeting of the company shall be entitled to inspect the proxies lodged provided he has given _______.
MCQ
5377
3. As the Company Secretary of the Company, advise the Board of Directors to reply to the question raised by a member in the meeting with respect to the prescribed period for which the company shall preserve the register of members and copies of documents filed with ROC respectively for _______ and _________.
MCQ
5378
4. Bharosa Insurance Company Ltd. (BICL) has issued certain instruments. Which among the following shall not be covered under the definition of "Securities"?
MCQ
5379
5. Classical Diagnostics Ltd. (CDL) proposed for variation in the shareholder's voting right. How much percentage of issued shares of that class shall be required for consent for passing such resolution?
MCQ
5380
6. Where the holders of at least ______ of the issued shares of a class who did not, consent to or vote in favour of the resolution for the variation, may apply to the Tribunal to have the variation cancelled, and where any such application is made, the variation shall not have effect unless and until it is confirmed by the Tribunal.
MCQ
5381
7. For his show in Canada, he needs to obtain prior approval for remittance of foreign exchange from:
MCQ
5382
8. Dr. Ronak Mosay has enquired from you that for which of the following purposes, is he allowed to draw foreign exchange?
MCQ
5383
9. Dr. Ronak Mosay desires to remit US $ 1,50,000 for payment of prize money to the winning team in a cricket tournament in Canada. He needs to obtain approval from which of the following?
MCQ
5384
10. As per the LLP Act, 2008, the term resident in India means a person who has stayed in India for a period of:
MCQ
5385
11. As per the LLP Act, 2008, whether above LLP fulfills the requirements of designated partner?
MCQ
5386
12. The term "Year" as per the General Clauses Act, 1897 means:
MCQ
5387
13. The General Clauses Act, 1897 (Act) was enacted on 11th March, 1897 to consolidate and extend the General Clauses Act, ________ and __________.
MCQ
5388
14. Jade Suites LLC is a chain of hotels and restaurants all over the world. It is proposing to establish a Hotel at Goa. It has appointed a Chartered Accountant Mr. B for taking care of the registration formalities of the company. While the registration process was ongoing, the company entered into a lease agreement with a land owner for the construction of its Hotel. After few months, the Directors of Jade Suites LLC withdrew their interest in establishing a Hotel at Goa due to the news in social media regarding the fall in the tourism industry there. The land owner refused to repay the advance received by him. Can Jade Suites LLC sue the land owner in the capacity of a foreign company? Referring to the provisions of the Companies Act, 2013, choose the correct option:
MCQ
5389
15. Any instrument in the form of depository receipt created by a Domestic Depository in India and authorized by a company incorporated outside India making an issue of such depository receipts, is called as:
MCQ
5390
6. Mohit Electronics Private Limited In terms of Rule 13
MCQ
5391
3. Issue of Certificate: As per Rule 8 (2) of the Companies (Registration of Charges) Rules, 2014, in case the Registrar enters a memorandum of satisfaction of charge in full, he shall issue a certificate of registration of satisfaction of charge in Form No. CHG-5. In the instant case, DNC Hydro Limited has to follow the above legal and procedural steps to remove the old charge from ROC records. Alternate Conclusion: As the SPM bank has already issued a no dues certificate, DNC Hydro Limited should file the form CHG-4 within the extended period of limitation i.e. within 30 to 300 days. Accordingly, the Registrar may, on an application by the company allow such intimation of payment or satisfaction to be made within a period of three hundred days of such payment or satisfaction on payment of prescribed fees. The Registrar shall not cause any notice to be sent to SPM Bank in this case as NOC has been issued by it and just register the satisfaction after payment of prescribed fees.
MCQ
5392
Question 1 (a) Amrish after completing his post-graduate degree in mechanical engineering from the United Kingdom returned back to India. Although he got a good placement in a UK based company but he thought to build his own business empire in India. Amrish belongs to Barmer district (Rajasthan) where his parents have agricultural land of 20 acres. He planned to manufacture commercial drones for the use of agricultural harvesting and assist in supply chain process. For this purpose, he planned to incorporate a private limited company having the following persons as the first subscribers to the Memorandum and Articles of Association: (i) Amrish (himself) (ii) Robert (He is a college friend of Amrish. He is a Citizen of UK. He has technical expertise and in order to incorporate the company visited India on a valid Business Visa). (iii) Eliza (She is college friend of Amrish. She is a Citizen of Netherlands and has good business contacts in European Countries which will be immensely useful in marketing of the company's products). (iv) Goma Devi (Mother of Amrish, who is illiterate. She has recently sold part of her agricultural land and has received ` 15 crores, out of which she agreed to subscribe ` 5 crores in the share capital of the proposed company). (v) Goodwork Technologies LLP (A Limited Liability Partnership having the expertise in the field of remote sensing devices). (vi) Mohit Electronics Private Ltd. (A Private Limited Company having expertise in the field of providing Electronics and Electricals). Amrish planned to have the Registered Office of the proposed company at Jaipur while the factory and works office shall be at the Barmer. CORPORATE AND OTHER LAWS For incorporation of a company, an application for registration is to be filed with the Registrar. In the given case, the initial subscribers to the company consists of one illiterate person, two foreign nationals, one LLP and one Private Limited Company. Discuss the procedure, how these persons shall subscribe to the Memorandum of Association and Articles of Association. (5 Marks) (b) Sangeeta was appointed as Statutory Auditor of ABC Ltd. in the Annual General Meeting (AGM) of the shareholders held on 20th August, 2023. However, Sangeeta met with an accident on 23rd December, 2023 and died. The Board of Directors of the ABC Ltd. filled up the casual vacancy caused by the sudden death of Sangeeta and appointed Keshav as the Statutory Auditor. The next AGM of the Company was scheduled for 28th August, 2024 in which the Board of Directors recommended for appointment of Aashish as Statutory Auditors before the shareholders. Keshav objected for the appointment of Aashish and gave representation to the Company Secretary mentioning therein that his (Keshav) appointment was approved by the Board of Directors after the demise of Sangeeta thus can continue as Statutory Auditor of the Company till the conclusion of the next 6th Annual General Meeting and also threatened to report the matter to the Registrar and the NCLT. Based on the above facts answer the followings: (i) Explain the procedure to fill up the casual vacancy of the office of Statutory Auditor. (ii) Whether the contention raised by Keshav is justified as per the provisions of the Companies Act, 2013? (iii) What shall be your answer, if the casual vacancy in the office of the Statutory Auditor in the company was caused by resignation of Sangeeta? (5 Marks) (c) Mr. V is a person of Indian origin who had moved to USA along with his wife in the year 1998 and had been living there until 2024. He was holding joint bank accounts with his wife in USA since 1998. On the demise of his wife on 17th November, 2024, he had returned permanently to India on 24th November, 2024. He also inherited his wife's money after her death, which got transferred to his bank account in USA. After few days of his return to India, he has paid premium from his bank account in USA of his insurance policy, which he had taken when he was in USA. Referring to the provisions of the Foreign Exchange Management Act, 1999, examine whether Mr. V is permitted to carry out the above transactions. (4 Marks)
Subjective
5393
Question 2 (a) Referring to the provisions of the Companies Act, 2013, state whether the following amounts received by the company constitute deposit or not: (i) IQ Books Limited received share application money of ` 50 crore from investors on 8th December, 2024. As the issue was under subscribed, the company refunded the amount to the investors on 20th February, 2025. (ii) Suraj, Raj and Tejas are the promoters of Precious Jewellers Limited. They borrowed a sum of ` 200 crore from ABC Bank Limited for its working capital purpose. The Bank imposed a stipulation that the promoters should contribute at least 20% of the amount borrowed. Hence, Suraj brought in ` 10 crore, Raj brought in ` 15 crore and Mr. K, father of Tejas brought in ` 15 crore. (iii) Pretty Cosmetics Limited issued non-convertible debentures for ` 125 crore and listed it on a recognized stock exchange adhering to SEBI rules and regulations. The company created a charge on its assets in favour of the debenture holders and duly registered the charge. (5 Marks) (b) Spark Services Limited issued a prospectus inviting public offer of securities on 18th June, 2024. The prospectus mentioned that Mr. T is one of the Directors of the Company. Mr. T is a famous social worker who helps in educating the poor children in Rajasthan. The prospectus also mentioned that a certain percentage of funds raised will be utilized towards that community service. Mr. C was impressed by these statements and subscribed to the shares of the company. He was allotted 1000 shares of the company. He subsequently sold 250 shares to Mr. D. On 15th December, 2024, he came to know that Mr. T was not a director and the company never had any intention of doing community service. Mr. C and Mr. D want to rescind the contract. Referring to the provisions of the Companies Act, 2013, examine whether Mr. C and Mr. D can rescind the contract. (5 Marks) (c) Purva Buildcon Ltd. (PBL) is a public company having two subsidiary companies namely Arihant Cements Ltd. (ACL) and Siddharth Bricks Ltd. (SBL). Purva is a Chief Financial Officer of PBL. Ashish and Mrinal, who were the CFO's of ACL and SBL resigned from their respective companies and Purva was offered to take charge of the office of CFO in ACL and SBL, which she accepted. Whether Purva can be designated as CFO simultaneously in two subsidiaries (i.e. in SBL and ACL) besides being CFO of PBL? Examine the matter with reference to the provisions contained in the Companies Act, 2013 as well as in the General Clauses Act, 1897. (4 Marks)
Subjective
5394
Question 3 (a) Comment on the following: (i) Disclosure required to be made on the face of the Prospectus. (ii) Conditions in regard to Experts' Statement. (iii) Date of publication of prospectus. (5 Marks) (b) Vital Pharmacy Limited is engaged in the manufacturing of medicines to cure skin diseases. It has established a unit in Germany. It registered few patents in Germany and raised funds by creating a charge on its stock in Germany and the patent rights. The company registered the charge. created on its stock but did not register the charge created on the patent rights. The Company received a notice from the Registrar of Companies for not filing the particulars of charge created by the Company on the property or assets situated outside India. The Company wants to defend the notice on the ground that it shall not be the duty of the company to register the particulars of the charge created on the patents obtained outside India and also as they are intangible in nature. Referring to the provisions of the Companies Act, 2013, examine the validity of the company's claim. OR (b) What do you mean by Floating Charge and when it converts into a Fixed Charge? (5 Marks) (c) ‘The meaning of a word is to be judged by the company it keeps'. Explain the concept of 'Noscitur A Sociis'. (4 Marks)
Subjective
5395
Question 4 (a) XYZ Ltd., uses an Accounting Software for recording its financial transactions. The statutory auditor of the company while auditing finds the following issues: Some journal entries were altered without creating edit logs for all such changes. The audit trail feature was disabled for certain modules (e.g., inventory adjustments, inter-company transactions). Keeping in view of the above issue, advice the company on the followings: CORPORATE AND OTHER LAWS (i) Audit trail and Edit Log requirements (ii) The back-up of books of accounts. (5 Marks) (b) Sun Roofings LLP has 6 partners. Mr. K, a partner is in-charge for the marketing division of the firm. He is literally the face of the firm and due to his acumen the business was doing very well. Mr. W is one of the senior most partner and a major investor in the firm. Mr. K met with a sudden demise. The LLP however continued its operations without dissolving the LLP. The firm incurred huge losses after his death and Mr. K's share in the firm was also utilised to repay the debts. Mr. W transferred his share to his son M who has previous experience in marketing. M wanted to take active part in the business but the remaining partners did not allow him. Referring to the provisions of the Limited Liability Partnership Act, 2008 state whether; (i) Mr. K's share can be used to repay the firm's debts after his death (ii) The remaining partners of Sun Roofings can forbid M to take part in the business. (5 Marks) (c) Whether Illustrations will have effect of modifying the language of the section in connection with Interpretation of Statutes? Explain with the help of an example (4 Marks)
Subjective
5396
Question 5 (a) Write down functions and duties of the National Financial Reporting Authority. (5 Marks) (b) Write down any five points on the distinction between LLP and Limited Liability Company. (5 Marks) (c) Dream Builders Limited was engaged in the activity of building and selling budget friendly apartments. It recently started a new project at Noida. Pending approval, the builders started the construction work. On verification of documents, the Corporation of Noida refused to sanction the permission and the Assistant Commissioner Mr. S issued a demolition order, signed by him under his authority. The builders filed an appeal at the court and stayed the demolition. After 6 months of court trials, the verdict was announced in favour of the Corporation of Noida. Mr. G, the present Assistant Commissioner initiated the demolition process. The builders argued that the order was passed by Mr. S and since he is no longer in the authority, the order stands cancelled and Mr. G cannot demolish the construction. Referring to the provisions of the General Clauses Act, 1897, determine the validity of the claim of the builders. (4 Marks) CORPORATE AND OTHER LAWS
Subjective
5397
Question 6 (a) DNC Hydro Limited, obtained a loan of ` 3,000 crores from SPM Bank in April, 2021 to finance its hydropower generation project. To secure the loan, the company created a charge on its assets including land, plant and machinery. The charge was registered with the ROC in form CHG-1. In September, 2024, DNC Hydro Limited fully repaid the loan and SPM Bank issued no dues certificate to the company. However, due to internal compliance oversight, DNC Hydro Limited failed to file form CHG-4 within the 30 days prescribed limit under Section 82 of the Companies Act, 2013. In January, 2025, RTS Bank approved a loan for ` 1,000 crore to DNC Hydro Limited for acquiring new plant and machinery. During the due diligence, RTS Bank discovered that the old charge was still active in the ROC records, thereby creating problems for the disbursement of the new loan. As a Financial Advisor of the company, advise what are the legal and procedural steps DNC Hydro Limited should follow to remove the old charge from ROC records. (5 Marks) (b) ABC Inc., a company based in USA, develops cyber security software and sells it to its Indian clients. CORPORATE AND OTHER LAWS ABC Inc. has entered into service agreement with PQR Private Limited, a company incorporated in India. PQR Private Limited provides support to the Indian customers for the software installation and after sale services. PQR Private Limited also holds 50% of shares of ABC Inc. Explain whether ABC Inc. is required to comply with the provisions of chapter XXII of the Companies Act, 2013. (5 Marks) (c) Define "Foreign Exchange" and "Foreign Security" as per the provisions of the Foreign Exchange Management Act, 1999. (4 Marks)
Subjective
5398
1. Advise ABC Publications Limited regarding the amount and the interest that can be repaid to Mr. Y:
MCQ
5399
2. Advise ABC Publications Limited regarding the request of Mr. U:
MCQ
5400
3. The Banker of ABC Publications Limited wanted a list of deposits accepted by the company. Advise the company on what among the following constitute deposit:
MCQ
5401
5. Combat Gaming Limited has made alteration in documents delivered to the Registrar, they shall intimate to Registrar of Companies by ______
MCQ
5402
6. Combat Gaming Limited has to deliver the required documents along with the appropriate fees to:
MCQ
5403
7. The name applied for has been approved by the Registrar. The approved name of LLP shall be valid for a period of _____________ from the date of intimation by the Registrar.
MCQ
5404
8. Which of the following combinations of partners, if appointed as designated partners, will not be in accordance with the provisions laid down by Limited Liability Partnership Act, 2008?
MCQ
5405
9. In how many days, a Limited Liability Partnership shall file with the Registrar, the particulars of every individual who has given his consent to act as designated partner?
MCQ
5406
10. For the purpose of cultural tours, approval of which Ministry is required to be obtained ?
MCQ
5407
11. For availing foreign exchange for studying abroad, which of the following option is correct:
MCQ
5408
12. The remittance of foreign exchange for arranging of cultural tour for the students is an example of:
MCQ
5409
13. Super Brain Coaching Limited was engaged in offline coaching of students for various competitive examinations. It was one of the pioneer in its field. It suffered losses due to various social and government restrictions imposed on study centers. On account of this, it defaulted in the repayment of term loan for the first two quarters of the financial year 2023-24. However, Super Brain Coaching Limited adapted itself to the changing circumstances and shifted to online mode of coaching and revived its financial conditions. On 31st December 2023, it cleared all the dues and regularized the term loan. Super Brain Coaching Limited wants to issue equity shares with differential rights. When can the issue be made?
MCQ
5410
14. An Act has been passed by the government and though sufficient time has elapsed since the Act was passed, it has not been brought into force by the Government. Which of the following is correct in the light of the provisions of the General Clauses Act, 1897?
MCQ
5411
15. With reference to the provisions of the General Clauses Act, 1897, in all Legislations and Regulations, unless there is anything repugnant in the subject or context, words importing the masculine gender shall be taken:
MCQ
5412
Question 1 (a) SAB Health Products Limited issued equity shares worth ` 5,00,00,000 (5,00,000 equity shares of ` 100 each) and it was fully subscribed and partly paid at ` 50 each. The company made a call to all its subscribers to pay a sum of ` 30 for each share held by them. Mr. GH, a subscriber to the shares of a company, holding 10,000 shares, paid all the money due on the shares held by him in advance. Later, Mr. GH claimed interest on the money advanced by him and also dividend in respect of the advance money paid. Is his claim justified? Another shareholder Mr. LK holding 15,000 shares did not pay the first call. So, the directors called upon him to pay the entire amount due by him in respect of the shares held by him. Referring to the provisions of the Companies Act, 2013 and Rules made there under, examine whether the directors of SAB Health Products Limited permitted to do so? (5 Marks) (b) (i) Right Trading Limited is a company engaged in trading of automobile spare parts. During the current financial year 2024-25, Mr. J the CFO retired due to bad health. The company appointed Mr. C as the new CFO. On verification of the financial statements and statutory returns of the company, Mr. C advised the Board of Right Trading Limited to revise the financial statements for the year 2021-22. Examine, with reference to the applicable provisions of the Companies Act, 2013, whether M/s Right Trading Limited can do so? (3 Marks) (ii) M/s DEF is conducting the audit of Right Trading Limited for the past 9 years. Now due to the requirement of rotation of auditors, M/s DEF is going to retire at the upcoming Annual General Meeting and in its place M/s XYZ will be appointed as the Auditor of Right Trading CORPORATE AND OTHER LAWS Limited. One of the partner Mr. F, who was in charge of the certification of the financial statements of the company retired from the firm of M/s DEF and joined the firm of M/s XYZ. Examine, considering the provisions of the Companies Act, 2013 about the validity of the appointment of M/s XYZ. (2 Marks) (c) Ms. Rose was an Indian citizen who got a job in a software company in USA. She went to USA and stayed there for 12 years. During her stay, she purchased a house in USA for her residence. Then due to some personal issues she moved back to India and joined a software company in India. As she had moved back to India, she let out her house in USA and deposited the rent in her account in USA. Out of that amount, she purchased another house in USA. Based on the above facts, answer the following referring to the provisions of the Foreign Exchange Management Act, 1999. (i) Whether Ms. Rose can purchase the house in USA and continue to retain it even after returning to India? (ii) Whether Ms. Rose can purchase another house in USA after returning to India? (4 Marks)
Subjective
5413
Question 2 (a) Stuti Ceramic Pvt. Ltd. (SCPL) manufactures crockery items which are predominantly used only by the domestic household customers. Now the company wants to expand its area of operation to manufacture all types of crockery items and cutlery for the use of big hotels. For this expansion plan, the company needs funds of around ` 500 lakh. The company does not want to convert itself from private company to public company since the promoters do not want to dilute their equity stake otherwise the public company have the option to raise the funds through public issue. The company explored the other avenue of raising funds by issue of right shares to the existing shareholders, however only ` 100 lakh could be generated. CORPORATE AND OTHER LAWS The banks and financial institutions are also reluctant to increase their exposure in the company. Referring to the provisions of the Companies Act, 2013, advise the SCPL, whether the company can raise further funds through private placement issue. If so, are there any limit for fresh offer and time limit of allotment of securities? (5 Marks) (b) Dolls Toys Limited is having a net- worth of ` 310 crore, paid up share capital of ` 200 crore, free reserves and security premium of ` 110 crore and turnover of ` 300 crore. Dolls Toys Limited wants to accept deposits form public other than its members. (i) Referring to the provisions of the Companies Act, 2013, state whether Dolls Toys Limited is permitted to accept the deposits from public other than its members. (ii) It is further mentioned that Dolls Toys Limited is in urgent need of funds as one of its contract is on the verge of completion and it is promising to repay the deposits within a period of four months. Is Dolls Toys Limited permitted to accept deposits with repayment period of 4 months? (5 Marks) (c) Referring to the provisions of the General Clauses Act, 1897, answer the following questions: (i) Whenever a new law is enacted by the Government of India, what shall be its date of coming into force? (ii) Whenever a new law is enacted to replace the existing law, it repeals the old enactment. Describe the points which shall not have any effect of repeal of the old enactment. (4 Marks)
Subjective
5414
Question 3 (a) The paid up share capital of Star Furnishing Limited is ` 1,00,00,000 divided into 10,00,000 equity shares of ` 10 each as at 31stMarch, 2024. Out of this, Home Decor Limited is holding 6,00,000 equity shares and the remaining equity shares of 4,00,000 held by others. Simultaneously, Star Furnishing Limited is holding 7% equity shares of Home Decor Limited out of which 2% equity shares are held as a legal representative of a deceased member of Home Decor Limited. On the basis of the given information, examine and
Subjective
5415
Question 4 (a) XYZ Limited is a company having a paid up equity share capital of ` 75 crore. Though it was performing well in the recent years it suffered losses in the first and second quarter of the financial year 2023-2024. In order to sustain its image, the Board of Directors declared an interim dividend at the rate of 30 percent on the paid-up equity share capital on 4/10/2023. The following are the additional information extracted from the books of account for the past 5 Financial Years: Financial year ending 31st March Rate of Dividend declared 2019 20% 2020 15% 2021 15% 2022 15% 2023 30% Examining the provisions of the Companies Act, 2013, decide the validity of the Board's declaration of 30% interim dividend. (5 Marks) (b) M/s Strong Steels Limited Liability Partnership firm was incorporated on 01st April 2010 with ten partners. The LLP had very good business and made considerable profits during the past years. Recently due to obsolete practices, M/s Strong Steels Limited LLP started making loss. Also, M/s Strong Steels LLP did not file its annual returns from 2020-21. Three partners decided that the LLP be wound up by the Tribunal. The remaining partners objected to it. Referring to section 64 of the Limited Liability Partnership Act, 2008, can the Tribunal pass an order to wound up M/s Strong Steels LLP? Also state the provisions and penalty for not filling annual return with the Registrar. (5 Marks) (c) (i) What is the purpose of inclusion of ‘definitions’ of certain words and expressions in the body of any statute? (ii) The definition sometimes includes the words 'mean', 'include', 'means and include' and 'to apply to and include'. What is the meaning of such words? (4 Marks)
Subjective
5416
Question 5 (a) Sanjana joined a company named as Designers Cloths Ltd. as an Independent Director. In order to know more about the company, she wanted to inspect the books of account and minutes books of the Board Meetings held during the previous three years. The company is keeping the books of account and other records at its Registered Office, which is at Mumbai whereas Sanjana resides in Kolkata. Therefore, through power of attorney, Sanjana authorised her friend Avantika, who is a Chartered Accountant and does practice in Mumbai, to make an inspection of the books of accounts and minutes books of the meetings of the Board. Giving the relevant provisions of the Companies Act, 2013 and its Rules made thereunder, examine, whether Avantika can make inspection on behalf of Sanjana. (5 Marks) (b) A, B, C and D are the partners of Alpha LLP and have equal share in the profits and losses of the LLP. A has made an agreement to transfer 70% of his share in the profits of Alpha LLP to his daughter X. X wanted to access information about the trading transactions of Alpha LLP claiming that she is entitled to the information as she receives a percentage of profits from the LLP. The partners refused to grant her access. Does X have any remedy against the denial according to the provisions of the Limited Liability Partnership Act, 2008? Are the partners correct in denying access to X? (5 Marks) (c) (i) In a contract of sale, Mr. A fraudulently sold certain unmarketable goods to Mr. B. Now Mr. A is liable for the fraudulent activity under both the Indian Contract Act, 1872 and the Sale of Goods Act, 1930. State the provision as per the General Clauses Act, 1897 as to whether his offence is punishable under the both the Acts? (ii) Mr. P bought a car from Mr. G who was his friend. Mr. P did not check the car or test drive it. Whether the purchase made could be said to be made in good faith? Explain with reference to the provisions of the General Clauses Act, 1897. (4 Marks)
Subjective
5417
Question 6 (a) Silk Textile Limited is a company which is incorporated in India. It holds two subsidiaries- Print Limited (in which it holds 80% of shares) and Stitch Limited (a wholly owned subsidiary). Both the subsidiaries are incorporated outside India. The Board of Directors of Silk Textile Limited intends to call an Extraordinary General Meeting (EGM) of Silk Textile Limited. During the same time, the Board of Print Limited also wanted to hold an EGM on urgent basis at Dubai. The Chairman with the consent of his Board wanted to hold the EGM of Silk Textile Limited at Dubai so that he can attend both the EGM. But the Company Secretary advised the Chairman that he cannot hold the EGM outside India. Referring to the provisions of the Companies Act, 2013, advise the Board of Directors on the following: (i) Whether the Board of Silk Textile Limited can hold its EGM at Dubai? (ii) Whether the EGM of Print Limited can be held at Dubai? (5 Marks) OR (a) Creative Textiles Ltd. is an unlisted public company. The company's paid-up share capital is ` 50 lakh consisting of 5 lakh shares having face value of ` 10 each. Raman is having 50,000 shares in the company. He is not happy with Somnath, who is a director in the company. He believed that Somnath is acting against the interest of the company. Raman wanted to remove Somnath from the directorship. Removal of a person from the directorship requires the approval of the shareholders in the general meeting. The Annual General Meeting (AGM) of the company has recently been concluded and the next AGM will be held in the next year. Considering the case and referring to the provisions of the Companies Act, 2013, advise: (i) Can Raman as an individual shareholder make a requisition to the company for calling of the Extra-ordinary General Meeting for putting such resolution? (ii) If the company does not call the EGM on the requisition of Raman, whether Raman can himself call the EGM? (5 Marks) (b) Beauty Cosmetics, a company incorporated in Korea has established its branch office in Chennai for conducting its business in India. The structure of paid-up share capital of Beauty Cosmetics as at 31st March 2024 is as below: The company does not have any Preference Share Capital. Equity share capital held by Mr. L, an Indian citizen: 10% Equity share capital held by Mr. R, an Indian Citizen: 20% CORPORATE AND OTHER LAWS Equity share capital held by Fairness Cosmetics Limited, an Indian company: 20% You being a Chartered Accountant are asked to explain with reference to the provisions of the Companies Act, 2013: (i) Whether Beauty Cosmetics shall be deemed to be a Foreign Company or an Indian Company for the business carried on by it in India, and (ii) for the business carried on by it in India, will it be required to comply with the relevant provisions of the Companies Act, 2013 as if it is an Indian Company? (5 Marks) (c) Mitali Diamonds Limited is a company engaged in the business of cutting, polishing and trading of diamonds in and outside India. The company exports the diamonds to USA. For the last five financial years, the foreign exchange earned by the company in exporting diamonds is as under: FY 2023-24 USD 1,25,000 FY 2022-23 USD 1,10,000 FY 2021-22 USD 95,000 FY 2020-21 USD 98,000 FY 2019-20 USD 93,000 The company wants to give donation of USD 10,000 to an institution situated in USA which provides technical support and training in the field of cutting and polishing of raw diamonds. This will help the company in guiding its own employees, posted in USA to get the requisite training. Referring to the provisions of the Foreign Exchange Management Act, 1999, state whether the company can give donation to such institution in USA? (4 Marks)
Subjective

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