Sets, Relations and Functions

217 Practice MCQs available for CA Foundation

Paper

Paper 3: Quantitative Aptitude

Exam Weightage

3-5 Marks

Key Topics

Sets, Relations, Functions

This chapter covers Sets, Relations, Functions and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

Exam Strategy Tip

This topic carries 3-5 Marks weightage. Focus on understanding core concepts rather than memorizing.

Key Terms

Quick Ratio

A stringent liquidity ratio (also called Acid-Test Ratio) that measures the ability to meet short-term obligations using only the most liquid assets, excluding inventories and prepaid expenses. Formula: (Current Assets − Stock − Prepaid Expenses) ÷ Current Liabilities. Ideal is 1:1.

Set

A well-defined collection of distinct objects (called elements or members). Sets are denoted by capital letters and elements are listed within curly braces. Key operations include Union (∪), Intersection (∩), and Complement.

Function

A relation from a set A (Domain) to a set B (Codomain) such that every element in A is associated with exactly one element in B. Written as f: A→B. Types include Linear, Quadratic, Polynomial, and Exponential functions.

Comparison Tables

Consignment vs Sale: Key Accounting Differences

All 217 Questions

1938
If A={1,2,3,4,5}\displaystyle A = \{1, 2, 3, 4, 5\}, B={2,4}\displaystyle B = \{2, 4\} and C={1,3,5}\displaystyle C = \{1, 3, 5\} then (A−C)×B\displaystyle (A - C) \times B is:
MCQ
1997
If f(x)=x2−5\displaystyle f(x)=x^2-5, evaluate f(3)\displaystyle f(3), f(−4)\displaystyle f(-4), f(5)\displaystyle f(5), and f(1)\displaystyle f(1).
MCQ
1900
Out of a group of 20\displaystyle 20 teachers in a school, 10\displaystyle 10 teach Mathematics, 9\displaystyle 9 teach Physics and 7\displaystyle 7 teach Chemistry. 4\displaystyle 4 teach Mathematics and Physics but none teach both Mathematics and Chemistry. How many teach Chemistry and Physics; how many teach only Physics?
MCQ
1901
If A={1,2,3,4,5,7,8,9}\displaystyle A = \{1, 2, 3, 4, 5, 7, 8, 9\} and B={2,4,6,7,9}\displaystyle B = \{2, 4, 6, 7, 9\} then how many proper subset of A∩B\displaystyle A \cap B can be created?
MCQ
1902
The number of subsets of the set {0,1,2,3}\displaystyle \{0, 1, 2, 3\} is:
MCQ
1973
If f(x)=x2+x−1\displaystyle f(x) = x^2+x-1 and 4f(x)=f(2x)\displaystyle 4f(x) = f(2x), then find the value of 'x'.
MCQ
1986
Find the f∘g\displaystyle f \circ g for the functions f(x)=x2\displaystyle f(x) = x^2, g(x)=x+1\displaystyle g(x) = x+1.
MCQ
1903
A survey shows that 74%\displaystyle 74\% of the Canadian like grapes, whereas 68%\displaystyle 68\% like bananas. What percentage of the Canadians like both grapes and bananas, if everybody like either of two?
MCQ
1904
If A={a,b,c}\displaystyle A = \{a, b, c\}, B={b,c,d}\displaystyle B = \{b, c, d\} and C={a,d}\displaystyle C = \{a, d\} then (A−B)×(B∩C)\displaystyle (A - B) \times (B \cap C) is equal to:
MCQ
1905
In a survey of 100\displaystyle 100 boys it was found that 50\displaystyle 50 used white shirts, 40\displaystyle 40 red shirts and 30\displaystyle 30 blue shirts. 20\displaystyle 20 were habituated in using both white and red shirts. 15\displaystyle 15 were using both red and blue shirts and 10\displaystyle 10 were using blue and white shirts. Find the number of boys who are using all colours.
MCQ
1906
If A={1,2,4}\displaystyle A = \{1, 2, 4\} and B={1,2,3}\displaystyle B = \{1, 2, 3\} then (A∪B)×(A∩B)\displaystyle (A \cup B) \times (A \cap B) is equal to:
MCQ
1907
If B={1,2,3,4,5}\displaystyle B = \{1, 2, 3, 4, 5\}, then the number of proper subsets of B\displaystyle B is
MCQ
1908
If A={1,2}\displaystyle A = \{1, 2\}, B={3,4}\displaystyle B = \{3, 4\}, C={5,6}\displaystyle C = \{5, 6\} then the value of A×(B∪C)\displaystyle A \times (B \cup C)
MCQ
1909
If a set contain n\displaystyle n elements, then the total number of proper subsets of set is:
MCQ
1910
A team has a total population of 50,000\displaystyle 50,000. Out of it 28,000\displaystyle 28,000 read the newspaper 'X' and 23,000\displaystyle 23,000 read newspaper 'Y', while 4,000\displaystyle 4,000 read both the newspaper. The number of persons not reading any of the two newspapers are:
MCQ
1911
The number of proper subsets of the set 3,4,5,6,7\displaystyle {3, 4, 5, 6, 7} is
MCQ
1912
If A={1,2,3,4}\displaystyle A = \{1, 2, 3, 4\} and B={2,3,4,5}\displaystyle B = \{2, 3, 4, 5\} then (A−B)∪(B−A)\displaystyle (A - B) \cup (B - A) is
MCQ
1913
The number of subsets 1,2,5\displaystyle {1, 2, 5} is
MCQ
1914
If A={1,2,3,4,5,6,7}\displaystyle A = \{1, 2, 3, 4, 5, 6, 7\} and B={2,4,6}\displaystyle B = \{2, 4, 6\} Cardinal number of A∪B\displaystyle A \cup B
MCQ
1915
If A={1,2,3,4}\displaystyle A = \{1, 2, 3, 4\} and B={5,6,7,6}\displaystyle B = \{5, 6, 7, 6\}, then cardinal number of the set A∩B\displaystyle A \cap B is
MCQ
1916
If A={1,2,3,4}\displaystyle A = \{1, 2, 3, 4\} and B={6,7,8}\displaystyle B = \{6, 7, 8\}, then cardinal number of A×B\displaystyle A \times B is:
MCQ
1917
The number of subsets of the set A={1,2,3,4,5,6,7,8}\displaystyle A = \{1, 2, 3, 4, 5, 6, 7, 8\} is
MCQ
1918
(A∪B)′\displaystyle (A \cup B)' is equal to
MCQ
1919
If A={p,q,r,s}\displaystyle A = \{p, q, r, s\}, B={q,s,t}\displaystyle B = \{q, s, t\} and C={m,q,n}\displaystyle C = \{m, q, n\} find C−(A∩B)\displaystyle C - (A \cap B)
MCQ
1920
The set having no element is called
MCQ
1921
If A={1,2,3,4,5}\displaystyle A = \{1, 2, 3, 4, 5\} and B={6,7,8,9}\displaystyle B = \{6, 7, 8, 9\}, then cardinal number of A×B\displaystyle A \times B is:
MCQ
1922
If A={1,2,3,4,5}\displaystyle A = \{1, 2, 3, 4, 5\} B={2,4}\displaystyle B = \{2, 4\} and C={1,3,5}\displaystyle C = \{1, 3, 5\} then (A−C)×B\displaystyle (A - C) \times B is
MCQ
1923
Let Z\displaystyle Z be the universal set for two sets A\displaystyle A and B\displaystyle B. If n(A)=300\displaystyle n(A) = 300, n(B)=400\displaystyle n(B) = 400 and n(A∪B)=200\displaystyle n(A \cup B) = 200, then n(A′∩B′)\displaystyle n(A' \cap B') is equal to 400 provided n(Z)\displaystyle n(Z) is equal to
MCQ
1924
If A={4,5}\displaystyle A = \{4, 5\}, B={2,3}\displaystyle B = \{2, 3\}, C={5,6}\displaystyle C = \{5, 6\} then A×(B∩C)\displaystyle A \times (B \cap C)
MCQ
1925
If A={1,2,3}\displaystyle A = \{1, 2, 3\}, B={3,4}\displaystyle B = \{3, 4\} and C={4,5,6}\displaystyle C = \{4, 5, 6\}, then A×(B∩C)\displaystyle A \times (B \cap C)
MCQ
1927
Let A\displaystyle A be the set of squares of natural numbers and let x∈A,y∈A\displaystyle x \in A, y \in A, then
MCQ
1928
A town has a total population of 50,000. Out of it 28,000 read the newspaper X and 23,000 read Y while 4,000 read both the papers. The number of persons not reading X and Y both is
MCQ
1929
In a survey of 300 companies, the number of companies using different Media-Newspapers N(N), Radio (R) and Television (T) are as follows: N(N)=200\displaystyle N(N) = 200, N(R)=100\displaystyle N(R) = 100, N(T)=40\displaystyle N(T) = 40, N(N∩R)=20\displaystyle N(N \cap R) = 20, N(R∩T)=20\displaystyle N(R \cap T) = 20, N(N∩T)=30\displaystyle N(N \cap T) = 30 and N(N∩R∩T)=5\displaystyle N(N \cap R \cap T) = 5. Find the numbers of companies using none of these media:
MCQ
1931
Out of total 150 students, 45 passed in Accounts, 30 in Economics and 50 in Maths, 30 in both Accounts and Maths, 32 in both Maths and Economics, 35 in both Accounts and Economics, 25 students passed in all the three subjects. Find the numbers who passed at least in any one of the subjects:
MCQ
1932
If A={0,1,2,3,4,5}\displaystyle A = \{0, 1, 2, 3, 4, 5\} then the no. of subsets of A\displaystyle A
MCQ
1933
The number of proper subsets of A∩B\displaystyle A \cap B, if A={1,2,3,4,5,7,8,9,10}\displaystyle A = \{1, 2, 3, 4, 5, 7, 8, 9, 10\} and B={2,4,6,7,9}\displaystyle B = \{2, 4, 6, 7, 9\}
MCQ
1934
Out of 20 members in a family, 11 like to take tea and 14 like coffee. Assume that each one likes at least one of the two drinks. Find how many like both coffee and tea:
MCQ
1935
In a survey of 300 companies, the number of companies using different media-Newspapers (N), Radio (R) and Television (T) are as follows: N(N)=200\displaystyle N(N) = 200, N(R)=100\displaystyle N(R) = 100, N(T)=40\displaystyle N(T) = 40, N(N∩R)=20\displaystyle N(N \cap R) = 20, N(R∩T)=20\displaystyle N(R \cap T) = 20, N(N∩T)=30\displaystyle N(N \cap T) = 30 and N(N∩R∩T)=5\displaystyle N(N \cap R \cap T) = 5. Find the numbers of companies using none of these media:
MCQ
1936
If A={p,q,r,s}\displaystyle A = \{p, q, r, s\}, B={q,s,t}\displaystyle B = \{q, s, t\}, C={m,q,n}\displaystyle C = \{m, q, n\} Find C−[A∩B]\displaystyle C - [A \cap B]
MCQ
1885
The numbers of proper subset of the set (3,4,5,6,7)\displaystyle (3, 4, 5, 6, 7) is
MCQ
1886
If A=(1,2,3,4,5,6,7)\displaystyle A = (1, 2, 3, 4, 5, 6, 7) and B=(2,4,6,8)\displaystyle B = (2, 4, 6, 8). Cardinal number of A−B\displaystyle A - B is:
MCQ
1887
If A=(1,2,3,4,5,6,7,8,9)\displaystyle A = (1, 2, 3, 4, 5, 6, 7, 8, 9) B=(1,3,4,5,7,8)\displaystyle B = (1, 3, 4, 5, 7, 8) C=(2,6,8)\displaystyle C = (2, 6, 8) then find (A−B)∪C\displaystyle (A - B) \cup C
MCQ
1888
The no. of subsets of the set (3,4,5)\displaystyle (3, 4, 5) is:
MCQ
1889
(Ac)c=?\displaystyle (A^c)^c = ? Note: This que is from matrix (deleted topic).
MCQ
1890
Two finite sets respectively have x\displaystyle x and y\displaystyle y number of elements. The total number of subsets of the first is 56\displaystyle 56 more than the total number of subsets of the second. The value of x\displaystyle x and y\displaystyle y respectively.
MCQ
1891
The set of cubes of the natural number is:
MCQ
1892
The set of cubes of natural number is
MCQ
4032
Which of the following relations is transitive but not reflexive for the set S={3,4,6}\displaystyle S = \{3, 4, 6\}?
MCQ
4033
If A={1,2,3,4}\displaystyle A = \{1, 2, 3, 4\}, B={2,4,6,8}\displaystyle B = \{2, 4, 6, 8\} and C={3,4,5,6}\displaystyle C = \{3, 4, 5, 6\} the value of A−(B∪C)\displaystyle A - (B \cup C) is -
MCQ
4034
The range of the function f(x)=3x−2\displaystyle f(x) = 3x - 2 is
MCQ
4132
For a relation R, aRb represents that a is related to b. If for all a, b, c, aRb and bRc gives that aRc, then the relation is
MCQ
4133
Let S={a,b,c,d,e}\displaystyle S = \{a, b, c, d, e\}. The number of non-empty proper subsets of S is
MCQ
4134
If f(y)=11+y\displaystyle f(y) = \frac{1}{1+y} and g(y)=y+1y\displaystyle g(y) = \frac{y+1}{y} then fog(y)=\displaystyle fog(y)=
MCQ
4135
The inverse of the function f(x)=2+3xx+5\displaystyle f(x) = \frac{2+3x}{x+5}, by taking f(x)\displaystyle f(x) as y\displaystyle y, is
MCQ
4216
If A={2,3}\displaystyle A = \{2, 3\}, B={4,5}\displaystyle B = \{4, 5\} and C={5,6}\displaystyle C = \{5, 6\} then the A×(B∩C)\displaystyle A \times (B \cap C) is
MCQ
4265
If f(x)=1+1x\displaystyle f(x)=1+\frac{1}{x}, then the value of f(f(1x))\displaystyle f\left(f\left(\frac{1}{x}\right)\right) is
MCQ
4266
The function f(x)=x2−25x−5\displaystyle f(x) = \frac{x^2 - 25}{x - 5} is undefined at x=5\displaystyle x=5. What value must be assigned to f(5) if f(x) is to be continuous at x=5\displaystyle x=5?
MCQ
4268
Let R is the set of real numbers such that the function f:R→R\displaystyle f: R \to R and g:R→R\displaystyle g: R \to R are defined by f(x)=x2+3x+1\displaystyle f(x) = x^2 + 3x + 1 and g(x)=2x−3\displaystyle g(x) = 2x - 3 then f∘g(x)\displaystyle f \circ g(x) is:
MCQ
1930
In a group of students 80 can speak Hindi, 60 can speak English and 40 can speak Hindi and English both, then number of students is:
MCQ
1958
If A={1,2,3,4}\displaystyle A = \{1, 2, 3, 4\} and B={1,4,9,16,25}\displaystyle B = \{1, 4, 9, 16, 25\} is a function f\displaystyle f is defined from set A\displaystyle A to B\displaystyle B where f(x)=x2\displaystyle f(x) = x^2 then the range of f\displaystyle f is:
MCQ
1948
Consider the following relations on A={1,2,3}\displaystyle A = \{1,2,3\}. R={(1,1),(1,2),(2,1),(2,2),(3,3)}\displaystyle R = \{(1,1), (1,2), (2,1), (2,2), (3,3)\}, S={(1,1),(1,2),(2,2),(2,3)}\displaystyle S = \{(1,1), (1,2), (2,2), (2,3)\} and Φ=empty set\displaystyle \Phi = \text{empty set}. Which one of these forms an equivalence relation?
MCQ
1942
A={1,2,3,4,…,10}\displaystyle A = \{1, 2, 3, 4, \dots, 10\} a relation on A\displaystyle A, R={(x,y)/x+y=10,x∈A,y∈A}\displaystyle R = \{(x, y) / x + y = 10, x \in A, y \in A\}, then domain of R−1\displaystyle R^{-1} is
MCQ
1926
Two Finite sets have m\displaystyle m and n\displaystyle n elements. The total number of subsets of first set is 56 more than the total number of subsets of the second set. The value of m\displaystyle m and n\displaystyle n are
MCQ
1951
On the set of lines, being perpendicular is a ______ relation.
MCQ
1959
Identify the function from the following: (1,1), (1,2), (1,3)
MCQ
1957
Let N\displaystyle N be the set of all natural numbers; E\displaystyle E be the set of all even natural numbers then the function f:N→E\displaystyle f: N \to E defined f(x)=2x,x∈N\displaystyle f(x) = 2x, x \in N
MCQ
4332
Which of the following relations is transitive but not reflexive for the set S={3,4,6}\displaystyle S = \{3, 4, 6\}?
MCQ
4333
If A={1,2,3,4}\displaystyle A = \{1, 2, 3, 4\}, B={2,4,6,8}\displaystyle B = \{2, 4, 6, 8\} and C={3,4,5,6}\displaystyle C = \{3, 4, 5, 6\} the value of A−(B∪C)\displaystyle A - (B \cup C) is -
MCQ
4334
The range of the function f(x)=3x−2\displaystyle f(x) = 3x - 2 is
MCQ
4432
For a relation R, aRb represents that a is related to b. If for all a, b, c, aRb and bRc gives that aRc, then the relation is
MCQ
4433
Let S={a,b,c,d,e}\displaystyle S = \{a, b, c, d, e\}. The number of non-empty proper subsets of S is
MCQ
4434
If f(y)=11+y\displaystyle f(y) = \frac{1}{1+y} and g(y)=y+1y\displaystyle g(y) = \frac{y+1}{y} then fog(y)=\displaystyle fog(y)=
MCQ
4435
The inverse of the function f(x)=2+3xx+5\displaystyle f(x) = \frac{2+3x}{x+5}, by taking f(x)\displaystyle f(x) as y\displaystyle y, is
MCQ
4516
If A={2,3}\displaystyle A = \{2, 3\}, B={4,5}\displaystyle B = \{4, 5\} and C={5,6}\displaystyle C = \{5, 6\} then the A×(B∩C)\displaystyle A \times (B \cap C) is
MCQ
4565
If f(x)=1+1x\displaystyle f(x)=1+\frac{1}{x}, then the value of f(f(1x))\displaystyle f\left(f\left(\frac{1}{x}\right)\right) is
MCQ
4566
The function f(x)=x2−25x−5\displaystyle f(x) = \frac{x^2 - 25}{x - 5} is undefined at x=5\displaystyle x=5. What value must be assigned to f(5) if f(x) is to be continuous at x=5\displaystyle x=5?
MCQ
4568
Let R is the set of real numbers such that the function f:R→R\displaystyle f: R \to R and g:R→R\displaystyle g: R \to R are defined by f(x)=x2+3x+1\displaystyle f(x) = x^2 + 3x + 1 and g(x)=2x−3\displaystyle g(x) = 2x - 3 then f∘g(x)\displaystyle f \circ g(x) is:
MCQ
5548
1. What is the Profit before Taxes for the Year 2, Year 3 and Year 4 of the investment proposal ?
MCQ
5549
2. What is the Cash Inflow after Taxes for the Year 1, Year 2 and Year 3 of the investment proposal ?
MCQ
5550
3. What is the Discounted Cash Inflow after Taxes for the Year 1, Year 2 and Year 3 of the investment proposal ?
MCQ
5551
4. What is the Net Present Value of the investment proposal?
MCQ
5498
1. What would be the Earnings Per Share (EPS) of the company in Plan-I and Plan-II?
MCQ
5499
2. What would be the Market Price per Share (MPS) of the company if Price Earnings Ratio (PE ratio) in Plan-1 is 12 times and Plan-II is 15 times?
MCQ
5500
3. What would be the financial Break Even Point (BEP) in Plan-I and Plan-II?
MCQ
5501
4. What would be the indifference point between Plan-1 and Plan-11?
MCQ
5502
5. What would be the Earnings Per Share (EPS) in Plan-1 and Plan-II at the indifference point as calculated by you above?
MCQ
5503
6. Inventory and Receivables would be:
MCQ
5504
7. Current Assets and Current Liabilities would be:
MCQ
5505
8. JKL Company Ltd. has current assets of ` 1,00,00,000 and current liabilities of ` 50,00,000. The Financial manager of the company desires to make a provision for contingencies @20% of working capital. Accordingly, what would be the amount of working capital requirement for the company?
MCQ
5506
9. The business through private airways is at which phase of product life cycle?
MCQ
5507
10. Tool for identifying the strongest and weakest competitors is known as:
MCQ
5508
11. The strategy being followed by PNL is:
MCQ
5509
12. Relationship being considered between PNL and CMP is indicating:
MCQ
5510
13. The activity of marketing team will be called as:
MCQ
5511
14. Farm Fresh Ltd., a family-owned organic farming business has been operating successfully over the past 10 years. Currently the company is facing stiff competition from the large farming houses. Hence to maintain status quo, the management of the company decided to adopt stability strategy. Which of the following initiatives best support Farm Fresh Ltd.'s stability strategy?
MCQ
5512
15. The role played by middle management is diminishing as the tasks performed by them are increasingly being replaced by new and improved technological tools. As a result, in a three layer organizational structure, middle level is constricted. Which one of the following is a suitable name to such structure?
MCQ
5513
16. In the framework of strategic analysis, which one is a constituent of internal analysis?
MCQ
5514
Question No. 1 is compulsory. Attempt any two questions out of the remaining three questions. In case, any candidate answers extra question(s)/ sub-question(s) over and above the required number, then only the requisite number of questions first
Subjective
5515
Question 1 (a) KP Ltd. has provided the following information: (i) Estimated monthly sales: Month ` in Lakh April-2024 10 May-2024 12 June-2024 15 July-2024 10 August-2024 13 September-2024 14 (ii) Gross Profit Ratio is 20%. (iii) Cost of Goods sold is paid in next month. (iv) Sales are in credit and credit period is allowed for 2 months. (v) Indirect Expenses are paid in the same month. Monthly indirect expenses are as follows: Month ` in Lakh June-2024 1.0 July-2024 1.2 August-2024 1.0 September-2024 1.3 FINANCIAL MANAGEMENT AND STRATEGIC MANAGEMENT (vi) Dividend amounting September 2024, 3 Lakh will be paid in the month of September 2024 (vii) Cash Balance on 01/07/2024 was 1.5 Lakh. (viii)The company has to maintain minimum cash balance of 1 Lakh. If there is cash balance deficit in any month, company would take a temporary short term loan and if cash balance exceed 2 Lakh, then company would invest for short term excess amount of 2 Lakh. (ix) Ignore the interest on short term loans and short term investment. You are required to prepare Cash Budget for three months starting from July 2024. (5 Marks) (b) Following is the Balance Sheet of EXIM Ltd. as on 31stMarch, 2024: Liabilities ` Assets ` Equity Share Capital of ` 100 each 20,00,000 Fixed Assets 50,00,000 Retained Earnings 4,00,000 Current Assets 30,00,000 12.5% Debenture 40,00,000 Current Liabilities 16,00,000 80,00,000 80,00,000 The additional information is given as under: Fixed costs per annum (exclusive interest) : ` 16,00,000 Variable operating cost ratio : 70% Total Assets turnover ratio : 2.5 Income tax rate : 30% You are required to calculate: (i) Earnings Per Share (ii) Operating Leverage (iii) Financial Leverage (iv) Combined Leverage (2 + 1 + 1 + 1 = 5 Marks) (c) Following information have been provided by LP Ltd.: Profit before Tax ` 40 Lakh Tax Rate 30% Equity Share Capital (` 10) ` 40 Lakh Return on Investment 18% Cost of Equity 15% Dividend Payout Ratio 50% You are required: (i) to determine the price of Equity Share of the company as per Walter's Model; (ii) to determine the Dividend Pay-out Ratio by applying Walter's Model assuming the price of equity share of the company is ` 48. (3+2=5 Marks)
Subjective
5516
Question 2 (a) The following information pertain to CMC Limited: Number of Equity Shares 20,00,000 Book Value of 10% Convertible Debentures ` 1,00,00,000 Book Value of 12% Bank Term Loan ` 25,00,000 Market Price of Equity Share ` 55 Market Value of 10% Convertible Debenture ` 108 Face Value of Equity Share ` 10 Face Value of 10% Convertible Debenture ` 100 Beta coefficient of Equity shares of CMC Ltd. 1.5 Risk free rate of return 4.5% Equity risk Premium 9% Rate of taxation 30% The company expects that the share prices will rise in future at an average rate of 6% per annum. The 10% convertible debentures of 100 each will be converted in six years' time into equity shares of the company in the ratio of 1: 4 (4 equity shares for each debenture). The market value of 12% bank term loan is at par. You are required to calculate: (i) Cost of Equity Share Capital by applying Capital Asset Pricing Model (CAPM) Approach (ii) Cost of Convertible Debenture by using approximation method, (iii) Cost of Bank Term Loan (iv) Weighted Average Cost of Capital using Market Value weights (1+2+1+3=7 Marks) (b) The following information pertain to MSD Limited for the year ending 31st March, 2024: Particulars Number of days Raw material storage period 61 days Work-in -progress conversion period 20 days Finished goods storge period 30 days Debt collection period 45 days Creditors payment period 60 days The annual operating cost (including depreciation of ` 4,80,000) was ` 60,00,000. Assume 360 days in a year. You are required to calculate: (i) Operating cycle period (ii) Number of operating cycles in a year (iii) Amount of working capital required for the company (1 + 1 + 1 = 3 Marks) FINANCIAL MANAGEMENT AND STRATEGIC MANAGEMENT
Subjective
5517
Question 3 (a) SRT Limited manufactures steel rods and is now considering to purchase a new aluminium smelting and moulding plant. This plant will have the cost of ` 20,00,000 to purchase and install the plant. It has a useful life of 5 years with a residual value of ` 1,00,000. Production and sales from the new plant are expected to be 1,00,000 units per year. Other estimates are as follows: Selling Price `150 per unit Direct Cost `100 per unit Fixed cost (including depreciation) is ` 8,00,000 per annum. Marketing and promotion cost not included in the above will be ` 1,00,000 and ` 1,60,000 for years 1 and 2, respectively. Additionally, investment in debtors and stocks will increase in year 1 by ` 1,50,000 and ` 2,00,000, respectively. Creditors will also increase by ` 1,00,000 in year 1. Thus, debtors, stocks, and creditors will be recouped at the end of the fifth year. The cost of capital is 18%. Corporate tax is 30% and is paid in the year in which profits are made. Depreciation is tax deductible. The company follows straight line method of depreciation. Required: (i) Calculate the Net Present Value and Profitability Index of the project. (ii) Advise SRT Limited whether the plant should be purchased. The PV factors at 18% are: Year 1 2 3 4 5 PV factor 0.847 0.718 0.609 0.516 0437 (5 + 1 = 6 Marks) FINANCIAL MANAGEMENT AND STRATEGIC MANAGEMENT (b) The equity share capital of Sky Pack Ltd. as on 31st March, 2024 was ` 2,00,000. The relevant ratios of the company are as follows: Current debt to Total debt 0.35 Total debt to Owner's equity 0.65 Fixed assets to Owner's equity 0.55 Total assets turnover 2.5 times Inventory turnover 10 times You are required to prepare the Balance Sheet of Sky Pack Ltd. as on 31stMarch, 2024. (4 Marks)
Subjective
5518
Question 4
Subjective
5519
Question 5 (a) ABC group of companies has five projects at different geographical locations. Each project is managed by a dedicated project manager. A Chief Executive Officer (CEO) is supported by a team of subject matter experts (SMEs) in each function at corporate level of the company. As an accepted practice, the authority and communication flow vertically and horizontally in the company. There are five common functions i.e. finance, human resource, operations, marketing and information technology facilitating each project. Each functional manager is having administrative relationship with respective project manager and functional relationship with related SME with a clear mutual understanding of his or her roles and responsibilities. Identify and explain the organizational structure best suited in the above scenario. State the advantages and disadvantages of the above structure. (1+2+1+1=5 Marks) (b) Ecro Ltd. is an e-commerce company that specializes in selling eco-friendly products. Although the company has been doing well, it still continues actively to strengthen its brand identity, launch creative and impactful marketing campaigns, and introduce new and innovative eco-friendly products. However, the company has started facing increasing competition from large retailers who are entering the eco-friendly space. To face competition the company quickly started to adapt to the changing market conditions, analyse the competitors' strategies, adopt different styles of marketing in response to competitors action and counteract competitors' pricing strategies. Discuss the strategic approaches taken by Ecro Ltd. in the two different situations to stay competitive. Explain the strategy that Ecro Ltd. should adopt in future to remain competitive and gain competitive advantage. (1 + 1 + 3 = 5 Marks) INTERMEDIATE EXAMINATION: JANUARY, 2025 (c) Organic Beverages has been manufacturing various soft drinks for over a decade. It has developed a sugar free beverage to cater to the needs of specific customers by spending heavily on research and development for this product. In addition, a lot of money was spent on marketing (branded as 'Say no to Sugar') and in obtaining licence for it. In a span of five months, company has gained a major share in the market for this new product and it is growing rapidly. Profitability of this product is also better. In order to take the advantage of best opportunity for expansion, it has to make heavy investment to maintain their position in current and new market. Classify 'Say no to Sugar' product in the most related category in the two dimensional growth share matrix as per Boston Consulting Group. Explain the strategies which can be pursued post identification and classification of products in such matrix. Also state the limitations of this technique as one of the strategic options. (1 + 2 + 2 = 5 Marks)
Subjective
5520
Question 6 (a) "International development is expensive and challenging". In the context of the statement, explain the internationalization of business and the steps involved in such strategic planning. (5 Marks) (b) "Managing stakeholders is critical to the success of a project". Explain how Mendelow's Matrix helps in managing stakeholders and categorizing the stakeholders into groups. (5 Marks)
Subjective
5521
Question 7 (a) Outline the main levels of management generally found in an organization. Also explain the types of networks of relationship between these levels and amongst the same levels of a business. (3 + 2 = 5 Marks) (b) What do you mean by strategic performance measures? State the reasons for the importance of strategic performance measures for an organization. (1 + 4 = 5 Marks)
Subjective
5522
Question 8 (a) As per one of the five forces of competition, Michael Porter stated that the more intensive is the rivalry, the less attractive is the industry. In view of this, explain the conditions in which rivalry among competitors tends to be cut throat and industry profitability is low. (5 Marks) (b) Explain the 'product market growth matrix' as propagated by Igor Ansoff as a device for identifying growth opportunities for the future. (5 Marks) OR INTERMEDIATE EXAMINATION: JANUARY, 2025 (b) Write a short note on the key strategic drivers of an organization. (5 Marks)
Subjective
5523
1. What will be the total manufacturing cost and total cost of sales on cash cost basis?
MCQ
5524
2. What will be the total estimated finished goods inventory and total debtors on cash cost basis?
MCQ
5525
3. What will be the total estimated current assets on cash cost basis?
MCQ
5526
4. What will be the total estimated current liabilities?
MCQ
5527
5. What will be the estimated working capital to be submitted by you in the proposal?
MCQ
5528
6. A company has net worth of ` 5,00,000. Its debt to equity ratio is 2. Interest on debt is 10%. The company earns an operating profit of ` 4,00,000. Tax rate is 30%. What will be the financial leverage of the company?
MCQ
5529
7. T Ltd. is looking for a capital project in order to replace its existing old machine. It got two proposals to consider; details of which are given below: Proposal X Proposal Y Initial investment ` 6,50,000 ` 7,80,000 Estimated useful life 5 Years 3 Years Annal cash inflows ` 1,90,000 ` 3,50,000 Cost of capital 10% 10% Year 1 2 3 4 5 PVIF0.10, t 0909 0.826 0.751 0.683 0.621 PVIFA0.10, t 0.909 1.736 2.487 3.170 3.791 What will be Equivalent Annual NPV for Proposal X and Proposal Y?
MCQ
5530
8. Q Ltd. is planning to pay dividend of ` 2 per share in next year. Growth rate of company is 8% p.a. Current market price per share is ` 51. Flotation cost is ` 1 per share. FINANCIAL MANAGEMENT AND STRATEGIC MANAGEMENT What will be cost of equity?
MCQ
5531
9. In order to position itself as the best service provider, stating year-on-year growth, indicates which one of the components of the strategic intent?
MCQ
5532
10. Analysis of strategic groups and cost structure can be termed as, which type of strategic analysis?
MCQ
5533
11. Entering into business of manufacturing of Robots can best be described as:
MCQ
5534
12. Elevating customer service to unprecedented level by providing better customer interface, online repair service and service on site is known as:
MCQ
5535
13. While preparing a Power Interest matrix of stakeholders, the position of Mr. X will be categorized in which one of the following quadrants? FINANCIAL MANAGEMENT AND STRATEGIC MANAGEMENT
MCQ
5536
14. In response to a scheme of subsidy by the state government, a company started manufacturing E-Vehicles. Some of the customers were not at ease with battery life and time consumed in recharging the battery. Some of the customers were apprehensive about frequent incidents of battery catching fire. All these resulted in half-hearted response from the customers in evolving EV market. Here, the customers' response is indicating towards which one of the limitations of strategic management?
MCQ
5537
15. M/s. A is providing mobile phones and Wi-Fi services in the country. M/s. B and M/s. C are other similar service providers already in operation. In competitive landscape, M/s. B and M/s. C decided to merge with each other. Such merger was an unexpected development in the industry. M/s. A decided to cope-up with such eventuality by intense review of its strategy and to form a core group to handle the situation. The situation where intense review of strategy is needed due to merger between M/s. B and M/s. C, indicates towards which type of strategic control for M/s. A?
MCQ
5538
16. M/s. SPG is a multi-product multi-business enterprise. It has four prominent divisions. Each division functions as an independent product center with its own set of activities managed by respective division head, which is responsible for its own performance and profitability. This organizational structure is known as:
MCQ
5539
Question No. 1 is compulsory. Attempt any two questions out of the remaining three questions. In case, any candidate answers extra question(s)/ sub-question(s) over and above the required number, then only the requisite number of questions first answered in the answer book shall be valued and subsequent extra question(s) answered shall be ignored. Working notes should form part of the answer.
Subjective
5540
Question 1 (a) The following information is available for S Ltd. for the year ended 31st March, 2025: Raw Material consumed: 20% of COGS Raw Material Inventory turnover ratio: 4.00 Finished Goods Inventory holding period: 0.75 month Gross profit (based on COGS): 12.50% Debtor collection period (all sales are credit sales): 3 months Proprietary ratio: 0.3125 Fixed Assets turnover ratio (based on sales): 3.00 Fixed Assets to Total Assets: 40% Fixed Assets = ₹12,00,000; Long-term Debt = ₹15,00,000 Prepare a Balance Sheet as on 31st March, 2025. (5 Marks) (b) Y Ltd. produces energy drinks. Rate of return on earnings = 25%. Currently retains 60% and distributes rest. Current P/E ratio = 8, EPS = ₹10. According to Gordon's Model: (i) Retention ratio if company wants P/E = 12, Ke = 20%? (2 Marks) (ii) Expected price per share after one year if targeted P/E of 12 is achieved? (1 Mark) (iii) Change in retention ratio if P/E = 10 and Ke = 17.50%? (2 Marks) (c) A Ltd. for year ended 31st March, 2025: P/V ratio = 24%, Operating leverage = 2.00, Financial leverage = 1.50 Interest Expenses = ₹12,000, Tax rate = 30%, No. of Equity Shares = 1,000 (i) Prepare Income Statement. (ii) Calculate EPS. (iii) % change in EPS if sales increase by 5%. (2+1+2 = 5 Marks)
Subjective
5541
Question 2 (a) Capital structure of B Ltd. for year ended 31st March, 2025: Equity share capital @₹10 each = ₹14,00,000 10% Preference share capital @₹1,000 each = ₹10,00,000 Debenture @₹100 each = ₹9,60,000 Bank Loan = ₹6,40,000 Risk-free rate = 14%, Market rate = 19%, Beta = 1.20 10% Preference shares redeemable at ₹1,065.40 after 3 years. Interest on bank loan = 1.30 times interest on debentures. Debentures redeemable at par after 5 years. Flotation cost = ₹4 per debenture. Tax rate = 30%. Cost of capital = 14%. Calculate: (i) Cost of Equity, (ii) Cost of Preference Share (YTM method), (iii) Post-tax cost of debenture (approximation method), (iv) Interest rate of bank loan. (1+2+3+2 = 8 Marks) (b) H Ltd.: EPS = ₹3.00, ROI = 20%, Cost of equity = 15%. As per Walter's Model, what is the maximum and minimum price of share? (2 Marks)
Subjective
5542
Question 3 (a) Capital project data: Annual interim cash inflows for first two years: ₹1,00,000 Annual interim cash inflows for next two years: ₹80,000 Useful life: 4 years; Salvage value at end: ₹50,000; IRR = 12%; Cost of capital = 10% Calculate: (i) Initial investment, (ii) NPV, (iii) Profitability Index, (iv) Discounted Payback Period, (v) MIRR (1+1+1+1+2 = 6 Marks) (b) Z Ltd. is an unlevered company. Wants to repurchase equity shares of ₹300 lakhs by issuing 12% debentures of same amount. Current MV of Z Ltd. = ₹1,400 lakhs, cost of capital = 18%, EBIT maintained, dividend payout = 100%, tax = 30%. As per MM approach, impact on: (i) Market Value of Z Ltd., (ii) Overall cost of capital, (iii) Cost of equity. (4 Marks)
Subjective
5543
Question 4 (a) What is agency cost and what are its types? How can a company minimize agency cost and align the interest of manager and shareholder? (4 Marks) (b) What are key features of bridge financing? (4 Marks) (c) What is hierarchy of financing under 'Pecking Order' theory, and why does it exist? (2 Marks) OR (c) "The total risk of any business is the combination of degree of operating and financial risk". Consider the table of DOL and DFL combinations and comment on total risk profile (Lower/Higher/Moderate). Also select the best combination. (2 Marks)
Subjective
5552
5. What is the Discounted Payback period of the investment proposal ?
MCQ
5553
6. A company has sales of ` 6,00,000, variable cost of ` 2,40,000, fixed operating cost of ` 2,70,000. The financial leverage is 2.5. The company wants to double its EBIT. The percentage change in ales required in order to double its EBIT will be :
MCQ
5554
7. The capital structure of KPS Limited includes 5,00,000 equity shares of ` 10 each. The market price of equity share (cum-dividend) is ` 75 per share. The company has declared to pay dividend on equity shares @ ` 6 per share which will be paid within next three days. The company has a history of consistent growth in its dividends. It has been predicted that in the next year KPS Limited will pay dividend on its equity shares@ ` 7.59 per share. The rate of dividend growth will be maintained in foreseeable future. The cost of equity is calculated as:
MCQ
5555
8. ZX Limited has total assets of ` 7,20,000 and its Shareholders' equity is ` 4,50,000. The net profit margin of ZX Limited is 12.5% and asset turnover ratio is 1.5. Using the DuPont model, the return on equity of ZX Limited is calculated as :
MCQ
5556
9. The strategy in which the company wants to keep ahead and reap the first mover advantages in the industry, is known as:
MCQ
5557
10. In context to service in transportation through railways, the company is analyzing a relationship between volume of business on one axis with respect to time on another axis. As per Product Life Cycle (PLC), which stage this service is passing through:
MCQ
5558
11. In Strategic Management, the concept of decrease in the overall per mile operating cost due to increase in efficiency and cumulative volume of services is depicted as:
MCQ
5559
12. As per strategies propagated by Michael Porter, niche marketing strategy for transporting goods through airways for a large customer segment on an assurance of 'delivery by next day', is known as:
MCQ
5560
13. The philosophy of the company stated as, 'to bring the best user experience to its customers through timely and safe delivery of goods', is indicating towards:
MCQ
5561
14. Super Products Ltd. is having four divisions, i.e. Alpha, Beta, Cos and Theta. All the divisions are independent product center and are also integral part of product Gama of the company. Each division contains its own set of activities under the control of respective general manager. Each general manager is responsible for his respective product line and its profitability. While having own set of competitors, each center has its own competitive advantages with the resources and capabilities they develop. Such structure is known as:
MCQ
5562
15. Always Ahead Ltd. is an established player in FMCG, Herbs, Health care and White goods. Company has classified its portfolio on investments in different businesses in four quadrants as suggested by Boston Consulting Group. On further analysis of relationship between market growth rate and relative market share for White goods business, it is found that opportunities to increase its market share are there. Emphasis need to be given to make a strong future with large market share even by foregoing short-term earnings for this business. Which strategy is being pursued by the company for White goods segment:
MCQ
5563
16. The correct sequence of the stages as per Kurt Lewin's model of change is:
MCQ
5564
3. Stress and Learning Challenges: The flatter structure and increased need for personal interactions may create stress for employees, especially those who lack the confidence for active participation in organization-sponsored learning programs. (
MCQ
5565
Question No. 1 is compulsory. Attempt any two questions out of the remaining three questions. In case, any candidate answers extra question(s)/ sub-question(s) over and above the required number, then only the requisite number of questions first
Subjective
5566
Question 1 (a) Financial information for the year 2023-24 of two companies, N Limited and C Limited are as under: Details N Limited C Limited Equity share capital (` 100 each) ` 10,00,000 ` 8,00,000 Debt ` 5,00,000@10% ` 7,00,000@8% Fixed Cost 3,00,000 3,36,000 Combined Leverage 8 4.5 Financial Leverage 2 1.5 You are required to calculate: (i) Contribution for N Ltd. and C Ltd. (ii) Margin of safety in % for N Ltd. and C. Ltd. (iii) Sales of C Ltd. (5 Marks) (b) The following information is available for SK Limited for the year ended on 31st March,2024: Particulars ` Cost of production 15,48,000 Cost of goods sold 14,61,000 Average stock of work-in-progress 94,600 Average stock of finished goods 2,43,500 Administration and Selling expenses 4,14,000 Receivables collection period 36 days Raw Material Storage period 65 days Creditors payment period 63 days You are required to calculate the working capital requirement by operating cycle method. Assume a 360 days year. (5 Marks) (c) Following information relates to MNP Limited for the year ended on 31sMarch, 2024: Inventory turnover ratio (based on cost of goods sold) 7.5 times Total assets turnover ratio 2.5 times Long term debt to Shareholders' fund 0.6:1 Debtors collection period 30 days Gross profit ratio 25% on sales Current Ratio 2.9:1 Balance Sheet as on 31st March,2024 Liabilities ` Assets ` Equity share capital 6,00,000 Fixed Assets ? Reserves & Surplus 3,00,000 Inventories ? Long term debt ? Debtors ? Creditors 3,00,000 Cash ? Total Total FINANCIAL MANAGEMENT AND STRATEGIC MANAGEMENT You are required to complete the Balance Sheet of MNP Limited as on 31st March,2024. Assume a 360 days year and all sales are credit sales. (5 Marks)
Subjective
5567
Question 2 (a) Capital structure of T Limited as on 1st April,2024 is as under: ` Equity Share Capital (` 10 per share) 50,00,000 10% Debentures (` 100 per Debenture) 40,00,000 12% Preference Share Capital (10,000 shares of ` 100 each) 10,00,000 Additional Information: (1) The risk free rate of return is 10%. The Beta of T Ltd. is 1.75 and the return on market portfolio is 12%. The Equity shares have a current market price of ` 70 per share. (2) The debentures are trading at a market price of ` 80 per debenture. The Debentures are to be redeemed after 5 years at par. (3) Preference shares are redeemable after 5 years at a premium of 5%, presently selling at ` 104 per share. (4) The Company pays tax at a rate of 30%. (5) The Cost of Debentures are to be calculated on Yield to Maturity approach. FINANCIAL MANAGEMENT AND STRATEGIC MANAGEMENT (6) The present value factors at 10% and 14% are: Year 1 2 3 4 5 PVIF0.10,t 0.909 0.826 0.751 0.683 0.621 PVIF0.14,t 0.877 0.769 0.675 0.592 0.519 You are required to calculate Weighted Average Cost of Capital (after tax) of T Limited using Market value weights. (8 Marks) (b) Explain Angel Financing. (2 Marks)
Subjective
5568
Question 3 (a) AB Enterprises deals in hardware materials having current turnover ` 30 Lakhs per annum. All sales are on credit and average collection period is 30 days with zero bad debts. The customers are requesting to increase the credit period. As a result of increase in credit period sales will also increase. Other information is as under: Credit policy | Increase in collection period (days) | Increase in sales (`) | Bad debts anticipated A | 15 | 3,00,000 | 1% B | 30 | 5,00,000 | 3.5% The Selling price is ` 100/- per unit. Variable cost per unit is ` 50/- and fixed cost is ` 5,00,000. Required rate of return on additional investment is 20%. Creditors for variable cost are ready to give 15 days extra credit for the additional cost incurred. Assume a 360 days year. You are required to analyse the present and proposed credit policies using the "Total Approach" method and recommend the credit policy to be adopted. (5 Marks) (b) ER Private Limited has a paid-up capital ` 2,50,000 consisting of 25,000 Equity shares of ` 10 each. The Market price per share is ` 24 with PE ratio of 8. The company is planning to purchase a plant which will cost ` 5,00,000. This plant is expected to yield earnings before interest and taxes of ` 2,00,000 per annum. It has two alternatives to finance the plant: Alternatives | Equity | Debt A | 100% | - B | 50% | 50% Other information is as under: (i) Cost of debt is 12%. (ii) Equity shares of face value of ` 10 each will be issued at a premium of ` 10 per share. (iii) PE ratio of Leveraged company will be 7. (iv) Tax rate -40%. Advise which alternative is the most suitable to raise the funds for additional capital, keeping in mind to maximize the benefit to its Shareholders. (5 Marks)
Subjective
5569
Question 4
Subjective
5570
Question 5 (a) M/s. MTS Ltd, is one of the mobile telephone service providers in India. It has its own mobile network, towers and distribution channels. It operates through its team of network operation, technicians, marketing, sales and after sales services. Currently all the team members are on its roll. Company knows that market is densely competitive. The environment is quite unstable and likely to remain so. Customer's taste and preferences are changing very fast. There is a strong need for innovation and quick response. While eliminating in-house business functions, company is considering outsourcing major activities and focusing on its core competencies. In the given situation identify the organizational structure suitable for the company. Also outline the merits and demerits in going for the identified structure. (5 Marks) (b) Symergy Ltd. is manufacturing a product since year 2010. The company was doing well till year 2022. After that its market share started declining. Accumulated losses started mounting and in turn carried a persistent negative impact on its cash flow. As a result morale of the employees was not up to mark. The Board of Directors (BoD) of the company thought it proper to continue in business by placing emphasis on improvement in internal efficiency. In view of the same, the BoD is evolving a workable action plan with intent to ensure a radical change in direction in strategy which includes revamping in top management. Which retrenchment strategy company should adopt in the given situation? Also state the stages in the action plan for the strategy. (5 Marks) (c) Market for baby care, readymade garments for new born, toys and strollers meant for babies are there. M/s. Maa ki Pasand is desirous to introduce new products for existing customers and new customers as well. The market for such products is narrow. On one side there are customers who are price conscious and on the other side there are customers who are ready to pay premium charges for an upscale product. The company wants to charge low price, relative to other firms that compete within the target market for customers who are price sensitive and also wants to charge premium based on uniqueness for rest of its products. Which of the strategy is being considered by the company, out of strategies as suggested by Michael Porter at business level. Also outline the advantages and disadvantages using such strategy. (5 Marks)
Subjective
5571
Question 6 (a) Explain in brief the term 'objectives' as part of strategic intent. Also outline the characteristics, the objectives of a company must possess to be meaningful and to serve the intended role. (5 Marks) (b) Value Chain Analysis consist two activities: Primary activities and Support activities. As per Michael Porter both the activities are intertwined. Do you agree with the statement? Also delineate the main areas in which primary activities of any organization are grouped. (5 Marks)
Subjective
5572
Question 7 (a) Explain the four specific criteria of sustainable competitive advantages that a company can use to determine the capabilities that are core competencies. (5 Marks) (b) Start-ups rarely aim for stability strategy. While agreeing with the statement or otherwise, support your point of view by briefly stating as to when the stability strategy is meaningful. State the major reasons for considering stability strategy as one of the corporate strategies by a company. (5 Marks)
Subjective
5573
Question 8 (a) In light of the five forces as propagated by Michael Porter, explain the common barriers which may cause restrain for the keenness of new entrepreneurs. (5 Marks) (b) Strategic performance measures are key indicators that organizations use to track the effectiveness of their strategies and make informed decisions about resource allocation. In light of the statement, state various types of Strategic performance measures. (5 Marks) OR (b) Explain the pointers for navigating change during digital transformation. (5 Marks)
Subjective
1893
The number of integers from 1\displaystyle 1 to 100\displaystyle 100 which are neither divisible by 3\displaystyle 3 nor by 5\displaystyle 5 nor by 7\displaystyle 7 is
MCQ
1894
Let U\displaystyle U be the universal set, A\displaystyle A and B\displaystyle B are the subsets of U\displaystyle U. If n(U)=650\displaystyle n(U) = 650, n(A)=310\displaystyle n(A) = 310 n(A∩B)=95\displaystyle n(A \cap B) = 95 and n(B)=190\displaystyle n(B) = 190, then n(A∩B)c\displaystyle n(A \cap B)^c is equal to (A\displaystyle A and B\displaystyle B are the complement of A\displaystyle A and B\displaystyle B respectively):
MCQ
1895
Two finite sets have x\displaystyle x and y\displaystyle y number of elements. The total number of subsets of first is 56\displaystyle 56 more than the total number of subsets of second. The value of x\displaystyle x and y\displaystyle y is:
MCQ
1896
Given A=(2,3)\displaystyle A = (2, 3), B=(4,5)\displaystyle B = (4, 5), C=(5,6)\displaystyle C = (5, 6) then A×(B∩C)\displaystyle A \times (B \cap C) is
MCQ
1897
If the universal set E={x∣x is a positive integer <25}\displaystyle E = \{x \mid x \text{ is a positive integer } < 25\}, A={2,6,8,14,22}\displaystyle A = \{2, 6, 8, 14, 22\}, B={4,8,10,14}\displaystyle B = \{4, 8, 10, 14\}
MCQ
1898
In a town of 20,000\displaystyle 20,000 families it was found that 40%\displaystyle 40\% families buy newspaper A\displaystyle A, 20%\displaystyle 20\% families buy newspaper B\displaystyle B and 10%\displaystyle 10\% families buy newspaper C\displaystyle C, 5%\displaystyle 5\% families buy A\displaystyle A and B\displaystyle B, 3%\displaystyle 3\% buy B\displaystyle B and C\displaystyle C and 4%\displaystyle 4\% buy A\displaystyle A and C\displaystyle C, if 2%\displaystyle 2\% families buy all the three newspaper, then the number of families which buy only A\displaystyle A is:
MCQ
1899
The number of items in the set A\displaystyle A is 40\displaystyle 40; in the set B\displaystyle B is 32\displaystyle 32; in the set C\displaystyle C is 50\displaystyle 50; in both A\displaystyle A and B\displaystyle B is 4\displaystyle 4, in both A\displaystyle A and C\displaystyle C is 5\displaystyle 5; in both B\displaystyle B and C\displaystyle C is 7\displaystyle 7 in all the sets 2\displaystyle 2. How many are in at least one of the set?
MCQ
1937
From a group of 200 persons, 100 are interested in music, 70 in photography and 40 in swimming, furthermore 40 are interested in both music and photography, 30 in both music and swimming, 20 in photography and swimming and 10 in all the three. How many are interested in photography but not in music and swimming?
MCQ
1939
In a town of 20,000 families it was found that 40% families buy newspaper A, 20% families buy newspaper B and 10% families buy newspaper C, 5% families buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three newspaper, then the number of families which buy A only is
MCQ
1940
The number of proper subsets of the set {3,4,5,6,7}\displaystyle \{3, 4, 5, 6, 7\} is
MCQ
1941
If A={1,2}\displaystyle A = \{1, 2\} and B={3,4}\displaystyle B = \{3, 4\}, Determine the number of relations from A\displaystyle A and B\displaystyle B:
MCQ
1943
In the set of all straight lines on a plane which of the following is not "TRUE"?
MCQ
1944
If AisrelatedtoBifandonlyifthedifferencein\displaystyle A is related to B if and only if the difference inAand\displaystyle andB$ is an even integer. This relation is
MCQ
1945
Let A={1,2,3}\displaystyle A = \{1, 2, 3\} and consider the relation R={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)}\displaystyle R = \{(1,1), (2,2), (3,3), (1,2), (2,3), (1,3)\} then R\displaystyle R is:
MCQ
1946
Given the relation R={(1,2),(2,3)}\displaystyle R = \{(1,2), (2,3)\} on the set A={1,2,3}\displaystyle A = \{1,2,3\}, the minimum number of ordered pairs which when added to R\displaystyle R make it equivalence relation is
MCQ
1947
If R\displaystyle R be a relation defined on the set of Natural numbers as "x\displaystyle x R\displaystyle R y⇔(x−y)\displaystyle y \Leftrightarrow (x-y) is divisible by 5\displaystyle 5" ∀x,y∈N\displaystyle \forall x, y \in N then the relation R\displaystyle R is
MCQ
1949
Let A={1,2,3}\displaystyle A = \{1,2,3\} and consider the relation R={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)}\displaystyle R = \{(1,1), (2,2), (3,3), (1,2), (2,3), (1,3)\} then R\displaystyle R is
MCQ
1950
On the sets of lines in a plane the Relation "is perpendicular to" is
MCQ
1952
Let A={1,2,3}\displaystyle A = \{1,2,3\} and R={(1,1),(2,2),(3,3),(1,2)}\displaystyle R = \{(1,1), (2,2), (3,3), (1,2)\} is
MCQ
1953
Let A={1,2,3}\displaystyle A = \{1,2,3\} then the relation R={(1,1),(2,3),(2,2),(3,3),(1,2)}\displaystyle R = \{(1,1), (2,3), (2,2), (3,3), (1,2)\} is called
MCQ
1954
On the set of lines, being perpendicular is a satisfies which property :
MCQ
1955
On the set of lines in a plane the Relation "is perpendicular to" is
MCQ
1956
R={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)}\displaystyle R = \{(1,1), (2,2), (3,3), (1,2), (2,3), (1,3)\} on the set A={1,2,3}\displaystyle A = \{1,2,3\} is:
MCQ
1960
If f(x)=x2\displaystyle f(x) = x^2 and g(x)=x\displaystyle g(x) = \sqrt{x}, then
MCQ
1961
If A={a,b,c,d}\displaystyle A = \{a, b, c, d\}, B={p,q,r,s}\displaystyle B = \{p, q, r, s\} which of the following relation is a function from A\displaystyle A to B\displaystyle B
MCQ
1962
If f(n)=f(n−1)+f(n−2)\displaystyle f(n) = f(n-1) + f(n-2) when n≥2\displaystyle n \ge 2, f(0)=0\displaystyle f(0) = 0, f(1)=1\displaystyle f(1) = 1 then f(7)=?\displaystyle f(7) = ?
MCQ
1963
If f(x)=x+1x−1\displaystyle f(x) = \frac{x+1}{x-1}, find f−1(x)\displaystyle f^{-1}(x).
MCQ
1964
The inverse function f−1\displaystyle f^{-1} of f(x)=3y\displaystyle f(x) = 3y is:
MCQ
1965
Let f:R→R\displaystyle f: R \to R be defined by f(x)={2x for x≤3x2+1 for 3<x≤63x for x>6\displaystyle f(x) = \begin{cases} 2x \text{ for } x \le 3 \\ x^2+1 \text{ for } 3 < x \le 6 \\ 3x \text{ for } x > 6 \end{cases} The value of f(−1)+f(2)+f(4)\displaystyle f(-1) + f(2) + f(4) is
MCQ
1966
The range of the function f\displaystyle f defined by f(x)=16−x2\displaystyle f(x) = \sqrt{16-x^2} is
MCQ
1967
Let A=R−{3}\displaystyle A = R - \{3\} and B=R−{1}\displaystyle B = R - \{1\}. Let f:A→B\displaystyle f: A \to B defined by f(x)=x−2x−3\displaystyle f(x) = \frac{x-2}{x-3}. What is the value of f−1(12)\displaystyle f^{-1}(\frac{1}{2})?
MCQ
1968
If f(x)=x2−1\displaystyle f(x) = x^2-1 and g(x)=2x+3\displaystyle g(x) = 2x+3, then [fog](3)−gof(−3)]\displaystyle [fog](3)-gof(-3)] is?
MCQ
1969
If u(x)=11−x\displaystyle u(x) = \frac{1}{1-x}, then u3(x)\displaystyle u^3(x) is:
MCQ
1970
If f={(2,2);(3,3);(4,4);(5,5);(6,6)}\displaystyle f = \{(2,2); (3,3); (4,4); (5,5); (6,6)\} be a relation on set A={2,3,4,5,6}\displaystyle A = \{2,3,4,5,6\}, then f\displaystyle f is:
MCQ
1971
If f(y)=y−1y\displaystyle f(y) = \frac{y-1}{y}, find f−1(x)\displaystyle f^{-1}(x).
MCQ
1972
If f(x):N→R\displaystyle f(x): N \to R is a function defined as f(x)=4x+3\displaystyle f(x) = 4x+3, ∀x∈N\displaystyle \forall x \in N, then f−1(x)\displaystyle f^{-1}(x) is:
MCQ
1974
If f(x)=x1−x\displaystyle f(x) = \frac{x}{1-x} & g(x)=x1+x\displaystyle g(x) = \frac{x}{1+x}, then gof(x)\displaystyle gof(x) is
MCQ
1975
Let f:R→R\displaystyle f: R \to R be such that f(x)=2x\displaystyle f(x) = 2^x, then f(x+y)\displaystyle f(x+y) equals
MCQ
1976
If f(x)=x2−4x−2\displaystyle f(x) = \frac{x^2-4}{x-2}, then f(2)\displaystyle f(2) is
MCQ
1977
If f(x)=x2−x\displaystyle f(x) = x^2-x and f(1)=−10\displaystyle f(1) = -10 then the value of K\displaystyle K is
MCQ
1978
Let R\displaystyle R be the set of real numbers such that the function f:R→R\displaystyle f: R \to R and g:R→R\displaystyle g: R \to R are defined by f(x)=x2+3x+1\displaystyle f(x) = x^2+3x+1 and g(x)=2x−3\displaystyle g(x) = 2x-3. Find (fog)\displaystyle (fog).
MCQ
1987
If f(x)=x2−4x−2then\displaystyle f(x) = \frac{x^2-4}{x-2} thenf(2)$ is.
MCQ
1979
If A={1,2,3,4}\displaystyle A = \{1,2,3,4\}, B={2,4,6,8}\displaystyle B = \{2,4,6,8\}, f:A→B\displaystyle f: A \to B then f−1\displaystyle f^{-1} is:
MCQ
1980
If f(x)=x2−1\displaystyle f(x) = x^2-1 and g(x)=2x+3\displaystyle g(x) = 2x+3 then gof(3)\displaystyle gof(3)
MCQ
1981
Find g∘f\displaystyle g \circ f for the functions f(x)=x\displaystyle f(x) = \sqrt{x}, g(x)=2x2+1\displaystyle g(x) = 2x^2+1.
MCQ
1982
Find f∘g\displaystyle f \circ g for the functions f(x)=x2\displaystyle f(x) = x^2, g(x)=2x2+1\displaystyle g(x) = 2x^2+1.
MCQ
1983
If A={1,2,3,4}\displaystyle A = \{1,2,3,4\} and B={1,4,9,16,25}\displaystyle B = \{1,4,9,16,25\} is a function f\displaystyle f is defined set A\displaystyle A to B\displaystyle B where f(x)=x2\displaystyle f(x) = x^2 then the range of f\displaystyle f is:
MCQ
1984
If f(x)=x+3\displaystyle f(x) = x+3 and g(x)=x2\displaystyle g(x) = x^2, then fog(x)\displaystyle fog(x)
MCQ
1985
A function f(x)\displaystyle f(x) is an even function, if
MCQ
1988
If f(x)=3x2+2x\displaystyle f(x) = 3x^2+2x & f(0)=0\displaystyle f(0) = 0 then find f(2)\displaystyle f(2).
MCQ
1989
If f(x)=x2−1\displaystyle f(x)=x^2-1 and g(x)=x+12\displaystyle g(x)=\frac{x+1}{2}, then f(3)f(3)+g(3)\displaystyle \frac{f(3)}{f(3)+g(3)} is
MCQ
1990
If f(x)=2+x2−x\displaystyle f(x)=\frac{2+x}{2-x}, then f−1(x)\displaystyle f^{-1}(x)
MCQ
1991
If f:R→R\displaystyle f: R \to R is a function, defined by f(x)=2x\displaystyle f(x)=2^x; then f(x+y)\displaystyle f(x+y) is
MCQ
1992
If f(x)=x+2,g(x)=7x\displaystyle f(x)=x+2, g(x)=7^x than g of (x)=\displaystyle g \text{ of } (x)=
MCQ
1993
Let R be a relation on N defined by x+2y=8\displaystyle x+2y=8. The domain of R is:
MCQ
1994
The domain of the function f(x)=x2+3x+5x2−5x+4\displaystyle f(x)=\frac{x^2+3x+5}{x^2-5x+4} is:
MCQ
1995
If f(p)=11−p\displaystyle f(p)=\frac{1}{1-p}, then f−1\displaystyle f^{-1} is
MCQ
1996
Determine f(x)\displaystyle f(x), given that f′(x)=12x2−4x\displaystyle f'(x)=12x^2-4x and f(−3)=17\displaystyle f(-3)=17
MCQ
1998
If f(x)=x1+x2\displaystyle f(x)=\frac{x}{\sqrt{1+x^2}} and g(x)=x1−x2\displaystyle g(x)=\frac{x}{\sqrt{1-x^2}} Find fog?\displaystyle fog?
MCQ
1999
The range of the relation {(1,0)(2,0)(3,0)(4,0)(0,0)}\displaystyle \{(1,0)(2,0)(3,0)(4,0)(0,0)\} is
MCQ
2000
If f(x)=x+2,g(x)=7x\displaystyle f(x)=x+2, g(x)=7^x, then gof(x)=\displaystyle go f(x)=
MCQ
2001
If f(x)=2x+2\displaystyle f(x)=2x+2 and g(x)=x2\displaystyle g(x)=x^2, then the value of fog(4)\displaystyle fog(4) is:
MCQ
2002
Let R is the set of real numbers, such that the function f:R→R\displaystyle f: R \to R and g:R→R\displaystyle g: R \to R are defined by f(x)=x2+3x+1\displaystyle f(x)=x^2+3x+1 and g(x)=2x−3\displaystyle g(x)=2x-3. Find (fog):\displaystyle (fog):
MCQ
2003
Let R is the set of real numbers such that the function f:R→R\displaystyle f: R \to R and g:R→R\displaystyle g: R \to R are defined by f(x)=x2+3x+1\displaystyle f(x)=x^2+3x+1 and g(x)=2x−3\displaystyle g(x)=2x-3 Find (fog):\displaystyle (fog):
MCQ
2004
Given the function f(x)=(2x+3)\displaystyle f(x)=(2x+3), then the value of f(2x)−2f(x)+3\displaystyle f(2x)-2f(x)+3 will be:
MCQ
2005
Find f∘g\displaystyle f \circ g for the functions f(x)=x8,g(x)=2x2+1\displaystyle f(x)=x^8, g(x)=2x^2+1
MCQ
2006
If f(x)=x+2,g(x)=7x\displaystyle f(x)=x+2, g(x)=7^x, then g∘f(x)=\displaystyle g \circ f(x)=
MCQ
2007
X={x,y,z,w};Y={1,2,3,4};H={(x,1);(y,2);(y,3);(z,4);(x,4)}\displaystyle X=\{x,y,z,w\}; Y=\{1,2,3,4\}; H=\{(x,1);(y,2);(y,3);(z,4);(x,4)\}
MCQ

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