The value of 6n+4+3n+3 × 2n+35 × 6n+6n is

Option c: 252. Solution: We want to evaluate the expression: 6n+4 + 3n+3 × 2n+35 × 6n + 6n First, simplify the terms using exponent laws: - In the numerator, we can combine 3n+3 × 2n+3 using the rule xa × ya = (xy)a : 3n+3 × 2n+3 = (3 × 2)n+3 = 6n+3 - In the denominator, combine the like terms: 5 × 6n + 6n = (5 + 1) × 6n = 6 × 6n = 6n+1 Substitute these back into the expression: 6n+4 + 6n+36n+1 Factor out the common term 6n+3 from the numerator: 6n+4 + 6n+3 = 6n+3(6 + 1) = 7 × 6n+3 Now, divide by the denominator: 7 × 6n+36n+1 = 7 × 6(n+3) - (n+1) = 7 × 62 Calculate the final value: 7 × 36 = 252 This matches Option C. Note: The textbook answer key incorrectly specifies Option D ( 262 ) as the correct choice. However, the exact mathematical calculation clearly shows that the result is 252 (Option C). Hence, Option C is the correct answer.

The value of $\frac{6^{n+4}+3^{n+3} \times 2^{n+3}}{5 \times 6^n+6^n}$ is

The correct answer is Option c: 252. We want to evaluate the expression: $$\frac{6^{n+4} + 3^{n+3} \times 2^{n+3}}{5 \times 6^n + 6^n}$$ First, simplify the terms using exponent laws: - In the numerator, we can combine $3^{n+3} \times 2^{n+3}$ using the rule $x^a \cdot y^a = (xy)^a$: $$3^{n+3} \times 2^{n+3} = (3 \times 2)^{n+3} = 6^{n+3}$$ - In the denominator, combine the like terms: $$5 \times 6^n + 6^n = (5 + 1) \times 6^n = 6 \times 6^n = 6^{n+1}$$ Substitute these back into the expression: $$\frac{6^{n+4} + 6^{n+3}}{6^{n+1}}$$ Factor out the common term $6^{n+3}$ from the numerator: $$6^{n+4} + 6^{n+3} = 6^{n+3}(6 + 1) = 7 \times 6^{n+3}$$ Now, divide by the denominator: $$\frac{7 \times 6^{n+3}}{6^{n+1}} = 7 \times 6^{(n+3) - (n+1)} = 7 \times 6^2$$ Calculate the final value: $$7 \times 36 = 252$$ This matches **Option C**. Note: The textbook answer key incorrectly specifies **Option D** ($262$) as the correct choice. However, the exact mathematical calculation clearly shows that the result is $252$ (Option C). Hence, **Option C** is the correct answer.

Ratio, Proportion, Indices, LogarithmMCQPYQ Dec. 21Question 883 of 305

All Questions

The value of $\displaystyle \frac{6^{n+4}+3^{n+3} \times 2^{n+3}}{5 \times 6^n+6^n}$ is

Options

A232

B242

C252

D262

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option c — 252

All Options:

A232
B242
C252
D262

Detailed Solution & Explanation

We want to evaluate the expression:

\frac{6^{n+4} + 3^{n+3} \times 2^{n+3}}{5 \times 6^n + 6^n}

First, simplify the terms using exponent laws:
- In the numerator, we can combine

\displaystyle 3^{n+3} \times 2^{n+3}

using the rule

\displaystyle x^a \cdot y^a = (xy)^a

3^{n+3} \times 2^{n+3} = (3 \times 2)^{n+3} = 6^{n+3}

- In the denominator, combine the like terms:

5 \times 6^n + 6^n = (5 + 1) \times 6^n = 6 \times 6^n = 6^{n+1}

Substitute these back into the expression:

\frac{6^{n+4} + 6^{n+3}}{6^{n+1}}

Factor out the common term

\displaystyle 6^{n+3}

from the numerator:

6^{n+4} + 6^{n+3} = 6^{n+3}(6 + 1) = 7 \times 6^{n+3}

Now, divide by the denominator:

\frac{7 \times 6^{n+3}}{6^{n+1}} = 7 \times 6^{(n+3) - (n+1)} = 7 \times 6^2

Calculate the final value:

7 \times 36 = 252

This matches **Option C**.
Note: The textbook answer key incorrectly specifies **Option D** (

\displaystyle 262

) as the correct choice. However, the exact mathematical calculation clearly shows that the result is

\displaystyle 252

(Option C).
Hence, **Option C** is the correct answer.

About This Chapter: Ratio, Proportion, Indices, Logarithm

Paper

Paper 3: Quantitative Aptitude

Weightage

5-7 Marks

Key Topics

Ratio, Proportion, Indices, Logarithms

This chapter covers Ratio, Proportion, Indices, Logarithms and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 5-7 Marks weightage. Focus on understanding core concepts rather than memorizing.

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The value of 6n+4+3n+3×2n+35×6n+6n\displaystyle \frac{6^{n+4}+3^{n+3} \times 2^{n+3}}{5 \times 6^n+6^n}5×6n+6n6n+4+3n+3×2n+3​ is