Surds and Indices are some of the basics of number system theory. The questions may include simplification of equations to find the simplified equations. Practice more questions on Surds and indices for CAT.

**Surds and Indices Questions for CAT PDF:**

DownloadÂ Surds and Indices Questions for CAT PDF

Enrol To CAT 2023 Online Course

Download CAT Quant Questions PDF

Take Free Mock Test for CAT 2023

**Question 1: Â **If $3^{2x + 3} – 244*3^x = -9$, then which of the following statements is true?

a) â€˜xâ€™ is a positive number

b) â€˜xâ€™ is a negative number

c) â€˜xâ€™ can be either a positive number or a negative number

d) None of the above

**Question 2: **If x = -0.5, then which of the following has the smallest value?

a) $2^{1/x}$

b) $1/x$

c) $1/x^2$

d) $2^x$

e)$1/\sqrt{-x}$

**Question 3:Â **Which of the following is true?

a) $7^{(3^2)} = (7^3)^2$

b) $7^{(3^2)} > (7^3)^2$

c) $7^{(3^2)} < (7^3)^2$

d) None of these

Download CAT 2023 Syllabus PDF

Enrol To CAT 2023 Online Course

**Question 4: **Which among $2^{1/2}, 3^{1/3}, 4^{1/4}, 6^{1/6}$, and $12^{1/12}$ is the largest?

a) $2^{1/2}$

b) $3^{1/3}$

c) $4^{1/4}$

d) $6^{1/6}$

e)$12^{1/12}$

**Question 5:Â **$2^{73}-2^{72}-2^{71}$ is the same as

a) $2^{69}$

b) $2^{70}$

c) $2^{71}$

d) $2^{72}$

**Solutions forÂ Surds and Indices Questions for CAT PDF:**

**Solutions:**

**1) Answer (C)**

The equation can be written as follow:

$3^{2x} * 3^3 – 244 * 3^x + 9 = 0$

Let $3^x = t$

=> $27t^2 – 244t + 9 = 0$

=> $27t^2 – 243t – t + 9 = 0$

=> $27t(t – 9) – 1(t – 9) = 0$

=> t = 9 or t = 1/27

=> $3^x = 9 or 3^x = 1/27$

=> $3^x = 3^2 or 3^x = 3^{-3}$

So, x = 2 or x = -3

So, â€˜xâ€™ can be either a positive number or a negative number. Option c) is the correct answer

Download Quantitative Ability for CAT

**2) Answer (B)**

$2^p$ is always positive

$x^2$ is always non negative.

$1/\sqrt{-x}$ is always positive.

$\frac{1}{x}$ is negative when x is negative.

In this case, x is negative => $\frac{1}{x}$ is smallest.

**3) Answer (B)**

$7^{(3^2)} = 7^9$

$(7^3)^2 = 7^6$

So $7^{(3^2)} > (7^3)^2$

**4) Answer (B)**

Make the power equal and compare the denominators.

$2^{1/2}$ can be written as $64^{1/12}$

$3^{1/3}$ can be written as $81^{1/12}$

$4^{1/4}$ can be written as $64^{1/12}$

$6^{1/6}$ can be written as $36^{1/12}$

Among these, $81^{1/12}$ is the greatest => $3^{1/3}$ is the greatest.

**5) Answer (C)**

$2^{71} (2^2 – 2^1 – 1)$

$2^{71} (4-2-1)$

$2^{71}$

Practice more surds and Indices CAT questions

[…] Surds and Indices for CAT QuestionsÂ – 6th February, 2018 […]