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**Q 1. What will come in place o f question mark in **

**ANSWER: 12**

**Explanation:****.**

**Q 2.**** What is value of (0.000001) ^{⅓} ?**

**ANSWER: 1/100**

**Explanation: **

If a cube has 6 decimals, then its cube

root will have 6/3 = 2 decimals

**Q 3.**** What will be value of **

**ANSWER: 6.84**

**Explanation: **

I f a square has 4 decimals, then its

square root will have 4/2 = 2 decimals

**Q 4. If value of is approximately 5.2915, then value of**

**ANSWER: 1.3228**

**Explanation: **

**Q 5. How many zeroes are there in 2000^{10}? **

**ANSWER: 30**

**Explanation: **

2000^{10} = 2000 x ... 10 times

2000 = 2 x 1000 i.e it has 3 zeroes.

So that means 3 zeroes x 10 times= 30 zeroes

**Q 6. What is value of (36)^{⅙}? **

**ANSWER:**

**Explanation: **

**Q 7. What is value of M in (p/q)^{2M+2} = (q/p)^{9-M} **

**ANSWER: -11**

**Explanation: **

Since the base is same i.e. p/q, we can equate the powers of both

∴ 2M+2 = -(9-M)

∴ 2M+2 = -9+M

∴ M = -11

**Q 8. What is value of 2^{2(-2)} **

**ANSWER:**

**Explanation: **

**Q 9. What is value of 2^{(-2)2} **

**ANSWER: 16**

**Explanation: **

Negative number raised to even power gives positive answer

**Q 10. There are four expressions given below separated by ‘=’ sign. Which one of the 4 expressions is not the same as the other three?**

6^{2} x 6 = (6^{1})^{3} = 2^{3}+3^{3} = 8^{3} - 14^{2} - 10^{2}

**ANSWER: 2 ^{3}+3^{3}**

**Explanation: **

This is very easy to solve

The first expression is 6^{2} x 6 = 6^{3} = 216.

The second expression is (6^{1})^{3} = 6^{1 x 3} = 6^{3} = 216

The third expression is 2^{3}+3^{3} = 8+27 = 35 = ≠ other two

So answer is Option C

**Question 11: ** = ?

a) 5

b) 6

c) 7

d) None of these**Answer (D)** **Explanation: **

= 14/3

**Question 12:** Find the value of x in 2^{|5x - 6|} = 8^{3}^{x - 2}

a) 2/3

b) 6/7

c) 9/5

d) cannot be determined **Answer (B)** **Explanation: **

Taking log on both sides we get,

⇒ |5x – 6| = 3(3x – 2) = 9x – 6

When x > 6/5, |5x – 6| = 5x – 6

Thus, 5x – 6 = 9x – 6

⇒ 5x = 9x which is not possible

When x < 6/5, |5x – 6| = 6 – 5x

Thus, 6 – 5x = 9x – 6

14x = 12

⇒ x = 6/7

**Question 13:** If log_{152} 729 = x, then what is the value of log_{81} 5625 ?

a)

b)

c)

d) **Answer (A)** **Explanation: ** log_{125} 729

= log_{5} 9

= x

⇒

⇒

=

**Question 14: **Find the number of digits in the number 2401^{27} when written in base 7.

a) 117

b) 181

c) 98

d) 109 **Answer (D)** **Explanation: ****The formula for finding the number of digits in a number ‘m’ in base ‘n’ is: **

[log_{n}(m)] + 1 , where [A] is greatest integer less than or equal to A.

2401 = 7^{4}

⇒

Thus, the answer is D.

**Question 15: **What is the value of

a) -2

b) -1

c) 0

d) None of these**Answer (A)** **Explanation:**

**Question 16: **If 3^{2x+3}-244*3^{x} = -9, then which of the following statements is true?

a) ‘x’ is a positive number

b) ‘x’ is a negative number

c) ‘x’ can be either a positive number or a negative number

d) None of the above**Answer (C)** **Explanation:**

The equation can be written as follow:

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

So, x = 2 or x = -3

So, ‘x’ can be either a positive number or a negative number. Option c) is the correct answer

**Question 17: **If x,y are natural numbers, log8+log5 = log(x+y)+log(x-y) and log8+log11 = log(x-y)+log(1+xy), then find the value of (x^{3} - y^{3})

a) 325

b) 316

c) 643

d) 602 **Answer (B)****Explanation:****log(x+y)(x-y) = log40(x+y)(x-y) = 40x+y = 10 and x-y = 4 or x+y = 20 and x-y = 2x = 7 and y = 3 or x = 11 and y = 9.log88 = log(x-y)(1+xy)x = 7 and y = 3 satisfy the equation. **

(x

**Question 18: **If log_{16 }5 = x and log_{5 }3 = y, find the value of log_{3} 6 in terms of x and y?

a)

b)

c)

d) 1 + 4xy**Answer (A)** **Explanation:**

log_{16} 5 = x

log_{5} 3 = y

We have to find the value of log_{3} 6

= 1+

= 1+

= 1+1/4xy =

**Question 19: **Find the value of log_{10}10 + log_{10}10^{2} + ..... +log_{10}10^{n}

a)

b)

c)

d) **Answer (B)** **Explanation:**

⇒

⇒

⇒

⇒

**Question 20: **If . Find x

a) 512

b) 289

c) 170

d) None of these**Answer (D)** **Explanation:**

⇒

⇒

⇒

⇒

⇒ x = 28900

Since there is no such option, the correct option to choose is D – None of these.

Logarithms, Surds and Indices questions will be asked in CAT quantitative aptitude section,

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