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 (684)^{2}= 467856?
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 is approximately
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)^{9M}
ANSWER: 11
Explanation:
Since the base is same i.e. p/q, we can equate the powers of both
∴ 2M+2 = (9M)
∴ 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}  243tt + 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(xy) and log8+log11 = log(xy)+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)(xy) = log40
(x+y)(xy) = 40
x+y = 10 and xy = 4 or x+y = 20 and xy = 2
x = 7 and y = 3 or x = 11 and y = 9.
log88 = log(xy)(1+xy)
x = 7 and y = 3 satisfy the equation.
(x^{3}  y^{3}) = 7^{3}  3^{3} = 316
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,
Use Code STAYHOME200 and get INR 200 additional OFF

Use Coupon Code 
153 videos129 docs131 tests
