Q 1. What will come in place o f question mark in
ANSWER: 12
Explanation:.
Q 2. What is value of (0.000001)â…“ ?
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 200010?
ANSWER: 30
Explanation:
200010 = 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)â…™?
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 22(-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?
62 x 6 = (61)3 = 23+33 = 83 - 142 - 102
ANSWER: 23+33
Explanation:
This is very easy to solve
The first expression is 62 x 6 = 63 = 216.
The second expression is (61)3 = 61 x 3 = 63 = 216
The third expression is 23+33 = 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| = 83x - 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 log152 729 = x, then what is the value of log81 5625 ?
a)
b)
c)
d)
Answer (A)
Explanation: log125 729
= log5 9
= x
⇒
⇒
=
Question 14: Find the number of digits in the number 240127 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:
[logn(m)] + 1 , where [A] is greatest integer less than or equal to A.
2401 = 74
⇒
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 32x+3-244*3x = -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 3x = t
⇒ 27t2 - 244t + 9 = 0
⇒ 27t2 - 243t-t + 9 = 0
⇒ 27t(t - 9)-1(t - 9) = 0
⇒ t = 9 or t = 1/27
⇒ 3x = 32 or 3x = 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 (x3 - y3)
a) 325
b) 316
c) 643
d) 602
Answer (B)
Explanation:
log(x+y)(x-y) = log40
(x+y)(x-y) = 40
x+y = 10 and x-y = 4 or x+y = 20 and x-y = 2
x = 7 and y = 3 or x = 11 and y = 9.
log88 = log(x-y)(1+xy)
x = 7 and y = 3 satisfy the equation.
(x3 - y3) = 73 - 33 = 316
Question 18: If log16 5 = x and log5 3 = y, find the value of log3 6 in terms of x and y?
a)
b)
c)
d) 1 + 4xy
Answer (A)
Explanation:
log16 5 = x
log5 3 = y
We have to find the value of log3 6
= 1+
= 1+
= 1+1/4xy =
Question 19: Find the value of log1010 + log10102 + ..... +log1010n
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,