CAT Questions On Exponents
Download important CAT Exponents Problems with Solutions PDF based on previously asked questions in CAT exam. Practice Exponents Problems with Solutions for CAT exam.
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Question 1: X and Y are the digits at the unit’s place of the numbers (408X) and (789Y) where X ≠ Y. However, the digits at the unit’s place of the numbers
a) 9
b) 10
c) 11
d) 12
e) None of the above
Question 2: For how many values of
a) 0
b) 1
c) 2
d) More than twice
Question 3: If
a) 58
b) 70
c) 31
d) None of These
Question 4: Suppose n is an integer such that the sum of digits on n is 2, and
a) 11
b) 10
c) 9
d) 8
Question 5:
a) -3
b) -1/3
c) 3
d) None of these
Question 6: Consider the expression
a) 5
b) 6
c) 7
d) 8
e) None of the above
Question 7:
a) 0.4520
b) 0.6020
c) 0.5039
d) None of these
Question 8: If
a) 683
b) 489
c) 583
d) 589
Question 9: If
a) 60
b) 61
c) 62
d) None of these
Question 10: What is the digit in the unit’s place of
a) 2
b) 8
c) 1
d) 4
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Question 11: Which of the following statements is false?
a) For all X>1,
b) For all X>1,
c) For all X>Y>1,
d) None of these
Question 12: What are the last two digits of
a) 21
b) 61
c) 01
d) 41
e) 81
Question 13: If
a) (x+y)/2xy
b) (x+y)/x
c) (y+2x)/xy
d) None of these
Question 14: The rightmost non-zero digit of the number
a) 1
b) 3
c) 7
d) 9
Question 15: If
a) 3
b) 4
c) 5
d) 6
Answers & Solutions:
1) Answer (B)
All numbers from 1 to 9 repeat their last digits over a cycle of 4.
63 can be written as 4k+3.
85 can be written as 4k+1.
Some number’s third power should yield the first digit as some number’s first power.
As we can see, X+Y = 10 in all the cases. Therefore, option B is the right answer.
2) Answer (B)
If
So,
The function
So, there exists exactly one Y between 2 and 3 such that
3) Answer (B)
So,
4) Answer (A)
The sum of digits should be 2. The possibilities are 1000000001,1000000010,10000000100,..these 10 cases . Also additional 1 case where 20000000000. Hence option A .
5) Answer (A)
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6) Answer (E)
=>
=>
On substituting b=1,and b=2, we get
7) Answer (B)
8) Answer (D)
Sum of digits =
9) Answer (B)
10) Answer (B)
The last digit of powers of 2 follow a pattern as given below.
The last digit of
The last digit of
The last digit of
The last digit of
The last digit of
The last digit of
The last digit of
The last digit of
Hence, the last digit of
11) Answer (D)
All three statements are true.
12) Answer (C)
So, any multiple of
Since 2008 is a multiple of 4,
13) Answer (A)
If
If
14) Answer (A)
Rightmost non-zero digit of
272 is of the form 4k.
All
=> Right most non-zero digit is 1.
15) Answer (A)
So,
Assuming
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