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Q.No: 1
Test Name : CAT Paper 1994
Q51 – 90 : Choose the best alternative.

If find the value of x.

A
1
B
0
C
2
D
None of these
Answer key/Solution
Solution:
Q.No: 2
Test Name : CAT Paper 1994
Q51 – 90 : Choose the best alternative.

A
3
B
C
D
None of these
Answer key/Solution
Solution:
Q.No: 3
Test Name : CAT Paper 2003 (R)
Directions for questions 60 to 93: Answer the following questions independently.

A
10
B
C
D
None of these
Answer key/Solution
Solution:
Q.No: 4
Test Name : CAT Paper 2003 (R)
Directions for questions 60 to 93: Answer the following questions independently.

A
B
C
D
Answer key/Solution
Solution:
Q.No: 5
Test Name : CAT Paper 2003 (R)
Directions for questions 60 to 93: Answer the following questions independently.

A
B
C
D
Answer key/Solution
Solution:
Q.No: 6
Test Name : CAT 2017 Actual Paper Slot 1


A
1/3
B
2/3
C
5/6
D
7/6
Answer key/Solution
Solution:
Q.No: 7
Test Name : CAT 2017 Actual Paper Slot 2

If x is a real number such that log3 5 = log5 (2 + x), then which of the following is true?

A
0 < x < 3
B
23 < x < 30
C
x > 30
D
3 < x < 23
Answer key/Solution
Solution:
Q.No: 8
Test Name : CAT 2017 Actual Paper Slot 2


Answer key/Solution
Solution:
Q.No: 9
Test Name : CAT 2018 Actual Paper Slot 1

A
log416
B
log28
C
log68
D
log616
Answer key/Solution
Solution:
Q.No: 10
Test Name : CAT 2018 Actual Paper Slot 1

If log2(5 + log3 a) = 3 and log5(4a + 12 + log2 b) = 3, then a + b is equal to

A
40
B
32
C
67
D
59
Answer key/Solution
Solution:
Q.No: 11
Test Name : CAT 2018 Actual Paper Slot 1

If x is a positive quantity such that 2x = 3log5 2 , then x is equal to

A
B
C
D
Answer key/Solution
Solution:
Q.No: 12
Test Name : CAT 2018 Actual Paper Slot 2

If p3 = q4 = r5 = s6, then the value of logs(pqr) is equal to

A
B
C
D
Answer key/Solution
Solution:
Q.No: 13
Test Name : CAT 2018 Actual Paper Slot 2

A
0
B
10
C
-4
D
Answer key/Solution
Solution:
Q.No: 14
Test Name : CAT 2019 Actual Paper Slot 1

Let x and y be positive real numbers such that log5 (x + y) + log5 (x – y) = 3, and log2 y – log2 x = 1 – log2 3. Then xy equals

A
25
B
100
C
150
D
250
Answer key/Solution
Solution:
Q.No: 15
Test Name : CAT 2019 Actual Paper Slot 2

Let A be a real number. Then the roots of the equation x2 – 4x – log2A = 0 are real and distinct if and only if

A
B
C
D
Answer key/Solution
Solution:
Q.No: 16
Test Name : CAT 2019 Actual Paper Slot 2


A
1 ≤ x ≤ 3
B
–1 ≤ x ≤ 3
C
–3 ≤ x ≤ 3
D
1 ≤ x ≤ 2
Answer key/Solution
Solution:
Q.No: 17
Test Name : CAT 2019 Actual Paper Slot 2

The real root of the equation 26x + 23x + 2 – 21 = 0 is

A
log29
B
log227
C
D
Answer key/Solution
Solution:
Q.No: 18
Test Name : CAT Actual Paper 2020 Slot-1


Answer key/Solution
Solution:
Q.No: 19
Test Name : CAT Actual Paper 2020 Slot-1


A
log2 (1/3)
B
–log2 (1/5)
C
–log2 (1/3)
D
log2 (1/5)
Answer key/Solution
Solution:
Q.No: 20
Test Name : CAT Actual Paper 2020 Slot-2


A
1
B
–0.5
C
–1
D
0
Answer key/Solution
Solution:
Q.No: 21
Test Name : CAT Actual Paper 2020 Slot-3


A
B
C
D
Answer key/Solution
Solution:
Q.No: 22
Test Name : CAT Actual Paper 2020 Slot-3


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Solution:
Q.No: 23
Test Name : CAT Actual Paper 2021 Slot-1


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Q.No: 24
Test Name : CAT Actual Paper 2021 Slot-2


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Q.No: 25
Test Name : CAT Actual Paper 2021 Slot-3


A
B
C
D
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Solution:
Q.No: 26
Test Name : CAT Actual Paper 2021 Slot-3


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Solution:
Q.No: 27
Test Name : CAT Actual Paper 2022 Slot-2


Answer key/Solution
Solution:
Q.No: 28
Test Name : CAT Actual Paper 2023 Slot 1

If x and y are positive real numbers such that logx(x2 + 12) = 4 and 3 logy x = 1, then x + y equals

A
11
B
10
C
68
D
20
Answer key/Solution
Solution:
Q.No: 29
Test Name : CAT Actual Paper 2023 Slot 2


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Q.No: 30
Test Name : CAT Actual Paper 2023 Slot 3


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D
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