Mastering CAT 2025: Your Guide to Practise Set Questions and Beyond- Day 52

CAT 2025 Practice Test: Online Free Mock Test

This free sectional mock test for CAT consists of subjects and topics-specific questions and answers. To get the best idea of what the CAT exam 2025 requirements are, candidates must download the best free mock test for CAT and complete the CAT online Practice Test Series from all three subjects. Based on the 51 days of lessons, this online free practice test includes comprehensive solutions. You can succeed on the exam in 2025 by using this free sectional mock test for the CAT.

This CAT previous year question paper of CAT 2025 Practice Test Series consists of three Sections:

CAT sample paper Part- A consists of 8 questions.

CAT sample paper Part- B consists of 11 questions.

CAT sample paper Part- C consists of 8 questions.

CAT Test Series Part- A: Quantitative Aptitude CAT Online Free Mock Test

Q1. Set A = {1, 4, 8, 9, 11, 13}, Set B = {p, q, r, s}. How many onto functions can be defined from Set A to Set B?

1. 20

2. 60

3. 120

4. None of the above

Ans: [3]

Number of onto function from Set A to Set B:

There are 4 elements in set B, all these elements need to be mapped to some element in set A.

For a function to exist every element of the domain has a unique value.

p of Set B can be mapped to any of the 6 elements of Set A

q of Set B can be mapped to any of the other 5 elements in Set A and

r of Set B can be mapped to any of the other 4 elements in Set A

So, Number of onto functions from set A to set B = 6x 5x 4 = 120.

Q2. In a survey conducted by a multilevel marketing company to know people’s preference for beauty products and Accessories, 74 preferred beauty products while 67 preferred accessories. There were 18 who liked both and may prefer any. If there was no one who didn’t prefer at least one of the phones, then on how many people was the survey conducted?

1. 120

2. 40

3. 123

4. 159

Ans: [3]

Using formula

n(AUB) = n(A) + n(B) – n(A∩B)

Here, n(A) = 74; n(B) = 67; n(A∩B) = 18

So, n(A) = 74 + 67 – 18 = 123.

Q3. Region R is defined as 5x - 8y < 40. Given that a point P with coordinates (a, b) lies within the region R, what is the probability that a > 4?

1. ¼

2. 1/3

3. 1/5

4. 1/2

Ans: [A]

5x – 8y = 40 is a straight-line intersecting x-axis at x= 8 and y-axis at y= -5.

So, 5x – 8y < 40 is a region inside the right triangle with the sides 5, 8, square root (5²+8²) i.e. 5, 8 and square root (89)

Area of this triangle = 5x 8/2 = 20 sq unit.

Line x = 4 and 5x – 8y = 40 intersect at (4, -2.5) which is also a right triangle with a base and height are 4 and 2.5 respectively.

The area of this triangle will be 5 sq units.

Probability of point lying inside the region = 5/20 = 1/4

Q4. The area of the region satisfying the inequalities 2|x| - y ≤ 2, y ≥ 1, and y ≤ 2 is [TITA]

Ans:

Plot the graph as shown

The shaded region is the required area (Trapezium of height 1 and parallel sides being 3 and 4)

Area = Area of Trapezium = ½ [3+ 4]x 1 = 3.5 sq unit.

Q5. PQRS is a rhombus with the diagonals PR and QS intersecting at the origin on the x-y plane. The equation of the straight-line PS is x + y = 2. What is the equation of QR?

1. x + y = –1

2. x – y = –2

3. x + y = -2

4. None of these

Ans: [C]

Since PQRS is a rhombus and using the given information, the coordinates of vertices are as shown in figure

So, equation of QR

{y-0}/{x-(-2)}=(-2-0)/(0+2)

⇒2y = -2x -4

⇒ y + x = -2

Q6. The Sum of the first 20 terms of an AP is equal to the sum of the first 28 terms in the same AP. If all terms in the series are integers, which of the following can be its common difference?

1. 9

2. -9

3. 4

4. 3

Ans: [C]

S₂₀ = 10[2a + 19d]

S₂₈ = 14[2a + 27d]

⇒10[2a + 19d] = 14[2a + 27d]

⇒20a + 190d = 28a + 378d

⇒ -8a = 188d

⇒ -2a = 47d

⇒ a = - (47/2) d

Clearly, from options, we can observe that the correct can be 4 because all terms are integers.

hence option d is correct.

Q7. If Sn = n³ - n² + n - 1, where Sn denotes the sum of the first n terms of a series and T_x = 70, then x is equal to?

1. 4

2. 6

3. 1

4. 14

Ans: [3]

S_x = x³ - x² + x - 1

S_x-1 = (x-1)³ – (x-1)² + (x -1) – 1

T_x = Sx – S_x-1 = x³ - x² + x – 1 – [(x-1)³ – (x-1)² + (x -1) – 1]

T_x = [x³ - (x-1)³]- [x² – (x-1)²] + x - (x -1) – 1 +1

T_x = [(x – x +1) (x² + (x-1)²+ x(x-1)]- [(x – x +1)(x +x +1) ]+ x² - x

T_x = [x² + x² +1 – 2x+ x²-x]- [2x +1]+ x² – x

T_x = 3x² +1 – 3x- 2x -1+ x² – x

T_x = 4x² – 6x

⇒ 4x² – 6x = 70

On solving, 4x² – 6x – 70 = 0

So, 4x² – 20x + 14x – 70 = 0

⇒ 4x (x- 5) +14 (x – 5) = 0

So, x = 5.

Q8. If (3n-1) + (3n - 3) + (3n - 5) + ... + (3n - 47) = 2880, then what is the value of 1+2+3+ ... +n? [TITA]

Ans: 1176

Let the number of terms in AP be x

therefore 3n-47 = (3n-1) + (x-1)(-2) as common difference is -2

form here we get value of x is 24 = Number of terms = 24

So, S₂₄ = 24/2 [2(3n – 1) + (24-1) (-2)] = 12 [6n- 2 – 46] = 2880

n= 48

So, 1+2+3+ ... +48 = 48 x 49/2 = 1176

Online Free Practice Test Part B: LRDI (Logical Reasoning and Data Interpretation)

Passage: (Q1-Q3)

The top three rankers of the class, Pranav, Qureshi, and Raja, not necessarily in the same order, made the following statements about their ranks.

Pranav:

I am not the top ranker.

Qureshi is not the second ranker.

Raja is the third ranker.

Qureshi:

Pranav’s first statement is false.

I am the third ranker.

I made two false statements.

Raja:

Pranav is the first rank.

Qureshi is not the second ranker.

I am the second rank.

It is known that each of Pranav and Raja made only one false statement. Qureshi made only one true statement.

Q1. Who is the first ranker?

1. Pranav

2. Qureshi

3. Raja

4. Cannot be determined

Q2. Which of the following represents the correct order of truth and false statements made by Raja?

1. True, False, True

2. True, True, False

3. False, True, True

4. Cannot be determined

Q3. Who is the third ranker?

1. Pranav

2. Qureshi

3. Raja

4. Cannot be determined

Solution:

It is given that Qureshi made only one true statement. It implies that he made two false statements.

⇒ Qureshi’s third statement is true and the other two are false.

⇒ Pranav’s first statement is true. (From Qureshi’s first statement) i.e. Pranav is not the top ranker.

⇒ Raja’s first statement is false and the other two are true.

⇒ Raja is the second ranker and Qureshi is not the second ranker. As Pranav is not the first ranker, Qureshi is the first ranker and Pranav is the third ranker.

⇒ Pranav’s second statement is true and the third one is false.

1. Qureshi is the first ranker. Choice (B)

2. Raja’s statements are in the order false, true and true. Choice (C)

3. Pranav is the third ranker. Choice (A)

Passage: (Q4- Q7)

A logician is telling his wife about four pieces of jewellery he has just seen in an exhibition. “I have seen a watch, a ring, a necklace and a brooch. The heavier of the necklace and the brooch is the costliest, while the costlier of the watch and ring is the lightest. The cheaper of the ring and the brooch is the heaviest, while the heavier of the necklace and the ring is the cheapest. Also, if the brooch is costlier than the necklace, then it is lighter than the watch.” His intelligent wife immediately ranks them in terms of their cost and weight and says, “We cannot determine the ranks of two of the pieces in one of the comparisons.”

Q4. Which of the following pairs is the wife of the logician talking about?

1. Necklace and Brooch

2. Brooch and Watch

3. Watch and Ring

4. Ring and Necklace

Q5. The logician then gave his wife an additional statement which was sufficient to determine the complete rank list in both comparisons. Which one of the following statements did the logician give his wife?

1. If the Ring is lighter than the Necklace, then the Necklace is costlier than the Brooch.

2. If the Necklace is lighter than the Brooch, then the Brooch is costlier than the Watch.

3. If the Watch is cheaper than the Ring, then the Ring is heavier than the Watch.

4. If the Ring is not lighter than the Watch, then the Watch is costlier than the Brooch.

Q6. Which of the following is the costliest?

1. Necklace

2. Brooch

3. Watch

4. Either (A) or (B)

Q7. Which of the following is the lightest?

1. Ring

2. Watch

3. Necklace

4. Either (B) or (C)

Solution:

Statement Ι: Costlier of the watch and ring is the lightest. Let us assume that the ring is the lightest.

Statement ΙΙ: Heavier of the necklace and ring is the cheapest.

Statement ΙΙΙ: Heavier of the necklace and brooch are the costliest.

Statement ΙV: Cheaper of the ring and brooch is the heaviest. If the ring is the lightest, it cannot be the heaviest. ⇒ Brooch is the heaviest [statement ΙV]

⇒ Brooch is the costliest [statement ΙΙΙ].

⇒ Necklace is the cheapest [statement ΙΙ]. But the brooch is the heaviest.

⇒ Brooch is heavier than the ring. ⇒ Brooch is cheaper than ring [statement ΙV]. “Brooch is the costliest”; and “Brooch is cheaper than ring” are contradicting each other. Hence, our assumption is wrong.

⇒ Ring is not the lightest.

⇒ Watch is the lightest.

Statement V: If a brooch is costlier than a necklace, then it is lighter than a watch. But we know that watch is the lightest.

⇒ Necklace is not lighter than a watch.

⇒ Brooch is not costlier than a necklace.

⇒ Necklace is costlier than brooch.

⇒ Necklace is the costliest [statement ΙΙΙ].

⇒ Necklace is heavier than brooch.

⇒ Brooch is not the heaviest. ⇒ Ring is the heaviest [statement ΙV].

⇒ Ring is the cheapest [statement ΙΙ].

In the above table, 1st rank represents the costliest or the heaviest as the case may be. Observation: We do not know the rank of the brooch and watch in terms of cost.

4. The logician's wife is talking about Brooch and Watch. Choice (B)

5. If we know the comparison between brooch and watch in terms of cost, we can determine the rank list in both comparisons. Choice (D)

6. The necklace is the costliest. Choice (A)

7. Watch is the lightest. Choice (B)

Passage:

Six football teams – Maharashtra, Tamil Nadu, West Bengal, Delhi, Karnataka and Andhra Pradesh participated in a tournament. After the first two rounds, it is known that every team played with two different teams, one in each round and won one of the matches and lost the other.

Each team scored a different number of goals among – 2, 3, 4, 5, 6 and 7 in the first round of the tournament and each team scored a different number of goals among 1, 3, 4, 5, 6 and 8 in their second round of the tournament. We know the following information about their scores.

West Bengal scored nine goals in total, but it scored less number of goals in the match they won with respect than in the match they lost.

The number of goals scored by Tamilnadu in the first round is the same as that conceded by it in the second round.

The number of goals conceded by Karnataka is the same in both rounds and in both matches, the difference in goals between the winner and the loser is two.

The total number of goals scored in each of the two matches of Maharashtra is 10 but the total number of goals scored by Maharashtra is not 10.

Delhi is the only team that scored the same number of goals in both matches. But in total, it scored less number of goals than any of the other teams.

Q8. What is the maximum number of goals scored in any match?

1. 14

2. 11

3. 12

4. 13

Q9. Which team scored the least number of goals in a match?

1. Delhi

2. Karnataka

3. Andhra Pradesh

4. West Bengal

Q10. Which team scored the maximum number of goals in both matches together?

1. West Bengal

2. Tamil Nadu

3. Karnataka

4. Maharashtra

Q11. Against which team did Delhi win the match in the first two rounds?

1. West Bengal

2. Maharashtra

3. Tamil Nadu

4. Andhra Pradesh

Solution:

From the given information. Ι round scores – 2, 3, 4, 5, 6, 7 ΙΙ round scores – 1, 3, 4, 5, 6, 8.

From (5), if Delhi scored 4 goals in each round, then the team which scored one goal in ΙΙ round can never score more goals than Delhi, which contradicts (5).

∴ Delhi scored 3 goals in each of the first two rounds.

From (4), the only possibility of getting 10 goals in a match is 6 and 4 in ΙΙ round. Now, as the total number of goals of Maharashtra is not 10, in the first match the number of goals scored must be 7 and the number of goals conceded must be 3. [∵ 3 goals scored by Delhi is known to us]

∴ In the first round, Delhi and Maharashtra played and Maharashtra won.

∴ Delhi won in the second round. ∴ It must have conceded 1 goal in the second round.

∴ In the second round, as the total number of goals scored is 10 in the match that Maharashtra played, Maharashtra loses it by scoring 4 goals and conceding 6 goals.

From (3) and the above results, Maharashtra conceded 6 goals in the second round; Karnataka cannot concede 6 goals each in the first two rounds. If Karnataka conceded 5 goals each in the first two matches, then in the first match it scored either 5 + 2 or 5 – 2 goals i.e., either 7 or 3 goals, which is not possible as Maharashtra and Delhi scored 7 and 3 goals respectively in the first round matches. For the same reason as above, it cannot concede 3 goals each in the first two matches.

∴ Karnataka conceded 4 goals each in the first two matches.

∴ It scored one of (4 + 2) and (4 – 2) are the number of goals in the first round and in the second round. In the second round, no team scored 2 goals.

∴ Karnataka scored 2 goals in the first round and 6 goals in the second round.

From (1) and the above results, as West Bengal scored a total of 9 goals, It must have scored 4 and 5 goals in the first two matches [∵ It cannot score 6 and 3 goals as Delhi scored 3 goals in each. of the first two rounds]. In the second round Maharashtra scored 4 goals, and West Bengal scored 4 goals and 5 goals in the first and the second rounds respectively. As Karnataka conceded 4 goals in the first round, it played against West Bengal in the first round.

As West Bengal won in the first round, it should lose in the second round.

∴It should concede 8 goals in the second round.

From (2) and the above results, Tamilnadu cannot score 6 goals in the first round, if so it has to concede 6 goals in the second round, which is not possible as Maharashtra conceded 6 goals in the second round. ∴ Tamilnadu must have scored 5 goals in the first round and conceded 5 goals in the second round.

∴ It scored 8 goals in the second round. (West Bengal scored 5 goals and conceded 8 goals in the second round) ∴ Tamil Nadu has to lose in the first round. So, it must have conceded 6 goals in the second round.

∴ AP scored 6 goals and Tamilnadu conceded 6 goals in the first round and Andhra Pradesh scored 1 goal and conceded 3 goals in the second round.

∴ The final table for Ι round will be as follows:

(1) AP - Tamilnadu

6 5

(2) West Bengal – Karnataka

4 2

(3) Delhi – Maharashtra

3 7

ΙΙ round

(1) AP - Delhi

1 3

(2) Karnataka - Maharashtra

6 4

(3) West Bengal - Tamil Nadu

5 8

8. The Maximum number of goals scored in any match is 5 + 8 = 13. Choice (D)

9. Andhra Pradesh scored the least number of goals (1) in the second-round match. Choice (C)

10. Tamilnadu scored 5 + 8 = 13 goals in the first two rounds, which is the maximum. Choice (B)

11. Against Andhra Pradesh, Delhi won the match in the first two rounds. Choice (D)

CAT Test Series Part C: VARC (Verbal Ability & Reading Comprehension)

Direction (Q1-Q4): You must find the part that contains an error and then choose accordingly the sequence of correct parts (excluding the part that is grammatically and contextually incorrect). That sequence will be your answer.

Q1- I bade him (A)/ to submit all the important documents (B)/ before he left (C) / for the meeting (D)/ No error (E)

1. A

2. B

3. C

4. D

5. E

Ans. Option B

Explanation- bade takes ‘plain infinitive’(V1) after it and not ‘infinitive’ (to + infinitive). So, change ‘to submit’ into ‘submit’.

Q2- when we reached (A)/ the station we found (B)/ that there was (C)/ no place to stand. (D)/ no error(E)

1. A

2. B

3. C

4. D

5. E

Ans- option D

Explanation- use ‘no room’ in place of ‘no place’. Room means ‘enough empty space for people or things to be fitted in’.

Q3- All the pupils (A)/ stood up respectively (B)/ as soon as the (C)/ guru entered the room. (D)/ No error (E)

1. A

2. B

3. C

4. D

5. E

Ans- option B

Explanation- change respectively and respectfully

Respectively- in the order already mentioned

Respectfully- marked by respect

Q4- The youth (A)/ is the time (B)/ when the seeds of (C)/ wisdom are sown. (D)/ No error (E)

1. A

2. B

3. C

4. D

5. E

Ans- option A

Explanation- the given sentence talks about ‘youth’ (the stage of life) in a general way. Hence, ‘the’ cannot be used before ‘youth’. However, if we talk about the youth in a particular way, we will have to use ‘the’ For eg. The youth of India is very hardworking.

Direction (Q5-Q7): Replace the word/ phrase printed in bold in the sentence to make it grammatically correct.

Q5- the space- crunched city throws up several stories of struggle that schools have had to put up with to win playgrounds for their students.

1. Have had to put up

2. Had put up to

3. Have had to put up with

4. Had to put up to

5. No correction required

Ans. Option D

Explanation- ‘had to put up to’ fits the sentence appropriately as it makes the sentence structure grammatically correct.

Q6- Emotions were high as both families were taken to the police station last night.

1. Emotions went higher

2. Emotions become high

3. Emotionally high

4. Emotions ran high

5. No correction required

Ans- option D

Explanation- ‘emotions run high’ fits the sentence appropriately and it is an idiom which means to be in a state of excitement or anger.

Q7- Work at all the court complexes was paralysed as lawyers went on a day-long strike as a mark of protest.

1. For a one-day strike

2. For a strike

3. On a day’s long strike

4. On a day-long striking

5. No correction required

Ans- option E

Explanation-no correction required

Q8- Rearrange para jumbles

1. It was the height of the cold war.

2. On the morning of 26 September 1983, alarms went off at Serpukhov-15, the secret command centre of the Soviet Air Defence Forces.

3. Russia had just a few minutes to respond before the missiles—which are no doubt aimed at its own strike capabilities—destroyed the country’s ability to retaliate.

4. Both the Soviet Union and the US were bristling with nuclear weapons and relations between the two global superpowers were at an all-time low.

5. Soviet satellites that comprised Russia’s early warning system were reporting that five Minuteman intercontinental ballistic missiles (ICBMs) had just been launched from an American base and were headed for the Soviet Union.

6. BECAD

7. EBCAD

8. BECDA

9. BEACD

10. ABCDE

Ans- option A

Explanation- introductory sentence can be sentence-B. sentence E follows sentence B. Russia's early warning is mentioned in sentence E and then sentence C seems to be an event after sentence E. then statement A. and the conclusion is in statement D. both sentences A and D can be ending sentences but sentence D is more appropriate.

Hope you all were able to solve the practice set questions, Day 53 will be uploaded tomorrow!

Till then!

Keep practising, keep learning

Thank you!

All the Best!