CAT 2025 Slot 2 QA Question Paper PDF with Solutions

CAT 2025 SLOT 2 QA - Question 1

CAT 2025

In a △ABC, points D and E are on the sides BC and AC , respectively. BE and AD intersect at point T such that AD:AT=4:3, and BE:BT=5:4. Point F lies on AC such that DF is parallel to BE. Then, BD:CD is

CAT 2025 SLOT 2 QA - Question 2

CAT 2025

A certain amount of money was divided among Pinu, Meena, Rinu and Seema. Pinu received 20% of the total amount and Meena received 40% of the remaining amount. If Seema received 20% less than Pinu, the ratio of the amounts received by Pinu and Rinu is

CAT 2025 SLOT 2 QA - Question 3

CAT 2025

Let $f(x)=\frac{x}{(2 x-1)}$ and $g(x)=\frac{x}{(x-1)}$ . Then, the domain of the function $h(x)=f(g(x))+g(f(x))$ is all real numbers except

CAT 2025 SLOT 2 QA - Question 4

CAT 2025

The equations 3x²-5x+p=0 and 2x²-2x+q=0 have one common root. The sum of the other roots of these two equations is

CAT 2025 SLOT 2 QA - Question 5

CAT 2025

If a,b,c and d are integers such that their sum is 46, then the minimum possible value of (a-b)²+(a-c)²+(a-d)² is

CAT 2025 SLOT 2 QA - Question 6

CAT 2025

If $\log _{64} x^2+\log _8 \sqrt{y}+3 \log _{512}(\sqrt{y} z)=4$ , where $x, y$ and $z$ are positive real numbers, then the minimum possible value of $(x+y+z)$ is

CAT 2025 SLOT 2 QA - Question 7

CAT 2025

An item with a cost price of Rs. 1650 is sold at a certain discount on a fixed marked price to earn a profit of 20% on the cost price. If the discount was doubled, the profit would have been Rs. 110. The rate of discount, in percentage, at which the profit percentage would be equal to the rate of discount, is nearest to

CAT 2025 SLOT 2 QA - Question 8

CAT 2025

Let a_{n }be the n^th term of a decreasing infinite geometric progression. If a_{1}+a_{2}+a_{3}=52 and a_{1} a_{2}+a_{2} a_{3}+a_{3} a_{1}=624, then the sum of this geometric progression is

CAT 2025 SLOT 2 QA - Question 9

CAT 2025

The number of divisors of (2⁶×3⁵×5³×7²), which are of the form (3r+1), where r is a non-negative integer, is

CAT 2025 SLOT 2 QA - Question 10

CAT 2025

The set of all real values of x for which (x²-|x+9|+x)>0, is

CAT 2025 SLOT 2 QA - Question 11

CAT 2025

The sum of digits of the number (625)⁶⁵×(128)³⁶, is

CAT 2025 SLOT 2 QA - Question 12

CAT 2025

A loan of Rs 1000 is fully repaid by two installments of Rs 530 and Rs 594, paid at the end of first and second year, respectively. If the interest is compounded annually, then the rate of interest, in percentage, is

CAT 2025 SLOT 2 QA - Question 13

CAT 2025

Rita and Sneha can row a boat at 5 km/h and 6 km/h in still water, respectively. In a river flowing with a constant velocity, Sneha takes 48 minutes more to row 14 km upstream than to row the same distance downstream. If Rita starts from a certain location in the river, and returns downstream to the same location, taking a total of 100 minutes, then the total distance, in km, Rita will cover is

CAT 2025 SLOT 2 QA - Question 14

CAT 2025

The ratio of expenditures of Lakshmi and Meenakshi is 2 : 3, and the ratio of income of Lakshmi to expenditure of Meenakshi is 6 : 7. If excess of income over expenditure is saved by Lakshmi and Meenakshi, and the ratio of their savings is 4 : 9, then the ratio of their incomes is

CAT 2025 SLOT 2 QA - Question 15

CAT 2025

Ankita is twice as efficient as Bipin, while Bipin is twice as efficient as Chandan. All three of them start together on a job, and Bipin leaves the job after 20 days. If the job got completed in 60 days, the number of days needed by Chandan to complete the job alone, is

CAT 2025 SLOT 2 QA - Question 16

CAT 2025

A mixture of coffee and cocoa, 16% of which is coffee, costs Rs 240 per kg. Another mixture of coffee and cocoa, of which 36% is coffee, costs Rs 320 per kg. If a new mixture of coffee and cocoa costs Rs 376 per kg, then the quantity, in kg, of coffee in 10 kg of this new mixture is

CAT 2025 SLOT 2 QA - Question 17

If $9^{x^2+2 x-3}-4\left(3^{x^2+2 x-2}\right)+27=0$ , then the product of all possible values of $x$ is

CAT 2025 SLOT 2 QA - Question 18

CAT 2025

Let ABCDEF be a regular hexagon and P and Q be the midpoints of AB and CD, respectively. Then, the ratio of the areas of trapezium PBCQ and hexagon ABCDEF is

CAT 2025 SLOT 2 QA - Question 19

CAT 2025

Suppose a,b,c are three distinct natural numbers, such that 3ac=8(a+b). Then, the smallest possible value of 3a+2b+c is

CAT 2025 SLOT 2 QA - Question 20

CAT 2025

If m and n are integers such that (m+2n)(2m+n)=27, then the maximum possible value of 2m-3n is

CAT 2025 SLOT 2 QA - Question 21

CAT 2025

Two tangents drawn from a point P touch a circle with center O at points Q and R. Points A and B lie on PQ and PR, respectively, such that AB is also a tangent to the same circle. If ∠AOB=50^∘, then ∠APB, in degrees, equals

CAT 2025 SLOT 2 QA - Question 22

CAT 2025

The average number of copies of a book sold per day by a shopkeeper is 60 in the initial seven days and 63 in the initial eight days, after the book launch. On the ninth day, she sells 11 copies less than the eighth day, and the average number of copies sold per day from second day to ninth day becomes 66. The number of copies sold on the first day of the book launch is