JIPMAT 2023

Given below are two statements:

Statement (I):
4 boys and 8 girls completed 1/3 of work in 5 days. After that 3 boys and 3 girls increased, and they completed another 1/3 of work in 3 days. If the remaining work is to be completed in 2 days, then the number of girls that should be increased is 32.

Statement (II):
The ratio of time taken by A and C to do a work is 1:2 respectively. B is 166 (2/3)% more efficient than C. Time taken by A to complete 6% of work is 6 days.

Then, the time taken by B and C together to complete the whole work is 54 (6/11) days.

In light of the above statements, choose the most appropriate answer from the options given below.

The number of integral solutions of the equation $7\left(y+\frac{1}{y}\right)-2\left(y^2+\frac{1}{y^2}\right)=9 \text { is }$

Given below are two statements:

Statement (I): The difference, the sum, and the product of two numbers are in the ratio 1: 5: 12. The product of the two numbers is 18.

Statement (II): The last digit in the decimal representation of 2$^{91}$ is 6.

In light of the above statements, choose the most appropriate answer from the options given below.

In a Women's Chess Championship having 300 entrants, a player is eliminated whenever she loses a match. It is given that no match results in a draw. The number of matches that are played in the entire Championship is:

The total number of seconds in P weeks, P days, P hours, P minutes, and P seconds is:

Sumit has Rs. 90000 with him. He purchases three items A, B, and C for Rs. 15000, Rs. 13000, and Rs. 35000 respectively and puts the remaining money in a bank deposit that pays compound interest @15% per annum. After 2 years, he sells off the three items at 80% of their original price and also withdraws his entire money from the bank by closing the account. What is the total change in his asset?

How many proper divisors (that is, divisors other than 1 or 7200) does 7200 have?

If the difference between the circumference and radius of a circle is 37 cm, using π = 22/7, what is the circumference (in cm) of the circle?

Let A and B be two events such that P(A)=0.25, P(B)=0.50 and P(A ∩ B)=0.14. The probability that neither A nor B occurs is:

Which of the following statements are True in the context of circles?

• A. A tangent of a circle touches it at two points.
• B. A circle can have two parallel tangents at the most.
• C. There is no tangent to a circle passing through a point inside the circle.

Choose the correct answer from the options given below:

$\sqrt{3+\sqrt{5}}=$

Which of the following statements are True?

• A. The mean of x, y, z is y. Then x + z = 2y.
• B. Median of 15, 28, 72, 56, 44, 32, 31, 43 and 51 is 43.
• C. Mode of 2, 3, 4, 5, 0, 1, 3, 3, 4, and 3 is 3.

Choose the correct answer from the options given below:

If k$^{2}$ - 1 is divisible by 8, then K is:

A 30 meter deep well, with a diameter of 7 meters is dug and the earth from digging is evenly spread out to form a platform of size 22 meters by 14 meters. The height of the platform is:

If the eight-digit number $5a32465b$ is divisible by $88$, then $2a+ 5b =$

Sonali buys 2 Pen Drives A and B, and their cost price is in the ratio of 5:6 respectively. If she sells them at a 10% profit each, she earns a total profit of ₹22. What will be her total profit, if she sells Pen Drive A at a 20% loss and Pen Drive B at a 30% profit?

If $\sin (θ) - \cos (θ) = 0$, the value of sin$^{4}$ (θ) + cos$^{4}$ (θ) is:

The mean of 25 observations is 36. If the mean of the first 13 observations is 32 and that of the last 13 observations is 39, then the 13th observation is:

The graph of a polynomial $y = f(x)$ is shown in figure below, then the number of its zeros is:

Enlarge diagram ↗

Given below are two statements:

Statement (I): The volume of a right circular cylinder of base radius 7 cm and height 10 cm is 1540 cm$^{3}$ (Take π = 22/7).

Statement (II): Total surface area of the cylinder having radius of base 14 cm and height 30 cm, is 3872 cm$^{2}$ (Take π= 22/7).

In light of the above statements, choose the most appropriate answer from the options given below.

If the pair of linear equations $2x + 3y = 7$ and $2px + (p + q) y = 28$ has an infinite number of solutions, then (p, q)

In $\triangle \mathrm{ABC}, \angle \mathrm{B}=90^{\circ}, \mathrm{BC}=5 \ \mathrm{cm}, \mathrm{AC}-\mathrm{AB}=1 \mathrm{~cm}$, then $\frac{1+\sin (\mathrm{C})}{1+\cos (\mathrm{C})}$ is

In a survey of 100 students, the number of students studying various languages were found to be:

1. English only-18
2. English but not Hindi-23
3. English and German-8
4. English-26
5. German-48
6. German and Hindi-8
7. No language-24

Then, which of the following statements are true?

A. Number of students who were studying Hindi is 18.

B. Number of students who were studying English and Hindi is 3.

C. Number of students who were studying English, Hindi and German is 3.

Amicable numbers are a pair of distinct natural numbers (a, b) such that the sum of the proper divisors of a equals b and the sum of the proper divisors of b equals a. Given that (220, y) is a pair of amicable numbers, y equals:

Given below are two statements in the context of throwing two different dice together:

Statement (I): The probability that the two numbers obtained have an even sum is 0.50.

Statement (II): The probability that the two numbers obtained have an even product is 0.75.

In light of the above statements, choose the most appropriate answer from the options given below.

The expression 2x$^{3}$ + ax$^{2}$ + bx + 3, where a and b are constants, has a factor of x-1 and leaves a remainder of 15 when divided by x + 2. Then, (a, b) =

Aman takes half the time in rowing a certain distance downstream than upstream.
Statement (I): Ratio of the speed of the boat in still water to the speed of the water current is 2: 1.
Statement (II): If the speed of the boat in still water is 6 km per hour, then the speed of the water current is 2 km per hour.
Choose the most appropriate answer from the options given below.

The probabilities that A, B, and D can solve a problem independently are 1/3, 1/3, and 1/4 respectively. The probability that only two of them are able to solve the problem is:

Given below are two statements:

Statement (I): (x$^{2}$ + 3x + 1) = (x - 2)$^{2}$ is not a quadratic equation.

Statement (II): The nature of roots of quadratic equations x$^{2}$ + 2x√3 + 3 = 0 are real and equal.

In light of the above statements, choose the most appropriate answer from the options given below.

Two identical solid cubes of side 5 cm are joined end to end. Then the total surface area of the resulting cuboid is:

Assertion [A]: Sum of the first hundred even natural numbers divisible by 5 is 45050.
Reason (R): Sum of the first n-terms of an Arithmetic Progression is given by $S = (n/2) *(a + l)$ where a=first term, l=last term.
Choose the correct answer from the options given below.

The area of the circle that can be inscribed in a square of side 6 cm is:

The radii of two cones are in the ratio 2:3 and their volumes are in the ratio 1:3. Then the ratio of their heights is: