JIPMAT 2024

What will be the least number which when divided by 12, 21 and 35 leaves 6 as a remainder in each case?

A candidate scoring $x \%$ marks in an examination fails by ' $a$ ' marks while another candidate who scores $y \%$ marks, gets ' $b$ ' marks more than the minimum required pass marks. What is the maximum marks for the examination ?

An equilateral triangle $A B C$ is inscribed in a circle of radius $20 \sqrt{3} \mathrm{~cm}$. The centroid of the triangle $A B C$ is at a distance $d$ from the vertex $A$. then $d$ is equal to ?

An amount doubles itself at compound interest in 5 years. How many years will it take to make the amount 16 times itself ?

A company offers four types of successive discounts A - D on the marked price of an article. Arrange these successive discounts A - D in ascending order based on the final price of the article after discounts.

(A) $25 \%$ and $15 \%$
(B) $30 \%$ and $10 \%$
(C) $35 \%$ and $5 \%$
(D) $15 \%$ and $20 \%$

A man sold $\frac{3}{5}^{\text {th }}$ of his articles at a gain of $20 \%$ and the remaining at the cost price. The gain earned in the transaction is

Given below are two statements :

Given that $a: b=5: 3$ and $b: c=2: 5$, then value of ( $c-a$ ) will be equal to

Statement I: $10(a+c)$
Statement II: $10 a+25 b$

In the light of the above statements, choose the correct answer from the options given below :

The HCF and LCM of two numbers $\mathrm{x}$ and $\mathrm{y}$ are respectively 6 and 210 .

If $x+y=72$, then $\frac{1}{x}+\frac{1}{y}$ is equal to :

The average of five consecutive numbers is a. If the next two numbers are also included, how will the average vary?

Choose the correct answer from the options given below :

If the seven digit number $94 a 29 b 6$ is divisible by 72 , then what is the value of $(2 a+3 b)$ for $a \neq b$ ?

An equilateral triangle $\mathrm{ABC}$ is inscribed in a circle of radius $20 \sqrt{3} \mathrm{~cm}$. What is the length of the side of the triangle ?

Given below are two statements :

In class ' $X$ ' of 30 students, 24 passed in first division; in another class ' $Y$ ' of 35 students, 28 passed in first division.

Statement I : Class ' $X$ ' has more percentage of students getting first division.

Statement II : Both classes have equal percentage of students getting first division.

Arrange the following fractions in descending order.

(A) $\frac{5}{9}$

(B) $\frac{7}{11}$

(C) $\frac{8}{15}$

(D) $\frac{11}{17}$

Simplify : $\dfrac{\sqrt[4]{0.0625}+\sqrt[3]{0.008}+\sqrt{0.09}-1}{\sqrt[3]{62 \cdot 5 \times \sqrt[5]{32}}}$

Ram and Shyam run a race between points $A$ and $B, 5 \mathrm{~km}$ apart. Ram starts at 9 AM from A at a speed of $5 \mathrm{~km} / \mathrm{hr}$, reaches $B$ and returns to $A$ at the same speed. Shyam starts at $9: 45 \mathrm{AM}$ from $\mathrm{A}$ at a speed of $10 \mathrm{~km} / \mathrm{hr}$, reaches $B$ and comes back to $A$ at the same speed.

At what time do Ram and Shyam meet each other ?

Ram and Shyam run a race between points $A$ and $B, 5 \mathrm{~km}$ apart. Ram starts at 9 AM from $A$ at a speed of $5 \mathrm{~km} / \mathrm{hr}$, reaches $B$ and returns to $A$ at the same speed. Shyam starts at $9: 45 \mathrm{AM}$ from $\mathrm{A}$ at a speed of $10 \mathrm{~km} / \mathrm{hr}$, reaches $B$ and comes back to $A$ at the same speed.

At what time does Shyam overtake Ram ?

If the roots of the equation $x^{2}-p x+54=0$ are in the ratio $2: 3$, then value of $p$ is:

If each side of a cube is decreased by $19 \%$, then the decrease in surface area is :

Given below are two statements:

Statement I: $\frac{\cot 30^{\circ}+1}{\cot 30^{\circ}-1}=2\left(\cos 30^{\circ}+1\right)$

Statement II : $2 \sin 45^{\circ} \cos 45^{\circ}-\tan 45^{\circ} \cot 45^{\circ}=0$

Given below are two statements, one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) :

The sum of $n$ terms of the Progression

$1+\frac{1}{2}+\frac{1}{2^{2}}+\frac{1}{2^{3}}+$ is $\frac{2^{n-1}-1}{2^{n-1}}$.

Reason (R) :

Sum of a geometric series having $n$ terms is given by $S_{n}=\frac{a\left(1-r^{n}\right)}{1-r}$, where $a$ is the $1^{\text {st }}$ term and $r$ is the common ratio.

A is $40 \%$ less efficient than $B$ who can do the same work in $20 \%$ less time than $C$. If $A$ and B together can complete $80 \%$ work in 12 days, then in how many days $60 \%$ work can be completed by $\mathrm{B}$ and $\mathrm{C}$ together ?

A speaks the truth in $75 \%$ cases and $B$ in $80 \%$ of the cases. In what percentage of cases are they likely to contradict each other in narrating the same incident?

By selling two articles for ₹ 800 , a person gains the cost price of three articles. The profit percent is :

A person travels three equal distances at a speed of 'a' $\mathrm{km} / \mathrm{hr}$, 'b' $\mathrm{km} / \mathrm{hr}$ and ' $c$ ' $\mathrm{km} / \mathrm{hr}$ respectively. What is the average speed for the whole journey?

If $\alpha$ and $\beta$ are the roots of the equation $a x^{2}+b x+c=0$, then value of

$\frac{1}{a \alpha+b}+\frac{1}{a \beta+b}$ is :

The sides of four triangles are given below. Which of them forms a right triangle ?

(A) $20 \mathrm{~cm}, 22 \mathrm{~cm}, 24 \mathrm{~cm}$

(B) $15 \mathrm{~cm}, 32 \mathrm{~cm}, 37 \mathrm{~cm}$

(C) $11 \mathrm{~cm}, 60 \mathrm{~cm}, 61 \mathrm{~cm}$

(D) $6 \mathrm{~cm}, 8 \mathrm{~cm}, 10 \mathrm{~cm}$

The factors of polynomial $x^{3}-6 x^{2}+11 x-6$ are :

A circle, square, equilateral triangle and regular pentagon have the same areas. Arrange the following in ascending order based on their perimeters.

(A) Circle

(B) Square

(C) Equilateral triangle

(D) Regular pentagon

If highest common factor of $x^{2}-p x-q$ and $5 x^{2}-3 p x-15 q$ is $(x-3)$, then value of ( $\left.p, q\right)$ will be :

If $\sin \theta+\cos \theta=\frac{\sqrt{7}}{2}$, then $(\sin \theta-\cos \theta)$ is equal to :

Fifteen people from different places come together for a family reunion. Each one of them had two gifts each for every other person. When the gifts were exchanged they hugged each other. What is the difference between the number of hugs and the number of gifts exchanged?

The points $(2,2),(6,3)$ and $(4,11)$ are vertices of :