IPMAT Indore 2019

If the compound interest earned on a certain sum for 2 years is twice the amount of simple interest for 2 years, then the rate of interest per annum is _______ percent

The maximum value of the natural number $n$ for which $21^n$ divides $50!$ is

The remainder when $(29^{29})^{29}$ is divided by $9$ is

Placing which of the following two digits at the right end of $4530$ makes the resultant six digit number divisible by $6, 7$ and $9$:

In a school $70\%$ of the boys like cricket and $50\%$ like football. If $x\%$ like both Cricket and Football, then

In a class of 65 students 40 like cricket, 25 like football and 20 like hockey. 10 students like both cricket and football, 8 students like football and hockey and 5 students like all three sports. If all the students like at least one sport, then the number of students who like both cricket and hockey is

If $x ∈ (a, b)$ satisfies the inequality $\dfrac{x - 3}{x^2 + 3x + 2} \geq 1$, then the largest possible value of $b - a$ is

If $a, b, c$ are real numbers and $a^2 + b^2 + c^2 = 1$, then the set of values $ab + bc + ca$ can take is:

The inequality $\log_{2} \frac{3x - 1}{2 - x} < 1$ holds true for

The set of values of $x$ which satisfy the inequality $0.7^{(2x^2 - 3x + 4)} < 0.343$ is

A chord is drawn inside a circle, such that the length of the chord is equal to the radius of the circle. Now, two circles are drawn, one on each side of the chord, each touching the chord at its midpoint and the original circle. Let k be the ratio of the areas of the bigger inscribed circle and the smaller inscribed circle, then k equals

Points $P$, $Q$, $R$, and $S$ are taken on sides $AB$, $BC$, $CD$, and $DA$ of square $ABCD$ respectively, so that $\frac{AP}{PB} = \frac{BQ}{QC} = \frac{CR}{RD} = \frac{DS}{SA} = \frac{1}{n}$. Then the ratio of the area of $PQRS$ to the area of $ABCD$ is

On a circular path of radius 6 m a boy starts from a point $A$ on the circumference and walks along a chord $AB$ of length 3 m. He then walks along another chord $BC$ of length 2 m to reach point $C$. The point $B$ lies on the minor arc $AC$. The distance between point $C$ from point $A$ is

The area enclosed by the curve $2|x| + 3|y| = 6$ is

Two points on a ground are 1 m apart. If a cow moves in the field in such a way that its distance from the two points is always in ratio $3: 2$ then

Given that $\cos x + \cos y = 1$, the range of $\sin x - \sin y$ is

If $sin \theta + cos \theta = m$, then $sin^6 \theta + cos^6 \theta$ equals

If inverse of the matrix $\left[\begin{array}{cc}2 & -0.5 \\ -1 & x\end{array}\right]$ is $\left[\begin{array}{ll}1 & 1 \\ 2 & 4 \end{array}\right]$, then the value of $x$ is

The function $f(x) = \dfrac{x^3 - 5x^2 - 8x}{3}$ is

For $a > b > c > 0$, the minimum value of the function $f(x) = |x - a| + |x - b| + |x - c|$ is

Let $\alpha, \beta$ be the roots of $x^2 - x + p = 0$ and $\gamma, \delta$ be the roots of $x^2 - 4x + q = 0$ where p and q are integers. If $\alpha, \beta, \gamma, \delta$ are in geometric progression then $p + q$ is

If $(1 + x - 2x^2)^6 = A_0 + \sum_{r=1}^{12} A_r x^r$, then the value of $A_2 + A_4 + A_6 + \cdots + A_{12}$ is

The number of terms common to both the arithmetic progressions $2, 5, 8, 11, ..., 179$ and $3, 5, 7, 9, ..., 101$ is

From a pack of 52 cards, we draw one by one, without replacement. If $f(n)$ is the probability that an Ace will appear at the $n^{\text{th}}$ turn, then

A die is thrown three times and the sum of the three numbers is found to be 15. The probability that the first throw was a four is

In a given village there are only three sizes of families: families with 2 members, families with 4 members and families with 6 members. The proportion of families with 2, 4 and 6 members are roughly equal. A poll is conducted in this village wherein a person is chosen at random and asked about his/her family size. The average family size computed by sampling 1000 such persons from the village would be closest to

The value of $(\log_{3} 30)^{-1} + (\log_{4} 900)^{-1} + (\log_{5} 30)^{-1}$ is

The inequality $\log_{a}{f(x)} < \log_{a}{g(x)}$ implies that

Three cubes with integer edge lengths are given. It is known that the sum of their surface areas is $564 \ \text{cm}^2$. Then the possible values of the sum of their volumes are

Determine the greatest number among the following four numbers:

The number of points, having both coordinates as integers, that lie in the interior of the triangle with vertices $(0, 0), (0, 31),$ and $(31, 0)$ is

Two small insects, which are $x$ metres apart, take $u$ minutes to pass each other when they are flying towards each other, and $v$ minutes to meet each other when they are flying in the same direction. Then, the ratio of the speed of the slower insect to that of the faster insect is

An alloy $P$ has copper and zinc in the proportion of $5:2$ (by weight), while another alloy $Q$ has the same metals in the proportion of $3:4$ (by weight). If these two alloys are mixed in the proportion of $a:b$ (by weight), a new alloy $R$ is formed, which has equal contents of copper and zinc. Then, the proportion of copper and zinc in the alloy $S$, formed by mixing the two alloys $P$ and $Q$ in the proportion of $b:a$ (by weight) is

How many different numbers can be formed by using only the digits 1 and 3 which are smaller than 3000000?

There are numbers $a_1, a_2, a_3, \ldots, a_n$ each of them being $+1$ or $-1$. If it is known that $a_1 a_2 + a_2 a_3 + a_3 a_4 + \ldots a_{n-1} a_n + a_n a_1 = 0$ then

Average annual exports for the given period 2006-2017 was approximately

The percentage decline in exports during the period 2006-2011 is more than the percentage decline in exports during 2012-2017 by approximately

The maximum difference between imports and exports is

Balance of trade is defined as imports subtracted from exports ( = exports - imports). Which of the following blocks of three years has witnessed the largest average negative balance of trade?

The percentage increase in imports over the previous year is maximum during