IPMAT Indore 2019 Question Paper with Answers

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 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 of 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

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