List of top Questions asked in KEAM- 2020

The equation of the line passing through the point (-3,7) with slope zero is

Which of the following sentences is/are statement(s)?
(i) 10 is less than 5.
(ii) All rational numbers are real numbers.
(iii) Today is a sunny day.

The values of x in $0\le x\le\pi$ such that $\cos 2x=\cos x$ are

The value of $\sin(45^{\circ}+\theta)-\cos(45^{\circ}-\theta)$ is equal to

The value of $\sin^{4}\frac{\pi}{8}+\sin^{4}\frac{3\pi}{8}$ is equal to

The value of $\sin^{2}1^{\circ}+\sin^{2}2^{\circ}+\sin^{2}3^{\circ}+\dots+\sin^{2}88^{\circ}+\sin^{2}89^{\circ}$ is equal to

The value of $\theta$ with $0\le\theta\le90^{\circ}$ and $\sin^{2}\theta+2\cos^{2}\theta=\frac{7}{4}$ is equal to

The solution set of the rational inequality $\frac{x+9}{x-6}\le0$ is

The system of equations $x+y+2z=4$, $3x+3y+6z=17$, $5x-3y+2z=27$ has

If \(A^{-1}=\frac{1}{11}\begin{pmatrix}-3 & 4\\5 & -3\end{pmatrix}\), then \(A=\)

The smallest prime number satisfying the inequality $\frac{2n-3}{3}\ge\frac{n-1}{6}+1$ is

The number of integers satisfying the inequality \(|n^{2}-100|<50\) is

If the matrix \(\begin{bmatrix}1 & 2 & -1\\-3 & 4 & k\\-4 & 2 & 6\end{bmatrix}\) is singular, then the value of \(k\) is equal to

The sum of the coefficients in the expansion of $(1+2x-x^{2})^{20}$ is

The number of ways a committee of 4 people can be chosen from a panel of 10 people is

If \(A=\begin{pmatrix}6 & 2\\7 & -5\end{pmatrix}\) and \(A-B=\begin{pmatrix}-2 & 1\\4 & -9\end{pmatrix}\) then \(B=\begin{pmatrix}8 & 1\\3 & 4\end{pmatrix}\)

If \(\begin{bmatrix}-1 & 3\\4 & -5\\0 & 2\end{bmatrix}\begin{bmatrix}1 & 2\\0 & 7\end{bmatrix}=\begin{bmatrix}-1 & 19\\\alpha & -27\\0 & 14\end{bmatrix}\), then the value of \(\alpha\) is

The value of the determinant \(\begin{vmatrix}bc & ca & ab\\ a^{3} & b^{3} & c^{3}\\ \frac{1}{a} & \frac{1}{b} & \frac{1}{c}\end{vmatrix}\) is

The middle term in the expansion of $\left(1+\frac{1}{5}\right)^{20}$ is

The 5th and 7th terms of a G.P. are 12 and 48 respectively. Then the $9^{\text{th}}$ term is

Five points are marked on a circle. The number of distinct polygons of three or more sides can be drawn using some (or all) of the five points as vertices is

The number of positive integers less than 1000 having only odd digits is

The value of ${}^{11}C_{0}+{}^{11}C_{1}+{}^{11}C_{2}+{}^{11}C_{3}+{}^{11}C_{4}+{}^{11}C_{5}$ is

If ${}^{n}P_{r}=840$ and ${}^{n}C_{r}=35$, then the value of $r$ is equal to

If p, q and 23 is an increasing arithmetic sequence and p and q are prime numbers, then $p+q=$