List of top Questions asked in KEAM

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

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

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

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

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

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

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

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

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

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

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

Consider the set of all positive rational numbers that are less than 1 and that have denominators as 30 in their lowest terms. Their sum is equal to

The numbers $a_1,a_2,a_3,\ldots$ form an arithmetic sequence with $a_1\ne a_2$. The three numbers $a_1,a_2$ and $a_6$ form a geometric sequence in that order. Then the common difference of the arithmetic sequence is

In an arithmetic sequence, the sum of first and third terms is 6 and the sum of second and fourth terms is 20. Then the $11^{\text{th}}$ term is

The value of $\sum_{k=1}^{10}(3k^2+2k-1)$ is

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