List of top Questions asked in KEAM

If $(x-1)(x^2 - 5x + 7) < (x-1)$, then $x$ belongs to

Let $L$ be an arc of a circle which subtends $45^\circ$ at the centre. If the radius of circle is $4$ cm, then the length of $L$ in centimeter is

If \(\tan\left(\frac{\pi}{4} + \theta\right) = \frac{1}{2}\) then the value of \(\sin 2\theta\) is

If \(1 + \cos x = \alpha\), \(0 \leq x \leq \frac{\pi}{2}\), then \(\sin \frac{x}{2}\) is equal to

The value of the determinant of the inverse of the matrix \(\begin{bmatrix} -4 & -5\\ 2 & 2 \end{bmatrix}\) is

If \(A=\begin{bmatrix}1 & 1\\ 0 & i\end{bmatrix}\) and \(A^{42}=\begin{bmatrix}a & b\\ c & d\end{bmatrix}\) then \(a+d\) is equal to

There are two women participants in a badminton tournament. The number of games the men played between themselves exceeds by 12 the number of games they played with women. If each player played one game with each other, then the number of men in the tournament was

Let \(f(x) = \begin{vmatrix} x & 1\\ \sin(2\pi x) & 2x^2 \end{vmatrix}\). If \(f(x)\) is an odd function, \(f(-x)=g(x)\) and \(\lambda f(1)g(1)=4\), then the value of \(\lambda\) is equal to

If \(A=\begin{bmatrix}3 & \lambda-3\\ -1 & 1\end{bmatrix}\) and \(B=\begin{bmatrix}3 & 2\\ 2 & 1\end{bmatrix}\) and \(AB=\begin{bmatrix}7 & 1\\ -1 & -1\end{bmatrix}\), then \(\lambda\) is equal to

If the 17th and 18th term in the expansion of \((2 + x)^{50}\) are equal, then the value of \(x\) is equal to

If three geometric means are inserted between 2 and 32, then the three numbers are

If $a,b,c$ are three unequal numbers such that $a,b,c$ are in arithmetic progression and $b-a, c-b, a-b$ are in geometric progression, then $a:b:c$ is

If \(\frac{{}^nP_{r-1}}{a} = \frac{{}^nP_r}{b} = \frac{{}^nP_{r+1}}{c}\), then

A geometric progression has an even number of terms. If the sum of all terms is five times the sum of all odd terms, then the common ratio is equal to

The number of ways in which we can choose a committee from 3 men and 6 women so that the committee includes at least two men and exactly twice as many women as men is

If \(\frac{1}{8!} + \frac{1}{9!} = \frac{x}{12!}\), then the value of \(x\) is equal to

In a geometric progression of positive terms, if any term is equal to the sum of the next two terms, then the common ratio of the geometric progression is equal to

The imaginary part of \(\frac{1 - i\sqrt{3}}{1 + i\sqrt{3}}\) is

The sum of $i^2 + i^4 + \cdots$ upto 25 terms is equal to

If $z(3 - i) = 2 + i$, then $z^2 =$

If $|z + 4| = 2|z + 1|$, where $z$ is a complex number then $|z|$ is equal to

The number of elements in the set \(\{(x,y): 2x^2 + 3y^2 = 35, x,y \in \mathbb{Z}\}\), where \(\mathbb{Z}\) is the set of all integers, is

The domain of \(f(x) = \frac{x^2 + 1}{x^2 + x + 1}\) is

Let \(R\) be a relation in \(\mathbb{N}\) defined by \(\{(x,y): x + 3y = 10, x,y \in \mathbb{N}\}\). Then the range of \(R\) is

Let $A$ and $B$ be two sets of having 3 and 2 elements respectively. Then the number of subsets of $A \times B$ having at least three elements is