List of top Questions asked in KEAM

Given that: \[ \frac{1}{\tan A - \tan B} = \]

Two circles \(C_1\) and \(C_2\) have radii 18 and 12 units, respectively. If an arc of length \( \ell \) of \(C_1\) subtends an angle 80° at the centre, then the angle subtended by an arc of same length \( \ell \) of \(C_2\) at the centre is:

Let \( A, B, C \) be three mutually and exhaustive events of an experiment. If \( 2P(A) = 3P(B) = 4P(C) \), then \( P(C) \) is equal to:
A bag contains 10 green balls and 5 red balls. If two balls are selected randomly, then the probability that both are green balls, is:
Three coins are tossed simultaneously. Then the probability that exactly two tails appear is:

An assignment of probabilities for outcomes of the sample space \( S = \{1, 2, 3, 4, 5, 6\} \) is as follows:

\[ \begin{array}{c|c c c c c c} 1 & 2 & 3 & 4 & 5 & 6 \\ \hline k & 3k & 5k & 7k & 9k & 11k \end{array} \]

If this assignment is valid, then the value of \( k \) is:

The first term and the 6th term of a G.P. are 2 and \( \frac{64}{243} \) respectively. Then the sum of first 10 terms of the G.P. is:

The second term of a G.P. is \( \frac{1}{2} \). If the product of first five terms is 32, then the common ratio of the G.P. is:

Let \( f(x) = 2 - 7 \sin{\left( \frac{2x}{7} \right)} \). Then the maximum value of \( f(x) \) is:

Let \[ A = \begin{pmatrix} 2 & -1 & 1 \\ -1 & 0 & 2 \\ 1 & -2 & -1 \end{pmatrix} \] and let \( B = \frac{1}{|A|} A \). Then the value of \( |B| \) is equal to:

The value of the sum \( 15 C_6 + 14 C_6 + 13 C_6 + 12 C_6 + 11 C_6 + 10 C_6 \) is equal to:
11\( (10P_7) \) =
There are 3 different mathematics books and 4 different physics books in a shelf. Then the number of ways these books can be arranged so that the mathematics books are together is:
Let \( A \) and \( B \) be two sets each containing more than one element. If \( n(A \times B) = 155 \), then \( n(A) \) is equal to:
The sum of the series \( \frac{1}{2^{10}} + \frac{1}{2^{11}} + \cdots + \frac{1}{2^{19}} \) is equal to:

The value of \( x \) that satisfies the equation:

\[ \begin{vmatrix} x & 1 & 1 \\ 2 & 2 & 0 \\ 1 & 0 & -2 \end{vmatrix} = 6 \]

The coefficient of \( x^{14}y \) in the expansion of \( (x^2 + \sqrt{y})^9 \) is:

If \( 2 \) is a solution of the inequality \( \frac{x-a}{a-2x}<-3 \), then \( a \) must lie in the interval:

Let \[ A = \begin{pmatrix} 3 & -2 & 1 \\ -1 & 3 & -1 \end{pmatrix} \] and \[ B = \begin{pmatrix} 1 \\ \alpha \\ -1 \end{pmatrix}. \] If \[ AB = \begin{pmatrix} -2 \\ 6 \end{pmatrix}, \] then the value of \( \alpha \) is equal to:

If \( 0 \leq x \leq 5 \), then the greatest value of \( \alpha \) and the least value of \( \beta \) satisfying the inequalities \( \alpha \leq 3x + 5 \leq \beta \) are, respectively,

The modulus of the complex number \[ \frac{(1 + i)^{10} (2 - i)^6}{(2i - 4)^4} \] is equal to:
The centre of a square is at the origin of the complex plane. If one of the vertices is at \( -3i \), then the area of the square is:
The value of \( \alpha \) for which the complex number \( \frac{2 - \alpha i}{\alpha - i} \) is purely imaginary, is:
The period of the function \( f(x) = \sin\left( \frac{3x}{2} \right) \) is equal to:

The value of \[ \left(\frac{10i}{(2-i)(3-i)}\right)^{2024} \] is equal to: