List of top Mathematics Questions asked in KEAM

If \( \frac{\sec^2 15^\circ - 1}{\sec^2 15^\circ} \) equals:
If \( B = \begin{bmatrix} 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{bmatrix} \) is the adjoint of a \( 3 \times 3 \) matrix \( A \) and \( |A| = 4 \), then the value of \( \alpha \) is:
If the determinant of the matrix \( \begin{bmatrix} |x| & 1 & 2 \\ 4 & 1 & x \\ 1 & -1 & 3 \end{bmatrix} \) equals -10, then the values of \( x \) are:
The coefficient of \( x^3 \) in the binomial expansion of \( \left( \frac{1}{\sqrt{x}} - x \right)^6 \) is:
If \( _nP_r = 480 \) and \( _nC_r = 20 \), then the value of \( r \) is equal to:
The constant term in the expansion of \( \left( x^3 + \frac{1}{x^2} \right)^{10} \) is:
If one end of a diameter of the circle \( x^2 + y^2 - 4x - 6y + 11 = 0 \) is \( (3, 4) \), then the coordinate of the other end of the diameter is:

If 

then the value of \( x - y \) is:

The minimum value of \( f(x) = 7x^4 + 28x^3 + 31 \) is:
If \( \sin \theta = \frac{b}{a} \), then \( \frac{\sqrt{a+b}} {\sqrt{a-b}} + \frac{\sqrt{a-b}} {\sqrt{a+b}} \) is equal to:
The numbers \( a, b, c, d \) are in G.P. with common ratio \( r \). If \( \frac{1}{a^3 + b^3} + \frac{1}{b^3 + c^3} + \frac{1}{c^3 + d^3} \) are also in G.P., then the common ratio is:
Evaluate \( \binom{10}{1} + \binom{10}{2} + \dots + \binom{10}{10} \):
The maximum value of \( y = 12 - |x - 12| \) in the range \( -11 \leq x \leq 11 \) is:
Let \( z \) be a complex number satisfying \( |z + 16| = 4|z + 1| \). Then:
If \( 2z = 7 + i\sqrt{3} \), then the value of \( z^2 - 7z + 4 \) is:
If \( \left( \frac{1 - i}{1 + i} \right)^{10} = a + ib \), then the values of \( a \) and \( b \) are, respectively:
The second term of a G.P. is 4, then the product of the first three terms is:
The integral \( \int \frac{dx}{1 + e^x} \) is:
The period of \( 2 \sin 4x \cos 4x \) is:
The common ratio of a G.P. is \( \frac{1}{2} \). If the product of the first three terms is 64, then the sum of the first 10 terms is:
The coefficient of \( x^7 \) in the expansion of \( \left( \frac{1}{x + x^2} \right)^8 \) is
If \( \frac{1}{\log_2 x} + \frac{1}{\log_3 x} + \frac{1}{\log_4 x} + \frac{1}{\log_5 x} + \frac{1}{\log_6 x} = 1 \), then the value of \( x \) is
If \( f(x) = \lfloor x \rfloor \), where \( \lfloor x \rfloor \) denotes the greatest integer function, and if the domain of \( f \) is \( \{-3.01, 2.99\} \), then the range of \( f \) is
The common ratio of a G.P. is 10. Then the ratio between its 11th term and its 6th term is:
If \( x + iy = \frac{3 + 4i}{5 - 12i} \), then \( x + y \) is equal to