List of top Mathematics Questions on Sequence and Series asked in KEAM

Evaluate \( \int x \cos x \, dx \):
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:
Let \( z \) be a complex number satisfying \( |z + 16| = 4|z + 1| \). Then:
If \[ \int \frac{dx}{\sqrt{16 - 9x^2}} = A \sin^{-1}(Bx) + C, { where } C { is an arbitrary constant, then } A + B = \]
Let \( A = (a_{ij}) \) be a square matrix of order 3 and let \( M_{ij} \) be the minors of \( a_{ij} \). If \( M_{11} = -40, M_{12} = -10, M_{13} = 35 \), and \( a_{11} = 1, a_{12} = 3, a_{13} = -2 \), then the value of \( |A| \) is equal to:
Evaluate \( \int \frac{dx}{x^2 (x^4 + 1)^{3/4}} \):
Evaluate \( \int_0^1 \log \left( \frac{1}{x - 1} \right) \, dx \):
The general solution of \( \frac{dy}{dx} + y = 5 \) is:
The period of \( 2 \sin 4x \cos 4x \) is:
If \( \frac{\sec^2 15^\circ - 1}{\sec^2 15^\circ} \) equals:
Evaluate \( \int_{-\pi/2}^{\pi/2} \sin^9 x \cos^2 x \, dx \):
Find the area bounded by the curves \( y = 2x \) and \( y = x^2 \):
If \( 2z = 7 + i\sqrt{3} \), then the value of \( z^2 - 7z + 4 \) 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 differential equation \( \frac{dy}{dx} + x = A \) (where A is constant) represents:

Let \( f(x) = \log_e(x) \) and let \( g(x) = \frac{x - 2}{x^2 + 1} \). Then the domain of the composite function \( f \circ g \) is:

For two sets \( A \) and \( B \), we have \( n(A \cup B) = 50 \), \( n(A \cap B) = 12 \), and \( n(A - B) = 15 \). Then \( n(B - A) \) is equal to:
The sum of the series \( \frac{1}{2^{10}} + \frac{1}{2^{11}} + \cdots + \frac{1}{2^{19}} \) is equal to:
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 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:

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:
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:

If \( 0 \leq \alpha \leq \frac{\pi}{2} \) and \(\sin \left(\alpha - \frac{\pi}{12}\right) = \frac{1}{2}\), then \(\alpha\) is equal to:

The equation of the line passing through the point \((-9,5)\) and parallel to the line \(5x - 13y = 19\) is:

The radius of the circle with centre at \((-4, 0)\) and passing through the point \((2, 8)\) is: