List of top Mathematics Questions on Sequence and Series

In a GP 9, 3, $ \frac{1}{3} $, $ \frac{1}{9} $, … find the 25th term.

Series Expansion $ n^6 + \frac{1}{2} n^4 + \frac{1}{3} n^2 + \cdots + \frac{1}{n} C_n + 1 \quad n \to \infty $
Let a relation \( R \) on the set of natural numbers be defined by \( (x, y) \in R \) if and only if \( x^2 - 4xy + 3y^2 = 0 \) for all \( x, y \in \mathbb{N} \). Then the relation is:
Evaluate \( \int \frac{e^{6 \log x} - e^{5 \log x}}{e^{4 \log x} - e^{3 \log x}} \, dx \):
If \[ \int \frac{dx}{\sqrt{16 - 9x^2}} = A \sin^{-1}(Bx) + C, { where } C { is an arbitrary constant, then } A + B = \]
The minimum value of \( f(x) = 7x^4 + 28x^3 + 31 \) 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 axis of a parabola is parallel to the y-axis and its vertex is at \((5, 0)\). If it passes through the point \((2, 3)\), then its equation is:

The centre of a circle lies on the y-axis. If it passes through the points \( (-4, 3) \) and \( (3, -4) \), then its radius 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:

If \( \cos \theta = \frac{2 \cos \alpha + 1}{2 + \cos \alpha} \), then \( \tan^2 \left( \frac{\theta}{2} \right) \) is equal to:
The value of \( \sin^2 \left( \frac{3\pi}{8} \right) + \sin^2 \left( \frac{7\pi}{8} \right) \) is:
Choose the correct alternative that will continue the same pattern and fill in the blank spaces. 2, 7, 14, 23, —–, 47
The sum up to \( n \) terms of the series \( \frac{1}{\sqrt{1} + \sqrt{6}} + \frac{1}{\sqrt{6} + \sqrt{11}} + \cdots \) 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:

If \( a \text{ and } b \) are A.M. and G.M. of \( x \text{ and } y \) respectively, then \( x^2 + y^2 \) is equal to: 
 

If

\[ A = \begin{pmatrix} x & 2 \\ 2 & x \end{pmatrix} \quad \text{and} \quad \det(A^2) = 25, \] then \( x \) is equal to:
Let A and B be two events such that \( P(A) = 0.4 \), \( P(B) = 0.5 \) and \( P(A \cap B) = 0.1 \). Then
\[ P(A \mid B) = ? \]

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:

Let \( \overrightarrow{AB} = i + 2j - 2k \) and \( \overrightarrow{AC} = i - j + k. \) Then the area of \( \triangle ABC \) is:

The equation of the line passing through the point \((-9,5)\) and parallel to the line \(5x - 13y = 19\) 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:
The sum of the series \( \frac{1}{2^{10}} + \frac{1}{2^{11}} + \cdots + \frac{1}{2^{19}} \) is equal to:
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:

Let \( x \text{ and } y \) be two positive real numbers. Then
\[ \left( x + \frac{1}{x} \right) \left( y + \frac{1}{y} \right) \] is greater than or equal to: