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

Let $a_{1}, a_{2}, 6, a_{4}$ be in G.P. Then the value of $(6a_{1}+6a_{2}+a_{1}a_{4}+a_{2}a_{4})^{2}$ is equal to
The two geometric means between 2 and 8 are $g_{1}$ and $g_{2}$. Then $g_{1}^{3}+g_{2}^{3}$ is equal to
Let $t_{1},t_{2},t_{3},\dots,t_{n}$ be in G.P. Then $(\frac{t_{4}}{t_{2}})^{3}$ is equal to
The sum of the first $n$ terms in a G.P. is $s_{n}=100-100^{1-n}$. The common ratio $r$ is
The 1st and 20th term of a GP are 512 and \( \frac{1}{1024} \), respectively. Find the common ratio.

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

If \( \alpha = \tan^2 x + \cot^2 x \), where \( x \in \left( 0, \frac{\pi}{2} \right) \), then \( \alpha \) lies in the interval:
Evaluate \( \int \frac{e^{6 \log x} - e^{5 \log x}}{e^{4 \log x} - e^{3 \log x}} \, dx \):

The point of intersection of the lines \(\frac{x-3}{2} = \frac{y-2}{2} = \frac{z-6}{1}\) and \(\frac{x-2}{3} = \frac{y-4}{2} = \frac{z-1}{3}\) is:

The area bounded by the curves \( y = x^2 \) and \( y = 2x \) in the first quadrant, is equal to:
The value of \( \sin^2 \left( \frac{3\pi}{8} \right) + \sin^2 \left( \frac{7\pi}{8} \right) \) 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 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 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:
The minimum value of \( f(x) = 7x^4 + 28x^3 + 31 \) is:
Evaluate \( \binom{10}{1} + \binom{10}{2} + \dots + \binom{10}{10} \):
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:
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:
The constant term in the expansion of \( \left( x^3 + \frac{1}{x^2} \right)^{10} \) is:

If 

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

If \( f(x) = \begin{cases} x^2 & \text{for } x < 0 \\ 5x - 3 & \text{for } 0 \leq x \leq 2 \\ x^2 + 1 & \text{for } x > 2 \end{cases} \), then the positive value of \( x \) for which \( f(x) = 2 \) is:
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:
Let \( z \) be a complex number satisfying \( |z + 16| = 4|z + 1| \). Then: