List of top Mathematics Questions on Sequence and series asked in MHT CET

Number of switches in alternative equivalent simple circuit for the circuit is (are)

$\int_1^e \frac{e^x}{x}(1 + x \log x) dx =$

The derivative of $\tan^{-1} \left( \frac{\sqrt{1+x^2}-1}{x} \right)$ w.r.t. $\tan^{-1} \left( \frac{2x\sqrt{1-x^2}}{1-2x^2} \right)$ at $x = 0$ is

If \( \frac{1}{4}, a, b, \frac{1}{19} \) form a harmonic progression (H.P.), then the values of \( a \) and \( b \) are respectively

The micro-organisms double themselves in 3 hours. Assuming that the quantity increases at a rate proportional to itself, then the number of times it multiplies itself in 18 years is

The sum of first four terms of a G.P. is $160$ and the common ratio is $3$, then the $4^{\text{th}}$ term is

If the plane \[ 2x + 3y + 5z = 1 \] intersects the coordinate axes at the points A, B, C, then the centroid of \( \triangle ABC \) is

Evaluate the sum of the series: \[ \frac{1^2}{2} + \frac{1^2 + 2^2}{3} + \frac{1^2 + 2^2 + 3^2}{4} + \frac{1^2 + 2^2 + 3^2 + 4^2}{5} + \cdots \quad \text{upto 8 terms} \]

If the equation \[ kxy + 5x + 3y + 2 = 0 \text{ represents a pair of lines, then } k = \]

For a sequence \( (t_n) \), if \( s_n = 7(3^n - 1) \), then \( t_n = \)

Evaluate \( \int e^{\tan^{-1} x} \left( 1 + \frac{x}{1 + x^2} \right) dx \)

Bacteria increases at the rate proportional to the number of bacteria present. If the original number \( N \) doubles in \( 4 \) hours, then the number of bacteria will be \( 4N \) in

Let $\overrightarrow{a}=a_1\hat{i}+a_2\hat{j}+a_3\hat{k},\overrightarrow{b}=b_1\hat{i}+b_2\hat{j}+b_3\hat{k}$ be three non-zero vectors such that $\overrightarrow{c}$ is a vector perpendicular to both $\overrightarrow{a}$ and $\overrightarrow{b}$. If the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is $\frac{\pi }{6}$ then $\left|\begin{array}{lll}{a}_1& b_1& c_1\\ a_2& b_2& c_2\\ a_3& b_3& c_3\end{array}\right|=?$

What is ${\int }_0^a\frac{f(a-x)}{f(x)+f(a-x)}dx$ equal to?

In a binomial distribution, the mean is $\frac{2}{3}$ and variance is $\frac{5}{9}$. What is the probability that random variable $D=2?$

What is the sum of the measures of the angles ∠A, ∠B, ∠C, ∠D, ∠E, and ∠F in the given figure?

There are 20 cricket players, out of which 5 players can bowl. In how many ways can a team of 11 players be selected so, to include 4 bowlers?

The point of intersection of diagonals of a square ABCD is at the origin and one of its vertices is at A(4, 2). What is the equation of the diagonal BD?

The value of $k$ which makes $f(x)=\{\begin{array}{l}\sin x,x\ne 0\\ k,x=0\end{array}$ continuous at $x=0$, is: