List of top Mathematics Questions

$$ \int e^x (\tan x + \sec^2 x) \, dx = ? $$
$$ \int_{-\pi/4}^{\pi/4} \sin^{103} x \cos^{101} x \, dx = ? $$
$$ \lim_{x \to 0} \frac{1 - \cos x}{x^2} = $$
$$ \lim_{x \to \infty} \left[ \frac{1^x + 2^x + 3^x + \cdots + n^x}{n} \right]^{1/x} = $$
Let $A = \{x : x \in \mathbb{R}, \, x \text{ is not a positive integer}\}$. Define $f: A \to \mathbb{R}$ as $f(x) = \dfrac{2x}{x-1}$, then $f$ is:
The number of bijective functions from set $A$ to itself when $A$ contains $97$ elements, is:
Domain of $\cos^{-1}[x]$ is, where $[.]$ denotes greatest integer function:
Given $0 \le x \le \dfrac{1}{2}$ then the value of $\tan \left[ \sin^{-1} \left( \dfrac{x}{\sqrt{2}} + \dfrac{\sqrt{1-x^2}}{\sqrt{2}} \right) - \sin^{-1} x \right]$ is:
If $A$ and $B$ are two events such that $P(A) = \dfrac{1}{2}$, $P(B) = \dfrac{1}{3}$ and $P(A \mid B) = \dfrac{1}{4}$ then $P(A' \cap B')$ is:
Meera visits only one of the two temples $A$ and $B$ in her locality. Probability that she visits temple $A$ is $\dfrac{2}{5}$. If she visits temple $A$, $\dfrac{1}{3}$ is the probability that she meets her friend, whereas it is $\dfrac{2}{7}$ if she visits temple $B$. Meera met her friend at one of the two temples. The probability that she met her friend at temple $B$ is:
Which of the following functions is not invertible?
$\tan^{-1} \left( \frac{1}{1 + 1 \cdot 2} \right) + \tan^{-1} \left( \frac{1}{1 + 2 \cdot 3} \right) + \dots + \tan^{-1} \left( \frac{1}{1 + n \cdot (n+1)} \right) =$
The corner points of the feasible region determined by the system of linear constraints are (0, 10), (5, 5), (15, 15), (0, 20). Let $z = px + qy$, where $p, q>0$. The relation between $p$ and $q$, so that the maximum $z$ occurs at both points (15, 15) and (0, 20) is
In Linear Programming Problem (LPP), the objective function $Z = ax + by$ has the same maximum value at two corner points. The number of points at which $Z_{max}$ occurs is
Probability of obtaining an even prime number on each die when a pair of dice is rolled is
The probability that a man and his wife live after 20 years are $\frac{1}{4}$ and $\frac{1}{3}$ respectively. The probability that neither the man nor his wife live after 20 years is
Integrating factor of the differential equation $(1 - x^2)\frac{dy}{dx} - xy = 1$ is
Recent studies suggest that 12% of the world population is left handed. Depending on parents hand usage, the chances of having left handed children are as follows:
A: Both parents are left handed, chances of having left handed children = 24%
B: Both parents are right handed, chances of having left handed children = 9%
C: Father left handed and mother right handed, chances of having left handed children = 17%
D: Father right handed and mother left handed, chances of having left handed children = 22%
Given $P(A) = P(B) = P(C) = P(D) = 1/4$ and L denotes child is left handed. What is the probability that $P(A|L)$?
If the sum of the first \(n\) terms of an A.P. is \(S_n = 3n^2 + 5n\), find the \(10^{th}\) term.
If $\alpha$ and $\beta$ are acute angles such that $\alpha + \beta$ and $\alpha - \beta$ satisfy the equation $\tan^2 \theta - 4\tan \theta + 1 = 0$, then $\alpha$ and $\beta$ are respectively
$\sum_{r=1}^{n} (r \cdot r!) = $ ________
The solution of $3x - 5<2x - 4$ is
10 distinct points are taken on a circle. Then using these points
Statement I : The number of triangles that can be formed is 100
Statement II : The number of chords that can be formed is 45
Which of the following is correct?
How many ways can you arrange all the letters and numbers in "KCET 2025" which start with K and end with 5?
The value of $\lim_{x \to 2} \frac{x^3 + 3x^2 - 9x - 2}{x^3 - x^2 - 4x + 4}$ is ________