List of top Mathematics Questions

The integral $ \int e^x \left( \frac{x + 5}{(x + 6)^2} \right) dx $ is:

The integral $ \int_0^1 \frac{1}{2 + \sqrt{2e}} \, dx $ is:

The integral $ \int e^x \left( \frac{x + 5}{(x + 6)^2} \right) dx $ is:
In $ \triangle ABC $, with usual notations, $ \sin \left( \frac{A}{2} \right) \cdot \sin \left( \frac{C}{2} \right) = \sin \left( \frac{B}{2} \right) \quad \text{and} \quad 2s \text{ is the perimeter of the triangle. Find the value of } s. $ Then the value of $ s $ is:
Evaluate the limit $ \lim_{n \to \infty} \frac{6^n - 9x - 7^n + 1}{\sqrt{2} - \sqrt{11} + \cos n} $

The eccentricity of the curve represented by $ x = 3 (\cos t + \sin t) $, $ y = 4 (\cos t - \sin t) $ is:

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 $
If $ y = \frac{b}{a} $, then $ \frac{dy}{dx} $ is:
Binomial Expansion Series $ \left( \frac{(1 + x)}{(n + 1)} \right)' = n_0 x + n_1 \frac{x^2}{2} + n_2 \frac{x^3}{3} + \cdots + n_n \frac{x^n}{n+1} $
Which of the following expressions represents the Principal Solution
Principal Solution of $ (5 \sin \theta)(2 \cos \theta + 1) = 0 $
Curves Represented
Given the function \( F(x) = |\sin(3x)| - \cos(3x) \), for \( \frac{\pi}{6} \leq x \leq \frac{\pi}{3} \), find \( f' \left( \frac{\pi}{4} \right) \).
Evaluate the definite integral: \( \int_{-2}^{2} |x^2 - x - 2| \, dx \)
Find the value of the following expression: \[ \tan^2(\sec^{-1}4) + \cot(\csc^{-1}3) \]

In the following figure, four overlapping shapes (rectangle, triangle, circle, and hexagon) are given. The sum of the numbers which belong to only two overlapping shapes is ________

Given a series \( 5, 8, 11, 14, \dots \), if the \( n \)-th term of the given series is 320, then find \( n \) (where \( n \geq 1 \)):
If \( \times \) means \( + \), \( + \) means \( \div \), \( - \) means \( \times \), and \( \div \) means \( - \), then evaluate: 8 \( \times \) 7 \( - \) 8 \( + \) 40 \( \div \) 2.

The table shows the data of 450 candidates who appeared in the examination of three subjects – Social Science, Mathematics, and Science. How many candidates have passed in at least one subject? 

How many candidates have passed in at least one subject?

Solve the system of equations: \[ \begin{bmatrix} 4 & 9 \\ 12 & -3 \\ 8 & -2 \end{bmatrix} \begin{bmatrix} 7 \\ 9 \end{bmatrix} = \begin{bmatrix} \alpha \\ \beta \end{bmatrix} \]
Evaluate the integral: \[ \int e^x \sec(x) \left( \tan(x) + 1 \right) \, dx \]
Evaluate the integral: \[ \int \frac{x^2 + 2x}{\sqrt{x^2 + 1}} \, dx \]
If two dice are rolled, what is the probability of getting a sum of 7?
A bag contains 5 red balls, 7 green balls, and 8 blue balls. One ball is drawn at random. What is the probability that the ball is either red or green?
Find the roots of the quadratic equation \( x^2 - 5x + 6 = 0 \).