List of top Mathematics Questions

A bag contains 5 red and 3 blue balls. Two balls are drawn one by one with replacement. The probability that both are red is:
If \(A\) and \(B\) are two matrices such that \(AB\) is defined and \(AB = A\), then \(B\) is:
The value of \(\cos 15^\circ + \sin 15^\circ\) is:
The value of \(\displaystyle \int_{-\infty}^{\infty} e^{-x^2}\,dx\) is:
The angle between the planes \(2x-y+z=6\) and \(x+y+2z=7\) is:
If the roots of the equation \(x^3-6x^2+11x-6=0\) are in A.P., the common difference is:
The probability of getting exactly 2 heads in 4 tosses of a fair coin is:
A man is 4 times as old as his son. After 5 years, he will be 3 times as old as his son. The present age of the son is:
If the matrix \(\begin{bmatrix}1 & 2\\ 3 & 4\end{bmatrix}\) has determinant \(k\), then the determinant of its adjoint is:
The value of \(\lim_{x\to0}\frac{\sin 3x}{x}\) is:
The solution of the equation \(\sin x + \cos x = 0\) in \([0,2\pi]\) is:
The differential equation \(\frac{dy}{dx}=\frac{y}{x}\) represents:
If the vectors \(2\hat{i}+3\hat{j}+\hat{k}\) and \(4\hat{i}-\hat{j}+2\hat{k}\) are perpendicular, the value of \(\lambda\) in \(\lambda\hat{i}+2\hat{j}+3\hat{k}\) is:
The number of terms in the expansion of \((a+b+c)^5\) is:
If \(\sin\theta+\cos\theta=\sqrt{2}\), then \(\tan\theta+\cot\theta\) is:
If \(A=\{1,2,3\}\), \(B=\{3,4\}\), then \(A\cup B\) is:
The value of \( \int_0^{\pi/2} \sin^2 x \, dx \) is:
The sum of the infinite series \[ \sum_{n=1}^{\infty} \frac{(-1)^{n+1} \pi^{2n+1}}{2^{2n+1} (2n)!} \] is equal to
If \( f : \mathbb{R} \to \mathbb{R} \) and \( g : \mathbb{R} \to \mathbb{R} \) are two functions defined by \( f(x) = 2x - 3 \) and \( g(x) = 5x^2 - 2 \), then the least value of the function \((g \circ f)(x)\) is:
Find the equation of the tangent line to the curve \( y = x^2 - 3x + 2 \) at the point \( (1, 0) \).
Find the Cartesian equation of a line which passes through point (3, -2, -5) and is parallel to the vector \( (3\hat{i} + 2\hat{j} - 2\hat{k}) \).
How many numbers between 900 and 1000 are divisible by 13?
Evaluate the integral: \[ \int \frac{2x^2 + 4x + 3}{x^2 + x + 1} \, dx \]

Find the variance of the following frequency distribution:

Class Interval 
0--44--88--1212--16
Frequency1221
If \(\alpha, \beta, \gamma\) are the roots of the equation \[ x^3 - 13x^2 + kx + 189 = 0 \] such that \(\beta - \gamma = 2\), then find the ratio \(\beta + \gamma : k + \alpha\).