List of top Mathematics Questions

The length of the tangent from the point \((5,1)\) to the circle \[ x^2+y^2+6x-4y-3=0 \] is

In a circle with center \(O\), a \(6\) cm long chord is at a distance \(4\) cm from the center. Then the length of diameter is

Modulus of the complex number \[ \frac{(1+i)^{10}}{(2i-4)^4} \] is equal to

The real part of \[ \frac{1+2i}{(2-i)^2} \] is

If \(\sin\theta-\cos\theta=\frac{4}{5}\), then the value of \(\sin\theta+\cos\theta\) is

The value of \[ \cos\frac{5\pi}{17}+\cos\frac{7\pi}{17}+2\cos\frac{11\pi}{17}\cos\frac{\pi}{17} \] is

The general solution of the equation \(\tan^2x=1\) is

If \(\sin 5x+\sin 3x+\sin x=0\), then the value of \(x\) other than zero lying between \(0\leq x\leq \frac{\pi}{2}\) is

The maximum value of \(3\cos\theta+4\sin\theta\) is

\[ \sin^6\theta+\cos^6\theta+3\sin^2\theta\cos^2\theta= \]

For real \(x\) and if \(x+\frac{1}{x}=2\cos\theta\), then \(\cos\theta\) is

If \[ 5\sin\theta=4, \] then the value of \[ \frac{\cosec\theta-\cot\theta}{\cosec\theta+\cot\theta} \] is

If \[ \cos\theta \cosec\theta=-1 \] and \(\theta\) lies in the second quadrant, then \(\cos\theta=\)

If \[ \sin\theta=\frac{3}{5}, \] then \(\cos\theta=\)

If \[ \frac{3x-1}{(x-1)(x-2)(x-3)} = \frac{A}{x-1}+\frac{B}{x-2}+\frac{C}{x-3}, \] then the values of \((A,B,C)\) are

If \[ \frac{2x+5}{(x-1)(x+3)} = \frac{A}{x-1}+\frac{B}{x+3}, \] then \(A+B=\)

If the matrix \(A\) is of order \(3 \times 3\) and the system of equations \(AX=B\) has a unique solution, what can be concluded about the determinant of \(A\)?

If \[ A=\begin{bmatrix} a & b \\ c & d \end{bmatrix} \] and the determinant of \(A\) is \(5\), then determinant of the matrix \(2A\) is

\[ \int_{-a}^{a}|x|\,dx= \]

If \[ A=\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \quad \text{and} \quad B=\begin{bmatrix} 1 & 0 \\ 1 & 0 \end{bmatrix}, \] then \((AB)^T=\)

If \[ A=\begin{bmatrix} x & 3 \\ 2 & 4 \end{bmatrix} \quad \text{and} \quad A^{-1}=\begin{bmatrix} -2 & 1.5 \\ 1 & -0.5 \end{bmatrix}, \] then the value of \(x\) is

One card is drawn from a well shuffled deck of 52 cards. Then the probability that the card will be a face card is ________

If two unbiased dice are thrown at a time, then find the probability of getting the sum of the number on the dice is 10?

A sector of a circle with radius 14 cm makes an angle 90° at the centre. Then the perimeter of the sector is (in cm).

Match the following: