List of top Mathematics Questions

Write \( \int \cot{x} \, dx \).

Write the degree of the differential equation \( \frac{d^2y}{dx^2} + \frac{dy}{dx} = x \).

If the corner points of the feasible solution are \( (0, 10), (2, 2) \), and \( (4, 0) \), then the point of minimum \( z = 3x + 2y \) is

The integral of \( \cos^2x \) is

If \( y \) is a function of \( x \) and \( \log(x + y) = 2xy \), then the value of \( y'(0) \) is

The area of the triangle with vertices \( (1, 2, 0), (1, 0, 2) \), and \( (0, 3, 1) \) in square units is

Let  denote the (r + 2) digit number where the first and the last digits are 7 and the remaining r digits are 5. Consider the sum S = 77 + 757 + 7557 + …+ . If S = , where m and n are natural numbers less than 3000, then the value of m + n is ______.

The line integral \(\overrightarrow V = x^2\hat{î}-2y\hat{j} + z^2\hat{k}\) over the straight line path from the point (-1, 2, 3) to (2, 3, 5) is

Let $f$ be a twice differentiable function on $R$. 
If $f ^{\prime}(0)=4$ and $f(x)+\int\limits_0^x(x-t) f^{\prime}(t) d t=\left(e^{2 x}+e^{-2 x}\right) \cos 2 x+\frac{2}{a} x,$ 
then $(2 a+1)^5 a^2$ is equal to ______.

A particle moves along the curve \(\frac{x^2}{16}+\frac{y^2}{4}=1\). When the rate of change of abscissa is 4 times that of its ordinate, then the quadrant in which the particle lies is

Let f(x) = sin 2x + cos 2x and g(x)=x²-1, then g(f(x)) is invertible in the domain

If the center and radius of the circle $\left|\frac{z-2}{z-3}\right|=2$ are respectively $(\alpha, \beta)$ and $\gamma$, then $3(\alpha+\beta+\gamma)$ is equal to

Let $A = \begin{bmatrix} 1 & a & a \\ 0 & 1 & b \\ 0 & 0 & 1\end{bmatrix}, a , b \in R$. 
If for some $n \in N , A ^{ n }=\begin{bmatrix}1 & 48 & 2160 \\ 0 & 1 & 96 \\ 0 & 0 & 1\end{bmatrix}$ 
then $n + a + b$ is equal to _________.

The value of \(\begin{vmatrix}     \sin^2 14 \degree & \sin^2 66\degree & \tan 135\degree \\     \sin^2 66\degree & \tan 135\degree &     \sin^2 14 \degree \\     \tan 135\degree & \sin^2 14 \degree & \sin^2 66\degree \end{vmatrix}\)

If polynomial \(g(x) = 3x^2 - 7x + 2\), then the value of \(g(-1)\) is

If \(\alpha\) and \(\beta\) are zeroes of the polynomial \(p(x) = x^2 - 3x + 5\), then the value of \(4(\alpha + \beta)\) is

If \( p(x) = 3x^{3} + x^{2} + 2x + 5 \) is divided by \( q(x) = x^{2} + 2x + 1 \), then the degree of the quotient will be:

Evaluate \( \dfrac{\sin^{2}(90^\circ-\theta)+\sin^{2}\theta}{\csc^{2}(90^\circ-\theta)-\tan^{2}\theta} \).

If \(\sin\theta=\dfrac{\sqrt{3}}{2}\), then the value of \(\csc\theta+\cot\theta\) is

If \(\sin\theta=\cos\theta,\ 0^\circ\le \theta\le 90^\circ\), then the value of \(\theta\) is

\(\displaystyle \frac{\sin 30^\circ+\cos 45^\circ-\tan 60^\circ}{\cot 30^\circ-\sin 45^\circ-\cos 60^\circ}=\)

\(\tan30^\circ\cdot \sin30^\circ\cdot \cot60^\circ\cdot \csc30^\circ=\)

If \(\sec\theta+\tan\theta+1=0\), then the value of \(\sec\theta-\tan\theta\) is

If \((\tan\theta+\cot\theta)=6\), then the value of \(\tan^{2}\theta+\cot^{2}\theta\) is