List of top Mathematics Questions

If $f\left(x\right) = \frac{x^{2} -1}{x^{2} +1} ,x\in R$ then the minimum value of $f$ is

The area of the parallelogram with $\vec{a}$ and $\vec{b}$ as adjacent sides is $20\, s \,units$. Then the area of the parallelogram having $7\vec{a} + 5\vec{b}$ and $8\vec{a} + 11\vec{b}$ as adjacent sides is

If the area of a circle increases at a uniform rate, then its perimeter varies

The surface area of a ball is increasing at the rate of $2 \pi \, s cm/sec$. The rate at which the radius is increasing when the surface area is $16 \pi \, s cm$ is

Let $f (x)$ and $g(x)$ be differentiable functions on (0, 2] such that $f"(x) - g"(x) = 0, f'(1) = 2g'(1) = 4, f(2) = 3g(2) = 9.$ Then $f (x)- g(x)$ at $ x = 3/2$ is

If $A = \begin{bmatrix}3&2\\ 4&5\end{bmatrix} $ and $AC = \begin{bmatrix}19&24\\ 37&46\end{bmatrix}$ then $C= $

The length of the subtangent to the curv $x^2y^2 = a^4$ at $(-a, a)$ is

The point of contact of the tangent $x + 2y + 2 = 0$ with the parabola $x^2 = 16y$ is

The equation of the line passing through $ (0,0) $ and intersection of $ 3x-4y=2 $ and $ x+2y=-4 $ is

If $A = \begin{bmatrix}3&x-1\\ 2x+3&x+2\end{bmatrix}$ is a symmetric matrix, then the value of $x$ is

The coordinates of a moving point $p$ are $(2t^2 + 4, 4t + 6)$. Then its locus will be a

The number of solutions of $2\,\sin x + \cos\, x = 3$ is

If $\sin\,\theta$ and $\cos \theta $ are the roots of the equation $ax^2 - bx + c = 0$, then $a, b$ and $c$ satisfy the relation

If the three points $A(1,6), B(3, -4)$ and $C(x, y)$ are collinear then the equation satisfying by $x$ and $y$ is

Let $\tan \,\alpha = \frac{a}{a+1}$ and $\tan \,\beta = \frac{1}{2a + 1}$ then $\alpha + \beta$ is

The solution of $\frac{dy}{dx} = \frac{y}{x}+\tan \frac{y}{x}$ is

If sin $\theta = \frac{2t}{1+t^{2}}$ and $?$ lies in the second quadrant, then $cos\,\theta$ is equal to

If $\log_{7} \,2 = ?$, then the value of $\log_{49}\, \left(28\right)$ is

If $^nC_4,\, ^nC_5$ and $^nC_6$ are in $A.P.$, then $n$ is

Find the value of $(7.995)^{1/3}$ correct to four decimal places.