List of top Mathematics Questions

The perimeter of a certain sector of a circle is equal to the length of the arc of the semicircle. Then the angle at the centre of the sector in radians is
The tangents drawn at the extremeties of a focal chord of the parabola $y^2 = 16 x$
The point $(5, - 7)$ lies outside the circle
The equation to the normal to the hyperbola $\frac {x^2}{16}- \frac {y^2}{9}=1$ at $(-4,0)$ is
One possible condition for the three points $(a, 5), (b, a)$ and $(a^2, - b^2)$ to be collinear is
If $\,^{16}C_{r} =\, ^{16}C_{r+1}$, then the value of $\, ^{r}P_{r-3}$ is
The projection of $\vec{a}=3\hat{i}-\hat{j}+5\hat {k} $ on $\vec{b}=2 \hat {i}+3 \hat j+\hat k$ is
If $R$ be a relation defined as $aRb iff |a - b| > 0$, then the relation is
If $I =\int\frac{x^{5}}{\sqrt{1+x^{3}}}dx$ , then I is equal to
The solution of the differential equation $\frac{dy}{dx} = \frac{xy + y}{xy + x}$ is
The ten's digit in $1! + 4!+ 7! + 10!+12! + 13! + 15! +16! + 17!$ is divisible by
The characteristic roots of the matrix $\begin{bmatrix} {1}&{0} &{0}\\ {2}&{3}& {0} \\ {4}&{5}&{6}\\ \end{bmatrix} $ are
The probability that number selected at random from the number $1, 2, 3, 4, 5, 6, 7, 8, ..., 100$ is a prime, is
The value of $\tan^{-1} \frac{\sqrt{2+\sqrt{3}} -\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3} } +\sqrt{2-\sqrt{3}}} $
If $[x]$ denotes the greatest integer function, then $\int\limits_{1}^{4} \left(\left[x\right] -1\right)\left(\left[x\right] -2\right)\left(\left[x\right] -3\right)\left(\left[x\right] -4\right)dx = $
If $\log_2 \: \sin x - \log_2 \cos x -\log_2(1 - \tan^2x) = - 1$, then
If $u = f(x^2) , v = g(x^3) , f'(x) = \sin x $ and $g'(x) = \cos x,$ then $ \frac{du}{dv} = $
If $x= 3 \cos t - 2 \cos^{3} t , y = 3\sin t - 2 \sin^{3} t ,$ then $ \frac{d^{2}y}{dx^{2}} t = \frac{\pi}{6}$ is
If $\tan^{-1} \left(\frac{x}{y}\right) + \log \sqrt{x^{2} +y^{2}} = 0 $ , then $\frac{dx}{dy} = $
Let $f\left(x\right) = \frac{\log\left(1+ex\right)-\log\left(1-x\right)}{x} , x\ne0 $ . Then $f$ is continuous at $x = 0$ if $f(0)$ =
Rain is falling vertically downwards with a velocity of $4\, km / h$. A man walks in the rain with a velocity of $3 \,km / h$. The raindrops will fall on the man with a velocity of
The value of $\cos \frac{\pi}{15}\, \cos \frac{2\pi}{15}\, \cos \frac{4\pi}{15}\, \cos \frac{8\pi}{15} $ is
The order and degree of the following differential equation $\left[1+\left(\frac{dy}{dx}\right)^{2}\right]^{5/2} = \frac{d^{3}y}{dx^{3}}$ are respectively
The differential equation of the family of circles passing through the fixed points $(a, 0)$ and $(-a, 0)$ is
The value of the integral $\int\limits_{-a}^{a} \frac{xe^{x^2}}{1+x^{2}} dx $ is