List of top Mathematics Questions

The remainder when $3^{100} \times 2^{500}$ is divided by $5$ is
If the matrix $\begin{bmatrix}a&b\\ c&d\end{bmatrix}$ is commutative with the matrix $\begin{bmatrix}1&1\\ 0&1\end{bmatrix}$, then
The value of $x$ for which $f(x) = x^3 - 6x^2 - 36x + 7 $ is increasing, belong to
If $ y =\sin^{-1} \left(\frac{5x+12 \sqrt{1 -x^{2}}}{13}\right)$ , then $ \frac{dy}{dx} = $
If $\vec{a}\cdot\hat {i}= \vec{a} \cdot(\hat {i}+\hat {j})= \vec{a}\cdot (\hat {i}+\hat {j}+\hat {k})=1$ then $\vec{a}$=
Let $y$ be the number of people in a village at time $t$. Assume that the rate of change of the population is proportional to the number of people in the village at any time and further assume that the population never increases in time. Then the population of the village at any fixed time $t$ is given by
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} = $