List of top Mathematics Questions asked in MET

$ f(x)= \begin{cases} \frac{\sin^3(\sqrt{3}) \cdot \log(1+3x)}{(\tan^{-1}\sqrt{x})^2 (e^{5\sqrt{x}}-1)x}, & x\neq 0 \\ a, & x=0 \end{cases} $ is continuous in $ [0,1] $, then $ a $ equals to

If $ y = |\sin x|^{|x|} $, then the value of $ \frac{dy}{dx} $ at $ x = -\frac{\pi}{6} $ is

The function $x^x$ is increasing, when

The length of the longest interval, in which $f(x)=3\sin x - 4\sin^3 x$ is increasing, is

The triangle formed by the tangent to the curve $f(x)=x^2 + bx - b$ at the point $(1,1)$ and the coordinate axes lies in the first quadrant. If its area is 2, then the value of $b$ is

The equation of the tangent to the curve $\left(\frac{x}{a}\right)^n + \left(\frac{y}{b}\right)^n = 2$ at $(a, b)$ is

The minimum radius vector of the curve $ \frac{a^2}{x^2} + \frac{b^2}{y^2} = 1 $ is of length

The largest term in the sequence $ a_n = \frac{n^2}{n^3 + 200} $ is given by

$ f(x)= \begin{cases} |x^3 + x^2 + 3x + \sin x|\left(3 + \sin\frac{1}{x}\right), & x\neq 0 \\ 0, & x=0 \end{cases} $ The number of points, where $ f(x) $ attains its minimum value, is

$ \int \frac{x^2 - 1}{(x^4 + 3x^2 + 1)\tan^{-1}\left(x + \frac{1}{x}\right)} \, dx $ is equal to

$ \int \frac{\cos x}{\sin^2 x (\sin x + \cos x)} \, dx $ is equal to

$ \int \frac{dx}{\sin x - \cos x + \sqrt{2}} $ is equal to

Evaluate $ \int_{0}^{\frac{3\pi}{2}} \sin\left( \left\lfloor \frac{2x}{\pi} \right\rfloor \right) dx $, where $ \lfloor \cdot \rfloor $ denotes the greatest integer function.

Evaluate $ \int_{1/n}^{(n-1)/n} \frac{\sqrt{x}}{\sqrt{a-x} + \sqrt{x}} \, dx $.

The area bounded by $ y = x|\sin x| $ and X-axis between $ x = 0 $ and $ x = 2\pi $ is

The area enclosed by the curves $ |y + x| \le 1 $, $ |y - x| \le 1 $ and $ 2x^2 + 2y^2 = 1 $ is

The real value of $ m $ for which the substitution $ y = u^m $ will transform the differential equation $ 2x^4 y \frac{dy}{dx} + y^4 = 4x^6 $ into a homogeneous equation is

The equation of the curve for which the square of the ordinate is twice the rectangle contained by the abscissa and the intercept of the normal on the $x$-axis passing through $(2,1)$, is

If $|a|=1, |b|=4, a\cdot b = 2$ and $c = 2a \times b - 3b$, then the angle between $b$ and $c$ is

If $ a, b, c $ are $ p^{th}, q^{th} $ and $ r^{th} $ terms of a G.P, then the vectors $ \log a \,\hat{i} + \log b \,\hat{j} + \log c \,\hat{k} $ and $ (q-r)\hat{i} + (r-p)\hat{j} + (p-q)\hat{k} $ are

The line joining the points $ (1,1,2) $ and $ (3,-2,1) $ meets the plane $ 3x + 2y + z = 6 $ at the point

The distance of the point $ (1,-5,9) $, from the plane $ \vec{r}\cdot(\hat{i}-\hat{j}+\hat{k}) = 5 $ measured along the line $ \vec{r} = \hat{i} + \hat{j} + \hat{k} $ is