List of top Questions asked in MET

The slope of the tangent at \((x,y)\) to a curve passing through \(\left(1, \frac{\pi}{4}\right)\) is given by \(\frac{y}{x} - \cos^2\left(\frac{y}{x}\right)\) then the equation of the curve is

If \(\frac{1}{x(x+1)(x+2)\ldots(x+n)} = \frac{A_0}{x} + \frac{A_1}{x+1} + \frac{A_2}{x+2} + \ldots + \frac{A_n}{x+n}\) then \(A_r\) is equal to

The solution of the equation \(\frac{dy}{dx} = \frac{x(2\log x + 1)}{\sin y + y\cos y}\) is

The curve for which the length of the normal is equal to the length of the radius vector, are

The degree of the differential equation \(\left(\frac{d^2y}{dx^2}\right)^2 + \left(\frac{dy}{dx}\right)^2 = x\sin\left(\frac{d^2y}{dx^2}\right)\) is

The value of \(\lim_{n \to \infty} \left\{\frac{1}{na} + \frac{1}{na+1} + \frac{1}{na+2} + \ldots + \frac{1}{nb}\right\}\) is

The value of \(\int_a^b \frac{|x|}{x} dx\) is

If \(\int \frac{dx}{x^2(x^n + 1)^{(n-1)/n}} = -[f(x)]^{1/n} + c\) then \(f(x)\) is

\(y = \int_{1/8}^{\sin^2 x} \sin^{-1}\sqrt{t} dt + \int_{1/8}^{\cos^2 x} \cos^{-1}\sqrt{t} dt, 0 \leq x \leq \pi/2\)

The area of the region \([(x,y): x^2 + y^2 \leq 1 \leq x + y]\) is

The area of the figure bounded by the parabola \((y-2)^2 = x-1\), the tangent to it at the point with the ordinate 3 and the \(x\)-axis is

If \(x, y \in [0, 2\pi]\) then the total number of ordered pairs \((x, y)\) satisfying \(\sin x \cdot \cos y = 1\) is equal to

\(\int \sqrt{1 + \csc x} dx\) is equal to

\(\int x^x \log(ex) dx\) is equal to

The value of \(\tan\left(\frac{1}{2}\cos^{-1}\left(\frac{\sqrt{5}}{3}\right)\right)\) is

The number of solutions of the equation \(1 + \sin x \cdot \sin^2 \frac{x}{2} = 0\) in \([-\pi, \pi]\) is

The interval for which \(2\tan^{-1}x + \sin^{-1}\frac{2x}{1+x^2}\) is independent of \(x\) is

If \(y = \sqrt{(a-x)(x-b)} - (a-b)\tan^{-1}\sqrt{\frac{a-x}{x-b}}\), then \(\frac{dy}{dx}\) is equal to

Let \(f(xy) = f(x) \cdot f(y)\) for all \(x, y \in \mathbb{R}\). If \(f'(1) = 2\) and \(f(4) = 4\), then \(f'(4)\) equal to

\(AB\) is a diameter of a circle and \(C\) is any point on the circumference of the circle. Then

If \(\sin^{-1}\left(\frac{x^2 - y^2}{x^2 + y^2}\right) = \log a\), then \(\frac{d^2y}{dx^2}\) equals

The value \(P\) such that the length of subtangent and subnormal is equal for the curve \(y = e^{Px} + Px\) at the point \((0,1)\) is

A man \(1.6\mathrm{m}\) high walks at the rate of \(30\mathrm{m/min}\) away from a lamp which is \(4\mathrm{m}\) above ground. How fast is the man's shadow lengthening?

If \(\cos \alpha + \cos \beta + \cos \gamma = \sin \alpha + \sin \beta + \sin \gamma = 0\) then the value of \(\cos 3\alpha + \cos 3\beta + \cos 3\gamma\) is

Which one of the following is independent of \(\alpha\) in the hyperbola \((0<\alpha<\pi/2)\) \(\frac{x^2}{\cos^2 \alpha} - \frac{y^2}{\sin^2 \alpha} = 1\)?