List of top Questions asked in MET- 2020

The solution of the differential equation \[ \sqrt{a+x}\,\frac{dy}{dx} + xy = 0 \] is
If \(\sin^{-1} x + \cot^{-1}\left(\frac{1}{2}\right) = \frac{\pi}{2}\), then value of \(x\) will be
If \(m\) things are distributed among \(a\) men and \(b\) women, then the chance that the number of things received by men is odd is:
The values of \( a \), if \( f(x) = 2e^x - a e^{-x} + (2a+1)x - 3 \) increases for all \( x \), are in
By Newton-Raphson method, the positive root of \(x^4 - x - 10 = 0\) is:
The value of \(\int_{0}^{\sqrt{\ln\left(\frac{\pi}{2}\right)}} \cos\left(e^{x^2}\right)\, 2x e^{x^2}\, dx\) is
The radius of a cylinder is increasing at \(2\,m/s\) and height is decreasing at \(3\,m/s\). When \(r=3\,m, h=5\,m\), rate of change of volume is:
By trapezoidal rule, approximate value of \(\int_0^6 \frac{dx}{1+x^2}\)
The number of unit vectors perpendicular to \(\vec{a} = \hat{i}+\hat{j}\) and \(\vec{b} = \hat{j}+\hat{k}\) is:
The point on the straight line \(y = 2x + 11\) which is nearest to the circle \(16(x^2 + y^2) + 32x - 8y - 50 = 0\), is
The locus of the extremities of the latus rectum of the family of ellipses \(b^2x^2 + y^2 = a^2b^2\) having a given major axis is
The solution of differential equation \(y\log x - y\,dx = x\,dy\) is
If \(\vec{a}, \vec{b}, \vec{c}\) are three non-coplanar vectors, then \([\vec{a}\times\vec{b},\ \vec{b}\times\vec{c},\ \vec{c}\times\vec{a}]\) is equal to:
If geometric mean and harmonic mean of two numbers are \(16\) and \(\frac{64}{5}\) respectively, then \(a:b\) is:
If sum of four numbers in GP is 60 and AM of first and last is 18, then the numbers are:
Who said, “Number of transistors per square inch on integrated circuits double every year…”?
The quadratic equation whose roots are \(\frac{1}{3+\sqrt{2}}\) and \(\frac{1}{3-\sqrt{2}}\), will be:
The sum of the real solutions of equation \(2|x|^2 + 51 = |1 + 20x|\) is
If \(A(-1,3,2), B(2,3,5), C(3,5,-2)\) are vertices of a triangle ABC, then angles of Triangle ABC are :
The equation of the curve through \((1,0)\), whose slope is \(\frac{y-1}{x^2+x}\), is:
If \(1, \omega\) and \(\omega^2\) are the cube roots of unity, then the value of \((1-\omega+\omega^2)(1+\omega-\omega^2)\) is equal to
Number of points where \(f(x)=[\sin x + \cos x]\) is not continuous in \((0,2\pi)\) is:
Evaluate: \[ \lim_{x \to 0} \frac{\int_0^{x^2} \sin\sqrt{t}\,dt}{x^3} \]
Evaluate: \[ \cot^{-1}\!\left(\frac{\sqrt{1+\sin x} + \sqrt{1-\sin x}}{\sqrt{1+\sin x} - \sqrt{1-\sin x}}\right) \]
Solution of the equation \[ \cos^2 x \frac{dy}{dx} - (\tan 2x)\,y = \cos^4 x,\quad |x|<\frac{\pi}{4}, \] where \(y\!\left(\frac{\pi}{6}\right)=\frac{3\sqrt{3}}{8}\), is given by: