List of top Questions asked in MET- 2020

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:
The sum of the real solutions of equation \(2|x|^2 + 51 = |1 + 20x|\) is
The quadratic equation whose roots are \(\frac{1}{3+\sqrt{2}}\) and \(\frac{1}{3-\sqrt{2}}\), will be:
Who said, “Number of transistors per square inch on integrated circuits double every year…”?
By trapezoidal rule, approximate value of \(\int_0^6 \frac{dx}{1+x^2}\)
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:
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 \(m\) things are distributed among \(a\) men and \(b\) women, then the chance that the number of things received by men is odd is:
The solution of the differential equation \[ \sqrt{a+x}\,\frac{dy}{dx} + xy = 0 \] 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:
In \(\triangle ABC\), if \(3a = b + c\), then value of \(\cot\frac{B}{2}\cot\frac{C}{2}\) 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

API stands for:
If \(z = i\log(2 - \sqrt{3})\), then the value of \(\cos z\) will be:

\(\lim_{x \to 2} \frac{2 - \sqrt{2 + x}}{2^{1/3} - (4 - x)^{1/3}}\) is equal to

The three lines of a triangle are given by \((x^2 - y^2)(2x + 3y - 6) = 0\). If the point \((-2,\lambda)\) lies inside and \((\mu,1)\) lies outside the triangle, then
The number of common tangents to two circles \(x^2 + y^2 = 4\) and \(x^2 + y^2 - 8x + 12 = 0\) is:
If \(2a + 3b + 6c = 0\), then the equation \(ax^2 + bx + c = 0\) has at least one real root in
If for all \(x,y \in \mathbb{N}\), there exists a function \(f(x)\) satisfying \(f(x+y)=f(x)f(y)\) such that \(f(1)=3\) and \(\sum_{x=1}^{n} f(x)=120\), then value of \(n\) is:
If \( f(x) = \begin{cases} \sin\left(\frac{\pi x}{2}\right), & x<1 \\ 3 - 2x, & x \ge 1 \end{cases} \), then \( f(x) \) has:
The general solution of the differential equation \(\frac{dy}{dx} = y\tan x - y^2\sec x\) is: