List of top Questions asked in MET

The passage gives primarily a history of
The graph of equation \(y^2 + z^2 = 0\) in three dimensional space is
If \(z_1 = 1 + i,\; z_2 = -2 + 3i,\; z_3 = \frac{ai}{3}\) are collinear, where \(i^2 = -1\), then value of \(a\) is:
A die is rolled three times. The probability of getting a larger number than the previous number is
If \(a, b\) and \(c\) are in HP, then for any \(n \in \mathbb{N}\), which one of the following is true?
By Simpson’s \(1/3\)rd rule, the approximate value of the integral \(\int_1^2 e^{-x/2}dx\) using four intervals, is
If \( f(x) = \ln(6 - |x^2 + x - 6|) \), then domain of \( f(x) \) has how many integral values of \( x \)
The values of \(\lambda\) such that \((x,y,z) \ne (0,0,0)\) and \[ (\hat{i} + \hat{j} + 3\hat{k})x + (3\hat{i} - 3\hat{j} + \hat{k})y + (-4\hat{i} + 5\hat{j})z = \lambda(x\hat{i} + y\hat{j} + z\hat{k}) \]
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:
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:
The general solution of the differential equation \(\frac{dy}{dx} = y\tan x - y^2\sec x\) is:
If \(2a + 3b + 6c = 0\), then the equation \(ax^2 + bx + c = 0\) has at least one real root in
In \(\triangle ABC\), if \(\cot A, \cot B\) and \(\cot C\) are in AP, then \(a^2, b^2\) and \(c^2\) are in
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
\(\lim_{x \to 2} \frac{2 - \sqrt{2 + x}}{2^{1/3} - (4 - x)^{1/3}}\) is equal to
API stands for:
System software : Utility software ::
The number of common tangents to two circles \(x^2 + y^2 = 4\) and \(x^2 + y^2 - 8x + 12 = 0\) is:
If \(z = i\log(2 - \sqrt{3})\), then the value of \(\cos z\) will be:
By Newton-Raphson method, the positive root of \(x^4 - x - 10 = 0\) is:
If \(\sin^{-1} x + \cot^{-1}\left(\frac{1}{2}\right) = \frac{\pi}{2}\), then value of \(x\) will be
The values of \( a \), if \( f(x) = 2e^x - a e^{-x} + (2a+1)x - 3 \) increases for all \( x \), are in
The value of \(\int_{0}^{\sqrt{\ln\left(\frac{\pi}{2}\right)}} \cos\left(e^{x^2}\right)\, 2x e^{x^2}\, dx\) is
In \(\triangle ABC\), if \(3a = b + c\), then value of \(\cot\frac{B}{2}\cot\frac{C}{2}\) 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: