List of top Questions asked in MET

If \(A\) and \(B\) are two such events that \(P(A \cup B) = P(A \cap B)\), then which of the following is true?
The number of unit vectors perpendicular to \(\vec{a} = \hat{i}+\hat{j}\) and \(\vec{b} = \hat{j}+\hat{k}\) is:

If \(\sin^{-1} x + \cot^{-1}\left(\frac{1}{2}\right) = \frac{\pi}{2}\), then value of \(x\) will be

Let \(f(x)\) be differentiable on the interval \((0,\infty)\) such that \(f(1)=1\) and \[ \lim_{t \to x} \frac{t^2 f(x) - x^2 f(t)}{t - x} = 1 \quad \text{for each } x>0. \] Then, \(f(x)\) is equal to
The locus of centre of circles which cut orthogonally the circle \(x^2 + y^2 - 4x + 8 = 0\) and touches \(x + 1 = 0\), is
The lawyer has plenty of ........... .
‘‘The project is good, but there is ........... missing’’
Orthopaedic : Bones :: Dermatologist : ?
Basilica : Church :: Dormer : ?
Although : Nevertheless :: Though : ?
Find the odd word.
Find the odd word.
Find the odd word.
In the English alphabet, find the position of P from right:
Which of the following letters is 14th to the right of 6th letter from the left in the English alphabet?
Alphabet reversed, 13th left of 3rd from right:
23, 28, 34, 41, 49, ?
11, 13, 17, 19, 23, 25, ?
Find the missing number in the given pattern:
Find the missing number in the triangle:
Among the following, compound with the lowest \(pK_a\) value is:
Equation of tangent to the circle \(x^2 + y^2 - 2x - 2y + 1 = 0\) perpendicular to \(y = x\) is given by
If point \(D\) divides base \(BC\) of \(\triangle ABC\) in ratio \(m:n\), then value of \(mBD^2 + nCD^2 + (m+n)AD^2\) is:
A man is standing on the horizontal plane. The angle of elevation of top of the pole is \(\alpha\). If he walks a distance double the height of the pole, then the elevation of the pole is \(2\alpha\). The value of \(\alpha\) is

If \( f(x) = \begin{cases} \frac{\sin |x|}{x}, & \text{for } [x] \ne 0 \\ 0, & \text{for } [x] = 0 \end{cases} \) where, \([x]\) denotes the greatest integer less than or equal to \(x\), then \(\lim_{x \to 0} f(x)\) is equal to