List of top Questions asked in MET- 2016

Area bounded by the curves \(y = x^2\) and \(y = 2 - x^2\) is

The coordinates of the point on the parabola \(y = x^2 + 7x + 2\), which is nearest to the straight line \(y = 3x - 3\), are

The equation of the circle passing through the point \((2a, 0)\) and whose radical axis is \(x = \frac{a}{2}\) with respect to the circle \(x^2 + y^2 = a^2\), will be

\(\lim_{n \to \infty} \left( \frac{1^2}{1 - n^3} + \frac{2^2}{1 - n^3} + \dots + \frac{n^2}{1 - n^3} \right)\) is equal to

The value of \(\int \frac{\sin x + \cos x}{3 + \sin 2x} dx\) is

The derivative of \(\sin^{-1}(2x\sqrt{1-x^2})\) with respect to \(\sin^{-1}(3x - 4x^3)\) is

The differential equation of the family of curves \(y = Ae^{3x} + Be^{5x}\), where \(A\) and \(B\) are arbitrary constants, is

If \(\begin{bmatrix} \alpha & \beta \gamma & -\alpha \end{bmatrix}\) is to be the square root of the two-rowed unit matrix, then \(\alpha, \beta\) and \(\gamma\) should satisfy the relation

If \(\cos^{-1}p + \cos^{-1}q + \cos^{-1}r = 3\pi\), then \(p^2 + q^2 + r^2 + 2pqr\) is equal to

The statement \(p \rightarrow (q \rightarrow p)\) is equivalent to

Total number of polynomials of the form \(x^3 + ax^2 + bx + c\) that are divisible by \(x^2 + 1\), where \(a,b,c \in \{1, 2, 3, \dots, 10\}\) is equal to

Total number of regions in which 'n' coplanar lines can divide the plane, it is known that no two lines are parallel and no three of them are concurrent, is equal to

The value of \(\lim_{n \to \infty} \left[\sqrt[3]{n^2 - n^3} + n\right]\) is

The points on the curve \(xy^2 = 1\) which are nearest to the origin, are

If \(\theta = \sin^{-1}x + \cos^{-1}x - \tan^{-1}x\), \(1 \le x < \infty\), then the smallest interval in which \(\theta\) lies is

If \(X\) follows a binomial distribution with parameters \(n = 8\) and \(p = \frac{1}{2}\), then \(P(|x - 4| \le 2)\) is equal to

If \(f(x)\) is a non-negative continuous function for all \(x \ge 1\) such that \(f'(x) \le p f(x)\), where \(p > 0\) and \(f(1) = 0\), then \([f(\sqrt{e}) + f(\sqrt{\pi})]\) is equal to

Which of the following anions is present in the chain structure of silicates?

Myosin(s) is/are

If \(aN = \{an : n \in N\}\) and \(bN \cap cN = dN\), where \(a,b,c \in N\) and \(b,c\) are coprime, then

If a and b be two perpendicular unit vectors such that \(\mathbf{x} = \mathbf{b} - (\mathbf{a} \times \mathbf{x})\), then \(|\mathbf{x}|\) is equal to

If \(2a + 3b + 6c = 0\), then at least one root of the equation \(ax^2 + bx + c = 0\) lies in the interval

The mean deviation from the mean for the set of observations \(-1, 0, 4\) is

In which of the following the pyrophosphate bond of ATP is broken down and linkage takes place between two molecules?

Which of the following options best describes the 'hydrogen economy'?