List of top Mathematics Questions asked in MET

Let \(h(x) = \min(x, x^2)\), for every real number \(x\). Then,

Fifteen coupons are numbered 1, 2, …, 15, respectively. Seven coupons are selected at random one at a time with replacement. The probability that the largest number appearing on a selected coupon is 9, is

The solution of the differential equation \(\frac{dy}{dx} = \sin(x + y) \tan(x + y) - 1\) is

The area bounded by the parabolas \(y^2 = 4a(x + a)\) and \(y^2 = -4a(x - a)\) is

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

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

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

The 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

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

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

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

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

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

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 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

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

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

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