List of top Mathematics Questions asked in MET

The greatest value of the function \(f(x) = xe^{-x}\) in \([0, \infty)\), is

If an isosceles triangle of vertical angle \(2\theta\) is inscribed in a circle of radius \(a\). Then, area of the triangle is maximum, when \(\theta\) is equal to

The range of the function \(f(x) = \log_5(25 - x^2)\) is

The image of the point \(P(1,3,4)\) in the plane \(2x - y + z + 3 = 0\), is

Equation of the plane that contains the lines \(\mathbf{r} = (\hat{\mathbf{i}}+\hat{\mathbf{j}}) + \lambda(\hat{\mathbf{i}}+2\hat{\mathbf{j}}-\hat{\mathbf{k}})\) and \(\mathbf{r} = (\hat{\mathbf{i}}+\hat{\mathbf{j}}) + \mu(-\hat{\mathbf{i}}+\hat{\mathbf{j}}-2\hat{\mathbf{k}})\), is

The distance of the point \((3,8,2)\) from the line \(\frac{x-1}{2} = \frac{y-3}{4} = \frac{z-2}{3}\) measured parallel to the plane \(3x + 2y - 2z + 15 = 0\), is

Let \(u_1\) and \(u_2\) be two urns such that \(u_1\) contains 3 white, 2 red balls and \(u_2\) contains only 1 white ball. A fair coin is tossed. If head appears, then 1 ball is drawn at random from urn \(u_1\) and put into \(u_2\). However, if tail appears, then 2 balls are drawn at random from \(u_1\) and put into \(u_2\). Now, 1 ball is drawn at random from \(u_2\). Then, probability of the drawn ball from \(u_2\) being white is

The eccentricity of the conic \(x^2 - 4x + 4y^2 = 12\) is

The equation of the plane through the intersection of the planes \(x + y + z = 1\) and \(2x + 3y - z + 4 = 0\) and parallel to X-axis, is

Let \(\mathbf{a} = 2\hat{\mathbf{i}} + \hat{\mathbf{j}} - 2\hat{\mathbf{k}}\) and \(\mathbf{b} = \hat{\mathbf{i}} + \hat{\mathbf{j}}\). If \(\mathbf{c}\) is a vector such that \(\mathbf{a} \cdot \mathbf{c} = |\mathbf{c}|\), \(|\mathbf{c} - \mathbf{a}| = 2\sqrt{2}\) and the angle between \(\mathbf{a} \times \mathbf{b}\) and \(\mathbf{c}\) is \(30^\circ\). Then \(|(\mathbf{a} \times \mathbf{b}) \times \mathbf{c}|\) is equal to

Order and degree of a differential equation \(\frac{d^2y}{dx^2} = \left\{ y + \left(\frac{dy}{dx}\right)^2 \right\}^{1/4}\) are

The sum to infinity of the series \(1 + \frac{2}{3} + \frac{6}{3^2} + \frac{10}{3^3} + \frac{14}{3^4} + ..........\) is

The equations of the straight lines passing through the point (4, 3) and making intercepts on the coordinate axes whose sum is -1, is

The number of positive integral solutions of \(x^2 + 9<(x+3)^2<8x + 25\), is

Two common tangents to the circle \(x^2 + y^2 = 2a^2\) and parabola \(y^2 = 8ax\) are

The value of \(\int \frac{1}{\sin\left(x - \frac{\pi}{3}\right)} dx\) is

Let \(D_k = \begin{vmatrix} 2^{2k} & 2^{2k-1} & 1 \\ 3^{4k} & 3^{4k-2} & 1 \\ 7^{8k} & 7^{8k-4} & 1 \end{vmatrix}\), then the value of \(\sum_{k=1}^{16} D_k\) is

One possible condition for the three points \((a,b), (b,a)\) and \((a^2, -b^2)\) to be collinear, is

A cone whose height is always equal to its diameter, is increasing in volume at the rate of \(40 \text{ cm}^3/\text{s}\). At what rate is the radius increasing when its circular base area is \(1 \text{ m}^2\)?

One mapping (function) is selected at random from all the mappings of the set \( A = \{1,2,3,\dots,n\} \) into itself. The probability that the mapping selected is one-one, is

If \( \begin{vmatrix} x+y+2z & x & y z & y+z+2x & y z & x & z+x+2y \end{vmatrix} = k(x+y+z)^3 \), then the value of \( k \) is

If \( \cos^2 A + \cos^2 C = \sin^2 B \), then \( \triangle ABC \) is

The minimum value of \( \frac{x}{\log x} \) is

In how many ways, can a student choose a program of 5 courses, if 9 courses are available and 2 specific courses are compulsory for every student?