List of top Questions asked in MET- 2019

Three blocks of masses \(2\ \mathrm{kg}\), \(3\ \mathrm{kg}\) and \(5\ \mathrm{kg}\) are connected to each other with light string and are then placed on a frictionless surface as shown in the figure. The system is pulled by a force \(\mathrm{F} = 10\ \mathrm{N}\), then tension \(\mathrm{T_1}\) is

The function \(f(x) = [x]\cos\left[\frac{2x - 1}{2}\right]\pi\), where \([\,\cdot\,]\) denotes the greatest integer function, is discontinuous at

A perpendicular is drawn from the point P(2, 4, -1) to the line \(\frac{x + 5}{1} = \frac{y + 3}{4} = \frac{z - 6}{-9}\). The equation of the perpendicular from P to the given line is

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 \(\mathbf{a} = -\hat{\mathbf{i}} + 2\hat{\mathbf{j}} - \hat{\mathbf{k}}\), \(\mathbf{b} = \hat{\mathbf{i}} + \hat{\mathbf{j}} - 3\hat{\mathbf{k}}\) and \(\mathbf{c} = -4\hat{\mathbf{i}} - \hat{\mathbf{k}}\), then \(\mathbf{a} \times (\mathbf{b} \times \mathbf{c}) + (\mathbf{a} \cdot \mathbf{b})\mathbf{c}\) is

The number of five digits numbers that can be formed without any restriction is

The maximum value of \(3\cos\theta + 4\sin\theta\) is

The vertex connectivity of any tree is

If \(\mathbf{a}, \mathbf{b}\) and \(\mathbf{c}\) are non-collinear vectors such that for some scalars \(x, y, z\), \(x\mathbf{a} + y\mathbf{b} + z\mathbf{c} = \mathbf{0}\), then

Which is the correct order for a given number \(\alpha\) in increasing order?

In \(\triangle ABC\), \(\frac{b - c}{r_1} + \frac{c - a}{r_2} + \frac{a - b}{r_3}\) is equal to

If \(n \in \mathbb{N}\), then \(|\sin nx|\)

If \(x\) follows a binomial distribution with parameters \(n = 100\) and \(p = \frac{1}{3}\), then \(P(X = r)\) is maximum when \(r\) equals

The direction cosines of any normal to the xy-plane are

If \(\int f(x) dx = F(x)\), then \(\int x^3 f(x^2) dx\) is equal to

The approximate value of \(\int_1^5 x^2 dx\) using trapezoidal rule with \(n = 4\) is

If the distance between the foci of an ellipse is 6 and the length of the minor axis is 8, then the eccentricity is

If \(I_n = \int \sin^n x dx\), then \(nI_n - (n - 1)I_{n-2}\) equals

The adjoining graph

The remainder obtained when \(5^{124}\) is divided by 124 is

Point out the grammatical category of the word 'very' in the passage.

He was very much ashamed ...... his mischief.

...... he stood first, he would have gone to America.

Of the sword and pen, the ...... is more powerful.

Antonym of Adverse