List of top Questions asked in MET

A circular disc is rotating with angular velocity \(\omega\). If a man standing at the edge of the disc walks towards its centre then the angular velocity of the disc will

\(n\) small balls, each of mass \(m\) impinge elastically each second on a surface with a velocity \(u\), then the force experienced by the surface in one second, will be

An earth satellite \(S\) has orbit radius which is 4 times that of communication satellite \(C\). The period of revolution of \(S\) will be

A running man has half the kinetic energy of that of a boy of half of his mass. The man speeds up by \(1\ \text{m/s}\) so as to have the same kinetic energy as that of the boy. The original speed of the man is

The moment of inertia of a body about a given axis is \(1.2\ \text{kg·m}^2\). To produce a rotational kinetic energy of \(1500\ \text{J}\) an angular acceleration of \(25\ \text{rad/s}^2\) must be applied for

A wet open umbrella is held vertical and it whirls about the handle at a uniform rate of 21 revolutions in \(44\ \text{s}\). If the rim of the umbrella is a circle of \(1\ \text{m}\) in diameter and the height of the rim above the floor is \(4.9\ \text{m}\), the locus of the drop is a circle of radius

An elevator car whose floor to ceiling distance is \(2.7\ \text{m}\) starts ascending with a constant acceleration of \(1.2\ \text{m/s}^2\). \(2\ \text{s}\) after a bolt begins to fall from the ceiling of the car. The free fall time of the bolt is \((g = 9.8\ \text{m/s}^2)\)

A prism of refractive index \(\sqrt{2}\) has refracting angle of \(60^{\circ}\). At what angle a ray must be incident on it so that it suffers minimum deviation?

Two similar coils are kept mutually perpendicular such that their centres coincide. At the centre, find the ratio of the magnetic field due to one coil and the resultant magnetic field through both coils, if the same current is flown

The radius \(R\) of a soap bubble is doubled under isothermal condition. If \(T\) be the surface tension of soap bubble, the work done in doing so is given by

The number of rational values of \(m\) for which the \(y\)-coordinate of the point of intersection of the lines \(3x + 2y = 10\) and \(x = my + 2\) is an integer is

A straight line cuts intercepts from the axis of coordinates the sum of the reciprocals of which is a constant \(K\). Then it always passes through a fixed point

If the line \(\frac{x}{a} + \frac{y}{b} = 1\) moves in such a way that \(\frac{1}{a^2} + \frac{1}{b^2} = \frac{1}{c^2}\) where \(c\) is a constant, then the locus of the foot of perpendicular from the origin on the straight line is

The pair of lines \(\sqrt{3}x^2 - 4xy + \sqrt{3}y^2 = 0\) are rotated about the origin by \(\frac{\pi}{6}\) in the anticlockwise sense. The equation of the pair in the new position is

The value of \(\lim_{x \to 1} \frac{\sum_{k=1}^{100} x^k - 100}{x - 1}\) is

The value of \(\lim_{x \to \infty} \frac{x}{x + \frac{\sqrt[3]{x}}{x + \frac{\sqrt[3]{x}}{x + \dots}}}\) is

If \(f(x)\) defined by \(f(x) = \begin{cases} \frac{|x^2 - x|}{x^2 - x}, & x \neq 0, 1 \\ 1, & x = 0 \\ -1, & x = 1 \end{cases}\) then \(f(x)\) is continuous for all

Function \(f(x)\) is defined as \(f(x) = \begin{cases} 3x, & x<1 \\ a-b, & x = 1 \\ 4b-a, & x>1 \end{cases}\) If \(f(x)\) is continuous at \(x = 1\), but discontinuous at \(x = 2\) then the locus of the point \((a, b)\) is a straight line excluding the point where it cuts the line

The maximum value of \((\cos \alpha_1) \cdot (\cos \alpha_2) \cdots (\cos \alpha_n)\) under the restrictions \(0 \leq \alpha_1, \alpha_2, \ldots, \alpha_n \leq \frac{\pi}{2}\) and \((\cot \alpha_1) \cdot (\cot \alpha_2) \cdots (\cot \alpha_n) = 1\) is

The minimum value of the expression \(\sin \alpha + \sin \beta + \sin \gamma\) where \(\alpha, \beta, \gamma\) are real numbers satisfying \(\alpha + \beta + \gamma = \pi\) is

If \(\theta\) be the angle between the unit vectors \(\mathbf{a}\) and \(\mathbf{b}\), then \(\cos \frac{\theta}{2}\) is equal to

If \(\mathbf{a} \cdot \mathbf{i} = \mathbf{a} \cdot (\mathbf{j} + \mathbf{i}) = \mathbf{a} \cdot (\mathbf{i} + \mathbf{j} + \mathbf{k})\), then \(\mathbf{a}\) is equal to

If the scalar projection of the vector \(x\mathbf{i} - \mathbf{j} + \mathbf{k}\) on the vector \(2\mathbf{i} - \mathbf{j} + 5\mathbf{k}\) is \(\frac{1}{\sqrt{30}}\) then value of \(x\) is equal to

If \(\mathbf{a} \times \mathbf{b} = \mathbf{c}\), \(\mathbf{b} \times \mathbf{c} = \mathbf{a}\) and \(a, b, c\) be the moduli of the vectors \(\mathbf{a}, \mathbf{b}, \mathbf{c}\) respectively, then

A unit vector coplanar with \(\mathbf{i} + \mathbf{j} + 2\mathbf{k}\) and \(\mathbf{i} + 2\mathbf{j} + \mathbf{k}\) and perpendicular to \(\mathbf{i} + \mathbf{j} + \mathbf{k}\) is