List of top Questions asked in MET

A short solenoid of length 4 cm, radius 2 cm and 100 turns is placed inside and on the axis of a long solenoid of length 80 cm and 1500 turns. A current of 3 A flows through the short solenoid. The mutual inductance of two solenoids is
The plane faces of two identical plano-convex lenses each having a focal length of 50 cm are placed against each other to form a usual biconvex lens. The distance from this lens combination at which an object must be placed to obtain a real, inverted image which has the same size as the object is
The momentum of a body is increased by 25%. The kinetic energy is increased by about
The ratio of the resistance of conductor at temperature 15\(^\circ\)C to its resistance at temperature 37.5\(^\circ\)C is 4:5. The temperature coefficient of resistance of the conductor is
The width of a single slit if the first minimum is observed at an angle 2\(^\circ\) with a light of wavelength 6980 \AA\ is
The apparent frequency of the whistle of an engine changes in the ratio 9:8 as the engine passes a stationary observer. If the velocity of the sound is 340 m s\(^{-1}\), then the velocity of the engine is
If \(\alpha\) and \(\beta\) are the current gain in the CB and CE configurations respectively of the transistor circuit, then \(\dfrac{\beta - \alpha}{\alpha\beta}\) is
In a gas, two waves of wavelengths 1 m and 1.01 m are superposed and produce 10 beats in 3 s. The velocity of sound in the medium is
The surface area of a black body is \(5 \times 10^{-4}\) m\(^2\) and its temperature is 727\(^\circ\)C. The energy radiated by it per minute is (\(\sigma = 5.67 \times 10^{-8}\) J/m\(^2\)-s-K\(^4\))
Water rises in a capillary tube to a height \(h\). Choose false statement regarding capillary rise from the following.
Force between two identical charges placed at a distance of \(r\) in vacuum is \(F\). Now a slab of dielectric of dielectric constant 4 is inserted between the charges. If the thickness of the slab is \(r/2\), then the force between the charges will become
Two identical cells whether connected in parallel or in series gives the same current when connected to an external resistance 1.5 \(\Omega\). Find the value of internal resistance of each cell.
Three blocks of masses \(m_1\), \(m_2\) and \(m_3\) are connected by massless strings as shown on a frictionless table. They are pulled with a force \(T_3 = 40\) N. If \(m_1 = 10\) kg, \(m_2 = 6\) kg and \(m_3 = 4\) kg, the tension \(T_2\) will be}
A string of density \(7.5\) g cm\(^{-3}\) and area of cross-section \(0.2\) mm\(^2\) is stretched under a tension of 20 N. When it is plucked at the mid-point, the speed of the transverse wave on the wire is
Two identical air core capacitors are connected in series to a voltage source of 15 V. If one of the capacitors is filled with a medium of dielectric constant 4, the new potential across this capacitor is
If $\Delta = \begin{vmatrix} 1 & a & a^2 \\ 1 & b & b^2 \\ 1 & c & c^2 \end{vmatrix} = k(a-b)(b-c)(c-a)$, then $k$ is equal to
$\vec{a} = \frac{1}{7}(2\hat{i} + 3\hat{j} + 6\hat{k})$, $\vec{b} = \frac{1}{7}(3\hat{i} - 2\hat{j} + \lambda \hat{k})$. If $\vec{a}$ and $\vec{b}$ are mutually perpendicular, then value of $\lambda$ is
The locus of the point of intersection of two perpendicular tangents to a circle is called
The area bounded by the curve $y = 4x^3 - 3x^2 + 2x + 3$ with x-axis and ordinates corresponding to the minima of y is
$\int \log_e (a^x + x^a) dx$ is equal to
$\lim_{n \to \infty} \left( \frac{1}{4n^2 - 1} + \frac{1}{4n^2 - 4} + \frac{1}{4n^2 - 9} + \ldots + \frac{1}{4n^2 - n^2} \right)$ is equal to
$\int \frac{dx}{x^2 + 4x + 13}$ is equal to
Consider the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$, the area of the triangle formed by the asymptotes and the tangent drawn to it at $(a,0)$ is
The differential equation of the family of lines passing through the origin is
If $P = \begin{bmatrix} 0 & i & i \\ -i & 0 & i \\ -i & -i & 0 \end{bmatrix}$ and $Q = \begin{bmatrix} 0 & 0 & -i \\ 0 & 0 & -i \\ i & i & 0 \end{bmatrix}$, then $PQ$ is equal to