List of top Questions asked in MHT CET

If \(E\), \(M\), \(L\) and \(G\) denote energy, mass, angular momentum and constant of gravitation respectively, then the quantity \( \left(\dfrac{EL^2}{G^2M^5}\right) \) has dimensions of
In the following network, \(I_1=-0.4\,\text{A}\), \(I_4=1\,\text{A}\) and \(I_5=0.4\,\text{A}\). The values of \(I_2\), \(I_3\) and \(I_6\) respectively are
In Young’s double slit experiment, the 6th maximum with wavelength \( \lambda_1 \) is at a distance \( d_1 \) from the central maximum and the 4th maximum with wavelength \( \lambda_2 \) is at distance \( d_2 \). Then \( \dfrac{d_1}{d_2} \) is
When an electron in a hydrogen atom jumps from the third orbit to the second orbit, it emits a photon of wavelength \( \lambda \). When it jumps from the fourth orbit to the third orbit, the wavelength emitted by the photon will be
A circular coil of radius \(R\) carries an electric current \(I\). The magnetic field due to the coil at a point on the axis of the coil located at a distance \(r\) from the centre of the coil, such that \(r \gg R\), the magnetic field at that point is proportional to
\( \vec{A} \) and \( \vec{B} \) are two non-zero vectors inclined at an angle \( \theta \). \( \hat{a} \) and \( \hat{b} \) are unit vectors along \( \vec{A} \) and \( \vec{B} \) respectively. The component of \( \vec{A} \) in the direction of \( \vec{B} \) is
An electron accelerated through potential difference \(V\) passes through a uniform transverse magnetic field and experiences a force \(F\). If the accelerating potential is increased to \(2V\), the electron in the same magnetic field will experience a force
A toroidal solenoid with air core has an average radius \(R\), number of turns \(N\) and area of cross-section \(A\). The self-inductance of the solenoid is (Neglect the field variation across the cross-section of the toroid)
The length of a potentiometer wire is \(L\). A cell of e.m.f. \(E\) is balanced at a length \( \frac{L}{5} \) from the positive end of the wire. If the length of the wire is increased by \( \frac{L}{2} \), at what distance will the same cell give a balance point?
A glass slab of thickness \(4\,\text{cm}\) contains the same number of waves as in \(x\,\text{cm}\) of water column when both are traversed by the same monochromatic light. If the refractive indices of glass and water for that light are \( \frac{5}{3} \) and \( \frac{4}{3} \) respectively, the value of \(x\) will be
Two springs of spring constants \(K\) and \(2K\) are stretched by the same force. If \(W_1\) and \(W_2\) are the energies stored in them respectively, then
If \( \vec{A} = 3\hat{i} - 2\hat{j} + \hat{k} \), \( \vec{B} = \hat{i} - 3\hat{j} + 5\hat{k} \) and \( \vec{C} = 2\hat{i} + \hat{j} - 4\hat{k} \) form a right angled triangle, then out of the following which one is satisfied?
A particle performs S.H.M. with amplitude \( A \). Its speed is tripled at the instant when it is at a distance of \( \frac{2A}{3} \) from the mean position. The new amplitude of the motion is
A Fraunhofer diffraction pattern due to a single slit of width \(0.3\,\text{mm}\) is obtained on a screen placed at a distance of \(3\,\text{m}\) from the slit. The first minima lie at \(5.5\,\text{mm}\) on either side of the central maximum on the screen. The wavelength of light used is
A donor impurity results in
A mass \( m \) is tied to one end of a spring and whirled in a horizontal circle with constant angular velocity. The elongation in the spring is 1 cm. If the angular speed is doubled, the elongation in the spring is 6 cm. The original length of the spring is
If \( A = \left[ \begin{array}{cc} 1 & 2 \\ 1 & 0 \end{array} \right] \), \( B = \left[ \begin{array}{cc} 1 & 2\\ 2 & 1 \end{array} \right] \), then \( (AB)^{-1} \) is
If the function given by \( f(x) = \left( \frac{4x + 1}{1 - 4x} \right)^{\frac{1}{3}} \) for \( x \neq 0 \) is continuous at \( x = 0 \), the value of \( f(0) \) is

Identify the product A in the following reaction: 
\(\text{CH\(_3\)-CH\(_2\)-CH\(_2\)Cl + 2 KOH\(_{aq}\) $\xrightarrow{\Delta}$ A + 2 KCl + H\(_2\)O} \)
 

What is the standard free energy change for the cell, having following cell reaction? 
\(\text{2 Ag\(^+\)(aq) + Cd(s) $\longrightarrow$ 2 Ag(s) + Cd\(^{2+}\)(aq), E\(_{\text{cell}}\) = 1.20 V} \)

In non-uniform circular motion, the ratio of tangential to radial acceleration is 
\(\textit{(r = radius, \( \alpha \) = angular acceleration, V = linear velocity)}\)

A body of mass 2 kg is acted upon by two forces, each of magnitude 1 N and inclined at \( 60^\circ \) with each other. The acceleration of the body in \( \text{m/s}^2 \) is 
\(\textit{(cos 60° = 0.5)}\)

A simple pendulum of length \( L \) has mass \( m \) and it oscillates freely with amplitude \( A \). At extreme position, its potential energy is 
\(\textit{(g = acceleration due to gravity)}\)

Evaluate \[ \int_0^1 \frac{x^2 - 2}{x^2 + 1} \, dx \]
The negation of the statement 'He is poor but happy' is