List of top Questions asked in MHT CET

$ \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

Binding energy of a revolving satellite at height $h$ is $3.5\times10^8\,\text{J}$. Its potential energy is

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

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

One end of thick horizontal copper wire of length $2L$ and radius $2R$ is welded to the end of another thin horizontal copper wire of length $L$ and radius $R$. When they are stretched by applying the same force at the two ends, the ratio of the elongation in the thick wire to that in the thin wire is

The non-zero potential difference across diode $D_1$ and that across diode $D_2$ are equal in the circuit shown in the figure (both diodes are identical in characteristics)

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 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 \[ A = \begin{bmatrix} 1 & 3 \\ 2 & 2 \end{bmatrix}, \quad B = \begin{bmatrix} 1 & 3 \\ 0 & 1 \end{bmatrix}, \] then \[ B^{-1} A^{-1} = \]

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

Among the given statements below
(a) $ \neg p \vee (\neg p \vee q) $
(b) $ \neg q \wedge (\neg p \vee \neg q) $
(c) $ (\neg p \vee \neg q) \wedge (p \vee \neg q) $
(d) $ (\neg p \vee \neg q) \vee (p \vee \neg q) $
.............. is a tautology.

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 'A' in the following reaction:
$\text{2 A + (C\(_6$H$_5$CH$_2$)$_2$Cd $\xrightarrow{}$ 2 CH$_3$-C-CH$_2$-C$_6$H$_5$ + CdCl$_2$} \)

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\(^+$(aq) + Cd(s) $\longrightarrow$ 2 Ag(s) + Cd$^{2+}$(aq), E$_{\text{cell}}$ = 1.20 V} \)

Identify Z in the following sequence of reactions:
CH$_3$-CH$_2$-OH + PCl$_3$ $\xrightarrow{\text{alcohol}}$ $X \xrightarrow{\text{KOH}}$ $Y \xrightarrow{\text{conc. H\(_2$SO$_4$}}\) $Z $

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
$\textit{(g = acceleration due to gravity)}$

If $ f(x) = \frac{2x + 3}{3x - 2}, \, x \neq \frac{2}{3}, $ then the function $ f \circ f $ is

The value of $ \sin^{-1} \left( -\frac{1}{2} \right) + \cos^{-1} \left( -\frac{\sqrt{3}}{2} \right) $ is

The integrating factor of the differential equation $\sin y \frac{dy}{dx} = \cos y (1 - x \cos y)$ is