List of top Questions asked in MHT CET- 2020

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

The domain of the function $ f(x) = \sqrt{x} $ is

For every value of $ x $, the function $ f(x) = \frac{1}{a^x}, a>0 $ is

If $ f(x) = \sin^{-1} \left( \sqrt{\frac{1 - x}{2}} \right) $, then \[ f'(x) = \]

Evaluate \[ \int_0^1 \frac{x^2 - 2}{x^2 + 1} \, dx \]

If $ a = \sin 175^\circ + \cos 175^\circ $, then

The rational form of the number $ 1.41 \overline{41} $ is

The order and degree of the differential equation \[ \left[ 1 + \left( \frac{dy}{dx} \right)^3 \right]^{\frac{3}{2}} = 7 \frac{d^2y}{dx^2} \] are respectively

The negation of the statement 'He is poor but happy' is

If the line \[ \vec{r} = (i - 2j + 3k) + \lambda(2i + j + 2k) \quad \text{is parallel to the plane} \quad \vec{r} \cdot (3i - 2j + mk) = 10, \] then the value of $ m $ is