List of top Questions asked in MHT CET- 2021

Water rises upto a height 10 cm in a capillary tube. It will rise to a height which is much more than 10 cm in a very long capillary tube if the apparatus is kept.

In LCR series resonant circuit, at resonance, voltage across \(L\) and \(C\) will cancel each other because they are

Two identical parallel plate air capacitors are connected in series to a battery of emf \(V\). If one of the capacitors is inserted in liquid of dielectric constant \(K\), then potential difference of the other capacitor will become

Two coherent sources of wavelength \(\lambda\) produce steady interference pattern. The path difference corresponding to \(10^{\text{th}}\) order maximum will be

The area of the parallelogram with vertices \( A(1, 2, 3) \), \( B(1, 3, a) \), \( C(3, 8, 6) \) and \( D(3, 7, 3) \) is \( \sqrt{265} \) sq. units, then \( a = \)

If \( y = \tan^{-1} \left\{ \frac{a \cos x - b \sin x}{b \cos x + a \sin x} \right\} \), then \( \frac{dy}{dx} = \)

If \( y = \tan^{-1} \left( \frac{a \cos x - b \sin x}{b \cos x + a \sin x} \right) \), then \( \frac{dy}{dx} = \)

With usual notations, perimeter of a triangle \( ABC \) is 6 times the arithmetic mean of sine of its angles. If \( a = 1 \), then measure of angle \( A = \)

If \( \theta + \phi = \alpha \) and \( \tan \theta = k \tan \phi \) (where \( k > 1 \)), then the value of \( \sin(\theta - \phi) \) is

If \( m \) is order and \( n \) is degree of the differential equation \[ \left( \frac{d^2y}{dx^2} \right)^5 + 4 \left( \frac{\frac{d^2y}{dx^2}}{\frac{d^3y}{dx^3}} \right) + \left( \frac{d^3y}{dx^3} \right) = x^2 \] then

If \[ \int \frac{5 \tan x}{\tan x - 2} dx = x + a \log | \sin x - 2 \cos x | + c \], then \( a = \) (Where \( c \) is constant of integration)

If \( p \to (\sim p \lor q) \) is false, then the truth values of \( p \) and \( q \) are, respectively

Let \( A = \{10, 11, 12, 14, 26\} \) and let \( f : A \to \mathbb{N} \) be such that \( f(a) = \) highest prime factor of \( a \), where \( a \in A \), then range of \( f = \)

For a set of five true or false questions, no student has written the all correct answers and no two students have given the same sequence of answers. The maximum number of students in the class for this to be possible is

The general solution of the differential equation. \[ \left( \frac{y}{x} \right) \cos \left( \frac{y}{x} \right) dx - \left[ \left( \frac{x}{y} \right) \sin \left( \frac{y}{x} \right) + \cos \left( \frac{y}{x} \right) \right] dy = 0 \] is

If the half life period of a substance is 5 years, then the total amount of the substance left after 15 years, when initial amount is 64 gms is

A bakerman sells 5 types of cakes. Profit due to sale of each type of cake is respectively ₹ 2.5, ₹ 3, ₹ 1.5, ₹ 1 and ₹ 2. The demands for these cakes are 20%, 5%, 10%, 50% and 15% respectively, then the expected profit per cake is

The logical statement \((p \to q) \land (q \to \sim p)\) is equivalent to

If \( y = \tan^{-1} \left[ \frac{1}{1+x+x^2} \right] + \tan^{-1} \left[ \frac{1}{x^2+3x+3} \right] \), \( x > 0 \), then \(\frac{dy}{dx} =\)

The number of solutions of \( \cos 2\theta = \sin \theta \) in \( (0, 2\pi) \) are

If \( \sin^{-1}\left(\frac{3}{5}\right) + \cos^{-1}\left(\frac{12}{13}\right) = \sin^{-1}\alpha \), then \( \alpha = \)

If \( z(2 - i) = (3 + i) \), then \( z^{38} = \), (where \( z = x + iy \))

The area bounded by the parabola \( y^2 = x \), the straight line \( y = 4 \) and \( Y \) axis is

The equation of circle with centre at \( (2, -3) \) and the circumference \( 10\pi \) units is

The equation of a line passing through $(3, -1, 2)$ and perpendicular to the lines $\bar{r} = (\hat{i} + \hat{j} - \hat{k}) + \lambda (2\hat{i} - 2\hat{j} + \hat{k})$ and $\bar{r} = (2\hat{i} + \hat{j} - 3\hat{k}) + \mu (\hat{i} - 2\hat{j} + 2\hat{k})$ is