List of top Questions asked in MHT CET- 2020

The value of \[ \tan^{-1} \left( \frac{1}{3} \right) + \tan^{-1} \left( \frac{1}{5} \right) + \tan^{-1} \left( \frac{1}{7} \right) + \tan^{-1} \left( \frac{1}{8} \right) \] is

The rate at which the metal cools in moving air is proportional to the difference of temperatures between the metal and air. If the air temperature is 290K and the metal temperature drops from 370K to 330K in 10 minutes, then the time required to drop the temperature up to 295K is

The radius of the circle passing through the points \[ (5, 7), \quad (2, -2), \quad (-2, 0) \] is

If the acute angle between the lines \[ x^2-4xy+y^2=0 \] is \(\tan^{-1}(k)\), then \(k=\)

The integral \[ \int \cot x \cdot \log \left[ \log (\sin x) \right] \, dx = \]

The symbolic form of the following circuit is (where \( p, q \) represents switches \( s_1 \) and \( s_2 \) closed respectively)

The points of discontinuity of the function \[ f(x) = \begin{cases} \frac{1}{x - 1} & \text{if } 0 \leq x \leq 2 \\ \frac{x + 5}{x + 3} & \text{if } 2<x \leq 4 \end{cases} \] in its domain are

The probability that a person wins a prize on a lottery ticket is \( \frac{1}{4} \). If he purchases 5 lottery tickets at random, then the probability that he wins at least one prize is

If the vectors \( i + j + k \), \( i - j + k \) and \( 2i + 3j + mk \) are coplanar, then \( m = \)

If \(3\cos x \ne 2\sin x\), then the general solution of \[ \sin^2 x-\cos 2x=2-\sin 2x \] is

If two angles of \( \triangle ABC \) are \( \frac{\pi}{4} \) and \( \frac{\pi}{3} \), then the ratio of the smallest and greatest side is

The micro-organisms double themselves in 3 hours. Assuming that the quantity increases at a rate proportional to itself, then the number of times it multiplies itself in 18 years is

If \[ f(x) = \left[ \tan \left( \frac{\pi}{4} + x \right) \right]^{\frac{1}{x}} \quad \text{if} \quad x \neq 0 \] \[ f(x) = k \quad \text{if} \quad x = 0 \] is continuous at \( x = 0 \), then \( k = \)

If the angle between the lines given by the equation \[ x^2 - 3xy + Ay^2 + 3x - 5y + 2 = 0, \quad \lambda \geq 0, \quad \text{is} \, \tan^{-1} \left( \frac{1}{3} \right), \, \text{then} \, \lambda = \]

Simplify \( \sqrt{2} + \sqrt{2} + 2 \cos 4\theta = \)

A die is thrown 100 times, then the standard deviation of getting an even number is

If \( f(x) = \begin{cases \dfrac{81^x - 9^x}{k^x - 1}, & x \neq 0
2, & x = 0 \end{cases} \) is continuous at \( x = 0 \), then the value of \( k \) is}

Evaluate: \[ \cos x \cos 7x - \cos 5x \cos 13x \]

If the error involved in making a certain measurement is continuous random variable \( X \) with probability density function \( f(x) = k (4 - x^2) \) for \( -2 \leq x \leq 2 \), and \( f(x) = 0 \) otherwise, then \[ P(|-1<X<1|) \]

The shortest distance between the lines \[ \vec{r} = (1 - t)\hat{i} + (t - 2)\hat{j} + (3 - 2t)\hat{k} \] and \[ \vec{r} = (p + 1)\hat{i} + (2p - 1)\hat{j} + (2p + 1)\hat{k} \] is

A body cools according to Newton’s law from \(100^\circ\text{C}\) to \(60^\circ\text{C}\) in 20 minutes. The temperature of the surroundings being \(20^\circ\text{C}\), the temperature of the body after one hour is

Which of the following statement patterns is a tautology? \[ S_1 \equiv \neg p \rightarrow (q \leftrightarrow p) \] \[ S_2 \equiv \neg p \vee q \] \[ S_3 \equiv (p \rightarrow q) \land (q \rightarrow p) \] \[ S_4 \equiv (q \rightarrow p) \vee (\neg p \leftrightarrow q) \]

The value of $\cos^{-1}\left(\cos\left(\frac{7\pi}{6}\right)\right)$ is

If the equation \[ x^2 - 3xy + y^2 + 3x - 5y + 2 = 0 \] represents a pair of lines, where \( \theta \) is the angle between them, then the value of \( \csc^2 \theta \) is

The volume of a tetrahedron whose vertices are \( A = (-1, 2, 3) \), \( B = (3, -2, 1) \), \( C = (2, 1, 3) \), and \( D = (-1, -2, 4) \) is