List of top Questions asked in MHT CET- 2020

The length of the latus rectum of the parabola whose focus is at \( (1,-2) \) and directrix is the line \( x + y + 3 = 0 \) is

If \( p, q \) are true statements and \( r \) is a false statement, then which of the following statements is a true statement?

If \( x = 3 \sin \theta \), \( y = 3 \cos \theta \cos \phi \), \( z = 3 \cos \theta \sin \phi \), then \( x^2 + y^2 + z^2 = \)

If the function \[ f(x)= \begin{cases} \dfrac{\log 10 + \log(0.1+2x)}{2x}, & x \neq 0 \\ k, & x=0 \end{cases} \] is continuous at \(x=0\), then \(k+2=\)

Solution of the differential equation \[ \frac{dy}{dx} + 2y = e^{-x} \text{ is:} \]

The solution of the differential equation \[ x^2 \frac{dy}{dx} = y^2 + xy \]

If \( f : \mathbb{R} \rightarrow \mathbb{R} \), \( g : \mathbb{R} \rightarrow \mathbb{R} \) are two functions defined by \( f(x) = 2x - 3 \), \( g(x) = x^3 + 5 \), then find \( (f \circ g)^{-1(x) \).}

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

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

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

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 \[ P(|-1<X<1|) \]

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

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

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

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

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

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

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}

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

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

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