List of top Mathematics Questions asked in MHT CET

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

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

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

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

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

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

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

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 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

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

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

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

With usual notations in \( \triangle ABC \), if \( C = 90^\circ \), then \( \tan^{-1}\left(\dfrac{a}{b+c}\right) + \tan^{-1}\left(\dfrac{b}{c+a}\right) \) is

If \( f(x) = \frac{|x|}{x} \) for \( x \neq 0 \) and \( f(x) = 1 \) for \( x = 0 \), then the function is

If $f(x)=\dfrac{4\sin \pi x}{5x}$ for $x\neq 0$ and $f(x)=2k$ for $x=0$, and $f(x)$ is continuous at $x=0$, then the value of $k$ is

If \[ \int_{0}^{\frac{\pi}{4}} \frac{\sin x + \cos x}{9 + 16 \sin 2x} \, dx = k \log 3, \text{ then } k = \]

If \( x + y = \frac{\pi}{2} \), then the maximum value of \( \sin x \cdot \sin y \) is

Given \(A = \{1,2,3,4,5\}\), \(B = \{1,4,5\}\). If \(R\) is a relation from \(A\) to \(B\) such that \((x,y) \in R\) with \(x>y\), then the range of \(R\) is

The line through the points \( (1, 4), (-5, 1) \) intersects the line \( 4x + 3y - 5 = 0 \) in the point

If line \( x + y = 0 \) touches the curve \( ax^2 = 2y^2 - b \) at \( (1, -1) \), then the values of \( a \) and \( b \) are respectively

If \(\displaystyle \sin\!\left(\frac{x+y}{x-y}\right) = \tan \frac{\pi}{5}\), then find \(\displaystyle \frac{dy}{dx}\).