List of top Questions asked in MHT CET- 2025

The distance of the point \(\mathrm{P}(3,4,4)\) from the point of intersection of the line joining the points \(\mathrm{Q}(3,-4,-5), \mathrm{R}(2,-3,1)\) and the plane \(2 x+y+z=7\) is

If \(y=\tan ^{-1}\left[\frac{4 \sin 2 x}{\cos 2 x-6 \sin ^2 x}\right]\), then \(\frac{\mathrm{d} y}{\mathrm{~d} x}\) at \(x=0\) is

The contrapositive of the statement \(\sim p \vee(q \wedge \sim r)\) is

The equation of the line passing through the point of intersection of \(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}\) and \(\frac{x-4}{5}=\frac{y-1}{2}=z\) and also through the point ( \(2,1,-2\) ) is

Which of the following is the negation of the statement " For all M>0, there exist \(x \in \mathrm{~s}\) such that \(x \geqslant \mathrm{M}^{\prime \prime}\)

The point on the curve \(4 y^2-4 y+2 x-1=0\) at which the tangent becomes parallel to Y -axis is

The value of \(\tan ^2\left(\sec ^{-1} 4\right)+\cot ^2\left(\operatorname{cosec}^{-1} 3\right)\) is

In a triangle ABC , with usual notations, if \(\mathrm{a}=5, \mathrm{~b}=4, \cos (\mathrm{~A}-\mathrm{B})=\frac{31}{32}\), then \(\mathrm{c}=\)

A particle moves along a curve \(y=\frac{2 x^3-1}{3}\). The points on the curve at which the \(y\) co-ordinate is changing 18 times the \(x\) co-ordinate are

\[ \int_3^5 \frac{\sqrt{x} \mathrm{~d} x}{\sqrt{8-x}+\sqrt{x}}= \]

\[ \int \frac{\mathrm{d} x}{\sqrt{x}+x}= \]

The value of \(\int_0^1 \tan ^{-1}\left(1-x+x^2\right) \mathrm{d} x\) is

\[ \int\left(\frac{x-3}{x^2+9}\right)^2 d x= \]

The maximum value of \(x^{2 / 3}+(x-2)^{2 / 3}\) is

\[ \int \frac{\mathrm{d} x}{\mathrm{e}^x-1}= \]

The order and degree of the differential equation \(\sqrt{\frac{\mathrm{d} y}{\mathrm{~d} x}}-4 \frac{\mathrm{~d} y}{\mathrm{~d} x}-7 x=0\) is respectively

If \(x \frac{\mathrm{~d} y}{\mathrm{~d} x}=y(\log y-\log x+1)\), then the solution of the equation is

The area of the rectangle having vertices \(\mathrm{P}, \quad \mathrm{Q}, \quad \mathrm{R}, \quad \mathrm{S}\) with position vectors \(-\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}, \hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}, \hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}},-\hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}}\) respectively is

The area bounded by the curve \(x^2=8 y\) and the straight line \(x-8 y+2=0\) is

In a triangle ABC with usual notations, \(\cot \frac{\mathrm{A}}{2}+\cot \frac{\mathrm{B}}{2}+\cot \frac{\mathrm{C}}{2}=\)

The differential equation of all circles touching the Y -axis at the origin and centre on the X -axis is

Let mean and standard deviation of probability distribution

\[ \begin{array}{|c|c|c|c|c|} \hline \mathrm{X}=x & -3 & 0 & 1 & \alpha \\ \hline \mathrm{P}(\mathrm{X}=x) & \frac{1}{4} & \mathrm{~K} & \frac{1}{4} & \frac{1}{3} \\ \hline \end{array} \]

be \(\mu\) and \(\sigma\) respectively and if \(\sigma-\mu=2\) then \(\sigma=\)

If A and B are non-singular matrices of order 2 such that \(\quad(A B)^{-1}=\frac{1}{6}\left[\begin{array}{cc}-7 & -3 \\ 2 & 3\end{array}\right] \quad\) and \(A^{-1}=\frac{1}{3}\left[\begin{array}{cc}4 & 3 \\ -1 & 0\end{array}\right]\) then \(B^{-1}=\)

In a game a man wins \(Rs \,\, 40\) if he gets 5 or 6 on a throw of a fair die and loses ₹ 20 for getting any other number on the die. If he decides to throw the die either till he gets a five or six or to a maximum of three throws, then his expected gain/loss (in rupees) is

\[ \mathop {\lim }\limits_{x \to 2} \frac{x+3 x^2+5 x^3+7 x^4-166}{x-2}= \]