List of top Mathematics Questions asked in MHT CET

The joint equation of the pair of lines through the origin and making an equilateral triangle with the line $x = 3$ is
A random variable X has the following probability distribution

then F(4) =
A differential equation for the temperature 'T' of a hot body as a function of time, when it is placed in a bath which is held at a constant temperature of $32^\circ\text{F}$, is given by (where k is a constant of proportionality)
$\int_0^{\pi / 4} \log (1+\tan x) \text{d}x=$
If the volume of a tetrahedron whose conterminous edges are $\vec{\mathrm{a}}+\vec{\mathrm{b}}$, $\vec{\mathrm{b}}+\vec{\mathrm{c}}$, $\vec{\mathrm{c}}+\vec{\mathrm{a}}$ is 24 cubic units, then the volume of parallelopiped whose coterminous edges are $\vec{\mathrm{a}}$, $\vec{\mathrm{b}}$, $\vec{\mathrm{c}}$ is
If the acute angle between the lines given by $ax^2 + 2hxy + by^2 = 0$ is $\frac{\pi}{4}$, then $4h^2 =$
The shaded part of the given figure indicates the feasible region. Then the constraints are
A wire of length 20 units is divided into two parts such that the product of one part and cube of the other part is maximum, then product of these parts is
If $A(\alpha)=\begin{bmatrix} \cos\alpha & \sin\alpha \\ -\sin\alpha & \cos\alpha \end{bmatrix}$, then $[A^2(\alpha)]^{-1} =$
Two dice are rolled simultaneously. The probability that the sum of the two numbers on the dice is a prime number, is
$\int \tan^{-1}(\sec x + \tan x) dx =$
The number of ways in which 8 different pearls can be arranged to form a necklace is
The curves $\frac{x^2}{a^2} + \frac{y^2}{4} = 1$ and $y^3 = 16x$ intersect each other orthogonally, then $a^2 =$
If $p, q$ are true statements and $r$ is false statement, then which of the following is correct.
For two data sets each of size 5, the variance are given to be 4 and 5 and the corresponding means are given to be 2 and 4 respectively. The variance of the combined data set is
$\lim _{x \rightarrow 1} \frac{(2 x-3)(\sqrt{x}-1)}{2 x^2+x-3}=$
$\int e^{\tan x}(\sec ^2 x+\sec ^3 x \sin x) d x=$
The product of the perpendicular distances from $(2,-1)$ to the pair of lines $2 x^2-5 x y+2 y^2=0$ is
The derivative of $(\log x)^x$ with respect to $\log x$ is
The function $f(x) = \cot^{-1} x + x$ is increasing in the interval.
If $|\bar{a}| = 3, |\bar{b}| = 4, |\bar{a} - \bar{b}| = 5$, then $|\bar{a} + \bar{b}| =$
The equation of a line passing through $(p \cos \alpha, p \sin \alpha)$ and making an angle $(90 + \alpha)$ with positive direction of X-axis is
$\tan ^{-1}\left(\frac{x-1}{x-2}\right)+\tan ^{-1}\left(\frac{x+1}{x+2}\right)=\frac{\pi}{4}$, then the values of $x$ are
A body at an unknown temperature is placed in a room which is held at a constant temperature of $30^{\circ}F$. If after 10 minutes the temperature of the body is $0^{\circ}F$ and after 20 minutes the temperature of the body is $15^{\circ}F$, then the expression for the temperature of the body at any time $t$ is
A stone is thrown into a quiet lake and the waves formed move in circles. If the radius of a circular wave increases at the rate of $4\ \text{cm/sec}$, then the rate of increase in its area, at the instant when its radius is $10\ \text{cm}$, is _________ $\text{cm}^2/\text{sec}$.