List of top Mathematics Questions asked in MHT CET

If $p^{3}=q^{4}=r^{6}=t^{7}=s^{2}$, then $\log_{t}(pqrs)=......$

$\int_{0}^{\frac{\pi}{2}}\frac{300 \sin x+100 \cos x}{\sin x+\cos x}dx=...$

$\lim_{x\rightarrow0}\frac{e^{x^{2}}-\cos 3x}{\sin x \log(1+2x)}=$

If A is a matrix of order 2 and I is the identity matrix of order 2 such that $A^{2}-4A+3I=0$ then $(A+3I)^{-1}=$

If $\cot^{-1}(\sqrt{\cos \alpha})-\tan^{-1}(\sqrt{\cos \alpha})=x$, then the value of $\sin x$ is}

In a triangle PQR with usual notations, $\angle R=\frac{\pi}{2}$. If $\tan\frac{P}{2}$ and $\tan\frac{Q}{2}$ are the roots of the equation $ax^{2}+bx+c=0(a\ne0),$ then}

In a triangle ABC with usual notations if $\angle A=30^{\circ}$, then the value of $(1+\frac{a}{c}+\frac{b}{c})(1+\frac{c}{b}-\frac{a}{b})=$

$\int_{0}^{1}x|x-\frac{1}{2}|dx=$

The function $f(x)=[x(x-2)]^{2}$ is increasing in the set}

If p,q,r,s are statements, where: $p:A^{2}-B^{2}=(A-B)(A+B)$ for matrices $AB\ne BA$; $q:5\le5$; $r:{^{8}C_{1}+{}^{8}C_{2}+...+^{8}C_{8}=256}$; $s$: Max value of ${}^{8}C_{r}$ is 70. The statement with truth value true is:

If $x$ and $y$ are sides of two squares such that $y=x-x^{2}$, then the rate of change of area of the second square with respect to that of the first square is}

The minimum value of $ax+by$ where $xy=c^{2}$ is}

The acute angle between the line $4x-2y+13=0$ and the line which makes equal intercepts with the co-ordinate axes is

Let $f(x)=\begin{cases}\frac{x^{4}-5x^{2}+4}{|(x-1)(x-2)|}&,x\ne1,2\\ 6&,x=1
12&,x=2\end{cases}$. Then $f(x)$ is continuous on the set}

Which of the following statement is a tautology?

Evaluate the integral: \[ \int \frac{1}{\sin^2 2x \cdot \cos^2 2x} \, dx \]

Given that \( \cot \left( \frac{A+B}{2} \right) \cdot \tan \left( \frac{A-B}{2} \right) = \), and the equation \( \frac{x}{2} + \frac{y}{3} + \frac{2}{6} - 1 = 0 \), find the area of \( \Delta ABC = 2 \).

Given the equation: \[ 81 \sin^2 x + 81 \cos^2 x = 30 \] Find the value of \( x \).

Find the value of the following expression: \[ \sin^2(30^\circ) + \cos^2(60^\circ) \]

If A and B are independent events such that \( P(A \cap B') = \frac{3}{25} \) and \( P(A' \cap B) = \frac{8}{25} \), then \( P(A) = \)}

If \( ^{15}C_4 + ^{15}C_5 + ^{16}C_6 + ^{17}C_7 + ^{18}C_8 = ^{19}C_r \), then the value of \( r \) is equal to}

In a triangle with one of the angles \( 120^\circ \), the lengths of the sides form an A.P. If the length of the greatest side is 7 m, then the area of the triangle is

If \( \bar{a} = \frac{1}{\sqrt{10}}(3\hat{i} + \hat{k}) \) and \( \bar{b} = \frac{1}{7}(2\hat{i} + 3\hat{j} - 6\hat{k}) \), then the value of \( (2\bar{a} - \bar{b}) \cdot ((\bar{a} \times \bar{b}) \times (\bar{a} + 2\bar{b})) = \)}