List of top Mathematics Questions asked in MHT CET

If the pair of lines $3x^{2}-5xy+py^{2}=0$ and $6x^{2}-xy-5y^{2}=0$ have one line common, then $p=$

$\int\frac{dx}{sin^{2}x~cos^{2}x}=$

Let $z$ be a complex number such that $|z|+z=3+i$ where $i=\sqrt{-1}$, then $|z|=$

Considering only principal values, the value of $\tan(\sin^{-1}(\frac{3}{5})-2 \cos^{-1}(\frac{2}{\sqrt{5}}))$ is}

The equation of the curve through (0,2) given the sum of ordinate and abscissa at any point exceeds the slope of tangent by 5 is

If the area bounded by $x^{2}=4y$, X-axis and $x=4$ is divided into equal areas by $x=\alpha$, then the value of $\alpha$ is}

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

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 $(1+\frac{a}{c}+\frac{b}{c})(1+\frac{c}{b}-\frac{a}{b})=$

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}

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

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

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

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

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