List of top Questions asked in MHT CET- 2025

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

The values of x for which the angle between $\vec{a}=2x^{2}\hat{i}+4x\hat{j}+\hat{k}$ and $\vec{b}=7\hat{i}-2\hat{j}+x\hat{k}$ is obtuse are}

A random variable X has the distribution: $P(X=1,2,3,4) = 0.1, 0.2, 0.3, 0.4$. The mean and standard deviation are:

If $u=\log(\sqrt{x+1}-\sqrt{x-1})$ and $v=\sqrt{x+1}+\sqrt{x-1}$ then $\frac{du}{dv}=...$

Two tangents to $x^{2}+y^{2}=4$ at A and B meet at $P(-4,0).$ Area of quadrilateral PAOB is}

Vectors $\vec{a}, \vec{b}, \vec{c}$ have magnitudes 2, 4, 4. Projection of $\vec{b}$ on $\vec{a}$ equals projection of $\vec{c}$ on $\vec{a}$ and $\vec{b} \perp \vec{c}$. Value of $|\vec{a}+\vec{b}-\vec{c}|$ is}

Population of towns A and B increases at a rate proportional to population. In 1984, both were 20,000. In 1989, A was 25,000 and B was 28,000. The difference in 1994 was

The lines $\frac{6x-6}{18}=\frac{y+1}{3}=\frac{z-1}{5}$ and $\frac{3x+6}{12}=\frac{y-1}{3}=\frac{z+1}{2}$ are...

$\int\frac{dx}{x^{\frac{1}{2}}+x^{\frac{1}{3}}}=Ax^{\frac{1}{2}}+Bx^{\frac{1}{3}}+Cx^{\frac{1}{6}}+D~log(x^{\frac{1}{6}}+1)+k$, then values of A, B, C and D are}

The probability that a non-leap year selected at random will contain 52 Saturdays or 53 Sundays is

The number of ways in which 6 boys and 4 girls can be seated around a round table such that 2 special boys and a special girl never sit together is

The solution of the differential equation $(1+x)\frac{dy}{dx}-xy=1-x$ is}

The differential equation representing the family of parabolas having vertex at the origin and axis along the positive Y-axis is

If the angles A, B and C of a triangle are in A.P. and if a, b and c denote the length of the sides opposite to A, B and C respectively, then the value of $\frac{a}{b}sin~2B+\frac{b}{a}sin~2A$ is}

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

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

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}

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 $\log_{t}(pqrs)=......$

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

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

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