List of top Questions asked in MHT CET- 2025

The equation of the tangent to $y=be^{-x/a}$ at the point where it crosses the Y axis is}

Two spherical black bodies have radii $R_{1}$ and $R_{2}$ and temperatures $T_{1}$ and $T_{2}$. If they radiate same power, then $R_2/R_1$ is}

A capacitor of unknown capacity is connected across a battery of V volt. The charge stored in it is Q coulomb. When potential across the capacitor is reduced by $V_{1}$ volt, the charge stored in it becomes $Q_{1}$ coulomb. The potential V is}

A same torque is applied to a disc and a ring of equal mass and radii then

If $f(x)=3x^{2}+2xf^{\prime}(1)+f^{\prime\prime}(2)$, then $f(x)=..........$

If $0\le x\le\pi$ and $81^{\sin^{2}x}+81^{\cos^{2}x}=30$ Then $x$ takes the value}

If $y=\tan^{-1}(\frac{1}{1+x+x^{2}})+\tan^{-1}(\frac{1}{x^{2}+3x+3})+\tan^{-1}(\frac{1}{x^{2}+5x+7})$ then $y^{\prime}(0)$ is}

A manufacturing company produces two items, A and B. Machine I (max 640 mins): A takes 20, B takes 15. Machine II (max 500 mins): A takes 5, B takes 8. Profit: A is Rs 25, B is Rs 18. Formulation is:

The equation of the plane passing through (1,1,1) and through the line of intersection of $x+2y-z+1=0$ and $3x-y-4z+3=0$ is

The unit vectors perpendicular to the plane determined by the points $A(1,-1,2)$, $B(2,0,-1)$, $C(0,2,1)$ is

The direction cosines of a normal to the plane passing through (4, 2, 3), (-1, 4, 2) and (3, 2, 1) are

P divides AC in 3:4 and Q divides BC in 4:3. Then M divides AQ in the ratio

A fair coin is tossed. If $P(5~tails) = P(7~tails)$, then $P(3~tails)$ is

A fair n-faced die is rolled until a number less than n appears. If the mean of tosses is $n/9$, then n =

The tangent to the ellipse $9x^{2}+16y^{2}=288$ making equal intercepts on the coordinate axes intersects the X-axis and the Y-axis in the points A and B respectively. Then $A(\triangle OAB)=$ (where O is origin)}

The distance of the point $A(3,-4,5)$ from the plane $2x+5y-6z=16$ measured along the line $\frac{x}{2}=\frac{y}{1}=\frac{z}{-2}$ is}

If $\vec{a}, \vec{b}, \vec{c}$ are coplanar, $|\vec{a}|=1, |\vec{b}|=2, \vec{b} \cdot \vec{c}=8$ and the angle between $\vec{b}, \vec{c}$ is $45^{\circ}$, then $|\vec{a}\times(\vec{b}\times\vec{c})|$ is}

The line $\frac{x-1}{2}=\frac{y+2}{-1}=\frac{z}{1}$ intersects the XY and YZ planes at A and B. The line through A and B is}

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 $\frac{du}{dv}=...$

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}

P divides AC in 3:4 and Q divides BC in 4:3. Then M divides AQ in the ratio

A fair n-faced die is rolled until a number less than n appears. If the mean of tosses is $n/9$, then n =

A fair coin is tossed. If $P(5~tails) = P(7~tails)$, then $P(3~tails)$ is

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...