List of top Questions asked in MHT CET

Two numbers are selected at random without replacement from the first \(n\) natural numbers. Let X denote the larger of the two numbers obtained. If \(E(X)=\frac{14}{3}\), then the value of \(n\) is

In \(\triangle ABC\), mid-points of the sides AB, BC and CA are respectively \((l,0,0),(0,m,0)\) and \((0,0,n)\). Then \(\frac{(AB)^{2}+(BC)^{2}+(CA)^{2}}{l^{2}+m^{2}+n^{2}}=\)

If the points \(A(1,p,1),B(2,5,-1),C(q,11,r)\) are collinear. If the line passing through these points is perpendicular to the vector \(4\hat{i}-2\hat{j}+\hat{k}\), then the value of \(p+q+r\) is

The point at which the maximum value of \(3x+2y\) subject to the constraints \(x+y\leq 2,x\geq 0,y\geq 0\) is obtained is

A coin is tossed n times. The probability of getting a head at least once is greater than \(0.8\), then the least value of n is

If \(\theta\) is the angle between the line \(\bar{r}=(\hat{i}+\hat{j}-\hat{k})+\lambda (\hat{i}-\hat{j}+\hat{k})\) and the plane \(\bar{r}\cdot (\hat{i}-2\hat{j}+3\hat{k})=5\) then the value of \(\cos ^{2}\theta\) is

The distance of the point \((4,5,3)\) from the plane \(x+y+z=2\) measured parallel to the line \(x=y=2z\) is ..... units

The equation of the line passing through the point of intersection of the lines \(\frac{x-3}{1}=\frac{y-5}{2}=\frac{z-1}{-1}\) & \(\frac{x-4}{2}=\frac{y-2}{-1}=\frac{z-4}{2}\) and in the direction of \(\hat{i}-2\hat{j}+\hat{k}\) is

The Cartesian equation of the line passing through \(A(3,2,1)\) and \(B(1,3,1)\) is:

If the function \(f(x)\) satisfying the equation \([f'(x)]^{2}+4f(x)f'(x)+f^{2}(x)=0\), then \(f(x)=\)
(where \(c\) is constant of integration)

A person's assets start reducing in such a way that the rate of reduction of assets is proportional to the square root of the assets existing at that moment. If the assets at the beginning are \(\text{₹}40\) lakhs and they dwindle down to \(\text{₹}40000\) after \(2\) years. Then the person will be bankrupt in k years from the start. Then \(k=\)

The differential equation of the equation \(x^{2}+(y-b)^{2}=1\) is

If the volume of tetrahedron with its coterminous edges \(\bar{a},\bar{b},\bar{c}\) is \(6\) cu. units then the volume of a tetrahedron with coterminous edges \((\bar{a}\times \bar{b}),(\bar{b}\times \bar{c}),(\bar{c}\times \bar{a})\) is

If \(\bar{p},\bar{q},\bar{r}\) are unit vectors such that \(\bar{p}\times (\bar{q}\times \bar{r})=\frac{1}{7}\bar{q}\), then the angle between \(\bar{p}\) and \(\bar{r}\) is

\(\int _{0}^{\pi /4}\log (1+\tan x)dx=\ldots\)

The value of the integral \(\int _{0}^{\pi /4}\frac{\cos x}{\sqrt{1-\sin ^{2}x}}dx\) is

\(\int _{0}^{1}\frac{\sin ^{-1}\sqrt{x(2-x)}}{\cos ^{-1}x+\sin ^{-1}\sqrt{x(2-x)}}dx=\ldots\)

The area of the region bounded by the parabola \(y^{2}=16x\) and the line \(x=4\) is

If Rolle's theorem holds for the function \(f(x)=x^{2}-px+10\), \(x\in [0,4]\) with \(c=2\), then \(p=\)

Evaluate \(\int e^{x}(\sin x+2\,\cos x)\sin xdx\)

If \(\int \sqrt{1+\sec x}dx=2\sin ^{-1}(f(x))+c\), then

The value of the integral \(\int \frac{dx}{x^{4}+x^{3}}\) is

\(\int \frac{x^{3}\sin (\tan ^{-1}(x^{4}))}{1+x^{8}}dx=\)

A rectangular sheet of paper has its area \(32\) meters\({}^{2}\). The margins at the top and bottom are \(50\) cm each and at the sides \(25\) cm each. If the area of the printed space is maximum, then the dimensions of the paper are

A stone is dropped into a quiet lake and waves move in circles at the speed of \(7\) cm s\({}^{-1}\). At the instant when the radius of circular wave is \(5\) cm, the enclosed area is increasing at the rate -------- cm\({}^{2}\) s\({}^{-1}\)