List of top Mathematics 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

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

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

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

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 \(\frac{(AB)^{2}+(BC)^{2}+(CA)^{2}}{l^{2}+m^{2}+n^{2}}=\)

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

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

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 \(k=\)

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

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

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

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

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

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

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

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

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

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

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

If \(x^{y}y^{x}=1\), then \(\frac{dy}{dx}\) is equal to

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\({}^{-1}\)