List of top Questions asked in MHT CET

Let \(X\) be a continuous r. v. with p. d. f.
\(f(x)=\begin{cases} kx^{3}, & 0\leq x\leq 1 \\ 0, & \text{otherwise} \end{cases}\)
then \(P\left(X\leq \frac{3}{4}|X>\frac{1}{4}\right)=\ldots\)

Suppose that \(60\%\) of all families own a mobile set. If \(11\) families are interviewed at random, then the probability that \(8\) families own a mobile set is..... (Given that \((0.6)^{8}=0.0168\))

If a fair die is thrown, then the odds in favor of getting a perfect square on the uppermost face are:

Let \(a\) and \(b\) be the distances from the point \((2,3,4)\) to the XY plane and Y-Axis respectively. Then \(a^{2}+b^{2}=\)

The minimum value of \(z=4x+2y\) subject to the constraints \(3x+y\geq 27,x+y\geq 21,x+2y\geq 30,x\geq 0,y\geq 0\) is

If \(M\) is the foot of the perpendicular drawn from \(A(4,3,2)\) on the line joining the points \(B(2,4,1)\) and \(C(4,5,3)\), the co-ordinates of \(M\) are _____

If the point \(Q(\alpha ,\beta ,\gamma )\) is the mirror image of \(P(10,15,20)\) in the plane \(\vec{r}=\hat{k}+\lambda (-\hat{i}+\hat{j})+\mu (-\hat{i}+\hat{k})\), \(\lambda ,\mu \in \mathbb{R}\) then the value of \(3(\alpha +\beta +\gamma )\) is

If the vector \(\vec{a}=x\hat{i}-\hat{j}+\hat{k}\) and \(\vec{b}=\hat{i}+y\hat{j}+z\hat{k}\) are collinear, then a possible unit vector parallel to the vector \(\hat{i}+y\hat{j}+z\hat{k}\) is...

If \(|\vec{a}+\vec{b}|=|\vec{a}-\vec{b}|\) then the angle between \(\vec{a}\) and \(\vec{b}\) is

\(\vec{a},\vec{b},\vec{c}\) represent three concurrent edges of a rectangular parallelopiped whose lengths are \(5,2\) and \(3\) units respectively, then \((\vec{a}+\vec{b}+\vec{c})\cdot (\vec{a}\times \vec{b}+\vec{b}\times \vec{c}+\vec{c}\times \vec{a})=\)

The vector equation of the plane determined by the lines \(x=y,z=0\) and \(x+y=0,z=0\) is

The cartesian equation of the line passing through the point \(\hat{i}+2\hat{j}+3\hat{k}\) and perpendicular to the vectors \(\hat{i}+\hat{j}+\hat{k}\) and \(2\hat{i}-\hat{j}+\hat{k}\) is

If \(\int _{0}^{\infty }\frac{1}{(x^{2}+1)(x^{2}+16)}dx=\frac{\pi }{k^{2}-9}\), then \(k=\ldots\)

The differential equation of the equation \(y=a\cos (x+b)\) is

If the curve \(y=f(x)\) passes through the point \((1,2)\) and satisfies the differential equation \(xdy+(y+x^{3}y^{2})dx=0\), then the equation of curve is...

The area between the curves \(y=1-|x|\) and \(y=|x|-1\) is ..... square units.

The differential equation of all parabolas which have \(4a\) as latus rectum and whose axis is parallel to the X-axis is \(2a\frac{d^{2}y}{dx^{2}}+\left(\frac{dy}{dx}\right)^{k}=0\), then the value of \(k\) is...

If \(\int _{-1}^{4}f(x)dx=4\) and \(\int _{2}^{4}(5-f(x))dx=7\) then \(\int _{2}^{-1}f(x)dx=\)

If \(f'(x)=k(\cos x-\sin x)\), \(f'(0)=5\), \(f\left(\frac{\pi }{2}\right)=19\), Then \(f(x)=\)

\(\int \frac{4x+5}{2x+1}dx=\)

If \(\int _{0}^{1}\tan ^{-1}\left[\frac{1}{1-x+x^{2}}\right]dx=2k\), then the value of \(k\) is:

\(\int \sqrt{x}\sec \left(x^{\frac{3}{2}}\right)\tan \left(x^{\frac{3}{2}}\right)dx=\)

The approximate value of \(\sin ^{-1}(0.51)\) is .......
[Given \(\pi =3.1416\), \(\frac{2}{\sqrt{3}}=1.1547\)]

If \(x^{y}\cdot y^{x}=1\) then the value of \(\frac{dy}{dx}\) is

If \(f(x)\) is a differentiable function of \(x\), then \(\lim _{h\rightarrow 0}\frac{[f(x+h)]^{2}-[f(x)]^{2}}{2h}=\)