List of top Questions asked in MHT CET

The minimum value of \(z=5x+8y\) subject to the constraints \(0\leq x\leq 4,\ 0\leq y\leq 2,\ x+y\geq 5\) is

The distance of the point \(2\hat{i}+\hat{j}-\hat{k}\) from the plane \(\bar{r}\cdot (\hat{i}-2\hat{j}+4\hat{k})=9\), is

The probability that a person hits a target is \(0.6\). If he fires \(5\) shots at the target, then the probability that he hits the target at least once is

Six faces of a die are marked with the numbers \(-3,-2,-1,0,1,2\). If such two dice are thrown simultaneously, then the probability of getting the product of the numbers on the uppermost surfaces as \(\pm 3\) or sum of the numbers on the uppermost surfaces is divisible by \(2\), is ....

Let \(L\) be a line \(\frac{x-1}{1}=\frac{y+2}{3}=\frac{z-7}{-1}\) and \(P\) be a plane passing through the midpoint of the segment joining \(M(-4,2,1)\) and \(N(2,-4,3)\) and perpendicular to segment MN. If the line \(L\) intersects the plane \(P\) at point \(S(\alpha ,\beta ,\gamma )\), then \(\alpha +\beta +\gamma =\ldots\)

Let X be a random variable with the probability density function defined by
\(f(x)=\frac{1}{x^{2}},\ 1\lt x\lt \infty\)
\(=0\) otherwise.
If \(C_{1}=\{x:1\lt x\lt 2\}\) and \(C_{2}=\{x:4\lt x\lt 5\}\) then \(P(C_{1}\cup C_{2})=\)

If \(\bar{a}=4\hat{i}-10\hat{j}+(1-p)\hat{k}\) and \(\bar{b}=12\hat{i}+(q-10)\hat{j}+3\hat{k}\) satisfy \(\bar{a}\times \bar{b}=\bar{0}\), then the values of \(p\) and \(q\) are respectively

If the vectors \(\bar{a}=2\bar{i}+\bar{j}+3\bar{k}\) and \(\bar{b}=p\bar{i}+2\bar{j}+2\bar{k}\) are perpendicular to each other, then ...

If the angle \(\theta\) between the line \(\frac{x+1}{1}=\frac{y-1}{2}=\frac{z-2}{2}\) and the plane \(2x-y+\sqrt{k}z+4=0\) is such that \(\cos \theta =\frac{\sqrt{8}}{3}\). Then \(k=\)

The acute angle between the line \(\bar{r}=2\hat{i}+2\hat{j}+\hat{k}+\lambda (2\hat{i}-3\hat{j}+2\hat{k})\) and the plane \(\bar{r}\cdot (3\hat{i}-2\hat{j}+5\hat{k})=4\) is

For two non-zero, non-collinear, non-orthogonal vectors \(\vec{a}\) and \(\vec{b}\) where \(\theta\) is angle between them, then \(\frac{(\vec{a}\cdot \vec{b})^{2}+|\vec{a}\times \vec{b}|^{2}}{(\vec{a}\cdot \vec{b})^{2}-|\vec{a}\times \vec{b}|^{2}}=\)

If \(\bar{a},\bar{b},\bar{c}\) are vectors such that \([\bar{a}\ \bar{b}\ \bar{c}]=3\), then \([\bar{a}\times \bar{b}\ \ \bar{b}\times \bar{c}\ \ \bar{c}\times \bar{a}]=\)

The area of the region bounded by the curves \(y^{2}=9x\) and \(x^{2}=9y\)

The differential equation of system of concentric circles with center \((1,2)\) is ____

If \(a>4\) and \(\int _{-2}^{1}\frac{1}{x^{2}+4x+a}dx=\frac{1}{3}\tan ^{-1}(1)\), then the value of \(a\) is

Let \(\vec{a}\) and \(\vec{b}\) be two unit vectors such that their sum is also a unit vector. If \(\vec{u}=\vec{a}+2\vec{b}\) and \(\vec{v}=2\vec{a}+\vec{b}\), then the angle between \(\vec{u}\) and \(\vec{v}\) is

Degree of differential equation \(\sqrt[3]{\left(\frac{dy}{dx}\right)^{2}+5}=\frac{1+\left(\frac{dx}{dy}\right)^{3}}{\sqrt{4+\left(\frac{dy}{dx}\right)^{5}}}\) is

The solution of the differential equation \(\frac{dy}{dx}+1=e^{x+y}\) is

In the Lagrange's Mean Value Theorem, \(f(b)-f(a)=(b-a)f'(c);\ (a\lt c\lt b)\). If \(a=2,b=4\) and \(f(x)=\sqrt{x^{2}-4}\), then the value of \(c\) is

\(\int f(x)dx=g(x)+c\), then \(\int xf(x^{2})dx=\)

\(\int \frac{1+\cos a\cos x}{\cos a+\cos x}dx=\)

If \(\int _{0}^{x}f(t)dt=x+\int _{x}^{0}t\cdot f(t)dt\) then the value of \(f(1)=\)

The point on the curve \(y=3x^{2}-9x+8\) where the tangent is parallel to x-axis is

If \(\int x^{3}e^{x}dx=e^{x}(px^{3}+qx^{2}+rx+s)+c\), then the value of \(p+q+r+s\) is

If \(\int \sqrt{e^{x}-1}dx=a\sqrt{e^{x}-1}+b\tan ^{-1}(\sqrt{e^{x}-1})+c\), then