List of top Questions asked in MHT CET

Two fair dice are thrown. The probability that the sum of the scores is \(7\) such that the number on the second die is greater than that on the first die is ...
The variance of random variable \(X\), for the following probability mass function (p. m. f.) is ...
\(X=x\)\(1\)\(2\)\(3\)
\(P(X=x)\)\(\frac{1}{5}\)\(\frac{2}{5}\)\(\frac{2}{5}\)
The planes \(5x-2y+3z=9\) and \(15x-6y+9z=-5\) are
If the lines \(\frac{x-1}{1}=\frac{y-1}{2}=\frac{z-1}{3}\) and \(\frac{x-3}{1}=\frac{y-k}{2}=\frac{z-5}{1}\) are intersect at the point \(P\), then the distance (in units) of the point \(P\) from the origin \(O(0,0,0)\) is ...
If \(X\) follows a Binomial distribution with parameters \(n=8\) and \(p=\frac{1}{2}\) then \(P(|X-4|\leq 2)\)
The foot of the perpendicular from the origin to the plane is \(N=(4,5,a),a>0\) and \(l(ON)=7\), then vector equation of the plane is ...
If \(8\vec{AB}-3\vec{AC}-5\vec{AD}=\vec{0}\), then the point \(C\) divides \(BD\) in the ratio ...
The equation of a plane passing through the intersection of two planes \(\vec{r}\cdot (\hat{i}-2\hat{j}+3\hat{k})=4\) and \(\vec{r}\cdot (2\hat{i}+\hat{j}-3\hat{k})=7\) and parallel to Y-axis is
Which of the following is not a correct pair of a linear differential equation and its integrating factor?
In a triangle PQR, L and M are the points on QR and PR respectively such that \(QL=2LR\) and \(PM=3MR\). Let S be the point of intersection of PL and QM; then S divides segment QM internally in the ratio ...
A parallelopiped is determined by vectors \(\vec{a}=\hat{i}+2\hat{k},\vec{b}=\hat{i}+\hat{j}-\hat{k}\) and \(\vec{c}=2\hat{i}+2\hat{j}+3\hat{k}\). The length (in units) of its altitude drawn to the base determined by vectors \(\vec{b}\) and \(\vec{c}\) is
If \(\vec{a}=\hat{i}+2\hat{j}+3\hat{k},\vec{b}=3\hat{i}+4\hat{j}+4\hat{k},\vec{c}=3\hat{i}+2\hat{j}+3\hat{k}\) are the position vectors of the vertices \(A\), \(B\) and \(C\) respectively of \(\triangle ABC\) and the bisector of \(\angle A\) meets side \(BC\) at \(D\) where \(B-D-C\), then \(|\vec{AD}|\) is...
If three coterminous edges of a parallelopiped are represented by \(\vec{a}-\vec{b},\vec{b}-\vec{c}\) and \(\vec{c}-\vec{a}\) then its volume is
The general solution of \(e^{\frac{dy}{dx}}=x\) is
The differential equation \(\frac{dy}{dx}=\frac{\sqrt{1-y^{2}}}{y}\) determines a family of circles with
The value of \(\int _{1}^{2}\frac{1}{x(1+\log x)^{2}}dx\) is.......
If \(\int _{0}^{\pi }\log (\sin x)dx=k\), then the value of \(\int _{0}^{\frac{\pi }{4}}\log (1+\tan x)dx\) in terms of \(k\) is...
The area bounded by the curve \(y=x^{2}+4,x=y,x=3\), and Y-axis is
\(\int _{0}^{\frac{\pi }{2}}(1+\sin x)^{3}dx=\)
If \(y=c_{1}\sin ^{2}x+c_{2}\), then its differential equation is:
\(\int \frac{dx}{(x+2)(x^{2}+1)}\) is equal to
If \(\int \frac{1}{f(x)}dx=\log |f(x)|^{2}+c\), then \(f(x)=\ldots\)
\(\int \sin ^{3}x\cos ^{3}xdx=\ldots\)
\(\int \frac{5x^{12}+6x^{11}}{(x^{6}+x+1)^{3}}dx=\)
If \(f(x)\) satisfy the condition of Rolle's Theorm in \([1,2]\) and \(f(x)\) is continuous in \([1,2]\) then \(\int _{1}^{2}f'(x)dx\) is equal to _____