List of top Questions asked in MHT CET

If the mean of a binomial distribution is twice its variance and \(n=18\), then the probability of success is...
The ratio and the coordinates of the point where the segment joining \((3,5,6)\) and \((4,6,-3)\) is divided by the YZ-plane are respectively:
The maximum value of \(Z=7x-6y\) subject to \(0\leq x\leq 5\) and \(0\leq y\leq 3\) is...
A fair die is thrown. The odds in favor of getting a number which is a perfect square on the uppermost face of the die are...
A continuous random variable X has the following probability distribution function (p.d.f.)
\(f(x)=\begin{cases} kx^{2} & \text{for }0\leq x\leq 3 \\ 0 & \text{otherwise} \end{cases}\)
If \(P(X>a)=0.5\), then the value of \(a\) is...
Let \(A\) be the point on line \(x-1=y-2=z-1\) and \(B\) be the foot of perpendicular drawn from \(A\) on a plane \(2x-y+z=8\) and \(AB=4\). If \(C\) is the point of intersection of the line and the plane, then the square of the distance between \(B\) and \(C\) is:
The plane passing through the point \((5,1,2)\) and perpendicular to the line \(2x-4=y-4=z-5\) will meet the line at the point
The equation of the plane passing through the point \((0,4,3)\) and containing the line \(\frac{x-1}{1}=\frac{y-3}{3}=\frac{z-2}{2}\) is \(ax+by+cz+d=0\), \((a\geq 0)\). The value of \((a+b+c+d)\) is
A line makes the same angle \(\alpha\) with each of the \(X\) and \(Z\) axes. If the angle \(\beta\) which it makes with the \(Y\)-axis is such that \(\sin ^{2}\beta =2\sin ^{2}\alpha\), then the value of \(\cos ^{2}\alpha\) is ...
The sum of the lengths of the projections of \(2\hat{i}+3\hat{j}+4\hat{k}\) on the coordinate axes is
Let the line \(\frac{x-2}{3}=\frac{y-1}{-5}=\frac{z+2}{2}\) lie in the plane \(x+3y-\alpha z+\beta =0\). Then \((\alpha ,\beta )\) equals
The solution of the differential equation \(y^{2}-x^{2}\frac{dy}{dx}=xy\frac{dy}{dx}\) is ...
The order of the differential equation representing the family of all parabolas having a fixed latus rectum of length \(4a\) and an axis parallel to the x-axis is...
Let \(\vec{u}\) and \(\vec{v}\) be unit vectors such that the angle between them is \(\theta =\frac{\pi }{6}\). If the adjacent sides of a parallelogram are represented by the vectors \(\vec{a}=2\vec{u}+3\vec{v}\) and \(\vec{b}=\vec{u}-\vec{v}\), then the area of the parallelogram is
The rate of disintegration of a radioactive element at any time t is proportional to its mass at that time. Then the time during which the original mass of \(4.5\) gm will disintegrate to a mass of \(1.5\) gm. is...(where \(k\) is proportionality constant)
The area bounded by \(5x^{2}-y=0\) and \(2x^{2}-y+9=0\) is (in sq.units)...
If the volume of a tetrahedron with coterminous edges \(\vec{a},\vec{b}\) and \(\vec{c}\), (where \(\vec{a}\) is a unit vector) is \(13\) cubic units and the angle between \(\vec{a}\) and \(\vec{b}\times \vec{c}\) is \(\frac{\pi }{3}\), then \(|\vec{b}\times \vec{c}|\) is
The value of the integral \(\int \frac{x^{2}+1}{(x+1)^{2}}dx=\) ............
The value of the integral \(\int \frac{dx}{3+\sin 2x+\sin ^{2}x}=\) .........
If \(\int \frac{\log (\log x)}{4x(\log x)^{2}}dx=k\left[\frac{1+\log (\log x)}{\log x}\right]+c\), then the value of \(k\) is...
The value of the integral \(\int _{10}^{20}\frac{1}{(x-3)(x-2)}dx\) is...
The values of \(a\) for which \(\int _{0}^{a}(3x^{2}+4x-5)dx\lt a^{3}-2\) are...
The value of the integral \(\int \frac{dx}{x\sqrt{1-x^{3}}}\) is equal to...
Let \(I_{n}=\int _{n}^{n+1}x[x]dx\), where \([x]\) denotes greatest integer function and \(n\in N\). If \(I_{n}=18\), then the value of \(n\) is...
If \(y=x-e^{x}\), then \(\frac{d^{2}x}{dy^{2}}=\) ...