List of top Questions asked in MHT CET, NEET (UG)

Two numbers are selected without replacement from the first six positive integers. Let X denote the number of prime numbers obtained. The mean value of X is .......

If the random variable \(X\sim B(4,0.5)\), then probability \(P(X\lt 3/X\geq 1)=\ldots\)

Let \(a\) and \(b\) be the numbers obtained in two trials of tossing a fair die. The probability that the matrix \(\begin{bmatrix} a & 2 \\ 6 & b \end{bmatrix}\) is not invertible is

The correct constraints for the given feasible region are ...

The direction cosines \(l,m,n\) of the two lines are connected by the relations \(l+m+n=0\) and \(lm=0\), then the angle between the lines is....

If the line \(\frac{x-2}{3}=\frac{y-1}{-5}=\frac{z+2}{2}\) lies in the plane \(x+3y+\alpha z+\beta =0\), then \((\alpha ,\beta )\) is

The position vector of the point at which the line joining the points \(\hat{i}+2\hat{j}-\hat{k}\) and \(3\hat{i}+4\hat{j}-2\hat{k}\) cuts the plane \(\vec{r}\cdot (\hat{j}-\hat{k})=-1\) is

If a parallelogram is constructed on vectors \(\vec{a}=3\vec{p}-\vec{q}\), \(\vec{b}=\vec{p}+3\vec{q}\) and \(|\vec{p}|=|\vec{q}|=2\) and the angle between \(\vec{p}\) and \(\vec{q}\) is \(\frac{\pi }{3}\), then \(|\vec{a}|:|\vec{b}|=\ldots\)

If \(\vec{r}=4\hat{i}+2\hat{j}+7\hat{k}+\lambda (3\hat{i}-5\hat{k})\) is the vector equation of the line passing through \((7,2,2)\), where \(\lambda\) is parameter, then the value of \(\lambda\) is...

The coordinates of the foot of the perpendicular and the length of perpendicular drawn from \((0,2,3)\) to the line \(\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}\) are respectively

If \(8\overline{AB}-3\overline{AC}-5\overline{AD}=\overline{O}\), then the ratio in which the point \(B\) divides segment \(CD\) is ....

If \(x\frac{dy}{dx}=y(\log y-\log x+1)\) and its solution is \(y=[h(x)]e^{cx}\), then \(h(x)=\ldots\)

The solution of the differential equation \(x^{2}ydx-(x^{3}+y^{3})dy=0\) is

In \(\triangle ABC\), \(P\) is a point on side \(BC\) such that \(BP:PC=4:1\) and \(Q\) is a point on the segment \(AP\) such that \(AQ:QP=3:2\). If \(\vec{BQ}\) is expressed as \(\vec{BQ}=x\vec{BA}+y\vec{BC}\), then the value of \(x+y\) is:

If \(\vec{a},\vec{b},\vec{c}\) are unit vectors satisfying \(\vec{a}-(\sqrt{3})\vec{b}+\vec{c}=\vec{0}\), then the angle between \(\vec{a}\) and \(\vec{c}\) is...

The differential equation which represents the family of curves \((a+bx)e^{y/x}=x\), (where \(a\) and \(b\) are arbitrary constants); is

If \(\int _{\alpha }^{2026-\alpha }\frac{(2026-x)^{2}}{x^{2}+(2026-x)^{2}}dx=100\), then \(\alpha =\)

The area between the parabola \(y=2x-x^{2}\) and the X-axis is .....

The area bounded by the curves \(y=|x|\) and \(y=4-|x|\) is ..... sq units.

\(\int _{0}^{2}|4x-5|dx=\)

If \(\int \frac{2\,\tan x+3}{3\,\tan x+4}dx=Ax+B\log |3\,\sin x+4\,\cos x|+c\), then the values of \(A\) and \(B\) respectively are

If \(f(x)=5x^{3}+2x^{2}-3x+1\) has a local maxima and a local minima at \(x=\sin \theta ,\pi \lt \theta \lt \frac{3\pi }{2}\) and \(x=\cos \phi ,\frac{3\pi }{2}\lt \phi \lt 2\pi\) respectively, then \((\tan \theta )(\tan \phi )=\ldots\)

If \(\int \frac{x+1}{x(1+xe^{x})^{2}}dx=\log |\frac{xe^{x}}{1+xe^{x}}|+f(x)+c\), then \(f(x)=\)

If \(\int \frac{\cos \frac{x}{2}-\sin \frac{x}{2}}{\sqrt{8-\sin x}}dx=2\sin ^{-1}\left(\frac{\phi (x)}{3}\right)+c\), then \([\phi (x)]^{2}\) is equal to _____

Let \(f(x)=(a+2)x^{3}-3ax^{2}+9ax-5\). If \(f(x)\) is strictly decreasing for all \(x\in R\), then the interval in which \(a\) lies is