List of top Mathematics Questions asked in MHT CET

The Incenter of the triangle whose vertices are \(A(0,3,0)\), \(B(0,0,4)\), and \(C(0,3,4)\) is;

The probability mass function (p.m.f.) of a random variable X is as follows:
\(P(X=0)=3k^{3},\ P(X=1)=4k-10k^{2},\ P(X=2)=5k-1,\ P(X=x)=0\) for any value of \(x\), then the value of \(k\) is:

If \(X\sim B(10,0.4)\), then the probability that \(X\) takes a value at least 2 is:

The L.P.P. Maximize \(Z=0.75x+0.5y\) subject to \(3x+2y\leq 6\), \(x+4y\leq 4\), \(x\geq 0\), \(y\geq 0\) has

Two fair dice are tossed simultaneously. Let \(A\) be the event that the sum of the numbers is prime, and \(B\) be the event that at least one die shows a number 5. The odds against the occurrence of event \(B\) given that event \(A\) has already occurred is:

If the angle between the line \(x=\frac{y-5}{2}=\frac{z+8}{k}\) and the plane \(2x-3y+3z=9\) is \(\cos ^{-1}\left(\sqrt{\frac{13}{22}}\right)\), then \(k=\ldots\)

Consider the lines
\(L_{1}:\frac{x}{2}=\frac{y}{2}=-z,\)
\(L_{2}:\frac{x-1}{1}=\frac{y-1}{2}=\frac{z-3}{2}.\)
The unit vector perpendicular to both \(L_{1}\) and \(L_{2}\) is:

The coordinates of the foot of the perpendicular drawn from the point \(P(-1,3,2)\) to the line formed by the intersection of the planes \(x+y+z=1\) and \(2x-y+z=2\) are:

If \(\bar{a}=\hat{i}+2\hat{j}+2\hat{k}\), \(\bar{b}=2\hat{i}-2\hat{j}+\hat{k}\) and \(\bar{c}\) is a vector projection of \(\bar{a}\) on the line of \(\bar{b}\), then the value of \([2\bar{a}\ 3\bar{b}\ \sqrt{3}\bar{c}]\) is

If the lines \(\frac{1-x}{3}=\frac{3y-1}{2\lambda +1}=4-z\) and \(\frac{x+2}{2\mu }=\frac{1-2y}{6}=\frac{5-z}{7}\) are perpendicular, then \(3\mu +\lambda =\ldots\)

If \(|\bar{a}|=24\), \(|\bar{b}|=7\), \(\bar{a}\cdot \bar{b}=0\), \(\bar{a}+\bar{b}+\bar{c}=\bar{0}\), then \(|\bar{c}|=\ldots\)

An ice ball melts. The rate at which it melts is proportional to the amount of the ice at that time. If half quantity of ice melts in \(20\) minutes, then the time when \((1/8)^{th}\) part of original amount of the ice is left is:

The order and degree of the differential equation \(e^{\frac{dy}{dx}}+\frac{dy}{dx}=x\) is

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

If the scalar products of a vector \(\bar{a}=x\hat{i}+y\hat{j}+z\hat{k}\) with \(2\hat{i}+\hat{j}+\hat{k},\ \hat{i}-\hat{j}+\hat{k},\ \hat{i}+2\hat{j}+3\hat{k}\) are \(5,3,\) and \(5\) respectively, then \(x+y+z=\ldots\)

Let \(\bar{a}=2\hat{i}+\hat{k},\ \bar{b}=\hat{i}+\hat{j}+\hat{k},\) and \(\bar{c}=4\hat{i}-3\hat{j}+7\hat{k}\). If \(\bar{r}\) is a vector such that \(\bar{r}\times \bar{b}=\bar{c}\times \bar{b}\) and \(\bar{r}\cdot \bar{a}=0\), then the value of the scalar product \(\bar{r}\cdot \hat{i}\) is:

The area of the region bounded by the line \(4x+3y=12\), the X-axis, and the lines \(x=-1\) and \(x=2\) (in sq units) is:

If \(\int _{-1}^{4}f(x)dx=9\) and \(\int _{2}^{4}(7-f(x))dx=10\), then \(\int _{2}^{-1}f(x)dx=\)

\(\int _{\pi /6}^{\pi /3}\sin 2x\log (\tan x)\ dx=\ldots\)

\(\int \frac{x}{x^{5/2}+4x^{3/2}}\ dx=\ldots\)

The integral \(\int \frac{\csc x}{\cos ^{2}[1+\log (\tan \frac{x}{2})]}\ dx\) is equal to:

\(\int e^{x}\left(\log (\sin x)+\sqrt{\frac{1+\cos 2x}{1-\cos 2x}}\right)dx=\ldots\)

A man of height \(1.2\) m is moving away from the lamp post at the rate \(0.6\) m/sec. If the height of the lamp post is \(4.8\) m, then the rate at which the shadow of the man is lengthening is:

The derivative of \(f(\cos x)\) with respect to \(g(\tan x)\) at \(x=\frac{\pi }{6}\), given that \(f'\left(\frac{\sqrt{3}}{2}\right)=4\) and \(g'\left(\frac{1}{\sqrt{3}}\right)=2\) is:

The approximate surface area of a sphere of radius \(2.01\) cm is