List of top Questions asked in MHT CET

The sum and product of mean and variance of a binomial distribution are 3 and 2 respectively. Then, \(P(X>0)=\ldots\)

The position vector of a point \(P\), such that \(OP\) inclined to the X axis at \(45^{\circ }\) and to the Y axis at \(60^{\circ }\) and \(|OP|=12\) units is:

A random variable X takes the values 0, 1, 2, 3 and its mean is \(1.3\). If \(P(X=3)=2P(X=1)\) and \(P(X=2)=0.3\), then \(P(X=0)\) is

The minimum value of \(Z=4x+6y\), subject to constraint \(x+2y\geq 80,3x+y\geq 75,x\geq 0,y\geq 0\) is:

The scalar triple product of the vectors \([2\bar{a}+3\bar{b}\ \ 3\bar{b}+\bar{c}\ \ \bar{c}+2\bar{a}]\) is equal to:

If the vector \(\bar{r}\) is perpendicular to \(\hat{i}-\hat{k}\) and \(\bar{r}\times (\hat{i}+x\hat{j}-\hat{k})=\hat{i}+2\hat{j}+3\hat{k}\), then the value of \(\bar{r}\cdot (\hat{i}+x\hat{j}-\hat{k})=\)

\(A(1,2)\), \(B(1,0)\) and \(C(0,2)\) are vertices of \(\Delta ABC\). The position vector of the point in which the bisector of angle \(A\) cuts \(BC\) is .....

The equation of the plane containing the line \(\frac{x+1}{4}=\frac{y-2}{-1}=\frac{z+5}{3}\) and parallel to the vector \(\hat{i}+\hat{j}-\hat{k}\) is \(ax+by+cz=9\). Then, the value of \(a+b-c\) is:

The equation of the plane that perpendicularly bisects the line segment joining the points \(A(2,-1,3)\) and \(B(3,1,0)\) is:

The angle between the line \(\frac{x+1}{1}=\frac{y-2}{2}=\frac{z-3}{3}\) and the plane \(3x+4y+z+5=0\) is:

The distance of the point \((1,1,1)\) from the line passing through the point \((2,3,4)\) whose direction ratios are \(2,-3,6\) is:

A body cools from \(100^{\circ }\)C to \(80^{\circ }\)C in 5 minutes in air at \(20^{\circ }\)C. The time taken to cool from \(80^{\circ }\)C to \(60^{\circ }\)C will be:

If the general solution of the differential equation \(\frac{dy}{dx}=\cos (2x-3y)-\cos (2x+3y)\) is \(\cos 2x=g(y)+c\), then \(g(y)=\ldots\)

If \(\int _{0}^{f(x)}dt=x\cos (\pi x)\) then \(f'(4)=\ldots\)

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

The value of \(\lim _{n\rightarrow \infty }\left(\frac{n}{(n+1)\sqrt{2n+1}}+\frac{n}{(n+2)\sqrt{2(2n+2)}}+\frac{n}{(n+3)\sqrt{3(2n+3)}}+\cdots +\frac{1}{2n\sqrt{3}}\right)\) is:

\(\int \frac{x^{3}+x^{2}+2x+1}{x^{2}-x+1}dx=\ldots\)

If \(\int [\sin (\log x)-\cos (\log x)]dx=xf(x)+c\), then the value of \(f(x)\) is:

A student learned 100 Math formulae for an examination. The number of formulae the student can remember in '\(t\)' days after learning is given by \(f(t)=100(1-0.1t)^{2}\). Then, the magnitude of the rate at which the student forgets the formula 3 days after learning is:

\(\int \sec ^{2}2x\cdot \text{cosec}^{2}2xdx=\ldots\)

Let \(f(x)\) be odd and continuous on \([-a,a]\). Then the value of \(\int _{-a}^{a}xf(x^{2})dx\) is:

\(\int \tan ^{-1}\sqrt{x}dx=\ldots\)

If \(y=\sin ^{-1}(y\cdot \cos 2x)\) such that \(\frac{dy}{dx}=\frac{2y\cdot f(x)}{g(x)-\cos y}\) then \(\{f(x)\}^{2}-\{g(x)\}^{2}=\)

Let \(f(x)\) be a twice differentiable function such that \(f^{''}(x)=-f(x)\), and \(f'(x)=g(x)\).
Let \(h(x)=\{f(x)\}^{2}+\{g(x)\}^{2}\). If \(h(2)=7\), then \(h(8)\) is equal to: