List of top Mathematics Questions asked in MHT CET

If a fair die is thrown, then the odds in favor of getting a perfect square on the uppermost face are:

Let \(a\) and \(b\) be the distances from the point \((2,3,4)\) to the XY plane and Y-Axis respectively. Then \(a^{2}+b^{2}=\)

Suppose that \(60\%\) of all families own a mobile set. If \(11\) families are interviewed at random, then the probability that \(8\) families own a mobile set is..... (Given that \((0.6)^{8}=0.0168\))

Let \(X\) be a continuous r. v. with p. d. f.
\(f(x)=\begin{cases} kx^{3}, & 0\leq x\leq 1 \\ 0, & \text{otherwise} \end{cases}\)
then \(P\left(X\leq \frac{3}{4}|X>\frac{1}{4}\right)=\ldots\)

If \(M\) is the foot of the perpendicular drawn from \(A(4,3,2)\) on the line joining the points \(B(2,4,1)\) and \(C(4,5,3)\), the co-ordinates of \(M\) are _____

The minimum value of \(z=4x+2y\) subject to the constraints \(3x+y\geq 27,x+y\geq 21,x+2y\geq 30,x\geq 0,y\geq 0\) is

\(\vec{a},\vec{b},\vec{c}\) represent three concurrent edges of a rectangular parallelopiped whose lengths are \(5,2\) and \(3\) units respectively, then \((\vec{a}+\vec{b}+\vec{c})\cdot (\vec{a}\times \vec{b}+\vec{b}\times \vec{c}+\vec{c}\times \vec{a})=\)

The cartesian equation of the line passing through the point \(\hat{i}+2\hat{j}+3\hat{k}\) and perpendicular to the vectors \(\hat{i}+\hat{j}+\hat{k}\) and \(2\hat{i}-\hat{j}+\hat{k}\) is

If the vector \(\vec{a}=x\hat{i}-\hat{j}+\hat{k}\) and \(\vec{b}=\hat{i}+y\hat{j}+z\hat{k}\) are collinear, then a possible unit vector parallel to the vector \(\hat{i}+y\hat{j}+z\hat{k}\) is...

The vector equation of the plane determined by the lines \(x=y,z=0\) and \(x+y=0,z=0\) is

If the point \(Q(\alpha ,\beta ,\gamma )\) is the mirror image of \(P(10,15,20)\) in the plane \(\vec{r}=\hat{k}+\lambda (-\hat{i}+\hat{j})+\mu (-\hat{i}+\hat{k})\), \(\lambda ,\mu \in \mathbb{R}\) then the value of \(3(\alpha +\beta +\gamma )\) is

If \(|\vec{a}+\vec{b}|=|\vec{a}-\vec{b}|\) then the angle between \(\vec{a}\) and \(\vec{b}\) is

The area between the curves \(y=1-|x|\) and \(y=|x|-1\) is ..... square units.

The differential equation of the equation \(y=a\cos (x+b)\) is

If \(\int _{-1}^{4}f(x)dx=4\) and \(\int _{2}^{4}(5-f(x))dx=7\) then \(\int _{2}^{-1}f(x)dx=\)

If the curve \(y=f(x)\) passes through the point \((1,2)\) and satisfies the differential equation \(xdy+(y+x^{3}y^{2})dx=0\), then the equation of curve is...

The differential equation of all parabolas which have \(4a\) as latus rectum and whose axis is parallel to the X-axis is \(2a\frac{d^{2}y}{dx^{2}}+\left(\frac{dy}{dx}\right)^{k}=0\), then the value of \(k\) is...

If \(\int _{0}^{\infty }\frac{1}{(x^{2}+1)(x^{2}+16)}dx=\frac{\pi }{k^{2}-9}\), then \(k=\ldots\)

If \(\int _{0}^{1}\tan ^{-1}\left[\frac{1}{1-x+x^{2}}\right]dx=2k\), then the value of \(k\) is:

\(\int \sqrt{x}\sec \left(x^{\frac{3}{2}}\right)\tan \left(x^{\frac{3}{2}}\right)dx=\)

\(\int \frac{4x+5}{2x+1}dx=\)

If \(f'(x)=k(\cos x-\sin x)\), \(f'(0)=5\), \(f\left(\frac{\pi }{2}\right)=19\), Then \(f(x)=\)

A water tank in the house of an inverted cone is being emptied at the rate of \(2\) cubic feet per second. The height of the cone is \(8\) feet and the radius is \(4\) feet, then the rate of change of the water level when the depth is \(6\) feet.

If \(x^{y}\cdot y^{x}=1\) then the value of \(\frac{dy}{dx}\) is

The radius of a spherical balloon increases at the rate of \(4\) cm/sec. The rate at which its surface area increases, when the radius is \(5\) metres is