List of top Mathematics Questions

The number of permutations of the letters of the word INSTITUTION are .......

A random variable \(X\sim B(n,p)\) follows a binomial distribution with \(n = 6\). If \(9P(X = 4) = P(X = 2)\), then the probability of success \(p\) is..

Let X be a continuous random variable with the probability density function(p.d.f.) given by
\(f(x) = \left\{ \begin{array}{cc}kx, & 0\leq x < 1 \\ k, & 1\leq x < 2 \\ -kx+3k, & 2\leq x < 3 \\ 0, & \text{otherwise}\end{array} \right.\)
\(P(2 < X\leq 3) = \cdots\)

In a certain city, the ratio of men to women is \(5:4\). It is found that \(80\%\) of men and \(90\%\) of women are literate. If a person selected at random is found to be illiterate, then the probability that the person is a man is....

The difference between the maximum value and the minimum value of the objective function \(z = 3x+y\) subject to the constraints \(2x+3y\leq 6\), \(x+y\geq 1\), \(x\geq 0\), \(y\geq 0\) is....

If M denotes the midpoint of the line joining A\((4,5,-10)\) and B\((-1,2,1)\), then the equation of the plane through M and perpendicular to AB is:

If \(\overset{̄}{a}\), \(\overset{̄}{b}\) and \(\overset{̄}{c}\) are three vectors such that \(|\overset{̄}{a}+\overset{̄}{b}+\overset{̄}{c}| = 1\), \(\overset{̄}{c} = λ(\overset{̄}{a}\times \overset{̄}{b})\) and \(|\overset{̄}{a}| = \frac{1}{\sqrt{3}}\), \(|\overset{̄}{b}| = \frac{1}{\sqrt{2}}\), \(|\overset{̄}{c}| = \frac{1}{\sqrt{6}}\), then the angle between \(\overset{̄}{a}\) and \(\overset{̄}{b}\) is

Let \(\overline{OD} = \hat{i}+2\hat{j}+6\hat{k}\), \(\overline{CB} = -3\hat{i}-2\hat{k}\) be the diagonals of the parallelogram OBDC and \(\overline{OA} = \hat{i}+2\hat{j}+3\hat{k}\) be another vector. Then the volume of a parallelopiped determined by vectors \(\overline{OA}\), \(\overline{OB}\), and \(\overline{OC}\) (in cubic units), is

The acute angle between the line \(\overset{⃗}{r} = (\hat{i}+2\hat{j}+\hat{k})+λ(\hat{i}+\hat{j}+\hat{k})\) and the plane \(\overset{⃗}{r}\cdot (2\hat{i}+p\hat{j}+\hat{k}) = 8\) is \(sin^{-1}(\frac{\sqrt{2}}{3})\), then the value of \(p\) are...

The shortest distance between the lines \(\frac{x-3}{3} = \frac{y-8}{-1} = \frac{z-3}{1}\) and \(\frac{x+3}{-3} = \frac{y+7}{2} = \frac{z-6}{4}\) is

A plane meets the co-ordinate axes in A, B, C such that the centroid of the triangle ABC is the point \((1,r,r^2)\), then the equation of the plane is,

If \(\overset{̄}{a}\) and \(\overset{̄}{b}\) are unit vectors perpendicular to each other, then \([\overset{̄}{a}+(\overset{̄}{a}\times \overset{̄}{b})\,\overset{̄}{b}+(\overset{̄}{a}\times \overset{̄}{b})\,(\overset{̄}{a}\times \overset{̄}{b})] = \cdots\)

The volume of the tetrahedron whose vertices are A\((-1,2,3)\), B\((3,-2,1)\), C\((p,1,3)\), D\((-1,-2,4)\) is \(\frac{16}{3}\) cubic units then the value of p is

Let \(\overset{̄}{a} = \hat{i}+\hat{j}+\hat{k}\), \(\overset{̄}{b} = \hat{i}-3\hat{j}+2\hat{k}\) and \(\overset{̄}{c} = 3\hat{i}-2\hat{k}\). If a vector \(\overset{̄}{p}\) satisfies the conditions \(\overset{̄}{p}\cdot \overset{̄}{c} = 0\) and \(\overset{̄}{p}\times \overset{̄}{a} = \overset{̄}{b}\times \overset{̄}{a}\), then the value of \(|\overset{̄}{p}| =\)...

If \(tanx\) is an integrating factor of the differential equation \(\frac{dy}{dx}+Py = Q\), then \(P\) can be

If \(y = f(x)\) is a monotonically increasing function such that \((\frac{dy}{dx})^2 = 6-\frac{dy}{dx}\) and \(y(0) = 5\), then \(y(3) = \cdots\)

The order and degree of the differential equation \((\frac{d^3y}{dx^3})^{\frac{2}{3}}-3\frac{d^2y}{dx^2}+5\frac{dy}{dx}+4 = 0\) are respectively

The area of the region lying in the first quadrant and bounded by the curve \(y = 4x^2\), the Y-axis, and the lines \(y = 2\), \(y = 4\) is...

The value of \(\int sin4xcos3x\,dx\) is

The area bounded by the curves \(y = |x|-1\) and \(y = -|x|+1\) is

If \(\int _0^1\frac{dx}{\sqrt{x+1}-\sqrt{x}} = \sqrt{2}k\), then the value of \(k\) is...

If \([x]\) denotes the greatest integer less than or equal to \(x\), then the value of the integral \(\int _0^2x^2[x]\,dx\) is equal to

\(\int (e^{log(sinx)}+cosx)x\,dx =\)

A spherical iron ball \(10\) cm in radius is coated with a layer of ice of uniform thickness that melts at a rate of \(50 \text{cm}^3/\text{min}\). When the thickness of ice is \(5\) cm, the rate at which the thickness of ice decreases is...

If the line \(ax+by+5 = 0\) is a normal to the curve \(xy = 1\) then .....