List of top Mathematics Questions

If a random variable \(X\) has a probability mass function \(P(x) = \{\begin{array}{cc}kx^2, & \text{for }x = 1,2,3,4 \\ 0, & \text{otherwise}\end{array}\), then the mean of \(X\) is ...

If \(d\) is the distance of point (2, 5, 10) from the plane containing the lines \(\overset{̄}{r} = (4\hat{j}-\hat{k})+λ(\hat{i}+2\hat{j}-2\hat{k})\) and \(\overset{̄}{r} = (2\hat{i}+\hat{j})+μ(\hat{i}+2\hat{j}-2\hat{k})\), then \(d^2 =\)

If a fair coin is tossed 8 times, then the probability of getting at most 2 heads is...

The vector equation of plane in parametric form, passing through the points (-1, 2, 0), (2, 2, -1) and parallel to the line \(\frac{x-1}{1} = \frac{2y+1}{2} = \frac{z+1}{-1}\) is

Let \(\overset{̄}{a},\overset{̄}{b}\) and \(\overset{̄}{c}\) be three coplanar unit vectors. A unit vector \(\overset{̄}{d}\) is perpendicular to them. If \((\overset{̄}{a}\times \overset{̄}{b})\times (\overset{̄}{c}\times \overset{̄}{d}) = \frac{3}{26}\hat{i}-\frac{2}{13}\hat{j}+\frac{6}{13}\hat{k}\) and the angle between \(\overset{̄}{a}\) and \(\overset{̄}{b}\) is \(30^{\circ}\), then \(\overset{̄}{c}\) is equal to...

If \(\overset{̄}{a} = 4\hat{i}+\hat{j}+\hat{k}\), \(\overset{̄}{b} = 2\hat{i}+\hat{j}+2\hat{k}\) and \(\overset{̄}{c} = 3\hat{i}+4\hat{j}+5\hat{k}\), then \((\overset{̄}{a}+\overset{̄}{b})\cdot (\overset{̄}{b}+\overset{̄}{c}) =\)

The volume of a parallelopiped with coterminous edges \(\overset{̄}{a},\overset{̄}{b},\overset{̄}{c}\) is 3 cubic units. The volume (in cubic units) of a tetrahedron with coterminous edges \((\overset{̄}{a}\times \overset{̄}{b}),(\overset{̄}{a}\times 2\overset{̄}{c}),(\overset{̄}{b}\times 2\overset{̄}{c})\) is...

If the lines \(2x = ky = -z\) and \(6x = -y = -4z\) are perpendicular to each other then the value of \(k\) is ...

If \(\overset{̄}{a} = 2\hat{i}+\hat{j}-\hat{k}\), \(\overset{̄}{b} = \hat{i}+3\hat{k}\) and \(\overset{̄}{c}\) is a unit vector, then the maximum value of the scalar triple product \([\overset{̄}{a} \overset{̄}{b} \overset{̄}{c}]\) is

For the differential equation \(\frac{d^3y}{dx^3}+cos(\frac{d^2y}{dx^2}) = 0\), which of the following is true ?

If water at \(100^{\circ}\text{C}\) cools in 10 minutes to \(80^{\circ}\text{C}\) and to \(65^{\circ}\text{C}\) in the next 10 minutes, then the room temperature will be ...

The equation of a line in cartesian form passing through (0, 0, 0) and (4, 3, c) and parallel to \(\overset{⃗}{a}\times \overset{⃗}{b}\) where \(\overset{⃗}{a} = 2\hat{i}+\hat{j}+2\hat{k}\), \(\overset{⃗}{b} = 3\hat{i}-4\hat{j}\) is

If \(f(x)\) is a polynomial such that \(f(x) = [f^'(x)]^2\) and \(f(2) = 0\), then \(f(-2) = \ldots\)

The equation of the curve passing through the point (0, 1) and having a slope of the tangent at point \(P(x,y)\) is equal to \(\frac{y}{x+y}\), is

The area of the region enclosed by the lines \(y = 2x,2y = x\) and \(x = 2\) (in sq.units) is...

\(\int \frac{x^4+1}{x^6+1}dx =\)

If \(a > 0,b > 0\) and \(\int \frac{1}{ax^2+b}dx = \frac{1}{\sqrt{6}}tan^{-1}(\frac{\sqrt{2}x}{\sqrt{3}})+c\), then \(\int \frac{1}{bx^2+a}dx = \ldots\)

The value of \(\int _{-π}^π\frac{2x(1+sinx)}{1+cos^2x}dx\) is...

The area of the region common to the parabolas \(4y^2 = 9x\) and \(3x^2 = 16y\) is...

The value of integral \(\int _0^1cot^{-1}(1+x^2-x)\,dx\) is...

The equation of tangent to the curves \(x = 1-3t^2\) and \(y = t-3t^3\) at the point \((-2,2)\) is...

If \(y = cos^{-1}(\frac{1-4^x}{1+4^x})\), then \(\frac{dy}{dx}\) at \(x = 1\) is

A spherical snow ball is melting so that its volume is decreasing at the rate of 8 c.c./sec then the rate of change of radius when the radius is 2 cm, is :

If \(f(x) = cosx\), then the value of \(\int \frac{e^{f(x)}(xsin^3x+f(x))}{1-(f(x))^2}dx =\)

A cylindrical tank without a top lid is being manufactured to hold a fixed volume of \(125π\) cubic cm. The minimum surface area required to construct this tank is ............square cm