List of top Mathematics Questions

If \(w\) is a complex cube root of unity , then the value of \(w^{10}-w^7+w^5-w^2+1\) is.
Bag A contains 3 white and 5 black balls while bag B contains 4 white and 3 black balls. A ball is selected at random from bag A and put in bag B. If a ball is now selected at random from bag B then the probability that this ball is white ball is...
The lengths of the shadows of a tree of height p, thrown by sun's rays at three different moments are p, 2p and 3p. The sum of the angles of elevation of the sun's rays at these three moments is equal to...
The probability that a bomb will hit the target is \(0.8\). Out of 6 bombs dropped, probability that at least 1 will miss the target is...
A line passing through the points \((1,-1,2)\) and \((2,0,1)\) meets the XY plane and the YZ plane at points A and B respectively. The distance AB is equal to...
The shortest distance between the lines \(\overset{⃗}{r} = (4\hat{i}-\hat{j})+λ(\hat{i}+2\hat{j}-3\hat{k})\) and \(\overset{⃗}{r} = (\hat{i}-\hat{j}+2\hat{k})+μ(\hat{i}+4\hat{j}-5\hat{k})\) is...
An airplane can carry a maximum of \(250\) passengers. A profit of Rs \(1500\) is made on each executive class ticket and a profit of Rs \(900\) is made on each economy class ticket. The airline reserves at least \(30\) seats for executive class. However at least \(4\) times as many passengers prefer to travel by economy class than by executive class. Let \(x_1\) be the number of passengers of executive class and \(x_2\) be the number of passengers of economy class. Formulate the LPP in order to maximize the profit for the airline...
Let \(\overset{⃗}{r}\cdot (3\hat{i}-2\hat{j}+7\hat{k}) = 32\) is the equation of a plane and the line having direction ratios \((5,b,3)\) is parallel to the plane, then the value of b is...
Two cards are drawn at random from a box which contains 5 cards numbered 1, 1, 2, 2 & 3. If X denotes the sum of the numbers, then the expected value of X is...
Let O\((0,0)\), A\((-1,2)\) and B\((1,3)\) be the vertices of \(△\)OAB. The bisector of angle O intersects side AB at point D. The value of \(\overset{⃗}{OD}\cdot \overset{⃗}{AB}\) is equal to...
The solution of the differential equation \(\frac{dy}{dx} = cos(x+y)\) is...
The perpendicular distance from the origin to the plane containing the points \((1,-2,1),(2,-1,-3)\) and \((0,1,5)\) is...(in units)
The maximum volume of a parallelopiped (in cubic units) with vectors \((2a\hat{i}+\hat{k}),(a\hat{j}-a\hat{k})\), and \((3\hat{i}+a\hat{j})\), where \(a\in [0,1]\), as its coterminous edges is...
If \(\overset{⃗}{a},\overset{⃗}{b},\overset{⃗}{c}\) are three vectors such that \(\overset{⃗}{a}⟂(\overset{⃗}{b}+\overset{⃗}{c}),\overset{⃗}{b}⟂(\overset{⃗}{c}+\overset{⃗}{a}),\) and \(\overset{⃗}{c}⟂(\overset{⃗}{a}+\overset{⃗}{b})\) and \(|\overset{⃗}{a}| = 1,|\overset{⃗}{b}| = 2,|\overset{⃗}{c}| = 3\), then \(|\overset{⃗}{a}+\overset{⃗}{b}+\overset{⃗}{c}|\) is...
If \(α,β,γ\) are the direction angles of the line \(x = 4z+3\) and \(y = 2-3z\), then the value of \(cosα+cosβ+cosγ\) is...
The area (in sq. units) of the region bounded by the curve \(y = 2x-x^2\) and the X-axis is...
The area (in square units) of the region bounded by the circle \(x^2+y^2 = 9\) and the parabola \(y^2\leq 8x\) is...
If the solution of the differential equation \((1+x^3)\frac{dy}{dx}+6x^2y = 1+x^2\) is \(y = \frac{1}{(1+x^3)^s}[x+\frac{x^p}{p}+\frac{x^q}{q}+\frac{x^r}{r}+c]\), then the LCM of \(p,q,r\) and \(s\) is...
The differential equation of all lines where the length of the normal from the origin is p and the inclination of the normal is \(α\) is... (where p and \(α\) are arbitrary constants)
The value of integral \(\int _0^{\infty}\frac{1}{1+e^x}\,dx\) is...
If \(f(x)\) is an antiderivative of \(\frac{x+1}{\sqrt{x-1}}\) with respect to \(x\), then value of \(f(5)-f(2)\) is...
If the rate of increase of surface area of a spherical balloon is \(5\,\text{cm}^2/\text{sec}\) and rate of increase of volume of a spherical balloon is \(10\,\text{cm}^3/\text{sec}\), then the radius of the balloon at that time is...
If \(3y^2-2xy-x = 0\), then the value of \(\frac{dy}{dx}\) at \(y = 2\) is...
The value of integral \(\int x^3cosx\,dx\) is...
If \(f(x) = |5x-3|\) is defined on interval \([0,1]\), then the value of \(\int _0^1f(x)\,dx\) is...