List of top Mathematics Questions

The equation of the straight line passing through the point \((-5,3)\) such that the portion of the line intercepted between the axes is divided by the point in the ratio \(4:3\) (from the X-axis to the Y-axis) is...

If \(sin3α = 4sinα\cdot sin(x+α)\cdot sin(x-α)\) where \(α\neq nπ,n\in Z\), then all possible values of \(x\) are given as

The general solution of \(cosθ-sinθ = 1\) is

If the equation \(kx^2-5xy+6y^2+x-3y = 0\) represents a pair of straight lines, then the co-ordinates of their point of intersection are

If \(x = \sqrt{-1-\sqrt{-1-\sqrt{-1-\ldots \infty }}}\), where \(ω\) is a non-real complex cube root of unity, then the value of \(x\) is...

The quadratic polynomial \(p(x)\) has roots \(1\) and \(α\), while quadratic polynomial \(q(x)\) has roots \(1\) and \(β\). Let \(α\) and \(β\) be the roots of \(r(x) = p(x)+q(x)\). Then \(\underset{x\rightarrow \infty }{lim}[\sqrt{p(x)}-\sqrt{q(x)}] =\)

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

A random variable X has the following probability distribution

\(X = x\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)
\(P(X = x)\)	\(0.15\)	\(0.23\)	\(0.10\)	\(0.12\)	\(0.20\)	\(0.08\)	\(0.07\)	\(0.05\)

For the events \(E = \{X\text{ is a prime number}\}\), \(F = \{X < 4\}\), \(P(E\cup F)\) is

The odds in favour of A winning a game of table tennis against B are 1:2. If 3 games are to be played, then the probability of A winning at least two games out of the three is.....

Let \(X\sim B(6,\frac{1}{2})\). Then the maximum probability occurs at

The shortest distance between the lines, where the first line passes through \((0,0,0)\) and \((2,0,3)\) and the second line passes through \((2,5,0)\) and \((0,4,0)\) is

Let a plane P pass through the point \((3,7,-7)\) and contain the line \(\frac{x-2}{-3} = \frac{y-3}{2} = \frac{z+2}{1}\). If the distance of the plane P from the origin is d, then \(d^2\) is

The point having position vector \(4\hat{i}-11\hat{j}+2\hat{k}\) lies on the line

In L.P.P., the corner points of the feasible region for the constraints \(3x-y\geq 6,x\leq 3,y\leq 2,y\geq 0,x\geq 0\) are .....

A vector \(\overset{̄}{r}\) of magnitude \(3\sqrt{2}\) units which makes angles of \(\frac{π}{4}\) and \(\frac{π}{2}\) respectively with Y and Z axes is

The plane \(\frac{x}{2}+\frac{y}{3}+\frac{z}{4} = 1\) cuts the co-ordinate axes at the points A, B, C respectively. Then the area of triangle ABC is

Let \(\overset{̄}{a},\overset{̄}{b},\overset{̄}{c}\) be three vectors having magnitudes 1, 1 and 2 respectively. If \(\overset{̄}{a}\times (\overset{̄}{a}\times \overset{̄}{c})+\overset{̄}{b} = \overset{̄}{0}\), then the acute angle between \(\overset{̄}{a}\) and \(\overset{̄}{c}\) is

A spherical balloon expands at a rate proportional to its surface area. Initially its radius is 2 cm and 5 minutes later it increases upto 7 cm, then surface area of spherical balloon after 12 minutes will be

If a parallelogram is constructed on the vectors \(\overset{̄}{a} = 3\overset{̄}{p}-\overset{̄}{q},\overset{̄}{b} = \overset{̄}{p}+3\overset{̄}{q}\) and \(|\overset{̄}{p}| = 3,|\overset{̄}{q}| = 2\) and angle between \(\overset{̄}{p}\) and \(\overset{̄}{q}\) is \(\frac{π}{3}\), then the ratio of the lengths of adjacent sides \(\overset{̄}{a}\) and \(\overset{̄}{b}\) of the parallelogram is

Let \(\overset{̄}{a},\overset{̄}{b},\overset{̄}{c}\) be unit vectors such that \(\overset{̄}{a}\) is perpendicular to the plane of \(\overset{̄}{b}\) and \(\overset{̄}{c}\). If the angle between \(\overset{̄}{b}\) and \(\overset{̄}{c}\) is \(\frac{π}{3}\), then \(|\overset{̄}{a}+\overset{̄}{b}+\overset{̄}{c}| =\)

The volume of a tetrahedron with vertices \(5\hat{i}-\hat{j}+\hat{k},7\hat{i}-4\hat{j}+p\hat{k},\hat{i}-6\hat{j}+10\hat{k}\) and \(-\hat{i}-3\hat{j}+7\hat{k}\) is 11 cubic units, then one of the values of p is

The value of the integral \(\int _{-\sqrt{3}}^{\sqrt{3}}\frac{(2x^9+3x^8-5x^7+9x^6+4x^3-x+3)}{x^2+3}\,dx\) is

\(\int \frac{30x^{14}+15^xlog225}{x^{15}+15^x}\,dx =\)

If \(\int _0^a\frac{dx}{1+4x^2} = \frac{π}{8}\), then \(a =\)

\(\int e^{2x}\frac{2(sin2xcos2x-1)}{2sin^22x}\,dx = A\,e^{2x}cot2x+c\)
(Where c is the constant of integration.), then \(A^3 =\)