List of top Mathematics Questions

If the points \((a,0),(0,b)\) and \((1,1)\) are collinear, then \(\frac{1}{a}+\frac{1}{b} =\)
For any y∈R, let cot\(^{-1}\)(y) ∈ (0,π) and tan\(^{-1}\)(y) ∈ (\(-\frac{\pi}{2},\frac{\pi}{2}\)). Then the sum of all the solutions of the equation\(tan^{-1}(\frac{6y}{9-y^2})+cot^{-1}(\frac{9-y^2}{6y})=\frac{2\pi}{3}\, for\,0<|y|<3,\) is equal to

If the roots of the equation z2 - i = 0 are α and β, then | Arg β - Arg α | =

The period of function f(x) = \(e^{log(sinx)}+(tanx)^3 - cosec(3x - 5)\)is

Akhilesh and Javed started a business by investing 50,000 and 60,000 respectively. Akhilesh being an active partner receives 12.5% of the profit in addition to his share of profit. How much Akhilesh gets out of a profit of 8800?
A circle with centre 'O', 'P' is a point outside the circle and PA and PB are two tangents to the circle at the point of contacts 'A' and 'B' from 'P'. If the length of PA 10 cm, then the length of PB =
Distance between the points (4,-8), (5,-2) is
S $ \equiv x^2 + y^2 - 2x - 4y - 4 = 0 $ and $ S' \equiv x^2 + y^2 - 4x - 2y - 16 = 0 $ are two circles. The point $ (-2, -1) $ lies
The total number of terms in the expansion of $ (x + y)^{60} + (x - y)^{60} $ is
3 and 5 are intercepts of a line $L = 0$, then the distance of $L = 0$ from $(3, 7)$ is
The slope of lines which makes an angle $60^\circ$ with the line $y - 3x + 18 = 0$ is
The distance of the point (3, 4) from the line $3x + 2y + 7 = 0$ measured along the line parallel to $y - 2x + 7 = 0$ is equal to
Let the equation of pair of lines $ y = m_1x $ and $ y = m_2x $ be written as $ (y - m_1x)(y - m_2x) = 0 $. Then, the equation of the pair of the angle bisector of the line $ 3y^2 - 5xy - 2x^2 = 0 $ is
A polygon of $ n $ sides has 105 diagonals, then $ n $ is equal to
The total number of numbers greater than 1000 but less than 4000 that can be formed using 0, 2, 3, 4 (using repetition allowed) are
There are 10 points in a plane out of which 4 points are collinear. How many straight lines can be drawn by joining any two of them?
If $ \left( \frac{3}{2} + i \frac{\sqrt{3}}{2} \right)^{50} = 3^{25}(x + iy) $, where $x$ and $y$ are real, then the ordered pair $(2x, 2y)$ is
If $i = \sqrt{-1}$ and $n$ is a positive integer, then $i^n + i^{n+1} + i^{n+2} + i^{n+3}$ is equal to
If $ z = \sqrt{3} + i $, then the argument of $ z^2 e^{-i} $ is equal to
If $ n(A) = p $ and $ n(B) = q $, then the number of relations from the set $ A $ to the set $ B $ is
If $ A = \{a, b, c\}, B = \{b, c, d\} $ and $ C = \{a, d, c\} $, then $ (A - B) \times (B \cap C) $ is equal to
The solution x1 = 1, x2 = 1, x3 = 0 and z = 3 to the system of equations
x1+x2+x3=2
x1+x2-x3=2
x1,x2,x3≥0
which minimizes z = x1 + 2x2 + 3x3 is

A straight line parallel to the line y = √3 x passes through Q(2,3) and cuts the line 2x + 4y - 27 = 0 at P. Then the length of the line segment PQ is

If $2f(x^2) + 3f\left( \frac{1}{x^2} \right) = x^2 - 1$, for $x \in \mathbb{R} - \{0\}$, then $f(x^8)$ is equal to

The general solution of $ 2 \cos 4x + \sin^2 2x $= 0  is