List of top Mathematics Questions

The normal to the curve $y(x-2)(x-3)=x+6$ at the point where the curve intersects the y-axis passes through the point :

Let a vertical tower $AB$ have its end $A$ on the level ground. Let $C$ be the mid-point of $AB$ and $P$ be a point on the ground such that $AP = 2AB$. If $\angle BPC = \beta $, then tan $\beta$ is equal to :

Let $\omega$ be a complex number such that $2 \omega + 1 = z$ where $z = \sqrt{-3}$ ,If $\begin{vmatrix}1&1&1\\ 1&-\omega^{2} - 1 &\omega^{2}\\ 1&\omega^{2}& \omega^{7}\end{vmatrix} = 3 k , $ then $k$ is equal to :

If, for a positive integer n, the quadratic equation, $x(x+1)+(x+1)(x+2)+....+(x + \overline{ n - 1}) (x+ n)=10n$ has two consecutive integral solutions, then $n$ is equal to :

A box contains $15$ green and $10$ yellow balls. If $10$ balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls drawn is :

For any three positive real numbers a, b and c, $9(25a^2 + b^2) + 25 (c^2 - 3ac) = 15b (3a + c)$. Then :

The value of $\tan^{-1} \left[\frac{\sqrt{1+x^{2}} + \sqrt{1-x^{2}}}{\sqrt{1+x^{2}} - \sqrt{1-x^{2}}}\right] , \left|x\right| < \frac{1}{2}, x \ne0, $ is equal to :

The probability that among 7 persons, no 2 were born on the same day of a week is

For the events A and B, P(A) = \(\frac{3}{4}\), P(B) = \(\frac{1}{5}\), P(A ∩ B) = \(\frac{1}{20}\) then P(A/B) = _________

If A and B are events with P(A ∪ B) = \(\frac{3}{4}\), P(A') = \(\frac{2}{3}\) and P(A ∩ B) = \(\frac{1}{4}\) then P(B) is

Two dices are thrown simultaneously. The probability of obtaining a total score of 5 is

The angle between two diagonals of a cube is

The equation of the plane which bisects the line joining (3, 0, 5) and (1,2,-1) at right angles is

The equation of the line passing through the point (5, 3, 2) and perpendicular to the lines \(\frac{x-2}{1}=\frac{y-3}{-1}=\frac{z-4}{1}\) and \(\frac{x-1}{2}=\frac{y-1}{1}=\frac{z+1}{0}\) is

If ω is an imaginary cube root of 1, then the value of 1(2 - ω) (2 - ω²)+ 2(3 - ω) (3 - ω²)+ … + (n-1)(n - ω) (n - ω²) is

If the line \(2x+\sqrt6y=2\) touches the hyperbola x² - 2y² = 4, then the point of contact is

The equation of the tangent and normal to the ellipse x² + 2y² + 2x - 4y - 14 = 0 at (2, -1) is

The imaginary part of conjugate of \((\frac{1+i}{1-i})^5\) is

The general solution of \(\sqrt3\cos x+\sin x=\sqrt2\), for any integer “n” is

If \(\sin^{-1}(\frac{x}{5})+\cosec^{-1}(\frac{5}{4})=\frac{\pi}{2},\) then the value of x

The area enclosed between the parabolas y² = 16x and x² = 16y is

The solution of y' = e^x-y + x²e^-y is

The value of \(4\tan^{-1}(\frac{1}{5})-\frac{\pi}{4}=\)

If the function f(x) defined by
\(f(x)=\frac{x^{100}}{100}+\frac{x^{99}}{99}+...+\frac{x^2}{2}+x+1,\)
then f'(0)=

The value of the integral
∫e^x{f(x) + f'(x)} dx is