List of top Mathematics Questions

If \( \frac{1}{x^4 + 1} = \frac{Ax + B}{x^2 + \sqrt{2}x + 1} + \frac{Cx + D}{x^2 - \sqrt{2}x + 1} \), then \( BD - AC = \):
If \(\int \frac{\log(1+x^4)}{x^3} dx = f(x) \log(\frac{1}{g(x)}) + \tan^{-1}(h(x)) + c\), then \(h(x) [f(x) + f(\frac{1}{x})] =\)
A line \( L \) passes through \( (1,2,-3) \) and \( (3,3,-1) \), and a plane \( \pi \) passes through \( (2,1,-2), (-2,-3,6), (0,2,-1) \). If \( \theta \) is the angle between \( L \) and \( \pi \), then \( 27 \cos^2 \theta = \) ?

\(\int\frac{2\cos 2x}{(1+\sin 2x)(1+\cos 2x)}dx=\)

\(\int\left(\frac{x}{x\cos x - \sin x}\right)^2 dx = \)
If \( y = f(x) \) is a thrice differentiable function and a bijection, then \[ \frac{d^2x}{dy^2} \left(\frac{dy}{dx}\right)^3 + \frac{d^2y}{dx^2} = ? \]

Let f(x) = \(\int \frac{x}{(x^2+1)(x^2+3)} dx\). If f(3) = \(\frac{1}{4} \log(\frac{5}{6})\), then f(0) =

The circle S = x2 + y2 − 2x − 4y + 1 = 0 cuts the y-axis at A, B (OA: OB). If the radical axis of S ≡ 0 and S′ = x2 + y2 − 4x − 2y + 4 = 0 cuts the y-axis at C, then the ratio in which C divides AB is:

A bag contains 2 white, 3 green, and 5 red balls. If three balls are drawn one after the other without replacement, then the probability that the last ball drawn was red is:
If $$ f(x) = \min \{ x, x^2 \} $$ Which of the following is true? 
If \(x^2 + 5ax + 6 = 0\) and \(x^2 + 3ax + 2 = 0\) have a common root, then that common root is:
The real part of \( \frac{\left( \cos a + i \sin a \right)^6}{\left( \sin b + i \cos b \right)^8} \) is:

Evaluate the following determinant: \( \begin{vmatrix} 1 & 1 & 1 \\ a^2 & {b^2} & {c^2} \\ {a^3} & {b^3} & {c^3} \\ \end{vmatrix} \)

A ray of light passing through the point (2, 3) reflects on the Y-axis at a point P. If the reflected ray passes through the point (3, 2) and P = (a, b), then 5b = ?
If m and M denote the mean deviations about mean and about median respectively of the data 20, 5, 15, 2, 7, 3, 11, then the mean deviation about the mean of m and M is:
Find the sum of the first 10 terms of the sequence \( 2.5 + 5.9 + 8.13 + 11.17 + \cdots \ to \ 10 \ terms =\):
If the roots of the equation \( x^3 - 13x^2 + Kx - 27 = 0 \) are in geometric progression, then \( K = \):

If the area of the circum-circle of the triangle formed by the line 2x + 5y + a = 0 and the positive coordinate axes is \(\frac{29\pi}{4}\) sq. units, then |a| =

Point (-1, 2) is changed to (a, b) when the origin is shifted to the point (2, -1) by translation of axes. Point (a, b) is changed to (c, d) when the axes are rotated through an angle of 45$^{\circ}$ about the new origin. (c, d) is changed to (e, f) when (c, d) is reflected through y = x. Then (e, f) = ?

Out of the first 5 consecutive natural numbers, if two different numbers x and y are chosen at random, then the probability that x4- y4 is divisible by 5 is:

There are 2 bags each containing 3 white and 5 black balls and 4 bags each containing 6 white and 4 black balls. If a ball drawn randomly from a bag is found to be black, then the probability that this ball is from the first set of bags is:
In a consignment of 15 articles, it is found that 3 are defective. If a sample of 5 articles is chosen at random from it, then the probability of having 2 defective articles is:
The smallest positive value (in degrees) of \( \theta \) for which \( \tan(\theta + 100^\circ) = \tan(\theta + 50^\circ) \tan(\theta - 50^\circ) \) is valid, is:
The value of \( 5 \cos \theta + 3 \cos \left( \theta + \frac{\pi}{3} \right) + 3 \) lies between:
Statement (S1): \( \sin 55^\circ + \sin 53^\circ - \sin 19^\circ - \sin 17^\circ = \cos 2^\circ \)
Statement (S2): The range of \( \frac{1}{3 - \cos 2x} \) is \( \left[ \frac{1}{4}, \frac{1}{2} \right] \) Which one of the following is correct?