List of top Mathematics Questions

$\cos(13^\circ)\sin(17^\circ)\sin(21^\circ)\cos(47^\circ) =$
$\sin\left(\frac{\pi}{5}\right) + \sin\left(\frac{2\pi}{5}\right) + \sin\left(\frac{3\pi}{5}\right) + \sin\left(\frac{4\pi}{5}\right) =$
The sum of the solutions of $\cos x \sqrt{16 \sin^2 x} = 1$ in $(0, 2\pi)$ is
If $\cot(\cos^{-1} x) = \sec\left(\tan^{-1}\left(\frac{a}{\sqrt{b^2 - a^2}}\right)\right)$, $b>a$, then $x =$
If $\frac{3x^2 - 7x + 1}{(x - 2)^3} = \frac{A}{x - 2} + \frac{B}{(x - 2)^2} + \frac{C}{(x - 2)^3}$, then $A(B + C + D + E) =$
The number of integers between 10 and 10,000 such that in every integer every digit is greater than its immediate preceding digit, is
Sum of the coefficients of $x^4$ and $x^6$ in the expansion of $(1 + x - x^2)^6$ is
The number of ways in which a cricket team of 11 members can be formed out of 6 batsmen, 6 bowlers, 4 all-rounders, and 4 wicket-keepers by selecting at least 4 batsmen, at least 3 bowlers, at least 2 all-rounders, and only one wicket-keeper is
If $y = \frac{3}{4} + \frac{3 \cdot 5}{4 \cdot 8} + \frac{3 \cdot 5 \cdot 7}{4 \cdot 8 \cdot 12} + ... \infty$, then
All letters of the word `AGAIN' are permuted in all possible ways, and the words so formed (with or without meaning) are written as in a dictionary. Then the $50^{th}$ word is
If $\alpha$, $\beta$, and $\gamma$ are the roots of the equation $2x^3 + 3x^2 - 5x - 7 = 0$, then $\frac{1}{\alpha^2} + \frac{1}{\beta^2} + \frac{1}{\gamma^2} =$
The set of all real values of $x$ for which $\frac{x^2-1}{(x-4)(x-3)} \ge 1$ is
Check whether the following system of equations is consistent or not. If consistent, solve graphically: \[ x - 2y + 4 = 0, \quad 2x - y - 4 = 0 \]
If the order and degree of the differential equation \(x \frac{d^2 y}{dx^2} = \left(1 + \left(\frac{d^2 y}{dx^2}\right)^2\right)^{-1/2}\) are \(k\) and \(l\) respectively, then \(k, l\) are the roots of
The general solution of the differential equation \( \left(x - (x + y)\log(x + y)\right) dx + x\,dy = 0 \) is:
The equation of the curve passing through the point \( (0, \pi) \) and satisfying the differential equation \( ydx = (x + y^3 \cos y)dy \) is
Area of the region (in sq. units) bounded by the curve $ y = x^2 - 5x + 4 $, $ x = 0 $, $ x = 2 $, and the X-axis is
Evaluate the integral \( \displaystyle \int_{1/5}^{1/2} \frac{\sqrt{x - x^2}}{x^3} \, dx \):
\( \int_{-\pi/2}^{\pi/2} \sin^2 x \cos^2 x (\sin x + \cos x) \, dx = \)
If \(\int \frac{1}{((x+4)^3 (x+1)^5)^{1/4}} \, dx = A \cdot \left(\frac{x+4}{x+1}\right)^n + c\), then
If \( \int e^{\sin x}(1 + \sec x \tan x)\, dx = e^{\sin x}f(x) + c \), then in \( 0 \leq x \leq 2\pi \), the number of solutions of \( f(x) = 1 \) is
Evaluate: \[ \int \frac{dx}{(x+1)\sqrt{x^2+1}} \]
If \( \int \left( x^6 + x^4 + x^2 \right) \sqrt{2x^4 + 3x^2 + 6} \, dx = f(x) + c \), then \( f(3) = \)
If \( m \) and \( M \) are the absolute minimum and absolute maximum values of the function \( f(x) = 2\sqrt{2 \sin x - \tan x} \) in the interval \( \left[0, \frac{\pi}{3} \right] \), then \( m + M = \)
The function \( f(x) = xe^{-x} \) for all \( x \in \mathbb{R} \) attains a maximum value at \( x = k \), then \( k = \)