List of top Mathematics Questions

Number of ways of distributing \(10\) identical chocolates among \(3\) children such that everyone gets at least one?

If \( f(x) = \displaystyle \int e^x \left(\frac{x^2 + x + 1}{\sqrt{x^2 + 1}}\right) dx \) such that the value of the function is \(1\) when \(x\) vanishes, find the value of \(f(1)\).

If \( \dfrac{d^2y}{dx^2} = \cos \left(\dfrac{dy}{dx}\right) \), find the order and the degree of the resulting differential equation.

Find the value of \( (125)^{\log_{625} 5} \)

If \( \omega \) is an imaginary cube root of unity, find the value of \( (1 + \omega - \omega^2)^7 \).

Find the value of \(k\) if the lines \[ \frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4} \] and \[ \frac{x-4}{5}=\frac{y-1}{2}=\frac{z}{k} \] are coplanar.

If \( S_n = 3n^2 + 5n \) represents the sum of \( n \) terms of an A.P., find the \(10^{th}\) term \( (a_{10}) \).

Evaluate the integral \( \displaystyle \int \frac{1}{x\log x}\,dx \).

If \[ \lim_{x\to 0} \frac{e^{(a-1)x}+2\cos bx+(c-2)e^{-x}} {x\cos x-\log_e(1+x)} =2, \] then \(a^2+b^2+c^2\) is equal to

Find the area of the region bounded by the curve \(y^2=4x\) and the line \(x=3\).

If \(A\) is a square matrix of order \(3\) such that \( |adj\,A| = 64 \), then find the value of \( |A| \).

The sum of the first \(10\) terms of an A.P. is \(150\). If the first term is \(10\), what is the common difference?

What is the distance of the point \((1,2,3)\) from the \(yz\)-plane?

Which one of the following point is not in a feasible region bounded by the inequalities $x \leq 4$, $y \leq 6$, $x + y \leq 6$, $x \geq 0$, $y \geq 0$

The area of the region bounded by the lines, $y = x + 2$, $x = 0$, $x = 1$ and $y = 0$ is

The solution of $(e^y + 1)\cos x\,dx + e^y \sin x\,dy = 0$ is

\(\int_{0}^{\pi/3} \frac{dx}{1 + \sqrt{\tan x}} =\)

\(\int_{0}^{\pi/4} \sqrt{1 + \sin 2x}\,dx =\)

The function \(y = be^x + ae^{-x}\), \(a\) and \(b\) are constants, is a solution of

$\int e^x \left(\frac{1 - \sin x}{1 - \cos x}\right) dx =$

If $\int \left(3t^2\sin\left(\frac{1}{t}\right) - t\cos\left(\frac{1}{t}\right)\right) dt = f(t)\sin\left(\frac{1}{t}\right) + c$ then $f(2)$ is equal to

\(\int \sin^3 x \, e^{\log \cos x} \, dx =\)

If \(\int_a^b x^3 \, dx = 0\) and \(\int_a^b x^2 \, dx = \frac{2}{3}\), then the values of \(a\) and \(b\) respectively are

If $u = \int e^x \cos x \, dx,\; v = \int e^x \sin x \, dx$, then $u + v =$

If \(\int \frac{2^{1/x}}{x^2} \, dx = k\,2^{1/x} + c\) then \(k\) is equal to