List of top Mathematics Questions

If \( \int e^{\sqrt{x}} / \sqrt{x} (x + \sqrt{x}) dx = e^{\sqrt{x}}[Ax + B\sqrt{x} + C] + K \), then \( A + B + C = \):
The number of solutions of the equations \[ x + y + z = 1,\quad x^2 + y^2 + z^2 = 1,\quad x^3 + y^3 + z^3 = 1 \] is:
What is the sum of the first \( n \) terms of the series, whose \( k \)-term is \( k! \cdot k \)?
The range of the data set: \( 35, 12, 21, 24, 15, 7, 16, 12, 30, 32, 13, 17 \) is:
Evaluate the limit: \[ \lim_{x \to \infty} \frac{A + e^{mx}}{x + Ae^{mx}} \]
\( \int_0^1 \alpha^k x^k dx = \)
Suppose a parabola passes through $(0, 4)$, $(1, 9)$ and $(4, 5)$ and has its axis parallel to the $y$-axis. Then the equation of the parabola is
Equation of tangent to the curve \( y = x + \frac{4}{x^2} \) which is parallel to x-axis is
If a and b are respectively the order and degree of a differential equation \( y^2(y'')^2 + 3x(y')^{1/3} + x^2y^2 = \sin x \), then
If $a$, $b$, $c$ are respectively the $5^{\text{th}$, $8^{\text{th}}$, $13^{\text{th}}$ terms of an arithmetic progression, then}
$\begin{vmatrix} a & 5 & 1 \\ b & 8 & 1\\ c & 13 & 1 \end{vmatrix} = $
Suppose a triangle is formed by $x + y = 10$ and the coordinate axes. Then the number of points $(x, y)$ where $x$ and $y$ are natural numbers, lying inside the triangle is
If 2, 3, 6 are the roots of the polynomial \(f(x) = x^3+ax^2+bx+c\), where \(a,b,c \in C\). Then the value of a--c is
If \( l \) and \( m \) are the order and degree of the differential equation of all the straight lines at constant distance \( P \) units from the origin, then \[ lm^2 + l^2 m = \]
If \( \lim_{x \to 0} x^2 \left( \frac{e^{x} - e^{-x}}{e^{x} + e^{-x}} \right) = k \), and \( \lim_{x \to 0} x^2 \left( \frac{e^{kx} - e^{-kx}}{e^{kx} + e^{-kx}} \right) = 1 \), then:
Evaluate: \( \int \frac{1 + \tan x \tan(x + \alpha)}{\tan x \tan(x + \alpha)} dx \):
The point on the curve $ y = x^2 + 4x + 3 $ that is closest to the line $ y = 3x + 2 $ is:
D, E, F are respectively the points on the sides $BC$, $CA$ and $AB$ of a $\triangle ABC$ dividing them in the ratio $2:3$, $1:2$, $3:1$ internally. The lines $BE$ and $CF$ intersect on the line $AD$ at $P$. If $\overrightarrow{AP} = x_1 \cdot \overrightarrow{AB} + y_1 \cdot \overrightarrow{AC}$, then $x_1 + y_1 =$
Let \(f: R \rightarrow R\) be defined by \(f(x) = 2x+3\). If \(\alpha, \beta\) are the roots of the equation \(f(x^2) - 2f(\frac{x}{2}) - 1 = 0\) then \(\alpha^2 + \beta^2 = \)
If the difference between the roots of $x^2 + ax + b = 0$ and that of $x^2 + bx + a = 0$ is same and $a \ne b$, then
The equation of circle with centre (2, -3) and touching x-axis is
\( 2\cot^2\theta - \cot\theta - 3 = \) (The question implies factorization of the quadratic in \(\cot\theta\))
If a polygon of $n$ sides has 560 diagonals, then $n$ = ?
If \( I_a = \int_0^{\pi/4} \tan^n x \, dx \), then \[ \frac{1}{I_2 + I_4} + \frac{1}{I_3 + I_5} + \frac{1}{I_4 + I_6} = \]
The value of $\dfrac{\sin\theta + \sin3\theta}{\cos\theta + \cos3\theta}$ is:
Solve: $iz^3 + z^2 - z + i = 0 \Rightarrow |z| = $ ?