List of top Mathematics Questions

$\int \frac{\text{d}x}{2\text{e}^{2x}+3\text{e}^x+1} =$
If $3 \sin \alpha = 5 \sin \beta$, then $\tan \left( \frac{\alpha+\beta}{2} \right) + \tan \left( \frac{\alpha-\beta}{2} \right) =$
The statement pattern $[(p \rightarrow q)\land \sim q] \rightarrow r$ is a tautology when $r$ is equivalent to
$\lim_{x \to 3} \frac{(84-x)^{\frac{1}{4}} - 3}{x - 3}$ is

A box contains 9 tickets numbered 1 to 9 both inclusive. If 3 tickets are drawn from the box one at a time, then the probability that they are alternatively either \(\{odd, even, odd\}\) or \(\{even, odd, even\}\) is

The point of intersection of the diagonals of the rectangle whose sides are contained in the lines $x = 8, x = 10, y = 11$ and $y = 12$ is
A plane passes through $(1, -2, 1)$ and is perpendicular to the planes $2x - 2y + z = 0$ and $x - y + 2z = 4$. The distance of the point $(1, 2, 2)$ from this plane is ________ units.
The distance of the point $(-3, 2, 3)$ from the line passing through $(4, 6, -2)$ and having direction ratios $-1, 2, 3$ is ________ units.
If $[2\bar{p} - 3\bar{r} \quad \bar{q} \quad \bar{s}] + [3\bar{p} + 2\bar{q} \quad \bar{r} \quad \bar{s}] = m [\bar{p} \quad \bar{r} \quad \bar{s}] + n [\bar{q} \quad \bar{r} \quad \bar{s}] + t [\bar{p} \quad \bar{q} \quad \bar{s}]$, then the values of m, n, t respectively are ....
The number of ways, in which 6 boys and 5 girls can sit at a round table, if no two girls are to sit together, is
The Cartesian equation of plane through A$(7, 8, 6)$ and parallel to the XY plane is
Let the line \(\frac{x-2}{3} = \frac{y-1}{-5} = \frac{z+2}{2}\) lie in the plane \(x + 3y - \alpha z + \beta = 0\), then the value of \((\beta - \alpha)\) is equal to
The number of solutions of \(16^{\sin^2 x} + 16^{\cos^2 x} = 10\) in \(0 \le x \le 2\pi\) are
If the difference between the maximum and minimum values of the objective function \(z = 7x - 8y\), subject to the constraints \(x + y \le 20, y \ge 5, x, y \ge 0\) is \(5k + 200\), then the value of k is

If \[ x = a\cos^3\theta, \qquad y = a\sin^3\theta, \] then find \[ \sqrt{1+\left(\frac{dy}{dx}\right)^2} = \, ? \] 

If \[ 3\sin^{-1}\left(\frac{2x}{1+x^2}\right) - 4\cos^{-1}\left(\frac{1-x^2}{1+x^2}\right) + 2\tan^{-1}\left(\frac{2x}{1-x^2}\right) = \frac{\pi}{3}, \] then the value of \[ x = \, ? \] 

If the tangent and the normal at the point \((\sqrt{3}, 1)\) to the circle \(x^2 + y^2 = 4\), and the X-axis form a triangle, then the area (in sq.units) of this triangle is
The line \(y = mx + 3\) is tangent to the parabola \(y^2 = 4x\), if the value of m is
If the lines \(\frac{x-1}{2} = \frac{y+1}{k} = \frac{z}{2}\) and \(\frac{x+1}{5} = \frac{y+1}{2} = \frac{z}{k}\) are coplanar, then the equation of the plane containing these lines are
The X and Y intercepts of the tangent to the hyperbola \(\frac{x^2}{20} - \frac{y^2}{5} = 1\) which is perpendicular to the line \(4x + 3y = 7\), are respectively
The approximate value of \(\sqrt[3]{64.04}\) is

If \[ f(x) = x \cdot e^{x(1-x)}, \] then \( f(x) \) is: 

In a single toss of a fair die, the odds against the event that number 4 or 5 turns up is
For \(N \in \mathbb{N}, \frac{d^n}{dx^n} (\log x) =\)

If \[ \int \frac{2x^2+3}{(x^2-1)(x^2-4)} \, dx = \log \left[ \left( \frac{x-2}{x+2} \right)^a \cdot \left( \frac{x+1}{x-1} \right)^b \right] + c \] where \( c \) is the constant of integration, then the value of \[ a+b = \, ? \]