List of top Mathematics Questions asked in MHT CET

The sum to infinite terms of the series $\tan^{-1} \left(\frac{1}{3}\right) + \tan^{-1} \left(\frac{2}{9}\right) + ..................... + \tan^{-1} \left(\frac{2^{n-1}}{1+2^{2n-1}}\right) + ..............$ is
The number of common tangents that can be drawn to the circles $x^2 + y^2 - 6x = 0$ and $x^2 + y^2 + 6x + 2y + 1 = 0$ is ________
If a random variable $X$ follows the Binomial distribution $\text{B}(33, \text{p})$ such that $3\text{P}(\text{X} = 0) = \text{P}(\text{X} = 1)$, then the variance of X is
In a bank, the principal increases continuously at a rate of $x%$ per year. Then the rate $x$, if Rs.\ 100 doubles itself in 10 years, is ($\log 2 = 0.6931$)
If $y = y(x)$ satisfies $\left(\frac{2+\sin x}{1+y}\right) \frac{dy}{dx} = -\cos x$ such that $y(0) = 2$, then $y\left(\frac{\pi}{2}\right)$ is equal to
If a random variable $X$ has the p.d.f. $f(x) = \begin{cases} \frac{k}{x^2+1} & , \text{if } 0<x<\infty \\ 0 & , \text{otherwise} \end{cases}$ then c.d.f. of X is
The probability distribution of a discrete random variable X is
If $\text{a} = \text{P}(x<3)$ and $\text{b} = \text{P}(2 \le \text{X}<4)$, then
The order and degree of differential equation of all tangent lines to the parabola $x^2 = 4y$ is respectively.
The value of $\int_1^4 \log[x]\text{d}x$, where $[x]$ is the greatest integer function is equal to
$\int \frac{\text{e}^{2030 \log x} - \text{e}^{2029 \log x}}{\text{e}^{2028 \log x} - \text{e}^{2027 \log x}} \text{d}x = .......$
$\int \frac{\text{d}x}{2\text{e}^{2x}+3\text{e}^x+1} =$
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 \[ \sqrt{1+\left(\frac{dy}{dx}\right)^2} = \, ? \]