List of top Questions asked in MHT CET

By dropping a stone in a quiet lake, a wave in the form of circle is generated. The radius of the circular wave increases at the rate of $2.1 \text{ cm/sec}$. Then the rate of increase of the enclosed circular region, when the radius of the circular wave is $10 \text{ cm}$ , is (Given $\pi = \frac{22}{7}$ )

The derivative of $\tan^{-1} \left(\sqrt{1+x^2}-1\right)$ is

If the directed line makes an angle $45^\circ$ and $60^\circ$ with the X and Y -axes respectively, then the obtuse angle $\theta$ made by the line with the Z -axis is

$f(x) = (\cos x + \text{i}\sin x) \cdot (\cos 3x + \text{i}\sin 3x) \cdots [\cos(2\text{n} - 1)x + \text{i}\sin(2\text{n} - 1)x] \text{n} \in \mathbb{N}$ Then $f''(x) = $ ________, (Where $\text{i} = \sqrt{-1}$ )

If the angle $\theta$ between the line $\frac{x+1}{1} = \frac{y-1}{2} = \frac{z-2}{2}$ and the plane $2x - y + \sqrt{\lambda}z + 4 = 0$ is such that $\sin \theta = \frac{1}{3}$, then $\lambda + 1 =$

The feasible region represented by the given constraints $2x + 3y \ge 12, -x + y \le 3, x \le 4, y \ge 3$ is denoted by

If the lines $\frac{3-x}{2} = \frac{5y-2}{3\lambda+1} = 5 - z$ and $\frac{x+2}{-1} = \frac{1-3y}{7} = \frac{4-z}{2\mu}$ are at right angles, then $7\lambda - 10\mu =$

For $\text{n} \in \mathbb{N}$ if $y = \text{a}x^{\text{n}+1} + \text{b}x^{-\text{n}}$, then $x^2 \frac{\text{d}^2 y}{\text{d}x^2} =$

$\int_1^e \frac{e^x}{x}(1 + x \log x) dx =$

The ratio of the areas bounded by the curves $y = \cos x$ and $y = \cos 2x$ between $x = 0, x = \frac{\pi}{3}$ and X -axis is

If the points $\text{A}(2 - x, 2, 2), \text{B}(2, 2 - y, 2), \text{C}(2, 2, 2 - z)$ and $\text{D}(1, 1, 1)$ are coplanar, then the locus of point $\text{P}(x, y, z)$ is

The volume of the tetrahedron whose co-terminus edges are $\bar{a}, \bar{b}, \bar{c}$ is 12 cubic units. If the scalar projection of $\bar{a}$ on $\bar{b} \times \bar{c}$ is 4 , then $|\bar{b} \times \bar{c}| =$

If the sum of the squares of the distance of the point $\text{P}(x, y, z)$ from the co-ordinate axes is 242 , then the distance of the point P from the origin is units.

The solution of the differential equation $x \frac{\text{d}^2 y}{\text{d}x^2} = 1$ at $x = y = 1$ with $\frac{\text{d}y}{\text{d}x} = 0$ at $x = 1$, is

If $4 \sin^{-1} x + \cos^{-1} x = \pi$ then $x =$

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 ($\log 2 = 0.6931$)

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 $y = y(x)$ 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

The ratios of sides in a triangle ABC are $5 : 12 : 13$ and its area is 270 . Then sides of the triangle are

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

$\int \frac{\text{d}x}{2\text{e}^{2x}+3\text{e}^x+1} =$

The value of $\int_1^4 \log[x]\text{d}x$, where $[x]$ is the greatest integer function is equal to

The order and degree of differential equation of all tangent lines to the parabola $x^2 = 4y$ is respectively.

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