List of top Questions asked in MHT CET

The smallest angle of the triangle whose sides are $6 + \sqrt{12}, \sqrt{48}, \sqrt{24}$ is

If $f(x)$ is continuous at point $x = 0$ where $f(x) = \begin{cases} \frac{3\sin x + 5\tan x}{\text{a}^x - 1} & , x<0 \\ \frac{2}{\log 2} & , x = 0 \\ \frac{8x + 2x\cos x}{\text{b}^x - 1} & , x>0 \end{cases}$ then the values of a and b, respectively, are ________

If $x + \log_{15}(5 + 3^x) = x \log_{15} 5 + \log_{15} 24$, then $x =$ ________

The modulus of the square root of the conjugate of $-7 + 24\sqrt{-1}$ is __________

If $m_1$ and $m_2$ are the slopes of the lines represented by $ax^2 + 2hxy + by^2 = 0$ satisfying the condition $16\text{h}^2 = 25\text{ab}$, then

$\int \frac{\sin 2x}{(a+b\cos x)^2} dx =$

In the mean value theorem, $f'(c) = \frac{f(b)-f(a)}{b-a}$, if $\text{a} = 0$, $\text{b} = \frac{1}{2}$ and $f(x) = x(x - 1)(x - 2)$, then the value of $c$ is

The angle between the curves $xy = 6$ and $x^2y = 12$ is

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

An ellipse has OB as semi-minor axis, S and S' are foci and angle SBS' is a right angle. Then the eccentricity of the ellipse is

A population $p(t)$ of 1000 bacteria introduced into a nutrient medium grows according to the relation $\text{p}(t) = 1000 + \frac{1000t}{100+t^2}$. The maximum size of this bacterial population 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 $\text{i} = \sqrt{-1}$ )

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

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 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 $\lambda + 1 =$

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 $7\lambda - 10\mu =$

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

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 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 $|\bar{b} \times \bar{c}| =$

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

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

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

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