List of top Questions asked in MHT CET

The circumradius of a triangle whose sides are 10 units, 8 units and 6 units is ______.

With usual notations in $\triangle ABC$, if $\angle B = \pi/2$, and $\tan A, \tan C$ are roots of equation $px^2 + qx + r = 0, p \neq 0$, then ______.

In L.P.P., the maximum value of objective function $Z = 6x + 3y$ subject to $x + y \leq 5, x + 2y \geq 4, 4x + y \leq 12, x, y \geq 0$ is \dots

The lines $\vec{r} = (\hat{i} + \hat{j} - \hat{k}) + \lambda(3\hat{i} - \hat{j})$ and $\vec{r} = (4\hat{i} - \hat{k}) + \mu(2\hat{i} + 3\hat{k})$ are \dots}

An object of mass 'm' moving with velocity 'u' collides with another stationary object of mass 'M' and stops just after the collision. The coefficient of restitution is ______.

$\int \frac{x^4 \cos(\tan^{-1} x^5)}{1 + x^{10}} dx$ equals ______.

$\int \frac{dx}{(x + a)^{9/7} (x - b)^{5/7}}$ = ______.

An a.c. source of frequency 'f' is connected to a circuit containing an inductance 'L' and resistance 'R' in series. The impedance of this circuit is ______.

If $\vec{b}$ and $\vec{c}$ are unit vectors and $|\vec{a}| = 7$, $\vec{a} \times (\vec{b} \times \vec{c}) + \vec{b} \times (\vec{c} \times \vec{a}) = \frac{1}{2} \vec{a}$, then angle between the vectors $\vec{a}$ and $\vec{c}$ and angle between the vectors $\vec{b}$ and $\vec{c}$ are respectively \dots
Note: The original question text displayed $\frac{1}{3}\vec{a}$, which is a known OCR/print typo in this standard exam question format. The correct standard value is $\frac{1}{2}\vec{a}$ to yield standard angular options.

A monobasic weak acid dissociates 2% in its 0.002 M solution. Calculate the dissociation constant of weak acid.

In hydrogen atom in its ground state, the first Bohr orbit has radius $r_1$. When the atom is raised to one of its excited states, the electron's orbital velocity becomes one-third. The radius of that orbit is \dots

If $(\tan^{-1} x)^2 + (\cot^{-1} x)^2 = 5\pi^2/8$, then $x^2 + 1 = \dots$

If $\sqrt{y} - \sqrt{y} - \dots = \sqrt{x} + \sqrt{x} + \dots$ then $dy/dx = \dots$

If $\theta$ is an obtuse angle between vectors $\vec{a}$ and $\vec{b}$ such that $|\vec{a}| = 5, |\vec{b}| = 3$ and $|\vec{a} \times \vec{b}| = 5\sqrt{5}$ then $\vec{a} \cdot \vec{b} = \dots$

Identify the correct increasing order of field strength of ligands from following.

$\cos^4(\pi/8) + \cos^4(3\pi/8) + \cos^4(5\pi/8) + \cos^4(7\pi/8) = \dots$

The fundamental frequencies of vibrations of air column in pipe open at both ends and in pipe closed at one end are $n_1$ and $n_2$ respectively, then \dots

A black body emits radiation of maximum intensity at wavelength '$\lambda$' at temperature $T$ K. Its corresponding wavelength at temperature $1.5 T$ K will be ______.

Identify the product formed in the following reaction: $(CH_3CO)_2O \xrightarrow{H_2O} \text{Product}$

A copper ring having a cut such as not to form a complete loop is held horizontally and a bar magnet is dropped through the ring. The acceleration of the falling magnet is \dots

Heat supplied $dQ$ = increase in internal energy $dU$ is true for \dots

Let $f : \mathbb{R} - \{2\} \rightarrow \mathbb{R} - \{1\}$ defined by $f(x) = \frac{x-3}{x-2}$ and $g : \mathbb{R} \rightarrow \mathbb{R}$ defined by $g(x) = 3x - 2$, then sum of all values of $x$ for which $f^{-1}(x) + g^{-1}(x) = 19/6$ is ______.

A balloon is filled at 27$^\circ$C and 1 atmospheric pressure by volume 500 m$^3$ helium gas. At -3$^\circ$C and 0.5 atmospheric pressure, the volume of helium gas will be ______.

In an open end organ pipe of length 'L', if the velocity of sound is 'V', then the fundamental frequency will be (Neglect end correction) ______.

In Young's double slit experiment, at two points P and Q on screen, waves from slits $S_1$ and $S_2$ have a path difference of 0 and $\lambda/4$ respectively. The ratio of intensities at point P to that at Q will be \dots