List of top Questions asked in MHT CET

A coil of 'n' turns and resistance $R \Omega$ is connected in series with a resistance $R/2$. The combination is moved for time 't' second through magnetic flux $\phi_1$ to $\phi_2$. The induced current in the circuit is ______.

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

A particle P starts from $Z_0 = 1 + 2i$. It moves horizontally away from origin by 5 units, then vertically up by 3 units to $Z_1$. From $Z_1$ it moves $\sqrt{2}$ units in direction $\hat{i} + \hat{j}$, then moves through $\pi/2$ anticlockwise on a circle with centre at origin to reach $Z_2$. Then $Z_2 = \dots$

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

Identify the product formed when 2-Bromobutane is heated with aqueous solution of sodium hydroxide.

The moment of inertia of a solid sphere of mass 'm' and radius 'R' about its diametric axis is 'I'. Its moment of inertia about a tangent in the plane is ______.

Two girls are standing at the ends 'A' and 'B' of a ground where $AB = b$. The girl at 'B' starts running perpendicular to 'AB' with velocity $V_1$. The girl at 'A' starts running simultaneously with velocity $V_2$ and in shortest distance meets the other girl in time 't'. The value of 't' is ______.

What is the time required for 99% completion of a first order reaction if rate constant is 23.03 min$^{-1}$?

If instantaneous rate of reaction is stated as $-\frac{1}{2} \frac{d[x]}{dt} = -\frac{d[y]}{dt} = \frac{1}{2} \frac{d[z]}{dt}$, identify the reaction.

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

In an a.c. circuit, a resistance 'R' is connected in series with an inductance 'L'. If phase angle between voltage and current is 45$^\circ$, the value of inductive reactance will be ($\tan 45^\circ = 1$) ______.

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 ______.

If $f(x) = \log(1 + x) - \frac{2x}{2 + x}$, then $f(x)$ is increasing in ______.

Using Bohr's quantisation condition, what is the rotational energy in the second orbit for a diatomic molecule? ($I$ = moment of inertia and $h$ = Planck's constant) ______.

The order of the differential equation whose general solution is given by $y = (C_1 + C_2) \sin(x + C_3) - C_4 e^{x+C_5}$ is \dots}

A bob of mass 'm' is tied by a string wound on a flywheel (disc) of radius 'R' and mass 'm'. If the bob has covered a vertical distance 'h', then the angular speed of the wheel will be \dots

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

Find the volume of 56 g dinitrogen at STP.

What is oxidation number of sulphur in $SO_3$?

If standard reduction potential ($E^\circ$) of ($Mg^{2+} | Mg(s)$), ($Ag^+ | Ag(s)$), ($Zn^{2+}(aq) | Zn(s)$) and ($Cu^{2+}(aq) | Cu(s)$) are $-2.37$ V, $+0.79$ V, $-0.76$ V and $+0.34$ V respectively. Which of the following reaction is spontaneous?

If the line $\frac{x-3}{2} = \frac{y+5}{1} = \frac{z+2}{2}$ lies in the plane $\alpha x + 3y - z + \beta = 0$, then values of $\alpha$ and $\beta$ respectively are \dots}

As shown in the figure, $S_1$ and $S_2$ are identical springs with spring constant K each. The oscillation frequency of the mass 'm' is 'f'. If the spring $S_2$ is removed, the oscillation frequency will become ______.

Which of the following is used as reagent in Etard reaction?

If $y = \tan^{-1} \left[ \frac{12x - 64x^3}{1 - 48x^2} \right]$, then $dy/dx = \dots$

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 ______.