List of top Questions asked in MHT CET

The general solution of \( \tan \theta + \tan 2\theta = \tan 3\theta \)

If \[ \int_{0}^{\frac{\pi}{4}} \frac{\sin x + \cos x}{9 + 16 \sin 2x} \, dx = k \log 3, \text{ then } k = \]

The symbolic form of the following circuit is (where \( p, q, r \) represent switches \( s_1, s_2, s_3 \) which are closed respectively)

The equations of the lines which make intercepts on the axes whose sum is 8 and product is 15 are

If the population grows at the rate of 5% per year, then the time taken for the population to become double is (Given \(\log 2 = 0.6912\))

The particular solution of the differential equation \( x \, dy + 2y \, dx = 0 \), when \( x = 2 \) and \( y = 1 \) is

If \( \tan \theta = 2 \) and \( \theta \) lies in the third quadrant, then the value of \( \sec \theta \) is

The foot of the perpendicular drawn from the origin to the plane \( x + y + 3z - 4 = 0 \) is

If the probability density function of a continuous random variable is \[ f(x) = \frac{x^3}{3} \quad \text{if} \quad -1<x<2, \quad f(x) = 0 \quad \text{otherwise}, \] then the cumulative distribution function of \( X \) is

If \( y = \tan^{-1} \left( \frac{\sin 2x}{1 + \cos 2x} \right) \), then \[ \frac{dy}{dx} = \]

For the following reaction, the relation between \( \Delta H \) and \( \Delta U \) is
\[ \text{2SO}_3(\text{g}) + \text{O}_2(\text{g}) \rightarrow \text{2SO}_3(\text{g}) \]

Which among the following group -15 elements forms hydrogen bonding in its hydride compounds?

An element crystallizes in bcc type of unit cell having atomic radius \( 1.33 \times 10^{-8} \) cm, the edge length of unit cell will be

Which among the following compounds is treated with benzonitrile to obtain benzophenone in dry ether and then acid hydrolysis?

Identify the product C in the following reaction.
\[ \text{CH\(_3\)CH\(_2\)COOH} \xrightarrow{\text{NaOH}} A \xrightarrow{\text{CaO, }\Delta} B \xrightarrow{\text{HNO\(_3\)}} C \]

The cartesian co-ordinates of the point whose polar co-ordinates are \( \left( \frac{1}{2}, 120^\circ \right) \text{ are}

In aqueous phase the order of basic strength of alkylamine is

What is the number of moles and total number of atoms respectively present in 5.6 cm\(^3\) of ammonia gas at STP?

An element crystallizes in bcc type of unit cell, the density and edge length of unit cell is 4 g cm\(^{-3}\) and 500 pm respectively. What is the atomic mass of an element?

Identify product ‘A’ in the following reaction.
\[ \text{R - C} \equiv \text{N} \xrightarrow{\text{DIBAL-H}} \xrightarrow{\text{H}_3\text{O}^+} A \]

0.5 molal aqueous solution of a weak acid (HX) is 20% ionised. If Kf of water is 1.86 K kg mol⁻¹, the lowering in freezing point of solution is

Which polymer is obtained from monomers 3-Hydroxy butanoic acid and 3-Hydroxy pentanoic acid?

In an isothermal and reversible process, \(1.6 \times 10^{-2}\) kg O\(_2\) expands from 10 dm\(^3\) to 100 dm\(^3\) at 300 K, work done in the process is (R = 8.314 J/mol·K)

The half life of a first order reaction is 6.0 hours. How long will it take for the concentration of reactant to decrease from 0.4 M to 0.12 M?

Identify the formula of potassium trioxalato aluminate (III).