List of top Questions asked in MHT CET

If \[ y = \tan^{-1}(\sec x + \tan x), \quad \text{then} \quad \frac{dy}{dx} = \]

The displacement of a particle at the time \( t \) is given by \[ s = \sqrt{1 + t}, \quad \text{then its acceleration } a \text{ is proportional to} \]

If \[ \mathbf{a} = \frac{1}{\sqrt{10}} (3i + k), \quad \mathbf{b} = \frac{1}{7} (2i + 3j - 6k), \quad \text{then the value of} \] \[ (2\mathbf{a} - \mathbf{b}) \cdot \left[ (\mathbf{a} \times \mathbf{b}) \times (\mathbf{a} + 2\mathbf{b}) \right] \]

If the body cools from \( 135^\circ C \) to \( 80^\circ C \) at room temperature of \( 25^\circ C \) in 60 minutes, then the temperature of the body after 2 hours is

The statement pattern \[ [(p \vee q) \wedge \neg p] \wedge (\neg q) \] is

Two cards are drawn from a pack of well shuffled 52 playing cards one by one without replacement. Then the probability that both cards are queens is

Evaluate the integral \[ \int_0^{\frac{\pi}{2}} \frac{\sin x \cos x}{1 + \sin^4 x} \, dx = \]

Evaluate the integral \[ \int \frac{dx}{\sqrt{5 + 4x - x^2}} = \]

Degree of the differential equation \[ \frac{dy}{dx} e^x + \left( \frac{dy}{dx} \right)^3 = x \]

If \( \cos 2\theta = \sin \alpha \), then \( \theta = \)

The solution of the differential equation \[ x^2 \frac{dy}{dx} = y^2 + xy \]

The maximum value of the function \[ y = e^{5 + \sqrt{3} \sin x + \cos x} \]

If \( Z = 7x + y \) subject to \[ 5x + y \geq 5, \quad x + y \geq 3, \quad x \geq 0, \quad y \geq 0, \quad \text{then the minimum value of } Z \text{ is} \]

Which among the following elements has the lowest density and is lightest?

What is the value of radius ratio of ionic crystal having coordination number six?

What is the molar conductivity of 0.1 M NaCl if its conductivity is \(1.06 \times 10^{-2} \, \Omega^{-1} \, \text{cm}^{-1}\text{cm}^{-1}\)?

If a mixture of iodomethane and iodethane is treated with sodium metal in presence of dry ether, it forms:

Which of the following reactions does NOT yield an amine?

Which of the following carbonyl compounds does NOT undergo aldol condensation?

What happens during Bessemerization process of extraction of copper from copper pyrites?

What is the common unit of conductivity if the dimensions are expressed in centimeter?

Blurring of vision is a side effect caused by the use of:

Identify 'Z' in the following series of reactions: \[ \text{Butan-2-ol} \xrightarrow{\text{PCl}_3} X \xrightarrow{\text{alc. KOH}} Y \xrightarrow{i) \, \text{H}_2\text{SO}_4, \, ii) \, \text{H}_2\text{O}/\text{heat}} Z \]

What is the boiling point of heavy water?

What is the effective atomic number of Fe in [Fe(CN)\(_6\)]\(^{4-}\) (At. no. of Fe = 26)?