List of top Questions asked in MHT CET

The auxiliary equation of the lines passing through the origin and having slopes \[ \sqrt{3} + 1 \quad \text{and} \quad \sqrt{3} - 1 \quad \text{is} \]

The equation of a plane containing the point \( (1, -1, 1) \) and parallel to the plane \[ 2x + 3y - 4z = 17 \text{ is} \]

The angle between the line \[ \frac{x - 1}{2} = \frac{y + 3}{1} = \frac{z + 7}{2} \] and the plane \[ \mathbf{r} \cdot (6\hat{i} - 2\hat{j} - 3\hat{k}) = 5 \] is

If \[ \frac{\sin(A + B)}{\sin(A - B)} = \frac{\cos(C + D)}{\cos(C - D)}, \] then \( \tan A \cot B = \)

If \[ f(x) = |x - 2|, \quad x \in [0, 4], \quad \text{then the Rolle's theorem cannot be applied to the function because} \]

The particular solution of the differential equation \[ \sin^2 y \frac{dx}{dy} + x = \cot y \quad \text{when} \quad x = 0 \quad \text{and} \quad y = \frac{3\pi}{4} \text{ is} \]

If \[ y = 3e^{5x} + 5e^{3x}, \quad \text{then} \quad \frac{d^2 y}{dx^2} - 8 \frac{dy}{dx} = \]

If \( \theta \) is a parameter, then the parametric equations of the circle \[ x^2 + y^2 - 6x + 4y - 3 = 0 \] are given by

If \[ | \mathbf{a} \times \mathbf{b} \times \mathbf{c} | = 4, \] then the volume of the parallelepiped with coterminous edges \[ \mathbf{a} + 2\mathbf{b}, \quad \mathbf{b} + 2\mathbf{c}, \quad \mathbf{c} + 2\mathbf{a} \] is

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

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

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

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

Which of the following reactions does NOT yield an amine?

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

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

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

What is the boiling point of heavy water?

The rate constant for a second-order reaction, A \(\rightarrow\) Product is 1.62 M\(^{-1}\)s\(^{-1}\). What will be the rate of reaction when the concentration of reactant is 2 \(\times\) 10\(^{-3}\) M?

Calcite crystals used in Nicol’s prism are formed of: