List of top Questions asked in MHT CET

Focal length of a convex lens will be maximum for

An electromagnetic wave of wavelength $\lambda$ is incident on a photosensitive surface of negligible work function. If the photoelectrons emitted from this surface have the de-Broglie wavelength $\lambda_1$, then

A graph of magnetic flux ($\phi$) versus current ($I$) is shown for four inductors A, B, C and D. Larger value of self-inductance is for inductor

The parametric equations of the line passing through \( A(3, 4, -7) \), \( B(1, -1, 6) \) are

A bus is moving with a velocity of 5 m/s towards a wall. The driver blows the horn of frequency 165 Hz. If the speed of sound in air is 335 m/s, then after reflection of the sound wave, the number of beats per second heard by the passengers in the bus will be

Evaluate the integral: \[ \int \frac{dx}{\cos x \sqrt{\cos 2x}}. \]

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 \( \tan A \cot B = \)

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

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

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

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

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

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

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 value of radius ratio of ionic crystal having coordination number six?

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

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