List of top Questions asked in MHT CET

In Young's double slit experiment, green light is incident on the two slits. The interference pattern is observed on a screen. Which one of the following changes would cause the observed fringes to be more closely spaced?

The ratio of speed of an electron in the ground state in an atom to the velocity of light (c) is
$(h = \text{Planck's constant}, \epsilon_0 = \text{permittivity of free space})$

If a point \( P \) on the line segment joining the points \( (3, 5, -1) \) and \( (6, 3, -2) \) has its \( y \)-coordinate 2, then its \( z \)-coordinate is

The growth of population is proportional to the number present. If the population of a colony doubles in 50 years, then the population will become triple in

The acute angle between the lines given by \( y - \sqrt{3}x + 1 = 0 \) and \( \sqrt{3}y - x + 7 = 0 \) is

The distance of the point \( (7, 5, 2) \) from the plane \( 3x + 4y + 2z - 8 = 0 \) measured parallel to the line \( \frac{x - 1}{3} = \frac{y - 2}{6} = \frac{z + 1}{2} \) is

If a fair coin is tossed 8 times, then the probability that it shows heads more than tails is

If \( 2f(x) = f'(x) \) and \( f(0) = 3 \), then the value of \( f(2) \) is

If \( f \) and \( g \) are differentiable functions satisfying \( g'(a) = 2 \), \( g(a) = b \), and \( f \circ g = 1 \), where 1 is an identity function, then \( f'(b) \) is equal to

Evaluate \( \int e^{\tan^{-1} x} \left( 1 + \frac{x}{1 + x^2} \right) dx \)

The angle between the two lines \( \frac{x-4}{1} = \frac{y+4}{2} = \frac{z+1}{2} \) and \( \frac{x+1}{2} = \frac{y+3}{2} = \frac{z-4}{-1} \) is

Evaluate \( \int 7^{7^{7x}} 7^{7x} dx = \)

The distance of the point \( (2, -1, 0) \) from the plane \( 2x + y + 2z + 8 = 0 \) is

The optimal solution of the L.P.P. \( Z = 8x + 3y \) subject to the constraints \( x + y \leq 3 \), \( 4x + y \leq 6 \), \( x \geq 0 \), \( y \geq 0 \) is

Evaluate the integral \( \int e^x \left( \frac{1 - x}{1 + x^2} \right)^2 dx = \)

If the sum of the slopes of the pair of lines given by \( 4x^2 + 2hxy - 7y^2 = 0 \) is equal to the product of the slopes, then \( h \) is

The solution of the differential equation \( \log \left( \frac{dy}{dx} \right) = 9x - 6y + 6 \) is (given that \( y = 1 \) when \( x = 0 \))

A line makes angles \( \alpha \), \( \beta \), \( \gamma \) with the co-ordinate axes, then \( \cos 2\alpha + \cos 2\beta + \cos 2\gamma \) is equal to

The number of solutions of the equation \( \tan x + \sec x = 2 \cos x \) lying in the interval \( [0, 2\pi] \) is

An ideal gas expands from 1 × 10\(^-3\) m\(^3\) to 1 × 10\(^-2\) m\(^3\) at 300 K against a constant external pressure of 1 × 10\(^5\) N/m\(^2\). Work done is

Identify the neohhexyl chloride from the following.

Which of the following oxide of nitrogen is coloured?

The coordination number of the sphere in cubic close packed (ccp) structure is

What is the coordination number of cation in ionic compound if the type of hole occupied by cation is cubic?

According to Andrews isothermals, the minimum temperature at which carbon dioxide gas obeys Boyle’s law is