List of top Questions asked in MHT CET

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 \( f \) 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

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

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

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

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

Identify the neohhexyl chloride from the following.

Which of the following oxide of nitrogen is coloured?

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

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

Which of the following is a synthetic estrogen derivative?

Identify 'B' in the following series of reactions:
Ethanol $\xrightarrow{\text{NaBr, H\(_2\)SO\(_4\), Δ}}$ A $\xrightarrow{\text{Mg, Dry ether}}$ B

An organic compound was found to contain 40.0% C and 6.66% H. Find its molecular formula (molar mass = 180).

Which of the following is dihydric phenol?

What is the oxidation number of Cr in K\(_2\)Cr\(_2\)O\(_7\)?

Identify the correct relation between depression in freezing point and freezing point of pure solvent.