List of top Questions asked in MHT CET

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

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

Simplify \( \sqrt{2} + \sqrt{2} + 2 \cos 4\theta = \)

The approximate value of the function \( f(x) = x^3 + 5x^2 - 7x + 10 \) at \( x = 1 \) is

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

If \( \sin(y + z - x) \), \( \sin(z + x - y) \), and \( \sin(x + y - z) \) are in A.P., then

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

If \( f(x) = 2x^2 + bx + c \), \( f(0) = 3 \) and \( f(2) = 1 \), then \( (f \circ f)(1) = \)

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

If \( y = \tan^{-1} \left( \frac{x - \sqrt{1 - x^2}}{x + \sqrt{1 - x^2}} \right) \), then \( \frac{dy}{dx} \) is

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

If \( CP \) and \( CD \) is a pair of semi-conjugate diameters of the ellipse \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \), then \( CP^2 + CD^2 = \)

Which of the following oxide of nitrogen is coloured?

Identify the neohhexyl chloride from the following.

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 derivative of \( f(\tan x) \) w.r.t. \( g(\sec x) \) at \( x = \frac{\pi}{4} \), where \( f'(1) = 2 \) and \( g'( \sqrt{2} ) = 4 \), is

In a single throw of three dice, the probability of getting a sum of at least 5 is

Radium decomposes at a rate proportional to the amount present. If half the original amount disappears in 1600 years, then the percentage loss in 100 years is

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

Which of the following does NOT give carbylamine test?

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

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

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

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

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