MHT CET 2026 May 12 Shift 1 PCM Question Paper- Download PDF with Solutions

Eight identical spherical liquid drops, each falling with a terminal velocity \(v\), coalesce to form a single large drop. The terminal velocity of the new large drop is:

• (A) \(2v\)
• (B) \(4v\)
• (C) \(8v\)
• (D) \(16v\)

A uniform solid sphere of mass \(M\) and radius \(R\) is placed on a smooth horizontal surface. It is struck by a horizontal cue at a height \(h\) above the center. For the sphere to roll without slipping immediately after the impact, the value of \(h\) must be:

• (A) \(\dfrac{R}{2}\)
• (B) \(\dfrac{2R}{5}\)
• (C) \(\dfrac{2R}{3}\)
• (D) \(\dfrac{3R}{5}\)

A disc of mass \(M\) and radius \(R\) has a concentric hole of radius \(\dfrac{R}{2}\). Its moment of inertia about an axis passing through its center and perpendicular to its plane is:

• (A) \(\dfrac{15}{32}MR^2\)
• (B) \(\dfrac{13}{32}MR^2\)
• (C) \(\dfrac{5}{16}MR^2\)
• (D) \(\dfrac{3}{8}MR^2\)

The work done in increasing the radius of a soap bubble from \(R\) to \(2R\) is \(W\). The work done in further increasing its radius from \(2R\) to \(3R\) will be:

• (A) \(\dfrac{5}{3}W\)
• (B) \(\dfrac{4}{3}W\)
• (C) \(\dfrac{7}{3}W\)
• (D) \(W\)

Water flows through a horizontal pipe. At one point, the velocity is \(2~m/s\) and the pressure is \(2~m\) of water column. What is the pressure at another point where the velocity is \(3~m/s\)?


(Density of water \(=10^3~kg/m^3\))

• (A) \(1.75~m\) of water
• (B) \(1.2~m\) of water
• (C) \(1~m\) of water
• (D) \(1.5~m\) of water

Identify the type of intermolecular force present between benzene and ammonia.

• (A) Hydrogen bonding
• (B) Dipole-induced dipole interaction
• (C) Dipole-dipole interaction
• (D) Ion-dipole interaction

What is the SI unit for rate of diffusion?

• (A) \(cm^3~minute^{-1}\)
• (B) \(dm^3~hour^{-1}\)
• (C) \(dm^3~s^{-1}\)
• (D) \(mL~hour^{-1}\)

Which of the following pair of liquids has dipole-induced dipole interaction?

• (A) Water and ammonia
• (B) Water and chloroform
• (C) Water and benzene
• (D) Water and ethyl alcohol

A certain mass of a gas occupies a volume of \(2.5~dm^3\) at NTP. Calculate the change in volume of gas at the same temperature, if pressure of gas is changed to \(1.25~atm\).

• (A) \(3.0~dm^3\)
• (B) \(0.5~dm^3\)
• (C) \(4.5~dm^3\)
• (D) \(1.5~dm^3\)

A gas occupies a volume of \(4.2~dm^3\) at \(101~kPa\) pressure. What volume will the gas occupy if the pressure is increased to \(235~kPa\) keeping the temperature constant?

• (A) \(1.8~dm^3\)
• (B) \(3.6~dm^3\)
• (C) \(0.9~dm^3\)
• (D) \(2.1~dm^3\)

Let
\[ f(x)=\int \frac{x\sqrt{x}}{(1+x)^2}\,dx \qquad (x\ge0) \]

Then \(f(3)-f(1)\) is equal to:

• (A) \(\dfrac{-1}{12}+\dfrac{1}{2}+\dfrac{\sqrt{3}}{4}\)
• (B) \(\dfrac{1}{12}+\dfrac{1}{2}-\dfrac{\sqrt{3}}{4}\)
• (C) \(\dfrac{-1}{6}+\dfrac{1}{2}+\dfrac{\sqrt{3}}{4}\)
• (D) \(\dfrac{1}{6}+\dfrac{1}{2}-\dfrac{\sqrt{3}}{4}\)

Gas is being pumped into a spherical balloon at the rate of \(30~ft^3/min\). Find the rate at which the radius increases when the radius becomes \(15~ft\).

• (A) \(\dfrac{1}{30}\,ft/min\)
• (B) \(\dfrac{1}{15}\,ft/min\)
• (C) \(\dfrac{1}{30\pi}\,ft/min\)
• (D) \(\dfrac{1}{20\pi}\,ft/min\)

Let the function
\[ f(x)=\frac{x-|x|}{x} \]

Then

• (A) the function is continuous everywhere
• (B) the function is not continuous
• (C) the function is continuous when \(x<0\)
• (D) the function is continuous for all \(x\) except zero

If the direction ratios of two lines are given by
\[ l+m+n=0 \]
\[ mn-2ln+lm=0 \]

then the angle between the lines is

• (A) \(\dfrac{\pi}{4}\)
• (B) \(\dfrac{\pi}{3}\)
• (C) \(\dfrac{\pi}{2}\)
• (D) \(0\)

The equation of normal to the curve
\[ y=\log_e x \]

at the point \(P(1,0)\) is

• (A) \(2x+y=2\)
• (B) \(x-2y=1\)
• (C) \(x-y=1\)
• (D) \(x+y=1\)