NEET Pattern Practice Questions

Thirty Questions. Thirty-Five Minutes. Go.

Sections 1 to 11 built this chapter slowly and worked more than forty problems through it. Section 14 then rebuilt the same material for speed: the statements asked word for word, the formula cards, the period lookup, the proportionality habits, the reference circle used as a clock, and the two special question formats. This section finds out whether any of that survives contact with a timer.

There is no new physics below. There are 30 questions built the way this paper builds them, and one rule that matters more than the rest: you are being tested on pace, not on cleverness. If a question here takes you five lines of algebra, you have misread it.

One syllabus note. Several items below rest on material that sits outside the body text of the rationalised syllabus — damped oscillation, forced oscillation and resonance, springs joined end to end, and the second's pendulum with its effective-gravity variants. NEET has asked about every one of them, so every one is drilled here.

How to attempt this set

Key Point: Blank sheet, pen, timer. Attempt all 30 questions in one unbroken sitting, and do not read a single explanation until your last answer is written. A drill you pause to check is a reading exercise, and reading exercises do not build speed.

The two symbols that decide half of these marks

Key Point: $\omega$ is the angular frequency in radians per second. $\nu$ is the frequency in hertz, oscillations per second. They are linked by $\omega = 2\pi\nu = \frac{2\pi}{T}$, and they are not interchangeable. A question asking for "the frequency" wants $\nu$; one asking for "the angular frequency" wants $\omega$. Read the last four words of every question before you circle anything.

The rest of the alphabet, fixed for all 30 questions.

Two more standing reminders, because two of the questions below are built on them.

Displacement is measured from the mean position, always. For a block hanging on a vertical spring the mean position is the stretched equilibrium, a distance $x_0 = \frac{mg}{k}$ below the spring's natural length. Measure from the natural length instead and every energy and every amplitude comes out wrong. The gravity term cancels exactly, which is why $T = 2\pi\sqrt{\frac{m}{k}}$ carries no $g$ in it at all.

The kinetic and potential energies repeat twice in every cycle of the motion. If $x$ has period $T$, then $K$ and $U$ each have period $\frac{T}{2}$ and frequency $2\nu$. Two questions below pay $+4$ or $-1$ on that single fact.

What this set covers

Five of the thirty are in a special format — two column-matching items and three assertion-reason items — which is about the share the real paper carries. Six more are pure proportionality: what happens to $T$ when the mass is quadrupled, the length made nine times larger, the spring cut or doubled up, or $g$ changed. Those six should take you fifteen seconds each, and if they do not, that is the most profitable thing you will learn from this set.

[Important] The 35-minute limit is the entire exercise. Most students can get 27 of these right given an hour — and an hour is exactly what the real paper will not give you. Finishing in 35 minutes with 24 correct puts you in far better shape than taking 55 minutes to get 27. Keep the timer where you can see it, and the moment a question passes 75 seconds, mark your best surviving option and move on.

Here is the arithmetic that makes that instruction safe. A blind guess among four options is worth $\frac{4 - 3}{4} = +0.25$, essentially nothing. But once you have eliminated two options, a guess between the survivors is worth $\frac{4 - 1}{2} = +1.5$ marks on average. Eliminate first, then commit. Leave blank only what you could not narrow down at all.

Mark It Honestly, Then Read Your Own Answer Sheet

Score with the real scheme: $+4$ for every correct answer, $-1$ for every wrong one, $0$ for every blank. No half marks for "I nearly had that one". The number you end up with is the number that means something.

The bands

Sort your mistakes into three piles

Do this before you read a single explanation. It is the most useful ten minutes in this section.

1. Did not know it. A formula you could not recall — whether $T = 2\pi\sqrt{\frac{m}{k}}$ or $2\pi\sqrt{\frac{k}{m}}$, whether springs joined end to end add their constants or add their reciprocals, whether $\omega^{\,\prime}$ is bigger or smaller than $\omega_0$. Cheapest to fix: it is a memory job, and it takes an evening.
2. Knew it, computed it wrong. You left a $2\pi$ out, took the square root of the wrong side, used the natural length of a hanging spring instead of its stretched equilibrium, or put an angle in degrees into a formula that wanted radians. Slow down for four seconds on the final line.
3. Knew it, answered a different question. You gave $\omega$ when it asked for $\nu$, the period of the energy when it asked for the period of the motion, the displacement where $K = 3U$ when it asked where $U = 3K$, the new period when it asked by what percentage the period changed. The distractors here are built specifically to reward this mistake.

Key Point: Two students both score 88. The first has four pile-1 mistakes and a memory gap that revision closes in a day. The second has nine pile-3 mistakes and a reading habit that will follow them into the exam hall. Pile 3 is the expensive one — count it before you explain it away.

The twelve facts this set keeps testing

• $\omega = 2\pi\nu = \frac{2\pi}{T}$, with $\omega$ in rad/s and $\nu$ in Hz. Every "the frequency is 100" trap lives here.
• $x = A\cos(\omega t + \phi)$; the whole bracket is the phase, $\phi$ alone is the phase constant, and the amplitude changes neither $T$ nor $\nu$.
• $v = -\omega A\sin(\omega t + \phi)$ and $a = -\omega^2 x$, so $v_m = \omega A$ at the mean position and $a_m = \omega^2 A$ at the extremes, and the two maxima never occur together.
• $v = \pm\omega\sqrt{A^2 - x^2}$ answers every "speed at this displacement" question in one line.
• $a$ against $x$ is a straight line of slope $-\omega^2$; $v$ against $x$ is an ellipse of semi-axes $A$ and $\omega A$.
• $T = 2\pi\sqrt{\frac{m}{k}}$ for a spring, with no $g$ in it even when the spring hangs vertically, and $x_0 = \frac{mg}{k}$ for the stretch at equilibrium.
• Side by side (parallel): $k_{\text{eq}} = k_1 + k_2$. End to end (series): $\frac{1}{k_{\text{eq}}} = \frac{1}{k_1} + \frac{1}{k_2}$. Cutting a spring into $n$ equal pieces makes each piece $n$ times stiffer.
• $E = \frac{1}{2}kA^2 = \frac{1}{2}m\omega^2A^2$, constant; $K$ and $U$ swap between $0$ and $E$ with period $\frac{T}{2}$; and $\langle K\rangle = \langle U\rangle = \frac{E}{2}$ over a cycle.
• $T = 2\pi\sqrt{\frac{L}{g}}$ for a pendulum, independent of the mass of the bob and of the amplitude while the amplitude stays small; $L$ runs to the centre of the bob.
• A second's pendulum has $T = 2$ seconds, which is about $0.99$ m where $g = 9.8$ m/s². For lift, car and liquid variants, replace $g$ by the effective $g$ and nothing else changes.
• Damping: $A(t) = A_0e^{-bt/2m}$, $E(t) = E_0e^{-bt/m}$, and $\omega^{\,\prime} = \sqrt{\omega_0^2 - \frac{b^2}{4m^2}} < \omega_0$. Critical damping returns fastest without a single overshoot.
• A driven body settles at the DRIVING frequency $\omega_d$, never its own; resonance is $\omega_d$ close to $\omega_0$, and the peak amplitude goes as $\frac{1}{b}$.

[Important] If you got fewer than 24 right, count how many of your errors were a lost or invented $2\pi$ and how many were an energy question answered with the period of the motion. In this chapter those two between them usually account for more marks than everything else put together, and both are cheap to fix: write the units — rad/s or Hz — beside every frequency the moment it appears, and write $\frac{T}{2}$ beside every energy question before you start it.