NEET (UG)

Practice Test 1 — Units, Dimensions & Measurement

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Section A — MCQ (Single Correct)

Question 1

Which of the following is a dimensionless quantity?

Solution: Strain is a ratio of two lengths, so it has no dimensions.

Question 2

The dimensional formula of momentum is:

Solution: Momentum $= mv = [\text{M}][\text{LT}^{-1}] = [\text{MLT}^{-1}]$.

Question 3

$1\ \text{femtometre}$ equals:

Solution: Femto = $10^{-15}$.

Question 4

Which quantity has the same dimensions as the Planck constant ($\text{J}\cdot\text{s}$)?

Solution: Both Planck's constant and angular momentum have dimensions $[\text{ML}^{2}\text{T}^{-1}]$.

Question 5

The percentage error in a measurement of $40.0\ \text{cm}$ with absolute error $0.2\ \text{cm}$ is:

Solution: $\dfrac{0.2}{40.0}\times100 = 0.5\%$.

Question 6

The number of significant figures in $1.20 \times 10^{-3}$ is:

Solution: 1, 2 and the trailing 0 are significant — three figures.

Question 7

If $X = a^{2}b^{3}$ and the percentage errors in $a$ and $b$ are $1\%$ and $2\%$, the maximum percentage error in $X$ is:

Solution: $2(1\%) + 3(2\%) = 2\% + 6\% = 8\%$.

Question 8

The order of magnitude of $89000$ is:

Solution: $89000 = 8.9\times10^{4}$; since $8.9 \ge 5$, the order of magnitude is $10^{5}$.

Question 9

Which pair does not have the same dimensions?

Solution: Force $[\text{MLT}^{-2}]$ and work $[\text{ML}^{2}\text{T}^{-2}]$ differ; the other pairs match.

Question 10

Light year is a unit of:

Solution: A light year is the distance light travels in one year — a unit of length.

Section B — Assertion & Reason

Question 11

Assertion (A): A dimensionally correct equation may still be physically wrong.
Reason (R): Dimensional analysis cannot detect dimensionless constants or numerical factors.

Solution: An equation can match dimensions yet have a wrong numerical factor — exactly because dimensional analysis ignores pure numbers.

Question 12

Assertion (A): The number $0.030$ has two significant figures.
Reason (R): Trailing zeros after a decimal point are significant.

Solution: $0.030$: the leading zeros don't count, 3 and the trailing 0 do — two figures, and R correctly explains why the trailing zero counts.

Question 13

Assertion (A): Systematic errors can be minimised by repeating the measurement many times and averaging.
Reason (R): Averaging cancels errors that are equally likely to be positive or negative.

Solution: Averaging reduces RANDOM (two-way) errors, not systematic (one-way) errors, so A is false; R correctly describes random errors, so R is true.

Question 14

Assertion (A): The argument of $\sin\theta$ must be dimensionless.
Reason (R): Trigonometric functions are defined only for pure numbers (angles in radians are dimensionless).

Solution: Arguments of trig functions must be dimensionless, precisely because such functions act on pure numbers.

Question 15

Assertion (A): Accuracy and precision mean the same thing.
Reason (R): Both describe the quality of a measurement.

Solution: Accuracy (closeness to true value) and precision (agreement of repeats) are different, so A is false; both do describe measurement quality, so R is true.