Question

Statement I: If three forces ${\overrightarrow{F}}_1, {\overrightarrow{F}}_2$ and ${\overrightarrow{F}}_3$ are represented by three sides of a triangle and $\overrightarrow{F_1}+\overrightarrow{F_2}=-{\overrightarrow{F}}_3,$ then these three forces are concurrent forces and satisfy the condition for equilibrium.
Statement II: A triangle made up of three forces $\overrightarrow{F_1}, \overrightarrow{F_2}$ and $\overrightarrow{F_3}$ as its sides were taken in the same order, satisfies the condition for translatory equilibrium.
In the light of the above statements, choose the most appropriate answer from the options given below:

JEE Main 2021 (31 Aug Shift 2)

Options

• A: Both Statement I and Statement II are true.
• B: Statement I is true but Statement II is false.
• C: Both Statement I and Statement II are false.
• D: Statement I is false but Statement II is true.

Question

Statement-I : Two forces $\left(\overrightarrow{P}+\overrightarrow{Q}\right)$ and $\left(\overrightarrow{P}-\overrightarrow{Q}\right)$ where $\overrightarrow{P}\perp \overrightarrow{Q},$ when act at an angle ${\theta }_1$ each other, the magnitude of their resultant is $\sqrt{3\left(P^2+Q^2\right)},$ when they act at an angle ${\theta }_2,$ the magnitude of their resultant becomes $\sqrt{2\left(P^2+Q^2\right)}.$ This is possible only when ${\theta }_1<{\theta }_2.$
Statement-II : In the situation given above.
${\theta }_1=60°$ and ${\theta }_2=90°$
In the light of the above statement, choose the most appropriate answer from the options given below :

JEE Main 2021 (31 Aug Shift 2)

Options

• A: Statement I is false but Statement II is true.
• B: Both Statement I and Statement II are true.
• C: Both Statement I and Statement II are false.
• D: Statement I is true but Statement II is false.

Question

Three students $S_1,{\mathit{ }\mathit{S}}_2$ and $S_3$ perform an experiment for determining the acceleration due to gravity $\left(g\right)$ using a simple pendulum. They use different lengths of pendulum and record time for different number of oscillations. The observations are as shown in the table.

Student No.	Length of pendulum $\left(\mathrm{cm}\right)$	Number of oscillations $\left(n\right)$	Total time for $n$ oscillations	Time period $\left(\mathrm{s}\right)$
$1.$	$64.0$	$8$	$128.0$	$16.0$
$2.$	$64.0$	$4$	$64.0$	$16.0$
$3.$	$20.0$	$4$	$36.0$	$9.0$

(Least count of length $=0.1 \mathrm{m}$, least count for time $=0.1 \mathrm{s}$)

If $E_1, E_2$ and $E_3$ are the percentage errors in $g$ for students $1, 2$ and $3$, respectively, then the minimum percentage error is obtained by student no $\underline{ }$ $.$

JEE Main 2021 (22 Jul Shift 1)

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Question

The maximum error in the measurement of resistance, current and time for which current flows in an electrical circuit are $1\%,2\%$ and $3\%$ respectively. The maximum percentage error in the detection of the dissipated heat will be:

JEE Main 2022 (25 Jul Shift 2)

Options

• A: $2$
• B: $4$
• C: $6$
• D: $8$

Question

A silver wire has a mass $\left(0.6\pm 0.006\right)\mathrm{g}$, radius $\left(0.5\pm 0.005\right)\mathrm{mm}$ and length $\left(4\pm 0.04\right)\mathrm{cm}$. The maximum percentage error in the measurement of its density will be

JEE Main 2022 (27 Jun Shift 1)

Options

• A: $7\%$
• B: $3\%$
• C: $4\%$
• D: $6\%$

Question

The length of a metallic wire is increased by $20\%$ and its area of cross-section is reduced by $4\%.$ The percentage change in resistance of the metallic wire is $\_\_\_\_\_\_\_\_.$

JEE Main 2023 (06 Apr Shift 1)

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Question

The angle between vector $\vec{Q}$ and the resultant of $(2 \vec{Q}+2 \vec{P})$ and $(2 \vec{Q}-2 \vec{P})$ is :

JEE Main 2024 (05 Apr Shift 1)

Options

• A: $\tan ^{-1} \frac{(2 \vec{Q}-2 \vec{P})}{2 \vec{Q}+2 \vec{P}}$
• B: $0^{\circ}$
• C: $\tan ^{-1}(\mathrm{P} / \mathrm{Q})$
• D: $\tan ^{-1}(2 \mathrm{Q} / \mathrm{P})$

Question

To find the spring constant $(k)$ of a spring experimentally, a student commits $2 \%$ positive error in the measurement of time and $1 \%$ negative error in measurement of mass. The percentage error in determining value of $k$ is :

JEE Main 2024 (06 Apr Shift 1)

Options

• A: $5 \%$
• B: $1 \%$
• C: $3 \%$
• D: $4 \%$

Question

The resultant of two vectors $\vec{A}$ and $\vec{B}$ is perpendicular to $\vec{A}$ and its magnitude is half that of $\vec{B}$. The angle between vectors $\vec{A}$ and $\vec{B}$ is ______ $\circ$.

JEE Main 2024 (09 Apr Shift 2)

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Question

Match List - I with List - II.

List - I (Number)		List - II (Signficant figure)
(A)	$1001$	(I)	$3$
(B)	$010.1$	(II)	$4$
(C)	$100.100$	(III)	$5$
(D)	$0.0010010$	(IV)	$6$

Choose the correct answer from the options given below:

JEE Main 2024 (01 Feb Shift 2)

Options

• A: (A)-(III), (B)-(IV), (C)-(II), (D)-(I)
• B: (A)-(IV), (B)-(III), (C)-(I), (D)-(II)
• C: (A)-(II), (B)-(I), (C)-(IV), (D)-(III)
• D: (A)-(I), (B)-(II), (C)-(III), (D)-(IV)