When a particle with charge \(+q\) is thrown with an initial velocity \(v\) towards another stationary change \(+Q,\) it is repelled back after reaching the nearest distance \(r\) from \(+Q.\) The closest distance that it can reach if it is thrown with an initial velocity \(2v,\) is:
1.
\(\dfrac{r}{4}\)
2.
\(\dfrac{r}{2}\)
3.
\(\dfrac{r}{16}\)
4.
\(\dfrac{r}{8}\)
The determination of the value of acceleration due to gravity \((g)\) by simple pendulum method employs the formula,
\(g=4\pi^2\frac{L}{T^2}\)
The expression for the relative error in the value of \(g\) is:
1. \(\frac{\Delta g}{g}=\frac{\Delta L}{L}+2\Big(\frac{\Delta T}{T}\Big)\)
2. \(\frac{\Delta g}{g}=4\pi^2\Big[\frac{\Delta L}{L}-2\frac{\Delta T}{T}\Big]\)
3. \(\frac{\Delta g}{g}=4\pi^2\Big[\frac{\Delta L}{L}+2\frac{\Delta T}{T}\Big]\)
4. \(\frac{\Delta g}{g}=\frac{\Delta L}{L}-2\Big(\frac{\Delta T}{T}\Big)\)
A monochromatic light of frequency \(500~\text{THz}\) is incident on the slits of Young's double slit experiment. If the distance between the slits is \(0.2~\text{mm}\) and the screen is placed at a distance \(1~\text{m}\) from the slits, the width of \(10\) fringes will be:
| 1. | \(1.5~\text{mm}\) | 2. | \(15~\text{mm}\) |
| 3. | \(30~\text{mm}\) | 4. | \(3~\text{mm}\) |
In a meter bridge experiment, the null point is at a distance of \(30~\text{cm}\) from \(A.\) If a resistance of \(16~\Omega\) is connected in parallel with resistance \(Y\), the null point occurs at \(50~\text{cm}\) from \(A.\) The value of the resistance \(Y\) is:
| 1. | \(\dfrac{112}{3}~\Omega\) | 2. | \(\dfrac{40}{3}~\Omega\) |
| 3. | \(\dfrac{64}{3}~\Omega\) | 4. | \(\dfrac{48}{3}~\Omega\) |
The temperature at which the RMS speed of atoms in neon gas is equal to the RMS speed of hydrogen molecules at \(15^{\circ} \text{C}\) is:
(the atomic mass of neon \(=20.2~\text u,\) molecular mass of hydrogen \(=2~\text u\))
1. \(2.9\times10^{3}~\text K\)
2. \(2.9~\text K\)
3. \(0.15\times10^{3}~\text K\)
4. \(0.29\times10^{3}~\text K\)
Two planets orbit a star in circular paths with radii \(R\) and \(4R,\) respectively. At a specific time, the two planets and the star are aligned in a straight line. If the orbital period of the planet closest to the star is \(T,\) what is the minimum time after which the star and the planets will again be aligned in a straight line?
| 1. | \((4)^2T\) | 2. | \((4)^{\frac13}T\) |
| 3. | \(2T\) | 4. | \(8T\) |
The correct order for boiling points of the following compounds is:
| 1. | AsH3 > PH3 > NH3 > SbH3 > BiH3 |
| 2. | BiH3 > SbH3 > NH3 > AsH3 > PH3 |
| 3. | NH3 > PH3 > AsH3 > SbH3 > BiH3 |
| 4. | PH3 > NH3 > AsH3 > SbH3 > BiH3 |
Match List-I with List-II:
| List-I (Quantities) |
List-II (Corresponding Values) |
||
| (a) | 4.48 litres of O2 at STP | (i) | 0.2 mole |
| (b) | 12.022 × 1022 molecules of H2O | (ii) | 12.044 × 1023 molecules |
| (c) | 96 g of O2 | (iii) | 6.4 g |
| (d) | 88 g of CO2 | (iv) | 67.2 litres at STP |
Choose the correct answer from the options given below:
| (a) | (b) | (c) | (d) | |
| 1. | (i) | (iii) | (iv) | (ii) |
| 2. | (iii) | (i) | (iv) | (ii) |
| 3. | (iv) | (i) | (ii) | (iii) |
| 4. | (iii) | (i) | (ii) | (iv) |
Given below are two statements:
| Statement I: | Aldehydes and ketones having at least one \(\alpha\)-hydrogen undergo aldol condensation in the presence of dilute alkali as catalyst. |
| Statement II: | When aldol condensation is carried out between two different aldehydes, it is called cross aldol condensation. Ketones do not give this reaction. |
In light of the above statements, choose the most appropriate answer from the options given below:
| 1. | Statement I is correct and Statement II is incorrect. |
| 2. | Statement I is incorrect and Statement II is correct. |
| 3. | Both Statement I and Statement II are correct. |
| 4. | Both Statement I and Statement II are incorrect. |
Match List-I with List-II:
| List-I Elements |
List-II Atomic radii (pm) |
||
| (a) | Oxygen (\(O\)) | (i) | 88 |
| (b) | Carbon (\(C\)) | (ii) | 74 |
| (c) | Boron (\(B\)) | (iii) | 66 |
| (d) | Nitrogen (\(N\)) | (iv) | 77 |
| (a) | (b) | (c) | (d) | |
| 1. | (ii) | (i) | (iv) | (iii) |
| 2. | (iv) | (iii) | (ii) | (i) |
| 3. | (i) | (iv) | (iii) | (ii) |
| 4. | (iii) | (iv) | (i) | (ii) |
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