The figure given below shows a long straight solid wire of circular cross-section of radius 'a' carrying steady current I. The current I is uniformly distributed across its cross-section. The plot which correctly represents the variation of magnetic field (B) with distance (r) from the axis of the conductor in the region is :
| 1. |  |
2. |  |
| 3. |  |
4. |  |
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Four statements are given (A is mass number) :
Choose the correct answer from the options given below :
| A. | The volume of a nucleus is proportional to \(A^{1/3 }\). |
| B. | The volume of a nucleus is proportional to A. |
| C. | The difference in mass of an atom and its nucleus is called the mass defect. |
| D. | The difference in mass of a nucleus and its constituents is called the mass defect. |
| 1. | A and D are true, but B and C are false |
| 2. | B and D are true, but A and C are false |
| 3. | B and C are true, but A and D are false |
| 4. | A and C are true, but B and D are false |
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Savitha, a XI standard student, while conducting an experiment to determine the effective length of a simple pendulum L, notes down the data of time taken to complete 30 oscillations as 60 s and hence calculates the length of the simple pendulum as:
\(\left(\text { Take } \pi^2=9 \cdot 8, \text { and } g=9 \cdot 8 \mathrm{~m} / \mathrm{s}^2\right)\)
1. 2 m
2. 1 m
3. \(0 \cdot 75 \mathrm{~m}\)
4. \(1 \cdot 5 \mathrm{~m}\)
\(\left(\text { Take } \pi^2=9 \cdot 8, \text { and } g=9 \cdot 8 \mathrm{~m} / \mathrm{s}^2\right)\)
1. 2 m
2. 1 m
3. \(0 \cdot 75 \mathrm{~m}\)
4. \(1 \cdot 5 \mathrm{~m}\)
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In a vernier callipers, 20 VSD coincide with 16 MSD (each division of length 1 mm). The least count of the vernier callipers is :
1. \(0 \cdot 1 \mathrm{~cm}\)
2. \(0 \cdot 02 \mathrm{~cm}\)
3. \(0 \cdot 01 \mathrm{~cm}\)
4. \(0 \cdot 2 \mathrm{~cm}\)
1. \(0 \cdot 1 \mathrm{~cm}\)
2. \(0 \cdot 02 \mathrm{~cm}\)
3. \(0 \cdot 01 \mathrm{~cm}\)
4. \(0 \cdot 2 \mathrm{~cm}\)
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Each side of a metallic cube of mass 5.580 kg is measured to be 9.0 cm. Keeping the significant figures in view, the density of the material of the cube can be best expressed as \(X \times 10^{3}\text{ kg m}^{-3}\), where the value of X is:
1. 7.654
2. 7.6
3. 7.65
4. 7.7
1. 7.654
2. 7.6
3. 7.65
4. 7.7
Subtopic: Significant Figures |
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In interference and diffraction, the light energy is redistributed. If it reduces in one region, producing a dark fringe, it increases in another region, producing a bright fringe.
Choose the correct answer from the options given below :
| A. | As there is no gain or loss of energy, these phenomena are consistent with the principle of conservation of energy. |
| B. | Diffraction and interference are characteristics exhibited only by light waves. |
Choose the correct answer from the options given below :
| 1. | A is false, but B is true. |
| 2. | A is true and B is also true. |
| 3. | A is true, but B is false. |
| 4. | Both A and B are false. |
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Five capacitors of capacitances;
\(C_1=C_2=C_3=C_4 = 10~\mu\text{F}\) and \(C_5 = 2.5~\mu\text{F}~\) are connected as shown, along with a battery of \(50\) V.
The equivalent capacitance and the charges on each capacitor, respectively, are:
\(C_1=C_2=C_3=C_4 = 10~\mu\text{F}\) and \(C_5 = 2.5~\mu\text{F}~\) are connected as shown, along with a battery of \(50\) V.
The equivalent capacitance and the charges on each capacitor, respectively, are:
| 1. | \(5~\mu\text{F}, 125~\mu\text{C}~\) on \(C_1\) to \(C_4\) and \(25~\mu\text{C}~\) on \(C_5\) |
| 2. | \(4~\mu\text{F}, 250~\mu\text{C}~\) on \(C_1\) to \(C_4\) and \(125~\mu\text{C}~\) on \(C_5\) |
| 3. | \(5~\mu\text{F}, 250~\mu\text{C}~\) on all capacitors |
| 4. | \(5~\mu\text{F}, 125~\mu\text{C}~\) on all capacitors |
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For a simple pendulum having a time period, \(T,\) the variation of kinetic energy \((K.E.)~\) with time \((t)~\) is represented by:
| 1 |  |
2. |  |
| 3. |  |
4. |  |
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A room heater is rated \(400\) W, \(220\) V. If the supply voltage drops to \(200\) V, what will be the power consumed (approximately)?
1. \(121~\text{W}\)
2. \(200~\text{W}\)
3. \(400~\text{W}\)
4. \(331~\text{W}\)
1. \(121~\text{W}\)
2. \(200~\text{W}\)
3. \(400~\text{W}\)
4. \(331~\text{W}\)
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The peak value of an alternating current is \(5\) A and frequency is \(60\) Hz. How long will the current, starting from zero, take to reach the peak value?
1. \(\dfrac{1}{60} ~\text{s}\)
2. \(\dfrac{1}{240} ~\text{s}\)
3. \(\dfrac{1}{30}~\text{s}\)
4. \(\dfrac{1}{120} ~\text{s}\)
1. \(\dfrac{1}{60} ~\text{s}\)
2. \(\dfrac{1}{240} ~\text{s}\)
3. \(\dfrac{1}{30}~\text{s}\)
4. \(\dfrac{1}{120} ~\text{s}\)
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