# Vibrations of rope tied by two rigid ends shown by equation $$y=cos2\pi t\sin2\pi x,$$ then the minimum length of the rope will be: 1. $$1$$ m 2. $$\frac12$$ m 3. $$5$$ m 4. $$2\pi$$ m

Subtopic:  Standing Waves |
64%
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If we change the value of $$R,$$ then:

1. voltage does not change on $$L$$

2. voltage does not change on $$LC$$ combination

3. voltage does not change on $$C$$

4. voltage changes on $$LC$$ combination

Subtopic:  Different Types of AC Circuits |
54%
From NCERT
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If $$V=ar$$ where $$a$$ is a constant and $$r$$ is the distance, then the electric field at a point will be proportional to:
1. $$r$$
2. $$r^{-1}$$
3. $$r^{-2}$$
4. $$r^{0}$$

Subtopic:  Relation between Field & Potential |
73%
From NCERT
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Electric field at point 20 cm away from the centre of a dielectric sphere is 100 V/m, the radius of the sphere is 10 cm, then the value of the electric field at a distance 3 cm from the centre is:

1. 100 V/m

2. 125 V/m

3. 120 V/m

4. 0

Subtopic:  Gauss's Law |
60%
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50 g ice at 0°C in insulator vessel, 50 g water of 100 °C is mixed in it, and then final temperature of the mixture is: (neglect the heat loss)
1. 10°C
2. 0°C << Tm < 20°C
3. 20°C
4. above 20°C

Subtopic:  Calorimetry |
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Real power consumption in a circuit is least when it contains:
1. High $$R$$, low $$L$$
2. High $$R$$, high $$L$$
3. Low $$R$$, high $$L$$
4. High $$R$$, low $$C$$

Subtopic:  Different Types of AC Circuits |
60%
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The linear density of a string is $$1.3\times 10^{-4}~\mathrm{kg/m}$$ and the wave equation is $$y=0.021\sin(x+30t)$$
What is the tension in the string, where $$x$$ is in meters and $$t$$ in seconds?
1. $$0.12 \mathrm{~N}$$
2. $$0.21 \mathrm{~N}$$
3. $$1.2 \mathrm{~N}$$
4. $$0.012 \mathrm{~N}$$

Subtopic:  Wave Motion |
56%
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Magnetic field at point O will be: (assume straight wire segments are infinite)

1. $$\frac{\mu_{_0}l}{2R}$$ interior
2. $$\frac{\mu_{_0}l}{2R}$$ exterior
3. $$\frac{\mu_{_0}l}{2R}1-\frac{l}{\pi}$$ interior
4. $$\frac{\mu_{_0}l}{2R}1-\frac{l}{\pi}$$ exterior

Subtopic:  Magnetic Field due to various cases |
60%
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In Young's double-slit experiment, the spacing between two slits is $$0.1$$ mm. If the screen is kept at $$1.0$$ m from the slits and the wavelength of light is $$5000$$ Å, then the fringe width is:
1. $$5$$ cm
2. $$0.5$$ m
3. $$1$$ cm
4. $$0.5$$ cm

Subtopic:  Young's Double Slit Experiment |
72%
From NCERT
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According to Bohr's model of a hydrogen atom, the relation between the principal quantum number $$n$$ and the radius of the stable orbit is:
1. $$r\propto\frac1n$$
2. $$r\propto n$$
3. $$r\propto\frac{1}{n^2}$$
4. $$r\propto n^2$$