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Given:

In 100 m race, A covers the distance in 36 seconds and B in 45 seconds.

Formula used:

Speed = distance/time

Distance = Speed × time

Calculation:

In 100 m race, A covers the distance in 36 seconds and B in 45 seconds.

According to the question,

A beats B by = (45 – 36) second

⇒ 9 second

Speed of B = 100/45

Distance covered by B in 9 second 

⇒ (100/45)× 9

⇒ 20 m

∴ A beats by B by 20 m.

Given:

Distance = 1500 meters

Rajiv beats Sanjay by 30 meters 

Rajiv beats Vijay by 100 meters 

Calculations:

Rajiv runs distance = 1500 meters

Sanjiv runs distance = 1500 - 30 

⇒ 1470 metes

Vijay runs distance = 1500 - 100

⇒ 1400 meters

At the same rate, Sanjiv runs 1500 meters while Vijay runs = 1500 × 1400/1470

⇒ 1428.57

Sanjay beats Vijay by =1500 - 1428.57

⇒ 71.42 meters

 ∴ Sanjiv ought to beat Vijay by 71.4 meters.

Given:

In a 200 metres race A beats B by 35 m or 7 seconds.

Formula used:

Time = Distance/speed

Calculation:

According to the question,

B runs 35 m in 7 second

Speed of B = Distance/time

⇒ 35/7

⇒ 5 m/sec

B covers 200 m in = 200/5

⇒ 40 second

A's time over the course = (40 – 7) second

⇒ 33 second.

∴ A's time over the course is 33 second.

Distance travelled by Nitin, when Rajat finishes the race = 1560 – 240 = 1320 m

As we know, the speed is directly proportional to the distance covered if the time taken is constant.

Thus, the ratio of speeds of Rajat and Nitin = 1560/1320 = 13/11

Let 13x and 11x be the speeds of Rajat and Nitin respectively.

On the slope,

New speed of Rajat = (1 – 10%)13x = (0.9)13x = 11.7x

New speed of Nitin = (1 + 3/22)11x = (25/22)11x = 12.5x

Let’s assume Rajat and Nitin met each other on the slope after t time.

Then, according to question, 12.5xt – 11.7xt = 20 ⇒ xt =20/0.8 = 25

Thus, total length of the slope = 12.5xt + 11.7xt = 24.2xt = 24.2 × 25 = 605 m

A. the highest energy of any electron

B. the individual contributions cancel each other

E. is much less than that of a proton

D. An insulator has a large energy separation between the highest filled band and the lowest empty band

A. increase the number of electrons in the conduction band 

E. near the center of the gap between the valence and conduction bands

B. the width of the depletion zone

B. is in a range below 1.5 × 10⁻⁶ m

E. the junction gets hot

E. none of the above

Answer is (1) 121 J

W = F.d = (10i - 3j + 6k).(10i – 2j + 7k - 6i - 5j + 3k) = (10i - 3j + 6k).(4i – 7j + 10k) 

= 40 + 21 + 60 = 121 J 

Option : (B) -7

Resistivity of metallic conductors commonly increases with a rise in temperature. But resistivity of semiconductors like carbon and silicon decreases generally with temperature rise. Good insulators, or dielectrics, have high resistivities and also low conductivities.

The first ionization energy decreases down a group in the periodic table. 
Because the atoms increases in atomic size down the group, the electron clouds of these non-polar atoms become increasingly polarized, which leads to weak van Der Waals forces among the atoms.  Thus, the formation of liquids and solids is more easily attainable for these heavier elements because of their melting and boiling points.

1) 200.450

Significant figure = 6

2) 10.50

Significant figure = 4

3) 4.005

Significant figure = 4

4) 50

= 5 x 10

Significant figure = 1

The sources of light, which emit continuous light waves of the same wavelength, same frequency and in same phase or having a constant phase difference are called coherent sources. When there is a single source of light, the distribution of light energy in the surrounding medium is uniform in all the directions. But, when we have two coherent sources of light emitting continuous waves of same amplitude, same wavelength and in the same phase (or with a constant phase difference), the distribution of light energy does not remain uniform in all the directions. At some points, where the crest of one wave falls on crest of the other, resultant amplitude is maximum. At certain other points, crest of one wave falls on trough of the other; and resultant amplitude becomes minimum (zero). 

This modification in energy distribution due to coherent sources gives rise to sustained interference pattern.

Option: (c) 6/7

Option : (b) f(A)=B

Even for a conductor in the form of a sheet or plate, an emf is induced when magnetic flux linked with it changes. But the difference is that there is no definite loop or path for induced current to flow away. As a result, the induced currents flow in concentric circular paths. As these electric currents resemble eddies of water, these are known as Eddy currents. They are also called Foucault currents.

(c) A very high current gain

(A) first overtone

Consider a waves moves along the positive direction of x with a velocity v. Let the displacement at any instant at time t at x = 0 is

y = a sin ωt

Here, v to be the wave velocity. We have form for λ displacement phase change is 2π so for x displacement the phase change Q = \(\frac {2π}λ\)x so we get 

y = a sin (ωt - Q)

y = a sin (ωt - \(\frac {2π}λ\)x)

y = t (vt - x)

y = a sin \(\frac {2π}λ\) (vt - x)