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λ = 2000 Å = (2000 × 10-10)m

W_o = 4.2eV

h = 6.63 × 10^-34 JS

(a) Using Einstein's photoelectric equation

K. E. = (6.2 – 4.2) eV = 2.0 eV

(b) The energy of the emitted electrons does not depend upon intensity of incident light; hence the energy remains unchanged.

(c) For this surface, electrons will not be emitted as the energy of incident light (6.2 eV) is less than the work function (6.5 eV) of the surface.

Number of atoms present in 2 g of deuterium = 6 × 10²³

Number of atoms present in 2.0 Kg of deuterium = 6 × 10²⁶

Energy released in fusion of 2 deuterium atoms

= 3.27 MeV

Energy released in fusion of 2.0 Kg of deuterium atoms

= \(\frac{3.27}{2}\) × 6 × 10²⁶ MeV

= 9.81 × 10²⁶ MeV

= 9.81 × 10²⁶ MeV

= 15.696 × 10¹³ J

Energy consumed by bulb per sec = 100 J

Time for which bulb will glow = \(\frac{15.696\times10^{13}}{100}\) s = 4.97 × 10⁴ year

We know that R = R₀ e^-λt

6080 = R₀ e^λt

4465 = R₀ e^-λ(t+60)

^{\(\frac {6080}{4465} = \frac {e^{-λt}}{e^{-λt}} e^{-60λ}\)}

e^+60λ =^{\(\frac {6080}{4465} \)}

e^+60λ= 1.354

60λ = ln (1.354)

λ = \(\frac {1}{60}\) ln (1.354)

λ = \(\frac {0.30}{60}\)

Decay constant λ = 0.005 m

Half life

T_1/2 = \(\frac {0.693}{λ}\)

 T_1/2 = \(\frac {0.693}{0.005}\)

 T_1/2 = 138.6 min

(2) If both assertion and reason are true but reason is not the correct explanation of assertion. 

(2) If both assertion and reason are true but reason is not the correct explanation of assertion. 

An optical devic forms an erect image of an object placed in front of it. If thr size of the image is one half that of the object, the optical device is a Convex mirror.

Incandescent bulbs typically use a tungsten filament because of tungsten’s high melting point. A tungsten filament inside a light bulb can reach temperatures as high as 4500˚F. A glass enclosure prevents oxygen in the air from reaching the hot filament. Tungsten has very high resistivity so it does not burn easily at room temperature.

• Krypton and Xenon filled light bulbs do not burn as hot as argon- filled ones. These gases also have larger atoms than argon gas, making them more effective at bouncing tungsten atoms back to the light filament. This in turn results in longer lasting light bulbs.  
• Avoid frequent switching on and off the bulbs
• Operate the bulbs at low power

Fuses are always connected in series with the device; so that any overcurrent blows the fuse and it will open the entire circuit and stop current through the component(s). An electric fuse in household’s works on the principle of Joule’s heating that heat produced due to the excess current flowing through it melts the fuse wire which cut off the circuit and hence the appliance is prevented from damage. Electrical fuses play the role of miniature circuit breakers.

Uses of concave mirror: 

I. Commonly used in torches, search- lights and vehicles headlights to get powerful parallel beams of light, 

II. Used as shaving mirrors to see a larger image of the face, 

III. Used by dentists, 

IV. Used to concentrate sunlight to produce heat in solar furnaces. 

Uses of convex mirror: 

I. Commonly used as rear- view mirrors in vehicles, 

II. Used in sunglasses and in magnifying glasses, 

III. As street light reflectors, 

IV. Used for security purposes like in ATM’s so that customers can check if someone is behind them.

Correct answer is: (b) 60˚

Ɵ/360˚xπr²=1/6x πr² 

Ɵ=60˚

Mean of the marks of 25 students of XA = 47 

∴Sum of the marks of 25 students = 25 × 47 = 1175 ......(i) 

Mean of the marks of 35 students of XB = 51 

∴Sum of the marks of 35 students = 35 × 51 = 1785 ........(ii) 

Mean of the marks of 30 students of XC = 53

Sum of the marks of 30 students = 30 × 53 = 1590.........(iii) 

Adding (i), (ii) and (iii) 

Sum of the marks of (25 + 35 + 30) i.e., 90 students 

= 1175 + 1785 + 1590 = 4550

Thus the combined mean of the marks of students of three sections 

= 4550/90 = 50.56

1. Correct answer is: (b) 5 units

AB =\(\sqrt{(4-1)^2+(0-4)^2}\)

=√(3²+4² )

AB = 5 units

2. Correct answer is: (a) x-y = 2

(x-7)² + (y-1)²=(x-3)2+(y-5)²

X² + 49-14x+y²+1-2y

= x²+9-6x+y²+25-10y

Simplifying

x-y=2

3. Correct answer is: (a) 3 : 4

3x + y – 9 = 0

Let R divide the line in ratio k:1

R( 2k+1/k+1, 7k+3/k+1)

3(2k+1/k+1) + (7k+3/k+1)-9 = 0

4k-3=0

K=3/4

3 : 4

4. Correct answer is: (c) 3 units

Distance of M from X - axis = √(2-2)²+(0-3)² = √9 = 3 units

5. Correct answer is: (b) (2, 9/2)

( (1+3)/2, (4+5)/2)

= (4/2, 9/2) = (2, 9/2)

PE/EQ = 4/4.5 = 8/9, PF/RF 

∴ PE/ EQ = PF/RF

∴ EF || QR

sin θ  + cosec θ  = 2 so sin θ  = 1 

sinⁿ θ  + cosecⁿ θ  = 2 

(1– cosθ)(1+ cosθ )/(1– sinθ)(1+ sinθ) 

= (1 -cos²θ/1-sin²θ) = tan² θ

= 64/49.

sin 3θ = cos (θ – 6)° 

where (θ – 6)° is an acute angle so 3θ + (θ – 6)° = 90°

∴ θ = 96/4 = 24°