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Tangents are drawn to a unit circle with centre at the origin from each point on the line 2x + y = 4. Then the equation to the locus of the middle point of the chord of contact is

Solution: Equation of unit circle with centre at origin is x2+y2 = 1. Given line, L: 2x+y = 4 Let A(x1, y1) be a point on the line L. Then... View Article

Surface tension of water is 0.072N/m. The excess pressure inside a water drop of a diameter 1.2 mm is:

a) 240 N/m2 b) 24 N/m2 c) 0.06 N/m2 d) 60 N/m2 Answer: b) 24 N/m2 Solution: Given : S= 0.072 N/m Diameter of... View Article

A small block of mass m is kept on rough inclined surface of inclination θ fixed in an elevator. The elevator goes up with a uniform velocity v and the block does not slide on the wedge. The work done by the force of friction on the block in time t will be

a) zero b) mgvt cos2θ c) mgvt sin2θ d) mgvt sin2θ Answer: c) mgvt sin2θ Solution: Wf =fsinθS... View Article

Stationary waves of frequency 200 Hz are formed in air. If the velocity of the wave is 360 m/s, the shortest distance between two antinodes is<

a) 1.8 m b) 3.6 m c) 0.9 m d) 0.45 m Answer: c) 0.9 m Solution: The shortest distance between two antinodes is equal to half of... View Article

What happens to the atomic number of an element when emits a β⁺ particle.

a) decrease by 1 b) increase by 1 c) remains unchanged d) becomes 1 Answer: a) decrease by 1 Solution: The atomic number decreases by... View Article

The time period of Jupiter is 11.6 years. How far is Jupiter from the Sun? The distance of the earth from the sun is 1.5 x 10¹¹ m.

a) 7.68 x 1011 m b) 9 x 1011 m c) 68 x 1011 m d) 8 x 1011 m Answer: a) 7.68 x 1011 m Solution: Kepler's relation (Tj2)/(Te2) =... View Article

A balloon is filled with hydrogen at room temperature, it will burst if pressure exceeds 0.2 bar. If at 1 bar pressure the gas occupies 2.27 L volume, up to what volume can the balloon be expanded?

Answer: 11.35 LSolution: According to Boyle's lawP1V1 = P2V2 V2 = (1 bar x 2.27 L)/0.2 bar = 11. 35 L Since the balloon bursts at 0.2bar... View Article

Power factor may be equal to 1 for :

a) pure inductor b) pure capacitor c) pure resistor d) an LCR circuit Answer: d) an LCR circuit Solution:... View Article

A potential difference of 20 kV is applied across an X-ray tube. The minimum wavelength of X-rays generated is ____________ À

a) 1.621 À b) 0.621 À c) 2.621 À d) 5.621 À Answer: b)... View Article

An object have a velocity [latex]overrightarrow{v}=(widehat{i}+widehat{j})[/latex] m/s at time t=0. It undergoes a constant acceleration [latex]a=(hat{i}-2hat{j})[/latex] ms⁻² for 4 second. The magnitude of velocity at the end of 4 s is:

a) √74 m/s b) √80 m/s c) √97 m/s d) √47 m/s Answer: a) √74 m/s Solution: Intial... View Article

Two small charged spheres A and B have charges of 10μC and 40μC respectively and are held at a separation of 90cm from each other. At what distance from A, electric field intensity would be zero?

a) 22.5 cm b) 18 cm c) 30 cm d) 36 cm Answer: c) 30 cm Solution: Electric field intensity = kq/x² Now the distance from B will... View Article

A cell of e.m.f E and internal resistance r is connected across a resistance r. The potential difference between the terminals of the cell must be

a) E b) E/2 c) 3E/4 d) 3E Answer: b) E/2 Solution: Current in the circuit, i = E/(r + r) = E/2r Potential difference across cell, V =... View Article

A particle of mass m is released on a smooth track in a vertical plane which transforms into a circular arc of radius R. Find the reaction force exerted at the bottom-most position.

a) 6mg b) 7mg c) 5mg d) 9mg Answer: a) 6mg Solution: The reaction force at the bottom is 6 mg... View Article

A ray of white light incident upon a glass prism is dispersed into various colour components. Which one of the following colours experiences the least refraction?

a) Red b) Yellow c) Orange d) Blue Answer: a) Red The light waves are refracted as they enter and leave the prism. The... View Article

Two small spheres, each of mass 0.1 gm and carrying same charge 10⁻⁹ C are suspended by threads of equal length from the same point. If the distance between the centres of the sphere is 3 cm, then find out the angle made by the thread with the vertical. (g = 10 m/s²) & tan⁻¹(1/100)=0.6⁰

Answer: 0.60 Solution: Tsinθ = Kq1q2/r2 Tcosθ = mg ⇒ tanθ = (Kq1q2/r2)/mg = [(9 x 109) x (10-19)2]/[(0.03)2 x 0.1 x 10-3 x 10] = 0.01... View Article

A body of mass m is placed on a rough surface with a coefficient of friction μ inclined at angle θ. If the mass is in limiting equilibrium, then

a) θ = tan-1 (m/μ) b) θ = tan-1 (μ) c) θ = tan-1 (μ/m) d) θ = tan-1 (1/μ) Answer: b) θ = tan-1 (μ) Solution: Given, mass of the body = m... View Article

The force [latex]overrightarrow{F}[/latex] experienced by a particle of charge q moving with a velocity [latex]overrightarrow{V}[/latex] in a magnetic field [latex]overrightarrow{B}[/latex] is given by [latex]overrightarrow{F}= q(overrightarrow{v}timesoverrightarrow{B})[/latex]. . Which pairs of vectors are always at right angles to each other?

a) b) c) d) Answer: a and b Solution: The pairs may have any angle between them.... View Article

A star that is emitting radiation at a wavelength of 5000 Å, is approaching the earth with a velocity of 1.5 x 104 m/s. The change in wavelength of the radiation as received on the earth is

(a) 25 Å (b) 100 Å (c) Zero (d) 2.5 Å Answer: (a) 25 Å Solution: Wavelength of the approaching star,... View Article

The logic gate realised from the circuit as shown in figure is (p and q are inputs and z is output)

a) XOR b) XOR c) NOR d) OR Answer: b) XOR Solution: P Q Y 0 0 0 0 1 1 1 0 1 1 1 0 Y = P ⊕ Q... View Article

Consider the situation given in the figure. The wire AB is slid on the fixed rails with a constant velocity. If the wire AB is replaced by a semicircular wire, the magnitude of the induced current will

a)decrease b) increases c)increase or decrease depending on whether the semicircle bulges towards the resistance or away from it d)remain same... View Article