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At each point (x, y) of a curve, the intercept of the tangent on the y-axis is equal to 2xy². Find the equation of the curve.

(a) (x/y) = x2+c (b) y/x = y2+c (c) x/y = y2+c (d) y/x = x2+c Solution: Equation of the tangent is y = mx+c Given that c = 2xy2 Slope m =... View Article

In the figure PQ, PR and BC are the tangents to the circle. BC touches the circle at X. If PQ = 7 cm, find the perimeter of ∆PBC.

Solution: Given PQ = 7 cm We know that the tangents from an external point to a circle are equal. So PQ = PR (tangents from point P) XC = CR... View Article

A Carnot engine absorbs 2000 J of heat energy from a reservoir at 127⁰C and rejects 800 J of heat energy during each cycle. The efficiency of engine and temperature of sink will be respectively

Answer: Solution: Efficiency of Carnot cycle is η = (Q1 - Q2)/Q1 = [(2000 - 800)/2000] x 100 = [1200/2000] x 100 = 60% Also,... View Article

A particle of mass 0.1kg executes SHM under a force F=(−10x)N. The speed of particles at the mean position is 6m/s. Then amplitude of oscillations is

a) 0.6 m b) 0.2 m c) 0.4 m d) 0.1 m Answer: a) 0.6 m Solution: From conservation fo mechanical energy. (1/2)KA2 = (1/2)mv2 A =... View Article

Effect of diffraction can be neglected when the distance between screen and lens/slit is

a) greater than a2/λ b) less than or equal to a2/λ c) any value greater than 50λ d) more than 10 km Answer: b)... View Article

What will be the input of A and B for Boolean expression

What will be the input of A and B for Boolean expression a) 0,0 b) 0,1 c) 1,0 d) 1,1 Answer: a) 0,0 Solution: A = 0, B = 0... View Article

An AND gate is followed by a NOT gate in series. With two inputs A & B, the Boolean expression for the output Y will be:

a) A.B b) A + B c) d) Answer: d) Solution: The Boolean expression for AND gate is A.B and if it is followed by a... View Article

ABC is an equilateral triangle. Charges +q are placed at each corner as shown in the figure. The electric intensity at centre O will be

a) (1/4πε0)(q/r) b) (1/4πε0)(q/r2) c) (1/4πε0)(3q/r2) d) zero Answer: d) zero Solution: E = (1/4πε0)(q/r2) EA = EB = EC... View Article

Three uniform spheres each having a mass M and radius a are kept in such a way that each touches the other two. Find the magnitude of the gravitational force on any of the spheres due to the other two

Answer: (√3/4)(GM2/a2] Solution: F1 = F2 = GM2/(2a)2 Fnet = F1cos 300 + F2cos300 = (√3/2) x 2 x GM2/(2a)2 = √3GM2/4a2... View Article

A particle is projected from the earth surface, at the topmost point of its path, the particle has an acceleration of magnitude

a) g/2 b) g c) 2g d) zero Answer: g Solution: At the topmost point, its acceleration will only be caused by the force of gravity. So the... View Article

A particle of mass m is projected with a velocity [latex]6hat{i}+8hat{j}[/latex]. Then the magnitude of change in momentum when it just touches the ground will be

a) 0 b) 12 m c) 16 m d) 20 m Answer: c) 16 m Solution: Initial velocity Final velocity Change in the momentum, ... View Article

The resultant of two forces has magnitude of 20N . if one of the forces is of magnitude 20√3 N and makes an angle of 30⁰ with the resultant then, the other forces must be of magnitude.

a) 10√3 N b) 20 N c) 20√3 N d) 10 N Answer: b) 20 N Solution: Given, A = 20√3 N, B = 20 N B2 = R2 + A2 - 2RAcos 300 = 400... View Article

Two different loops are concentric and lie in the same plane. The current in the outer loop is clockwise and increasing with time. The induced current in the inner loop then is

a) clockwise b) zero c) counter clockwise d) in a direction that depends on the ratio of the loop radii Answer: c) counter clockwise... View Article

A voltage of 10V and frequency 1000Hz is applied to a (1/π)μF capacitor in series with a resistor of 500 Ω. Find the power factor of the circuit and the average power dissipated.

a) 40.018 W b) 0.1 W c) 10.18 W d) 20.018 W Answer: b) 0.1 W Solution: Given, v = 10 V f = 1000 Hz C... View Article

A uniform rod is placed on two spinning wheels as shown in the figure. The axes of the wheels are separated by l = 20 cm, the coefficient of friction between the rod and the wheel is k = 0.18. Show that rod performs SHM and find the period of small oscillations.

Answer: 1.5s Solution: In the equilibrium position the C.M. of the rod lies betweent the two rotating wheels. Let us displace the rod... View Article

A Carnot engine whose sink is at 300 K has an efficiency of 40%. By how much should the temperature of the source be increased so as to increase its efficiency by 50% of original efficiency?

(a) 380 K (b) 275 K (b) 215 K (d) 250 K Answer: (d) 250 K Solution: The efficiency of a Carnot engine, η = 1 - (T2/T1)... View Article

The two ends of a train moving with constant acceleration pass a certain point with velocities u and 3u. The velocity with which the middle point of the train passes the same point is

a) 2u b) (3/2) u c) √5u d) √10u Answer: c) √5u Solution: Initial velocity, u = u final velocity, v =... View Article

The distance travelled by a freely falling body is given by the equation, y = v₀ t – (1/2)gt². Using principles of dimensions, check the correctness of the equation.

Answer: Formula is dimensionally correct Solution: For checking dimensional correction, the principle of Homogeneity is used According... View Article

If an AC ammeter reads I A in an AC circuit, then the peak value of the current is

a) I/√2 b) I c) √2I d) 2I Answer: c) √2I Solution: Irms = I A I = Io Sin ωt = Io /√2... View Article

The applied potential difference in the circuit shown is V=10sin100t where V is in volt and t is in second. If the power factor of the circuit is 1/√2, then the value of capacitance C of the circuit nearly is:

a) 111 μF b) 333 μF c) 222 μF d) 444 μF Answer: a) 111 μF Solution: C = 111 μF... View Article