A heater is designed to operate with a power of 1000 W in a 100 V line. It is connected in combination with a resistance of 10 Ω and a resistance R to a 100 V line as shown in the figure. What should be the value of R so that the heater operates with a power of 62.5 W?
A rectangular loop carrying a current i is situated near a long straight wire such that the wire is parallel to one of the sides of the loop. If a steady current is established in the wire, as shown in the figure, the loop will
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A ray of light travels from a medium of refractive index n1 to a medium of refractive index n2. If angle of incidence is i and the angle of refraction is r. Then sini/sinr is equal to
Transverse wave of amplitude 10 cm is generated at one end (x = 0) of a long string by a tuning fork of frequency 500 Hz. At a certain instant of time, the displacement of a particle A at x = 100 cm is -5 cm and of particle B at x = 200 cm is +5 cm. What is the wavelength of the wave?
Two masses of M and 4M are moving with equal kinetic energy. The ratio of their linear momentum is
A smooth sphere 'A' is moving on a frictionless horizontal surface with angular speed ω and centre of mass velocity v. It collides elastically and head-on with an identical sphere B at rest. Neglect friction everywhere. After the collision, their angular speeds are ωA and ωB, respectively. Then,
Two particles of masses ma and mb and and same charge are projected in a perpendicular magnetic field. They travel along circular paths of radius ra and rb and such that ra > rb. Then which is true?
Two progressive waves having equation x1=3 sin ωt sin and x2=4 sin (ωt + 90o) are super imposed. The amplitude of the resultant wave is :
If C(s) + O2(g) → CO2(g), ΔH = -X,
CO(g) + (1/2)O2(g) → CO2(g), ΔH = -Y,
Calculate ΔrH for CO(g) formation
Which of the following sets of solutions of urea (mol, mass 60 g mol-1) and sucrose (mol. mass 342 g mol-1) is isotonic?
Relationship between van't Hoff's factor (i) and degree of dissociation (α) is
The solution of the differential equation dθ/dt = - k(θ - θ0) where k is constant, is …….
The equation of the circle concentric with the circle x2 + y2 - 6x - 4y -12 = 0 and touching the Y-axis is ..........
The pdf of a random variable X is f(x) = 3(1 - 2x2), 0 < x="" />< 1="0" />
A player tosses 2 fair coins. He wins Rs. 5 if 2 heads appear, Rs. 2 If 1 head appear and Rs. 1 if no head appears, then the variance of his winning amount is
The particular solution of the differential equation log(dy/dx) = x, when x = 0, y = 1 is ...
If A, B, C and D are (3, 7, 4), (5, -2, 3), (-4, 5, 6) and (1, 2, 3) respectively, then the volume of the parallelepiped with AB, AC and AD as the coterminous edges, is ....... cubic units.
The set of all values of k for which (tan-1x)3 + (cot-1x)3 = kπ3, x ∈ R, is the interval:
Consider the line L given by the equation . Let Q be the mirror image of the point (2, 3, -1) with respect to L. Let a plane P be such that it passes through Q, and the line L is perpendicular to P. Then which of the following points is on the plane P?
Let f(x) be a polynomial function such that f(x) + f'(x) + f''(x) = x5 + 64 and fv(x) = 120. Then, the value of
Area of the region bounded by y = cosx, x = 0, x = π and X-axis is ...sq. units.
If f(x) is continuous at x = 3, where
f(x) = ax +1, for x ≤ 3
= bx + 3, for x > 3 then
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