Class 12th

Charge Q? and Q? are at point A and B of a right angle triangle OAB (see figure). The resultant electric field at point O is perpendicular to the hypotenuse, then Q?/Q? is proportional to:

An AC circuit has R = 100Ω, C = 2µF and L = 80mH, connected in series. The quality factor of the circuit is:

If f(x+y)=f(x)f(y) and Σₓ₌₁^∞ f(x)=2, x,y∈N where N is the set of all natural numbers, then the value of f(4)/f(2) is:

In the figure below, P and Q are two equally intense coherent sources emitting radiation of wavelength 20 m. The separation between P and Q is 5 m and the phase of P is ahead of that of Q by 90°. A, B and C are three distinct points of observation, each equidistant from the midpoint of PQ. The intensities of radiation at A, B, C will be in the ratio:

The general solution of the differential equation √(1+x²+y²+x²y²) + xy(dy/dx)=0 is: (where C is a constant of integration)

A sound source S is moving along a straight track with speed v, and is emitting sound of frequency v? (see figure). An observer is standing at a finite distance, at the point O, from the track. The time variation of frequency heard by the observer is best represented by:
(t? represents the instant when the distance between the source and observer is minimum)

The area (in sq. units) of the region A={(x,y): |x|+|y|≤1, 2y²≥|x|} is:

If α and β be two roots of the equation x² - 64x + 256 = 0. Then the value of (α³/β⁵)¹/⁸ + (β³/α⁵)¹/⁸ is:

The value of the definite integral ∫π/?π/? dx / (1 + ³√tan2x) is:

Let y = y(x) be the solution of the differential equation dy/dx = 1 + xe^(y-x), -√2 < x < 2, y(0) = 0, then the minimum value of y(x), x (-2,2) is equal to: