In the figure, ABC; is triangle in which C = 90º and AB = 5 cm. D is a point on AB such that AD = 3 cm and = 60º. Then the length of AC is –

If f(x) =, then equals

The figure shows four wire loops, with edge lengths of either L or 2L. All four loops will move through a region of uniform magnetic field (directed out of the page) at the same constant velocity. Rank the four loops according to the maximum magnitude of the e.m.f. induced as they move through the field, greatest first

A magnet is made to oscillate with a particular frequency, passing through a coil as shown in figure. The time variation of the magnitude of e.m.f. generated across the coil during one cycle is

A square loop of side 5 cm enters a magnetic field with 1 cms^-1. The front edge enters the magnetic field at t = 0 then which graph best depicts emf

Switch S of the circuit shown in figure. is closed at t = 0. If e denotes the induced

emf in L and i, the current flowing through the circuit at time t, which of the following graphs is correct

The current i in an induction coil varies with time t according to the graph shown

in figure. Which of the following graphs shows the induced emf (e) in the coil with time

A flexible wire bent in the form of a circle is placed in a uniform magnetic field perpendicular to the plane of the coil. The radius of the coil changes as shown in figure. The graph of induced emf in the coil is represented by

When a certain circuit consisting of a constant e.m.f. E an inductance L and a resistance R is closed, the current in, it increases with time according to curve 1. After one parameter (E, L or R) is changed, the increase in current follows curve 2 when the circuit is closed second time. Which parameter was changed and in what direction

In the following figure, the magnet is moved towards the coil with a speed v and induced emf is e. If magnet and coil recede away from one another each moving with speed v, the induced emf in the coil will be

The equation . where a, b, c are the sides of a ΔABC, and the equation have a common root. The measure of is-

in a right angled isosceles triangle, ratio of sides = 1:√2:1
base angles are = 45 degrees.

If in a ΔABC, (sin A + sin B + sin C)(sin A + sin B – sin C)= 3 sin A sin B, then –

the sine rule states that
a/sin A =b/sin B = c/sinC = 2R
this is used to find the relation of the angles and sides of the triangles.

In the adjacent figure 'P' is any interior point of the equilateral triangle ABC of side length 2 unit –

If xa, xb and xc represent the distance of P from the sides BC, CA and AB respectively then xa + xb + xc is equal to -

area of equilateral triangle = √3a²/4
area of triangle = 1/2 x base x height

The expression is equal to -

In a triangle ABC, cos A = (b²+c²-a²)/2bc
 

In the figure, if AB = AC, and AE = AD, then x is equal to

exterior angle = sum of interior opposite angles is a property of triangles
sum of interior angles of a triangle = 180 degree

Statement- (1) : The tangents drawn to the parabola y² = 4ax at the ends of any focal chord intersect on the directrix.
Statement- (2) : The point of intersection of the tangents at drawn at P(t₁) and Q(t₂) are the parabola y² = 4ax is {at₁t₂, a(t₁ + t₂)}