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

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)}

Statement- (1) : PQ is a focal chord of a parabola. Then the tangent at P to the parabola is parallel to the normal at Q.
Statement- (2) : If P(t₁) and Q(t₂) are the ends of a focal chord of the parabola y² = 4ax, then t₁t₂ = –1.

slopes at the two extremeties of a focal chord are : (t,-1/t)
this property is used to explain the behaviour of tangents and normals at the respective points.

Statement- (1) : Let () and () are the ends of a focal chord of = 4x then
Statement- (2) : PSQ is the focal of a parabola with focus S and latus rectum then SP + SQ = 2.

Statement- (1) : If 4 & 3 are length of two focal segments of focal chord of parabola y² = 4ax than latus rectum of parabola will be 48/7 units
Statement- (2) : If 1 & 2 are length of focal segments of focal chord than its latus rectum is .

The current i in an inductance coil varies with time, t according to the graph shown in fig. Which one of the following plots shows the variation of voltage in the coil with time

Figure (i) shows a conducting loop being pulled out of a magnetic field with a speed v. Which of the four plots shown in figure (ii) may represent the power delivered by the pulling agent as a function of the speed v

The graph gives the magnitude B(t) of a uniform magnetic field that exists throughout a conducting loop, perpendicular to the plane of the loop. Rank the five regions of the graph according to the magnitude of the emf induced in the loop, greatest first

Some magnetic flux is changed from a coil of resistance 10 ohm. As a result an induced current is developed in it, which varies with time as shown in figure. The magnitude of change in flux through the coil in webers is

A horizontal loop abcd is moved across the pole pieces of a magnet as shown in fig. with a constant speed v. When the edge ab of the loop enters the pole pieces at time t = 0 sec. Which one of the following graphs represents correctly the induced emf in the coil

An alternating current of frequency 200 rad/sec and peak value 1A as shown in the figure, is applied to the primary of a transformer. If the coefficient of mutual induction between the primary and the secondary is 1.5 H, the voltage induced in the secondary will be

The current through a 4.6 H inductor is shown in the following graph. The induced emf during the time interval t = 5 milli-sec to 6 milli-sec will be