A chain of length L weighing l per unit length begins to fall through a hole in the ceiling.

The velocity of the cart at time t

A rod of length 1000 mm and coefficient of linear expansion a = 10–4 per degree is placed symmetrically between fixed walls separated by 1001 mm. The Young’s modulus of the rod is 1011 N/m2 . If the temperature is increased by 20°C, then the stress developed in the rod is

If coefficient of friction between the two blocks is equal to 0.4, then magnitude of initial slope (in S.I. unit) versus t (in SI unit) will be:

If the angles of a triangle are in ratio 4 : 1 : 1 then the ratio of the longest side and perimeter of triangle is -

So, the ratio of the longest side and perimeter of triangle is

In a triangle PQR as shown in figure given that x : y : z :: 2 : 3 : 6, then the value of QPR is -

If the sides be a, b, c then (r + r₁) tan+ (r + r₂) tan+ (r + r₃) tan =

If in a triangle ABC; AD, BE and CF are the altitudes and R is the circum-radius, then the radius of the circle DEF is -

Therefore, the radius of the circle DEF is R/2.

In an equilateral triangle of side cms, the circum radius is -

The circumradius is 2cm.

If the lines and are concurrent then

is a unit vector such that 0 then a unit vector perpendicular to

The reflection of the point (2, –1, 3) in the plane 3x – 2y – z = 9 is :

A, B, C & D are four points in a plane with position vectors respectively such that Then for the triangle ABC, D is its:

Equation of the angle bisector of the angle between the lines

The sine of angle formed by the lateral face ADC and plane of the base ABC of the tetrahedron ABCD where A º (3, –2, 1) ; B º (3, 1, 5); C º (4, 0, 3) and D º (1, 0, 0) is -

Four coplanar forces are applied at a point O. Each of them is equal to k and the angle between two consecutive forces equals 45º as shown in the figure. Then the resultant has the magnitude equal to :