Mathematics Tes...

Let a, b and c be positive constants. The value of ‘a’ in terms of ‘c’ if the value of integral   is independent of ‘b’ equals

Let  are three vectors along the adjacent edges of a tetrahedron,  if  then volume of tetrahedron is

Let ω be a complex cube root of unity with ω ≠ 1. A fair die is thrown three times. If r₁, r₂ and r₃ are the numbers obtained on the die, then the probability that 

A ray of light travels along a line y = 4 and strikes the surface of a curves y² = 4 (x + y), then equations of the line along which reflected ray travel is

A triangle ABC having vertices A (5, 1), B (–1, –7) and C (1, 4) respectively. If L1 be the line mirror passing through C and parallel to AB, a light ray emanating from point A and goes along the direction of internal bisector of the angle A, which meets the mirror at E and BC at D. Then sum of the area of ΔACE and ΔABC is

The number of different ways in which the persons A, B, C having 6 one rupee coins, 7 one rupee coins, 8 one rupee coins respectively donate 10 one rupee coins collectively is equal

Let a = cos^–1 (cos 20), b = cos^–1 (cos 30) and c = sin^–1 sin (a + b) then maximum value of sin (2 (a+b+c) x) + cos² ((a+b+c) x) is

A rectangle ABCD of dimensions r and 2r is folded along diagonal BD such that planes ABD and CBD are perpendicular to each other. Let the position of the vertex A remains unchanged and C₁ is the new position of C.

The distance of C₁ from A is equal to

A rectangle ABCD of dimensions r and 2r is folded along diagonal BD such that planes ABD and CBD are perpendicular to each other. Let the position of the vertex A remains unchanged and C₁ is the new position of C.

If ∠∠ABC₁ = θ, then cos θ is equal to

A square ABCD of diagonal 2a is folded along the diagonal AC so that the planes DAC and BAC are at right angle. The shortest distance between DC and AB is