Mathematics Tes...

If the line ℓx + my + n = 0 is tangent to the circle x² + y² – 2ax = 0, then

 is equal to

then the value of (1/k) is equal to -

(Where C is constant of integration)

If a,b,c are unequal real numbers in G.P. and 'a' is their harmonic mean then 

(where [.] denotes greatest integer function)

Let  (k + ce^x2/2) sin y = 1be the solution of x siny tany dx = x tany dx + dy, then k is equal to - 

One of the possible equation of the chord of x² + y² = 100 that passes through (1,7) and subtends an angle 2π/3 at the origin, is -

A plane 2x + 3y + 5z = 1 has point P which is at minimum distance from the line segment joining A(1, 0, –3) and B(1, –5, 7), then distance AP is equal to -

The angle of intersection between the curves  dt and x-axis is (where x ≠ 0) -

Let y = g(x) be the inverse of a bijective mapping f : R → R, f(x) = 3x³ + 2x. The area bounded by graph of  g(x), the x-axis and the ordinate at x = 5 is -

A 12 digit number starts with 2 and all its digits are prime, then the probability that the sum of any two consecutive digits of the number is prime is 1/2^k, where k is equal to -