Maths

The tangent at a point where eccentric angle 60° on the ellipse x²/a² + y²/b² = 1(a > b) meet the auxiliary circle at L and M. If LM subtends a right angle at the centre, then eccentricity of the ellipse is:

Set of all possible values of k for which f(x) = sin x – cos x – kx + b decreases for all real values of x, is:

The value of 'a' for which the straight line 4x – 3y + 4z – 2 = 0 = 3x – 2y + z – 5 is parallel to the plane 2x – y + az – 7 = 0, is:

a, b, c are positive integers forming an increasing G.P. whose common ratio is a natural number. b – a is cube of a natural number and log? a + log₆ b + log_e c = 6, then a + b + c =

Let α and β are roots of the equation x² – 6x + 12 = 0. The value of the [removed]α – 2)¹² + (β−6)¹²/α¹² – 1 is:

The parabola y = x² – 9 and y = kx² intersect each other at the points A and B. If the length AB is equal to 10 units then the value of k is:

From first 100 natural numbers, 3 numbers are selected. If these numbers are in A.P., then the probability that these numbers are even is:

The statement p → (q → p) is equivalent is:

If Δ =
| 1 3cosθ 1 |
| sinθ 1 sinθ |
| 1 3cosθ 1 |
, then the maximum value of Δ is:

If value of $\frac{\left\{\left(\overrightarrow{a}-\overrightarrow{b}\right)*\left(\overrightarrow{a}-\overrightarrow{b}-\overrightarrow{c}\right)\right\}.\left(\overrightarrow{a}+2\overrightarrow{b}-\overrightarrow{c}\right)}{\left[\overrightarrow{a}\overrightarrow{b}\overrightarrow{c}\right]}$  is k then $\frac{k}{4}$  is