If 0 < x < π and cosx + sinx = 1/2 , then tanx is

If a₁, a₂, … , an are in H.P., then the expression a₁a₂ + a₂a₃ + … + a_n−1a_n is equal to

• n(a₁ − a_n)

• (n − 1) (a₁ − a_n)

• na₁a_n

• na₁a_n

23.

If x^m.yⁿ = (x+y)^m+n, then dy/dx is

• y/x

• x+y/xy

• xy

• xy

The number of values of x in the interval [0, 3π] satisfying the equation 2sin² x + 5sinx − 3 = 0 is

• 4

• 6

• 1

• 1

If A and B are square matrices of size n × n such that A² − B² = (A − B) (A + B), then which of the following will be always true?

• A = B

• AB = BA

• either of A or B is a zero matrix

• either of A or B is a zero matrix

Let  a , b ∈ N. Then

• there cannot exist any B such that AB = BA

• there exist more than one but finite number of B’s such that AB = BA

• there exists exactly one B such that AB = BA

• there exists exactly one B such that AB = BA

The set of points where x f(x) = x /1+|x| is differentiable is

• (−∞, 0) ∪ (0, ∞)

• (−∞, −1) ∪ (−1, ∞)

• (−∞, ∞)

• (−∞, ∞)

The differential equation whose solution is Ax² + By² = 1, where A and B are arbitrary constants is of

• second order and second degree

• first order and second degree

• first order and first degree

• first order and first degree

ABC is a triangle, right angled at A. The resultant of the forces acting along  respectively is the force along  where D is the foot of the perpendicular from A onto BC. The magnitude of the resultant is

The value of the integral, is

• 1/2

• 3/2

• 2

• 2