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

• 
• 
• 
• 

C.

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

• (n − 1)a₁a_n

D.

(n − 1)a₁a_n

If x^m.yⁿ = (x+y)^m+n, then dy/dx is

• y/x

• x+y/xy

• xy

• x/y

A.

y/x

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

• 4

• 6

• 1

• 2

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 an identity matrix