If p and q are positive real numbers such that p² + q² = 1, then the maximum value of (p + q) is

• 2

• 1/2

• 
• 

The sum of the series 

• e^-2

• e^–1

• e^-1/2

• e^-1/2

Let a₁, a₂, a₃, … be terms of an A.P. If  equals

• 41/11

• 7/2

• 2/7

• 2/7

If the coefficients of rth, (r+ 1)th and (r + 2)th terms in the binomial expansion of (1 + y)^m are in A.P., then m and r satisfy the equation

• m² – m(4r – 1) + 4r² – 2 = 0

• m² – m(4r+1) + 4r² + 2 = 0

• m² – m(4r + 1) + 4r² – 2 = 0

• m² – m(4r + 1) + 4r² – 2 = 0

If the letters of word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at serial number

• 601

• 600

• 602

• 602

If  where a, b, c are in A.P. and |a| < 1, |b|<1, |c|< 1, then x, y, z are in

• G.P.

• A.P.

• Arithmetic − Geometric Progression

• Arithmetic − Geometric Progression

167.

If in a triangle ABC, the altitudes from the vertices A, B, C on opposite sides are in H.P., then sin A, sin B, sin C are in

• G.P.

• A.P.

• Arithmetic − Geometric Progression

• Arithmetic − Geometric Progression

If non-zero numbers a, b, c are in H.P., then the straight line  always passes through a fixed point. That point is

• (-1, 2)

• (-1, -2)

• (1, -2)

• (1, -2)

The sum of the series 

If a₁, a₂, a₃ , ....,a_n , .... are in G.P., then the value of the determinant  is

• 0

• -2

• 1

• 1