The first two terms of a geometric progression add up to 12. The sum of the third and the fourth terms is 48. If the terms are alternately positive and negative the first term is

a) 4

b) -4

c) -12

d) 12

In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then the common ratio of the progression equals

a)

b)

c)

d)

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

a) 2

b)

c)

d)

Let a_1, a₂, a₃ ………. be terms of an arithmetic progression. If =  , p ≠ q then  equals

a)

b)

c)

d)

Let a_1, a₂, a₃ .  .  .  . a_n be in harmonic progression then the expression a₁a₂ + a₂a₃ + .  .  .  .+ a_{n – 1}a_n is equal to

a) (n – 1)( − )

b) n

c) (n −1)

d) n( − )

If   x = ,  y =  , z =  where a, b, c are in arithmetic progression and |a| < 1, |b| < 1, |c| < 1, then x, y and z are in

a) Harmonic Progression

b) Arithemetico–Geometric Progression

c) Arithmetic Progression

d) Harmonic Progression

The sum of the series     + .  .  .  . is

a)

b)

c)

d)

Let T_r be the r^th term of an AP whose first term is a and common difference is d. If for some positive integers m, n, m ≠ n, T_m =  and T_n =  then a – d equals

a) 0

b) 1

c)

d)  

The sum of the series  …… is

a)

b)

c)

d)

The sum of the series   …… up to  is equal to

a) 2ln2

b) ln2  1

c) ln2

d) ln

The value of  2^1/4 . 4^1/8 .  8^1/16 . .  .  .  .is

a)

b) 2

c)

d) 4

Fifth term of a geometric progression is 2 then the product of its 9 terms is

a) 256

b) 512

c) 1024

d) None of these

  is equal to

a) lnx

b) x

c)

d) None of these

is equal to

a) ln(x – 1)

b) lnx

c) x

d) None of these

If  α and β are roots of the equation x² – x + 1 = 0 then α²⁰⁰⁹ + β²⁰⁰⁹ is equal to

a) -2

b) -1

c) 1

d) 2

If roots of the equation bx² + cx + a = 0 be imaginary then for all real values of x the expression 3b²x² + 6bcx + 2c² is

a) Greater than 4ab

b) Less than 4ab

c) Greater than 4ab

d) Less than 4ab

The sum to infinity of the series
1 +   +   +  +  + ………. is

a) 3

b) 4

c) 6

d) 2

If α, β are roots of ax² + bx + c = 0 then ^{1/(x – α)}  is

a) log |a (α – β)|

b) e^{a(β – α)}

c) e^{a(α – β)}

d) None of these

If the system of linear equations

x + 2ay + az = 0
x + 3by + bz = 0 and
x + 4cy + cz = 0
has a non zero solution, then a, b, c

a) are in arithmetic progression

b) are in geometric progression

c) are in harmonic progression

d) satisfy a + 2b + 3c = 0

If a_n, b_n be two sequences given by
a_n =, b_n =   
for all n ε ℕ. Then  a₁ . a₂ . . a_n is equal to

a) x – y

b)

c)

d)

If one root of the equation (1 + i) x² – (7 + 3i) x + 6 + 8i = 0, where i =   is 4 – 3i, then the other root must be

a) 1 – i

b) i ( i – 1)

c) i + 1

d) 4 + 3i

If the equations ax² + bx + c = 0 and z² + 2z + 3 = 0 have a common root where a, b, c ε ℝ then a : b : c is

a) 1 : 2 : 3

b) 3 : 2 : 1

c) 3 : 1 : 2

d) 2 : 3 : 1

The value of 2. is

a)

b)

c)

d)