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 first n terms of the series 1² + 2.2²  + 3²  + 2.4² + 5² + 2.6² + … is   when n is even. When n is odd the sum is

a)

b)

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