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

• 1

• 3

• 4

• 4

In the binomial expansion of (a - b)n, n ≥ 5, the sum of 5th and 6th terms is zero, then
a/b equals

• 5/n −4

• 6 /n −5

• n -5 /6

• n -5 /6

The set S: {1, 2, 3, …, 12} is to be partitioned into three sets A, B, C of equal size. Thus, A ∪ B ∪ C = S, A ∩ B = B ∩ C = A ∩ C = φ. The number of ways to partition S is-

• 12!/3!(4!)³

• 12!/3!(3!)⁴

• 12!/(4!)³

• 12!/(4!)³

A body weighing 13 kg is suspended by two strings 5 m and 12 m long, their other ends being fastened to the extremities of a rod 13 m long. If the rod be so held that the body hangs immediately below the middle point. The tensions in the strings are 

• 12 kg and 13 kg

• 5 kg and 5 kg

• 5 kg and 12 kg

• 5 kg and 12 kg

6.

Consider a family of circles which are passing through the point (-1, 1) and are tangent to x-axis. If (h, K) are the co-ordinates of the centre of the circles, then the set of values of k is given by the interva

• 0 < k < 1/2

• k ≥ 1/2

• – 1/2 ≤ k ≤ 1/2

• – 1/2 ≤ k ≤ 1/2

The differential equation of all circles passing through the origin and having their centres on the x-axis is

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

• 2

• 1/2

• 
• 

A tower stands at the centre of a circular park. A and B are two points on the boundary of the park such that AB (= a) subtends an angle of 60º at the foot of the tower, and the angle of elevation of the top of the tower from A or B is 30º. The height of the tower is

The sum of the series ²⁰C₀ – ²⁰C₁ + ²⁰C₂ – ²⁰C₃ + …… - ….. + ²⁰C₁₀ is-

• – ²⁰C₁₀

• 

• 0

• 0