1.

Let α,  β be real and z be a complex number. If z² + αz + β = 0 has two distinct roots on the line Re z = 1, then it is necessary that

• β ∈(0, 1)

• β ∈(-1, 0)

• |β| = 1

• |β| = 1

The coefficient of x⁷ in the expansion of (1 - x - x² +x³)⁶ is :

• 144

• -132

• -144

• -144

A man saves Rs. 200 in each of the first three months of his service. In each of the subsequent months his saving increases by Rs. 40 more than the saving of immediately previous month. His total saving from the start of service will be Rs. 11040 after

• 18 Months

• 19 Months

• 20 Months

• 20 Months

Consider the following statements
P: Suman is brilliant
Q: Suman is rich
R: Suman is honest. The negation of the statement ì Suman is brilliant and dishonest if and only if Suman is richî can be ex- pressed as

•  ~ P ^ (Q ↔ ~ R)

• ~ (Q ↔ (P ^ ~R)

• ~ Q ↔ ~ P ^ R

• ~ Q ↔ ~ P ^ R

If ω(≠1) is a cube root of unity, and (1 + ω)⁷ = A + Bω.Then (A, B) equals

• (0,1)

• (1,1)

• (1,0)

• (1,0)

If the mean deviation about the median of the numbers a, 2a, ....., 50a is 50, then |a| equals 

• 2

• 3

• 4

• 4

Let R be the set of real numbers.
Statement-1 : A = {(x, y) ∈R × R : y - x is an integer} is an equivalence relation on R.
Statement-2 : B = {(x, y) ∈ R × R : x = αy for some rational number α} is an equivalence relation on R.

• Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1. 

• (2) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1. 

• Statement-1 is true, Statement-2 is false. 

• Statement-1 is true, Statement-2 is false. 

Consider 5 independent Bernoulliís trials each with a probability of success p. If the probability of at least one failure is greater than or equal to 31/32, then p lies in the interval

• (1/2, 3/4]

• (3/4, 11/12]

• [0, 1/2]

• [0, 1/2]

The value of p and q for which the function f(x) =

• p = 1/2. q = -3/2

• p = 5/2, q = 1/2

• p = - 3/2, q = 1/2

• p = - 3/2, q = 1/2