Q1. If f(x) = log [(1 + x)/(1-x), then f (2x )/(1 + x^2 ) is equal to

a) 2 f (x)

b) {f(x)}^2

c) {f(x)}^3

d) 3 f(x)

Q2. Evaluate f(1) + f(2) + f(3) + … + f(25)

a) -26

b) None of these

c) -24

d) -22

Q3. { (a, b): a^2 +b^2 = 1} on the set s has the following relation

a) Symmetric

b) Reflexive and transitive

c) None

d) Reflexive

Q4. Insert a.m.'s (arithmetic mean) between 7 and 71 in such a way that the 5th a.m. is 27. The number of  a.m.s  are

a) 12

b) 17

c) 15

d) 51

Q5. If log 27 = 1.431, then the value of log 9 is:

a) 0.934

b) 0.958

c) 0.945

d) 0.954

Q6. If a = cos θ + i sin θ, then (1 + a) / (1 – a) =

a) Cot θ / 2

b) Cot θ

c) I cot θ / 2

d) I tan θ / 2

Q7. If n arithmetic means are inserted between 1 and 31, such that the ratio of the first mean and the nth mean is 3 : 29, then the value of n is

a) 10

b) 12

c) 13

d) 14

Q8. Cube root of 5 x cube root of 7 is

a) Cube root of 35

b) Cube root of 12

c) Cube root of 7 / 5

d) Cube root of 2

Q9. The greatest possible number of points of intersection of 8 straight lines and 4 circles is

a) 32

b) 64

c) 76

d) 104

Q10. How many numbers greater than 10 lakhs be formed from 2, 3, 0, 3, 4, 2, 3?

a) 420

b) 360

c) 400

d) 300

Q11. In pert the span of time between the optimistic and pessimistic time estimates of an activity is ______________

a) 3σ

b) 12σ

c) 6σ

d) None of the above.

Q12. In a survey conducted in patna, it was found that 3/4ths of town owns color t.v., 85 % of the people own refrigerators and every 4 in 5 in the town own music systems, what is the minimum percentage of people who have all the three?

a) 30 %

b) 55 %

c) 40 %

d) None of these

Q13. Find the domain of the function y = f(x) which is defined as f(x) = (1 / √{x- [x]}) [x] is the greatest integer function

a) X is any real number other than an integer

b) And real value of x

c) All natural numbers

d) None of these

Q14. A relation R ={(1,1), (1,2)}ON a ={1,2,3}. A minimum number of elements required in R so that the enlarged relation becomes an equilance relation

a) {(2,2), (3,3)}

b) {(2,1) , (3,1), (3,3)}

c) {(2,2), (2,1), }

d) {(2,2), (3,3), (2,1)}

Q15. 55 cows can graze a field in 16 days. How many cows will graze the same field in 10 days?

a) 84 cows

b) 34 cows

c) 88 cows

d) 44 cows

Q16. The argument of (1 – i) / (1 + i) is

a) π / 2

b) π / 2

c) π 3 / 2

d) 5 π / 2

Q17. (- 3 / 2) + (5 / 4) – (- 7 / 4)

a) -2

b) 2

c) 7/4

d) 3 / 2

Q18. The union of infinite number of open sets is

a) An open set

b) A closed set

c) Need not be an open set

d) Not a set

Q19. In how many ways 4 men and 4 women can be seated in a row so that men and women are alternate?

a) 28

b) 36

c) 4! 4!

d) 2.4! 4!

Q20. Find the 5th term in the expansion ( 1 -2x )^-1

a) 15×3

b) 16×4

c) 17×5

d) 14×6