Q1. If in a group of n distinct objects, the number of arrangements of 4 objects is 12 times the number of arrangements of 2 objects, then the number of objects is

a) 10

b) 8

c) 6

d) None of these

Q2. In how much time will Rs 3000 amount to Rs 3993 at 40% p.a compounded quarterly.

a) 8 months

b) 6 months

c) 9months

d) 11 months

Q3. Using binomial theorem expansion of ( 3x + 2y) ^4

a) 72x^4  + 21x^3  y

b) 81x^4  +216x^3 .y + 216x^2 .y^2 + 96xy^3 + 16y^4

c) 81x^4  + 96x^3 .y + 16x^2 .y^2 +216x .y^3 + 81y^4

d) 37x^4 + 43x^3 .y +16y^4

Q4. The number of positive integral solution of abc = 30 is

a) 27

b) 81

c) 243

d) None of these

Q5. Solve a +b +c = 0

12a +2b -3c = 5

3a +4b +c = -4

a) a=1, b=2, c=3

b) a=1, b=-2, c=1

c) a=2, b=3, c=1

d) a=2, b=2, c=3

Q6. A triangular matrix can be

a) Upper triangular

b) Lower triangular

c) Both

d) None

Q7. Two matrices A and B are said to be equal if,

a) A and B are not of same order

b) A and B are of symmetric order

c) A and B are of null order

d) A and B are of same order

Q8. The area of a triangle whose vertices are ( 3, 8), ( -4, 2) and (5 ,1) is

a) 63/2

b) 51/2

c) 61/2

d) 55/2

Q9. Solve -x –y +z = -2

3x +2y -2z =7

x +3y -3z =0

a) y and z are linearly dependent

b) x, y, z are independent

c) x ,y and z are dependent

d) None of the above

Q10. The equation ax -3y +5z = 4 is inconsistent for

x –ay +3z =2

9x -7y +8az =0

a) a =2

b) a= 3

c) a =4

d) a =5

Q11. Solve x -2y +z =1

3x +y -2z =4

y -z =1

a) x=0, y=-2, z=-3

b) x=1, y=-1, z=3

c) x=-2, y=0, z=-3

d) x=2, y=-1, z=0

Q12. A set consisting of a definite number of elements is called a

a) Null set

b) Singleton set

c) Infinite set

d) Finite set

Q13. The range of the function f(X) = x / |x| is

a) R – {0}

b) R – {-1, 1}

c) {-1, 1}

d) None of these

Q14. f(x) = |x|+ |y| g(x) = max (x + y) (x – y) h(x) = min (x + y, x – y)

(i) g(x) f(x)

(ii) g(x) + h(x) f(x)

(iii) g(x) > f(x).

Which of the following are not necessarily true?

a) i and ii

b) i and iii

c) ii and iii

d) i, ii and iii

Q15. Find the sum of the series 2+5+8+ … +182

a) 5520

b) 5612

c) 5623

d) 5418

Q16. The polar form of (i^25)^3 is

a) Cos π/2 + i Sin π/2

b) Cos π + i Sin π

c) Cos π – i Sin π

d) Cos π/2 – i Sin π/2

Q17. -6 ÷ (-8 / 17)

a) 48 / 17

b) – 51 / 4

c) 51 / 4

d) – 48 / 17

Q18. √14 is called

a) Cubic surd

b) Compound surd

Q19. How many 3 digit numbers with distinct digits can be formed such that the product of the digits is the cube of a positive integer?

a) 21

b) 24

c) 36

d) 30

Q20. The cube root of 127 up to four places of decimal are

a) 5.0264

b) 4.1468

c) 5.0236

d) 4.1648