1) If A={7,8,9} and B={9,5} then (A∪B)x(A∩B) is
A){(7,9),(7,5),(8,9),(8,5),(9,9),(9,5)}
B){(5,9),(7,9),(8,9),(9,9)}
C) {(9,5),(9,7),(9,8),(9,9). D) none
2) If the number of elements in set A and in set B are m and n respectively, then the number of relations from A to B is
A) 2ᵐ⁺ⁿ B) 2ᵐⁿ C) m+n D) mn
3) If the relation R: A --> B, where A={1,2,3} and B={1,3,5} is defined by R= {(x,y): x< y, x ∈ B} then
A) R={(1,3),(2,3),(2,5),(3,5),(1,5)}
B) R={(1,1),(1,5),(2,3),(2,5)}
C) R⁻¹={(3,1),(5,1),(3,2),(5,3)}
D) R⁻¹={(1,1),(5,1),(3,2),(5,3)}
4) The domain of the real valued function f(x)= √(log₁₆ x² ) is
A) x> 0. B)|x|≥1 C) |x|≥4. D) x≥4
5) If x ∈ R then (x²-x+1)/(x²+x+1)
takes values in the interval.
A) (1/3, 3) B) (-1/3,3) C) (0,3) d) n
6) In a certain town, 25% families Own a phone and 15% own a car car a car car 65% families all neither a phone nor a car 2000 families own both a car and a phone. Consider the following statements in this regard.
I) 10% family own both car and a phone.
II) 35% families own either a car or a phone.
III) 40000 families live in the town.
Which of the above statements are correct ?
A) 1 and 2. B) 1 and 3
C) 2 and 3. D)1,2 and 3
7) Let A={1,2,3} and B= {a,b}. Which of the following subset of AxB is a mapping from A to B ?
A) {(1,a),(3,b),(2,a),(2,b)}
B) {(1,b),(2,a),(3,a)}
C) {(1,a),(2,b)}. D) none
8) A function f is defined for all positive integers and satisfies f(1) = 2014 and f(1)+ f(2) + ...+ f(n) = n² f(n), and n> 1. The value of f(2013) is
A) 2013/2014. B) 2015/2014
C)1/2013. D) 2/2013
9) The period the period of function cos(πx/3) + tan(πx/3)+3 is :
A) 2 B) 4 C) 6. D) none
10) Which of the following is the domain of sin⁻¹{log₂(x³/2)} ?
A) 1<x<2, -2<x< -1
B) 1≤ x≤2, -2≤x≤-1
C) 1≤ x<2, -2≤x≤-1. D) none
11) The domain of the function f(x)= ¹⁶⁻ˣ C ₂ₓ₋₁ + ²⁰⁻³ˣP ₄ₓ₋₅ , where the symbols have have their usual meaning meaning is the set.
A) {1,2,3,4,5}. B) {2,3,4}
C) {2,3}. D) none
12) The range of f(x)=
3sin√(π²/16 - x³) is
A) [-3,3]. B) [0,3]
C) [0, √3/2]. D)[0, e/√2]
13) If A={1,3,5,7,9,11,13,15,17} , B{2,4,6,8,10,12,14,16,18} and N is the universal universal set, then
A'∪{(A∪B)∩B'} is
A) A. B) A'. C) B. D) N
14) Let R be the relation on N defined by R={(a,b): a, b ∈N and a= b²}. Which of the following is True?
A) (a,a) ∈ R and a ∈ N
B) (a,b) ∈ R => (b,a) ∈ R
C) (a,b) ∈ R, (b,c) ∈ R => (a,c) ∈R
D) none of these
15) The range of
f(x)= cot⁻¹(log₄/₅ (5x²-8x+4) is
A) (0,π/2). B) (π/4,π)
C) (-π/2, π/2). D) (0, π/2)
16) The period of
f(x) = | sinx| + | cosx| is
A) π/2. B) π. C) 3π/2. D) 2π
17) If f(x) is an even function defined on (-5,5), then the sum of the squares the squares of all numbers satisfying the equation f(x)= f{(x+1)/(x+2)} is
A) 10. B) 12. C) 15. D) 8
18) If f(x)= (a - xⁿ)¹⁾ⁿ , a>0, n∈ N, then f(f(x))=
A) 1. B) n. C) x. D) nx
19) If f: R --> R is defined by
f(x)= x - [x] - 1/2 and x ∈ R, where [x] denotes the greatest integer function then { x ∈ R : f(x)= 1/2} is:
A) Z, the set of all integers.
B) N, the set of all natural numbers.
C) ¢, the empty set
D) R, the set of of all real numbers.
20) The domain of f(x)=1/√(4-x²)
A) set of all real numbers.
B) set of all positive real numbers
C) (-2, 2). D) [-2,2]
21) If A={1, 2, 3, 4, 5},
and B={2, 4, 6}, C={3, 4,6} then (A∪B)∩ C is :
A) {3,4,6} B) {1,2,3} C) {1,4,3} D) n
22) If A= {x:x is an even number}
B={ x:x is prime number}
C={x:x is a perfect square}
D={x:x is an odd number}
then which of the following two set are disjoint ?
A) A and B B) B and C
C) C and D D) D and B
23) Two sets A and B have 9 elements common. The number of common to each of the sets AxB and BxA are
A) 2⁹. B) 9². C) 10. D) 18
24)) The range of the function f(x)= sec⁻¹(1+ cos²x), If ([.] denotes the greatest integer function) is
A) (π/4, π/2). B) (0, π/2).
C) (0, sec⁻¹2). D) (0, π/3).
25) The function f(x)=(16ˣ - 1)/4ˣ
A) even function B) odd function
C) periodic function D) none.
26) If f(x) satisfy the functional equation x² f(x)+ f(1-x) = 2x - x⁴, then f(1/3)=
A) 1/3 B) 1/9. C) 8/9. D) 10/9
27) if [x] denotes greatest integer ≤ x, and 2[x/8]² + 3[x/8]= 20, then x lies in the smallest interval [a,b] where b - a is equals to
A) 6 B) 5 C) 4 D) 8
28) The value of n belongs to I for which the function
f(x)=(sin nx)/sin(x/n) has 4π as its period is
A) 2 B) 3 C) 4 D) 5
29) Let R be a relation in N defined by R={(x,y): x+2y=8}, then range of R is
A) {2, 4,6}. B) {1,2 ,3, 4, 6}
C) {1, 2,3}. D) none of these
30) The graph of f(x)= cosx cos(x+2) - cos²(x+1) is
A) A straight line through (π/2, - sin²1) and parallel to x-axis.
B) a parabola with vertex (1, - sin²1)
C) a straight line passing through origin. D) none of these.
31) If f(x)= (1-x)/(1+x), then
f(f(1/x)) will be
A) x. B) 1/x. C) - x. D) - 1/x
32) The domain of f(x)=√(log(2x-x²) is
A) 0<x≤1. B) 0<x<2
C) 0<x≤2. D) none
33) Let A={1,2,3} and B={2,3,4}, then which of the following relation is a function from A to B?
A) {(1,2),(2, 3),(3,4),(2,2)}
B) {(1,2),(2, 3),(11,3)}
C) {(1,3),(2, 3),(3,3)}
D) {(1,1),(2, 3),(3,4)}
34) if 2f(x) - 3f(1/x)= x² (x≠0), the value of f(2) will be
A) 5/2. B) -7/4. C) -1. D) none
35) The range of y= 1/(2 - sin 3x) for all x is
A) 1/3 < y ≤1. B) -1/3 < y ≤1.
C) 1/3 >y >1. D) 1/3 >y >1.
36) The function f (x) =
sin⁻¹[2x² -5], where [x] represents greatest integer function, has domain
A) [-√(7/2), -√2]. B) [√2, 7/2]
C) √[-7/2), √2]∪ [√2, 7/2]. D) n
37) Out of the 64 students, the number of students taking Mathematics is 55 and number of students taking both mathematics and Statistics is 10. then the number of students taking only statistics is
A) 19. B) 20. C) 15. D) 25
38) A and B are subset of the
universal set U set U such that n(U)= 800, n(A)= 300, n(B)= 400 and n(A ∩ B) = 100. The number of elements in the set A' ∩ B' is equal to:
A) 100 B) 200 C) 300 D) 400
39) If A, B and C are sets such that A∩B = A∩ C and A∪B)=A∪C then
A) A∩ B= null set. B) A= B
C) A= C. D) B= C
40) If A and B are two sets, then (A - B)∪(B - A) ∪(A∩B)(A∩B) = ?
A) A∪B B) A∩ B. C) A. D) B'
41) For any two sets A and
A - (A - B) equals to
A) B. B) A - B. C) A∩B. D) A'∩B'
42) If A and B are any two sets, then (A∪B)'∩(A'∪B)'
A) Complement of null set
B) A'. C) B'. D) universal set
43) Three sets A, B, C are such that A= B∩ C and B= C∩A, then
A) A is subset of B
B) B is subset of A
C) A= B D) A subset of complement B.
44) If A, B, C are subsets of set X, then
(A'∩B'∩C)∪(B∩ C)∪(A∩ C) =?
A) A. B) B. C) C D) X∩(A∪B∪)
45) If A= {a,b}, B={c,d}, C={d,c}, then {(a,c),(a,d),(a,e),(b,c),(b,d),(b,c)} is equal to
A) A∩(B∪C) B) A∪(B∩C)
C) Ax (B∪C) D) Ax(B∩ C)
46) In a group of 45 persons, 25 drink tea but not coffee, while 32 drink tea. How many persons drink coffee but not tea ?
A) 12. B) 13. C) 15. D) 20
47) Out of 800 students in a school, 224 played cricket, 240 played hockey and 336 played basketball. Of the total, 64 played both basketball in hockey, 80 played cricket and basketball, 40 played cricket and hockey, 24 played all the three games. The number of students who did not play any game is
A) 128 B) 216 C) 240 D) 160
48) On the annual sports day, school awarded 35 medal in athletics, 15 in Judo and 18 in swimming. If these medals goes to a total of 58 students and only three of them got medals in all the three sports, the number of students who received medals in exactly two of three sports are:
A) 9 B) 4 C) 5 D) 7
49) In a survey it is to be found that 70% of employees like bananas and 64% like apples. If x% like both bananas and apples, then
A) x≥34. B) x≤64
C) 34≤ x ≤ 64. D) All of these
50) A factory inspector examined the defects in hardness, finish and dimensions of an item. After examining 100 items he gave the following report; All three defects 5, defects in hardness and finish 10, defects in dimensions and finish 8, defect in dimensions and hardness 20. Defect in finish 30, in hardness 23 and in dimensions 50. The Inspector was fined because
A) The inspector took bribe.
B) the inspector's conduct towards the workers was not good.
C) the report of the Inspector was incorrect
D) none of these.
No comments:
Post a Comment