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1. Which German mathematician developed the theory of sets?
A) Carl Friedrich Gauss
B) David Hilbert
C) Georg Cantor
D) Jacobi
C) Georg Cantor
2. The symbol used to represent the set of all positive rational numbers is
A) Q+
B) Z
C) R+
D) I
A) Q+
Golden
3. A ∪ A = A - What is the name of this law?
A) Identity law
B) Idempotent law
C) Idempotent law
4. If A and B are two sets such that A ⊂ B, then what is A ∪ B?
A) B
B) A
C) A ∩ B
D) ∅
A) B
5. What is the name of these two laws? (A ∪ B)´ = A′ ∩ B′ and (A ∩ B)′ = A′ ∪ B′
A) De Morgan's laws
B) Identity laws
C) Absorption laws
D) Supplementary laws
A) De Morgan's laws
6. What is the cardinality of a set?
A) The number of elements in the set
B) The number of subsets of the set
C) The number of common elements in two sets
D) The sum of all elements in the set
A) The number of elements in the set
2 Answer
7. What does it mean for two sets to be disjoint?
A) They have the same elements
B) One set is a subset of the other
C) They have no elements in common
D) One set is the complement of the other
C) They have no elements in common
8. If x(cosA)−y(sinA)=a, x(sinA)+y(cosA)=b, then which is the correct answer
A) x²−y²=a²−b²
B) x²+y²=a²+b²
C) x²+y²=a²−b²
D) x²−y²=a²+b²
B) x²+y²=a²+b²
9. If x tan 45° sin 30° = cos 30° tan 30°, then x is equal to
A) √3
B) ½
C) 1/√2
D) 1
D) 1
10. The value of the expression [cosec (75° + θ) – sec (15° - θ) – tan (55° + θ) + cot (35° - θ)] is
A) 1
B) -1
C) 0
D) ½
C) 0
2 Answer
11. If A, B and C are interior angles of a ΔABC then cos((B+C)/2) is equal to
A) -sin A/2
B) sin A/2
C) cos A/2
D) -cos A/2
B) sin A/2
12. If A and (2A – 45°) are acute angles such that sin A = cos (2A – 45°), then tan A is equal to
A) 0
B) 1/√3
C) 1
D) √3
C) 1
2x Question
13. Find the area of a sector with radius 8 cm and angle 60°
A) 33.35 cm2
B) 30.35 cm2
C) 33.51 cm2
D) 30.51 cm2
C) 33.51 cm2
14. The length of the diagonal of a square is 10 cm. What is its area?
A) 60 cm2
B) 50 cm2
C) 20 cm2
D) 40 cm2
B) 50 cm2
Danger
15. A cuboid has dimensions: length = 10 cm, width = 6 cm, and height = 4 cm. Find the volume of the cuboid
A) 240 cm3
B) 200 cm3
C) 180 cm3
D) 250 cm3
E) 230 cm3
F) 140 cm3
A) 240 cm3
2x Question
16. Which of the following is not one of the Congruence rules?
A) SSS
B) ASA
C) SAS
D) AAA
D) AAA
17. The ratio of the angle subtended by an arc at the centre to the angle subtended by the arc at any point on the remaining part of the circle is
A) 2:1
B) 1:2
C) 1:3
D) 1:1
A) 2:1
2x Question
18. Who derived the famous formula for the area of a triangle in terms of its three sides?
A) Pythagoras
B) Srinivasa Ramanujan
C) Heron
D) Aryabhatta
C) Heron
Golden
19. The midpoint of the line joining two points (36, 6) and (16, 4) are _______
A) (5, 26)
B) (26, 5)
D) (26, 5)
Danger 20. The equation of the line passing through the point (-1, 4) and perpendicular to the line y = 2x + 1 is
A) y = −1/2x + 7/2
B) y = 1/2x + 3
C) y = −2x + 2
D) y = 2x – 6
E) y = 2/3x + 4
F) y = y = −1/4x + 3/7
A) y = -1/2x + 7/2
Golden
21. Which of the following is an obtuse angle?
A) 11/21 of a right angle
B) 8/20 from a right angle
B) 8/20 from a right angle
22. Which of the following is not a valid solution of the equation x + 2y = 6
A) (2,2)
B) (6,0)
C) (4,1)
D) (3,1)
D) (3.1)
Danger
23. What is the expansion of a⁴– b⁴
A) (a² - b²) (a + b) (a – b)
B) (a² + b²) (a + b) (a – b)
C) (a² + b²) (a - b) (a – b)
D) (a²- b²) (a + b) (a + b)
E) (a² + b²) (a - b) (a + b)
F) (a² - b²) (a - b) (a – b)
B) (a²+ b²) (a + b) (a – b)
2 Answer
24. Find the value of abc*1001 if abc is a three digit number (with the digits a,b and c)
A) abcba
B) aabbcc
C) abcabc
D) ababca
C) abcabc
25. Which of the following represents a linear function?
A) y=(x^2)+2
B) y=sin x
C) y=3x+2
D) y=x3 +2
C) y=3x+2
26. A box contains cards numbered 11 to 123. A card is drawn at random from the box. Find the probability that the number on the drawn card is a square number.
A) 7/113
B) 11/113
C) 6/113
D) 8/113
D) 8/113
27. A box contains 12 balls of which some are red in color. If 6 more red balls are put in the box and a ball is drawn at random, the probability of drawing a red ball doubles than what it was before. Find the number of red balls in the bag.
A) 3
B) 6
C) 4
C) 5
A) 3
2 Answer
28. There are two men X and Y who were born in the same year. If X's date of birth is on 19th December 1990.How many dates are possible for Y to be born such that he doesn't have the same birthday as?
A) 360
B) 362
C) 363
D) 364
D) 364
Golden
29. A record of a weather station shows that out of the past 200 consecutive days, its weather forecasts were correct 150 times. What is the probability that the weather report will be incorrect for the next day?
A) 0.25
B) 0.28
A) 0.25
Danger 30. Find the 12th term from the last term of the A. P - 2, -4,- 6, ... -100
A) -88
B) -78
C) -76
D) -86
E) -75
F) -85
B) -78
31. A bag contains 8 red balls and x blue balls, the odd against drawing a blue ball are 2:5. What is the value of x?
A) 24
B) 20
C) 18
D) 28
B) 20
2x Question
32. Find the domain of the function f(x)= (2x+3)/(x-7)
A) Except all the real values except 2
B) Except all the real values except 7
C) Except all the real values except 3
D) Except all the real values except 1
B) Except all the real values except 7
33. The relation R in the set Z on integers given by R = {(a, b): a - b is divisible by 5} is?
A) Reflexive but not symmetric
B) Reflexive
C) Symmetric and transitive
D) An equivalence relation
D) An equivalence relation
34. If (x² - 3x + 5, y – 4) = (3,1), find the values of x and y.
A) 1, 4
B) 2, 5
C) 5, 2
D) 5, 1
B) 2, 5
35. The function f(x) = x² + 4x + 4 is
A) Odd
B) Neither odd nor even
C) Even
D) Periodical
B) Neither odd nor even
36. Write the roaster form for A = {x: x² – 5x + 6 = 0}
A) {2, 3}
B) {3}
C) {2}
D) ϕ
A) {2, 3}