MATHEMATICS- PAGE 3
1. Let G be a group of order 15. Then the number of sylow subgroups of G of order 3 is
(A) 1 (B) 0 (C) 3 (D) 5
Ans: A
2. Let G be a group of order 28 and let A and B be two normal subgroups of orders 2 and 7
respectively. Then the order of the group G/AB is
(A) 14 (B) 2 (C) 4 (D) 7
Ans: B
3. If a square matrix of order 10 has exactly 6 distinct eigen values then the degree of its minimal polynomial is
(A) At least 4 (B) At most 4 (C) At least 6 (D) At most 6
Ans: C
4. Let A be a non-zero upper triangular matrix all of whose eigen values are 0. Then I + A is
(A) Singular matrix (B) Idempotent matrix (C) Invertible matrix (D) Nilpotent matrix
Ans: C
5. An orthogonal set of non-zero vectors
(A) is constant (B) is linearly dependents
(C) is linearly independent (D) may be or may not be linearly independent
Ans: C
6. The polynomial of least degree interpolating the data (0, 3), (1, 7), (2, 11) is of degree
(A) 4 (B) 1 (C) 2 (D) 3
Ans: B
7. If the dual Linear Programming Problem (L.P.P.) has an unbounded solution, then the primal LPP has
(A) An unbounded solution (B) A feasible solution
(C) An infeasible solution (D) Infinitely many optimal solutions
Ans: C
8:- The number of sides of a Polygon of 12 sides is
A:- 66 B:-64 C:- 62 D:-54
Ans: D
9:- The students in a class can be divided into groups of 2, 5, 6 and 10. What is the least number of students this class can have?
A:- 15 B:- 20 C:- 60 D:- 30
Ans: D
10:- In an examination the candidate must get 34% to pass. The one who gets 180 marks fails by 41 marks. Then what is the maximum marks for that examination.
A:-600 B:- 650 C:- 700 D:- 750
Ans: B
11:- Raju can do a work in 3 days. Tom can do the same work in 6 days. In how many days can they finish it if they work together.
A:-1 day 3:15 day C:- 2 days D:-2.5 days
Ans: C
12:- A person standing on a highway sees a firecracker light far away. He hears its sound 3 seconds later. What is the approximate distance of the firework from his place?
A:-1 Km B:-2 Kms C:- 300 m D:- 500 m
Ans: A
13:- How much time will a train 225 metres long take to cross a bridge of length 275 metres if it is running at a speed of 30 Km/hr.
A:-1.3 minutes B:-1.25 minutes C:- 1.5 minutes D:- 1 minute
Ans: D
14:- At what time between 4 & 5 will the hands of a clock coincide?
A:-21 ‘(5)/(9)‘ minutes past 4 B:-21 ‘(4)/(9)‘ minutes past 4
C:- 21 ‘(9)/(11)‘ minutes past 4 D:- 21 ‘(8)/(11)‘ minutes past 4
Ans: C
15:- Today is 25th July. The day of the week is Sunday. This is a leap year. What will be the day of the week on this day after 3 years.
A:-Wednesday B:-Thursday C:- Monday D:-Tuesday
Ans: A
16:- Ryan's age is 3 times that of Appu. In 12 years Tyans age will be double the age of Appu. Ryan's present age is
A:-12 years B:-36 years C:- 32 years D:-24 years
Ans: B
17:-Find the sum of the series 1 + 2 + 3 + + 100.
A:-5000 B:-5050 C:-4050 D:-4000
Ans: B
18:-What percentage of 33 is 44% of 27?
A:-28 B:-36 C:-40 D:-11.88
Ans: B
19:-Average age of 10 students is 12. If 3 students having age 9, 14 and 13 are included in the group. What is the average of all the students?
A:-14 B:-13 C:-12 D:-11
Ans: C
20:-The population of a town is 10,00,000. If the annual birth rate is 3.3% and death rate is 1.3%. What will be the population after 3 years? A:-10,55,000 B:-10,61,208
C:-10,54,000 D:-10,61,200
Ans: B
21:-Selling a radio for Rs. 1,230, there is a loss of 18%. What would have been gain or loss if it had been sold for Rs. 1,600.
A:-140 B:-100 C:-50 D:-150
Ans: B
22:-In an examination 75% of candidates passed in English 65% in Mathematics while 15% failed in English as well as in Mathematics. If 495 candidates passed in both subjects, find the total no. of candidates who took the examination.
A:-900 B:-550 C:-750 D:-600
Ans: A
23:-If the ratio of areas of two circles is ‘ 121/169‘. What is the ratio of their radii?
A:-‘ 13/11‘ B:-‘ 11/13‘
C:-‘ 121/169‘ D:-‘ 169/121‘
Ans: B
(A) 1 (B) 0 (C) 3 (D) 5
Ans: A
2. Let G be a group of order 28 and let A and B be two normal subgroups of orders 2 and 7
respectively. Then the order of the group G/AB is
(A) 14 (B) 2 (C) 4 (D) 7
Ans: B
3. If a square matrix of order 10 has exactly 6 distinct eigen values then the degree of its minimal polynomial is
(A) At least 4 (B) At most 4 (C) At least 6 (D) At most 6
Ans: C
4. Let A be a non-zero upper triangular matrix all of whose eigen values are 0. Then I + A is
(A) Singular matrix (B) Idempotent matrix (C) Invertible matrix (D) Nilpotent matrix
Ans: C
5. An orthogonal set of non-zero vectors
(A) is constant (B) is linearly dependents
(C) is linearly independent (D) may be or may not be linearly independent
Ans: C
6. The polynomial of least degree interpolating the data (0, 3), (1, 7), (2, 11) is of degree
(A) 4 (B) 1 (C) 2 (D) 3
Ans: B
7. If the dual Linear Programming Problem (L.P.P.) has an unbounded solution, then the primal LPP has
(A) An unbounded solution (B) A feasible solution
(C) An infeasible solution (D) Infinitely many optimal solutions
Ans: C
8:- The number of sides of a Polygon of 12 sides is
A:- 66 B:-64 C:- 62 D:-54
Ans: D
9:- The students in a class can be divided into groups of 2, 5, 6 and 10. What is the least number of students this class can have?
A:- 15 B:- 20 C:- 60 D:- 30
Ans: D
10:- In an examination the candidate must get 34% to pass. The one who gets 180 marks fails by 41 marks. Then what is the maximum marks for that examination.
A:-600 B:- 650 C:- 700 D:- 750
Ans: B
11:- Raju can do a work in 3 days. Tom can do the same work in 6 days. In how many days can they finish it if they work together.
A:-1 day 3:15 day C:- 2 days D:-2.5 days
Ans: C
12:- A person standing on a highway sees a firecracker light far away. He hears its sound 3 seconds later. What is the approximate distance of the firework from his place?
A:-1 Km B:-2 Kms C:- 300 m D:- 500 m
Ans: A
13:- How much time will a train 225 metres long take to cross a bridge of length 275 metres if it is running at a speed of 30 Km/hr.
A:-1.3 minutes B:-1.25 minutes C:- 1.5 minutes D:- 1 minute
Ans: D
14:- At what time between 4 & 5 will the hands of a clock coincide?
A:-21 ‘(5)/(9)‘ minutes past 4 B:-21 ‘(4)/(9)‘ minutes past 4
C:- 21 ‘(9)/(11)‘ minutes past 4 D:- 21 ‘(8)/(11)‘ minutes past 4
Ans: C
15:- Today is 25th July. The day of the week is Sunday. This is a leap year. What will be the day of the week on this day after 3 years.
A:-Wednesday B:-Thursday C:- Monday D:-Tuesday
Ans: A
16:- Ryan's age is 3 times that of Appu. In 12 years Tyans age will be double the age of Appu. Ryan's present age is
A:-12 years B:-36 years C:- 32 years D:-24 years
Ans: B
17:-Find the sum of the series 1 + 2 + 3 + + 100.
A:-5000 B:-5050 C:-4050 D:-4000
Ans: B
18:-What percentage of 33 is 44% of 27?
A:-28 B:-36 C:-40 D:-11.88
Ans: B
19:-Average age of 10 students is 12. If 3 students having age 9, 14 and 13 are included in the group. What is the average of all the students?
A:-14 B:-13 C:-12 D:-11
Ans: C
20:-The population of a town is 10,00,000. If the annual birth rate is 3.3% and death rate is 1.3%. What will be the population after 3 years? A:-10,55,000 B:-10,61,208
C:-10,54,000 D:-10,61,200
Ans: B
21:-Selling a radio for Rs. 1,230, there is a loss of 18%. What would have been gain or loss if it had been sold for Rs. 1,600.
A:-140 B:-100 C:-50 D:-150
Ans: B
22:-In an examination 75% of candidates passed in English 65% in Mathematics while 15% failed in English as well as in Mathematics. If 495 candidates passed in both subjects, find the total no. of candidates who took the examination.
A:-900 B:-550 C:-750 D:-600
Ans: A
23:-If the ratio of areas of two circles is ‘ 121/169‘. What is the ratio of their radii?
A:-‘ 13/11‘ B:-‘ 11/13‘
C:-‘ 121/169‘ D:-‘ 169/121‘
Ans: B