Engineering Maths - Numbers and Algebra - Numbers and Algebra Section 1 Online Exam Quiz

Important questions about Engineering Maths - Numbers and Algebra - Numbers and Algebra Section 1. Engineering Maths - Numbers and Algebra - Numbers and Algebra Section 1 MCQ questions with answers. Engineering Maths - Numbers and Algebra - Numbers and Algebra Section 1 exam questions and answers for students and interviews.

1. If x - y = 1, then x 3 - y 3 - 3xy equals

Options

A : 0

B : 1

C : 2

D : x 2 - y 2

3. If (a, n)! is defined as product of n consecutive numbers starting from a, where a and n are both natural numbers, and if H is the HCF of (a, n)! and n!, then what can be said about H?

Options

A : h = a!

B : h = n!

C : h ≥ n!

D : h ≥ a * n

46. A gardener had a number of shrubs to plant in horizontal rows. At first he tried to plant 5 shrubs in each row, then 6, then 8 and then 12, but had always 1 left. On trying 13, in one row he had none left. What is the smallest number of shrubs that he could have had?

Options

A : 481

B : 477

C : 468

D : 121

47. What is the sum to infinity of the series, 3 + 6x 2 + 9x 4 + 12x 6 + ... given |x| < 1?

Options

A : 3 / (1+x²)

B : 3 / (1-x²)²

C : 3 / (1+x²)²

D : 3 / (1-x²)

48. What is the ratio of common differences d1 and d2 of two arithmetic progressions if respective nth terms are in the ratio of 2n + 3 : n -11?

Options

A : 1 : 2

B : 2 : 3

C : 2 : 1

D : 1 : 3

49. A group of four numbers has only one prime number amongst them. Which of the following must be true about the group? I. HCF of the four numbers of the group is .either 1 or equal to that prime number. II. LCM of the four numbers of the group is same as product of the prime number and LCM of the remaining three numbers. III. Product of four numbers is equal to product of the prime number * HCF of the group * LCM of the group.

Options

A : I only

B : II only

C : I and II only

D : All of these

8. What is the harmonic mean of two numbers whose geometric mean and arithmetic mean is 8 and 5 respectively?

Options

A : 12.8

B : 12

C : 13.5

D : 14.6

9. Anil wants to divide Rs.100 into a number of bags so that one can ask for any amount between Rs.1 and Rs.100, he can give the proper amount by giving certain number of these bags without taking out the amount from them. What is the minimum number of bags he will require if each bag has whole number of rupees?

Options

A : 5

B : 6

C : 7

D : 8

10. When x + y + z = 9 and xy + yz + zx = 11, then x 3 - y 3 - z 3 - 3xyz equals

Options

A : 384

B : 192

C : 432

D : 48

11. HCF and LCM of two numbers is given. It is possible to find out the two numbers uniquely if I. either sum or difference between the two numbers is known. II. HCF of two numbers = LCM of two numbers. III. (LCM/HCF)= Prime number.

Options

A : I and II only

B : II only

C : II and III only

D : II and III only

12. A number when divided by sum of 555 and 445 gives two times their difference as quotient and 30 as remainder. The number is

Options

A : 1220

B : 1250

C : 22030

D : 220030

13. What is the remainder when 2050 x 2071 x 2095 is divided by 23?

Options

A : 17

B : 12

C : 6

D : 3

14. HCF of y 3 - 4y and 4y (y 3 + 8) is

Options

A : y(y + 2)

B : y - 2

C : 2 (y + 2)

D : (y + 2)(y 2 - 2y + 4)

15. A ball is dropped from a height of 12 m and it rebounds 1/2 of the distance it falls. If it continues to fall and rebound in this way, how far will it travel before coming to rest?

Options

A : 36 m

B : 30 m

C : 48 m

D : 60 m

16. Sum of three prime numbers is 100. If one of them exceeds another by 36, then one of the numbers is

Options

A : 7

B : 29

C : 41

D : 67

17. A school has 5 divisions in a class IX having 60, 50, 55, 62 and 58 students. Mean marks obtained in a History test were 56, 64, 72, 63 and 50 by each division respectively. What is overall average of the marks per students?

Options

A : 56.8

B : 58.2

C : 62.4

D : 60.8

18. What is the smallest number which when increased by 3 is divisible by 27, 35, 25 and 21?

Options

A : 4722

B : 4725

C : 4728

D : 4731

19. Which of the following is true?

Options

A : Sum of four consecutive even numbers is always divisible by 8.

B : Sum of four consecutive odd numbers is always divisible by 8.

C : Product of any n consecutive natural numbers may not be divisible by n!.

D : Product of 4 consecutive odd numbers is always divisible by 15.

20. Sum of all odd numbers up to 100 is

Options

A : 5050

B : 2500

C : 2525

D : 5000

21. If x+y+z=0,then x 2 /yx + y 2 /zx + z 2 /xy equal

Options

A : 0

B : 1

C : 2

D : 3

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