Number System - Set 3

Number System – Set 3

Dear ! This is Number System – Set 3 Quiz and it contains 50 questions.

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1) If a and b are positive integers, a > b and (a + b)² – (a – b)² > 29 Then the smallest value of a is –

2 / 50

2) 1234 + 2345 – 3456 + 4567 = ?

None of these

4670

4880

4690

3 / 50

3) 2 “> \sqrt is a/an-

irrational number

rational number

integer

natural number

4 / 50

4) How many numbers less than 1000 are multiple of both 10 and 13 ?

5 / 50

5) If m = – 4, n = – 2, then the value of m³ – 3m² + 3m + 3n + 3n² + n³ is :

-126

-129

-127

-128

6 / 50

6) What is sum of all natural numbers from 1 to 100 ?

5055

5060

5050

5065

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7) Given that (1² + 2² + 3² + ….. + 20²) = 2870, the value of (2² + 4² + 6² + … + 40² ) is :

11470

11490

11438

11480

8 / 50

8) Two numbers when divided by a certain divisor leave the remainders 4375 and 2986 respectively but when the sum of two numbers is divided by the same divisor, the remainder is 2361. The divisor in question is :

4000

6000

5000

None of these

9 / 50

9) 8 + 88 + 888 + 8888 + 88888 + 888888 = ?

897648

986748

987648

896748

10 / 50

10) The smallest number which must be subtracted from 8112 to make it exactly divisible by 99 is :

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11) What least number must be added to 1056 to get a number exactly divisible by 23 ?

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12) A 9 digit number in which zero does not appear and no digits are repeated has the following properties: The number comprising the left most two digits is divisible by 2, that comprising the left most three digits is divisible by 3, and so on?

381654729

456789321

987654321

432156789

13 / 50

13) If the seven digit number 876p37q is divided by 225, then the value of p and q respectively are :

0 and 5

0 and 1

0 and 9

0 and 7

14 / 50

14) The numbers from 1 to 29 are written side by side as follows : 1234567891011121314…..2829 If this number is divided by 9, then what is the remainder ?

None of these

15 / 50

15) Among the following statements, the statement which is not correct is :

Every real number is a rational number.

Every natural number is a real number.

Every integer is a rational number.

Every natural number is an integer

16 / 50

16) Which of the following numbers is exactly divisible by 24 ?

537804

35718

63810

3125736

17 / 50

17) (800 ÷ 64) × (1296 ÷ 36) = ?

None of these

470

460

480

18 / 50

18) If x and y are two digits of the number 653xy such that the number is divisible by 80, then x + y is equal to :

19 / 50

19) How many prime numbers are there between 100 to 200 ?

20 / 50

20) The greatest number by which the product of three consecutive multiples of 3 is always divisible is :

192

132

100

162

21 / 50

21) The number of times 99 is subtracted from 1111 so that the remainder is less then 99 is :

22 / 50

22) Which of the following numbers is divisible by 3, 7, 9 and 11 ?

2078

2079

2080

2077

23 / 50

23) If a number is divisible by both 11 and 13, then it must be necessarily :

Divisible by (11 + 13)

Divisible by (13 – 11)

Divisible by (11 × 13)

429

24 / 50

24) If a = 7, b = 5, c = 3, then the value of a² + b² + c² – ab – bc – ca is :

25 / 50

25) The digit in the unit’s place of the product (2464)¹⁷⁹³ × (615)³¹⁷ × (131)⁴⁹¹ is :

26 / 50

26) The digit in the unit’s place of the number (67)²⁵ – 1 must be –

None of these

27 / 50

27) (46351 – 36418 – 4505) ÷ ? = 1357

28 / 50

28) 98th term of the infinite series 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, …. is :

29 / 50

29) What is the remainder when 2³¹ is divided by 5 ?

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30) If n = 1 + x, where x is the product of four consecutive positive integers, then which of the following is/are true ? I. n is odd II. n is prime III. n is a perfect square

I and III only

None of these

I only

I and II only

31 / 50

31) The digits indicated by * in 3422213** so that this number is divisible by 99 are :

7,5

2,4

3,6

1,9

32 / 50

32) If x is a rational number and y is an irrational number, then-

xy is necessarily irrational, but x + y can be either rational or irrational

Both x + y and xy are necessarily rational

x + y can be either x + y is necessarily irrational, but xy can be either rational or irrational

Both x + y and xy are necessarily irrational

33 / 50

33) If p³ – q³ = (p – q) (p – q)² – xpq, then find the value of x :

-3

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34) The digit in the unit’s place of [(251)⁹⁸ + (21)²⁹ – (106)¹⁰⁰ + (705)³⁵ – 16⁴ + 259] is :

35 / 50

35) If a + b + c = 0, (a + b) (b + c) (c + a) equals

(a + b + c)2

a2 + b2 + c2

ab (a + b)

– abc

36 / 50

36) Which of the following digits will replace the H marks in the following equation ? 9H + H8 + H6 = 230

None of these

37 / 50

37) P and Q are two positive integers such that PQ = 64. Which of the following cannot be the value of P + Q = ?

38 / 50

38) 397 × 397 + 104 × 104 + 2 × 397 × 104 = ?

251004

251001

251005

251000

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39) For the integer n, if n³ is odd, then which of the following statements are true ? I. n is odd II. n² is odd III. n² is even

I and III only

I only

I and II only

II only

40 / 50

40) If (10¹² + 25)² – (10¹² – 25)² = 10ⁿ, then the value of n is :

41 / 50

41) If the sum of two numbers is 14 and their difference is 10, find the product of these two numbers.

42 / 50

42) The smallest three-digit prime number is :

103

101

102

104

43 / 50

43) 25²⁵ is divided by 26, the remainder is :

44 / 50

44) (4⁶¹ + 4⁶² + 4⁶³ + 4⁶⁴) is divisible by :

45 / 50

45) (xⁿ – aⁿ) is divisible by (x – a)

only for prime values of n

only for odd values of n

for all values of n

only for even values of n

46 / 50

46) The remainder obtained when any prime number greater than 6 is divided by 6 must be :

either 1 or 3

either 1 or 2

either 3 or 5

either 1 or 5

47 / 50

47) If the number 357*25* is divisible by both 3 and 5, then the missing digits in the unit’s place and the thousandth’s place respectively are :

None of these

4,7

4,8

3,6

48 / 50

48) In the relation x > y + z, x + y > p and z < p, which of the following is necessarily true ?

Insufficient data

y + p > x

y > p

x + y > z

49 / 50

49) 287 × 287 + 269 × 269 – 2 × 287 × 269 = ?

325

322

323

324

50 / 50

50) While writing all the numbers from 700 to 1000, how many numbers occur in which the first digits greater than the second digit, and the second digit is greater than the third digit ?