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) 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?

987654321

456789321

432156789

381654729

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

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

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

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

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6) 25²⁵ is divided by 26, the remainder is :

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

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

132

162

100

192

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9) 397 × 397 + 104 × 104 + 2 × 397 × 104 = ?

251005

251004

251001

251000

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

5065

5055

5050

5060

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

None of these

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12) 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

I and II only

None of these

I only

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13) 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

II only

I only

I and III only

I and II only

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

537804

63810

35718

3125736

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15) (4⁶¹ + 4⁶² + 4⁶³ + 4⁶⁴) is divisible by :

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16) 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 :

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17) (800 ÷ 64) × (1296 ÷ 36) = ?

470

None of these

480

460

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

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19) 8 + 88 + 888 + 8888 + 88888 + 888888 = ?

986748

896748

897648

987648

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20) 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

4,8

4,7

3,6

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21) 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 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

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

(a + b + c)2

ab (a + b)

– abc

a2 + b2 + c2

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23) (xⁿ – aⁿ) is divisible by (x – a)

for all values of n

only for even values of n

only for odd values of n

only for prime values of n

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24) 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 ?

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25) (46351 – 36418 – 4505) ÷ ? = 1357

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26) 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 :

None of these

5000

6000

4000

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

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

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

None of these

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

Every natural number is an integer

Every real number is a rational number.

Every natural number is a real number.

Every integer is a rational number.

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

2077

2078

2080

2079

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32) The smallest three-digit prime number is :

102

103

104

101

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33) 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 7

0 and 9

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

7,5

1,9

2,4

3,6

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

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

-129

-127

-126

-128

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

y > p

Insufficient data

x + y > z

y + p > x

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

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39) 98th term of the infinite series 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, …. is :

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

either 3 or 5

either 1 or 5

either 1 or 3

either 1 or 2

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

Divisible by (11 × 13)

429

Divisible by (11 + 13)

Divisible by (13 – 11)

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42) 287 × 287 + 269 × 269 – 2 × 287 × 269 = ?

323

322

325

324

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43) 1234 + 2345 – 3456 + 4567 = ?

None of these

4690

4880

4670

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

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

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46) 2 “> \sqrt is a/an-

natural number

irrational number

integer

rational number

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47) 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