Number System – Set 3

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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?

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

 

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

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4) The smallest three-digit prime number is :

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5) 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 :

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6) 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 :

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7) 2525 is divided by 26, the remainder is :

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

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9) (461 + 462 + 463 + 464) is divisible by :

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

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

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

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

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14) 1234 + 2345 – 3456 + 4567 = ?

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15) 287 × 287 + 269 × 269 – 2 × 287 × 269 = ?

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

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

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

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20) (46351 – 36418 – 4505) ÷ ? = 1357

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21) 98th term of the infinite series 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, …. is :

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

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

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

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26) 2“>√2 is a/an-

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27) 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 ?

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

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29) 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

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

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31) 8 + 88 + 888 + 8888 + 88888 + 888888 = ?

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

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

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34) (800 ÷ 64) × (1296 ÷ 36) = ?

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

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36) 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

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

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

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39) (xn – an) is divisible by (x – a)

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

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

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

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

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

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

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

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

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

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