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
A. 183654729
B. 381654729
C. 983654721
D. 981654723
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The remainder obtained when any prime number greater than 6 is divided by 6 must be :
A. either 1 or 2
B. either 1 or 3
C. either 1 or 5
D. either 3 or 5
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The smallest number which must be subtracted from 8112 to make it exactly divisible by 99 is :
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If the sum of two numbers is 14 and their difference is 10, find the product of these two numbers.
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The greatest number by which the product of three consecutive multiples of 3 is always divisible is :
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If p3 - q3 = (p - q) (p - q)2 - xpq, then find the value of x :
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If n = 1 + x, where x is the product of four consecutive positive integers, then which of the following is/are true ?
A. I only
B. I and II only
C. I and III only
D. None of these
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If the seven digit number 876p37q is divided by 225, then the value of p and q respectively are :
A. 0 and 0
B. 9 and 0
C. 0 and 5
D. 9 and 5
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What is the remainder when 231 is divided by 5 ?
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(800 ÷ 64) × (1296 ÷ 36) = ?
A. 420
B. 460
C. 500
D. 540
E. None of these
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The number of times 99 is subtracted from 1111 so that the remainder is less then 99 is :
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If p is a positive fraction less than 1, then
A. p 1
B. p 1
C. p2 is less than p
D. p 2
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Given that (12 + 22 + 32 + ..... + 202 ) = 2870, the value of (22 + 42 + 62 + ... + 402 ) is :
A. 2870
B. 5740
C. 11480
D. 28700
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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 :
A. 0, 6
B. 5, 1
C. 5, 4
D. None of these
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In the relation x > y + z, x + y > p and z < p, which of the following is necessarily true ?
A. y > p
B. x + y > z
C. y + p > x
D. Insufficient data
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(xn - an ) is divisible by (x - a)
A. for all values of n
B. only for even values of n
C. only for odd values of n
D. only for prime values of n
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8 + 88 + 888 + 8888 + 88888 + 888888 = ?
A. 897648
B. 896748
C. 986748
D. 987648
E. None of these
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If a + b + c = 0, (a + b) (b + c) (c + a) equals
A. ab (a + b)
B. (a + b + c)2
C. - abc
D. a2 + b2 + c2
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If x is a rational number and y is an irrational number, then-
A. Both x + y and xy are necessarily rational
B. Both x + y and xy are necessarily irrational
C. xy is necessarily irrational, but x + y can be either rational or irrational
D. x + y is necessarily irrational, but xy can be either rational or irrational
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The digit in the unit's place of [(251)98 + (21)29 - (106)100 + (705)35 - 164 + 259] is :
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