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HCF and LCM

Multiple Choice Questions

11.

If the students of 9th class are arranged in a row of 6, 8, 12 or 16, no student is left behind. Then the possible number of students in the class is

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12.

In a division sum, the divisor is 4 times the quotient and twice the remainder. If a and b are respectively the divisor and the dividend, then

$fraction numerator 4 straight b minus straight a squared over denominator straight a end fraction equals 3$
$fraction numerator 4 straight b minus 2 straight a over denominator straight a squared end fraction space equals space 2$
$left parenthesis straight a plus 1 right parenthesis squared space equals space 4 straight b$
$left parenthesis straight a plus 1 right parenthesis squared space equals space 4 straight b$

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13.

H.C.F. of $2 over 3 comma space space 4 over 5 space and space space 6 over 7$ is

$48 over 105$
$2 over 105$
$1 over 105$
$1 over 105$

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14.

There are five bells which start ringing together at intervals of 3, 6, 9, 12 and 15 seconds respectively. In 36 minutes, how many times will the bells ring simultaneously?

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15.
The greatest number among $square root of 5 comma space space space cube root of 4 comma space space fifth root of 2 space comma space root index 7 of 3 space$ is

$cube root of 4$
$root index 7 of 3$
$square root of 5$
$square root of 5$

square root of 5

LCM of the orders of the surds = LCM of 2, 3, 5 and 7 = 210
Now,
$5 to the power of 1 half end exponent space equals space 5 to the power of 105 over 210 end exponent space equals space left parenthesis 5 to the power of 105 right parenthesis to the power of 1 over 210 end exponent 4 to the power of 1 third end exponent space equals space 4 to the power of 70 over 210 end exponent space equals space left parenthesis 4 to the power of 70 right parenthesis to the power of 1 over 210 end exponent 2 to the power of 1 fifth end exponent space equals space 2 to the power of 42 over 210 end exponent space equals space left parenthesis 2 to the power of 42 right parenthesis to the power of 1 over 210 end exponent 3 to the power of 1 over 7 end exponent space equals space 3 to the power of 30 over 210 end exponent space equals left parenthesis 3 to the power of 30 right parenthesis to the power of 1 over 210 end exponent$
∴ The largest number
$equals space 5 to the power of 1 half end exponent space equals space square root of 5$