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A school group charters three identical buses and occupies $4 over 5$ of the seats. After $1 fourth$ of the passengers leave, the remaining passengers use only two of the buses. The fraction of the seats on the two buses that are now occupied is

$8 over 9$
$7 over 10$
$7 over 9$
$7 over 9$

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22.

Find the value of:
$square root of 30 plus square root of 30 plus square root of 30 plus....... end root end root end root$

5
$3 square root of 10$
6
6

116 Views

23.

The value of $fraction numerator left parenthesis 8.3 right parenthesis to the power of 3.6 end exponent cross times space left parenthesis 9 right parenthesis to the power of 2.7 end exponent over denominator left parenthesis 81 right parenthesis to the power of 4.2 end exponent space cross times space left parenthesis 3 right parenthesis end fraction$ is

126 Views

24. $square root of 6 plus square root of 6 plus 6 plus.... end root end root$ is equal to

2

5

4

4

Let $straight x equals space square root of 6 plus square root of 6 plus square root of 6 plus.... end root end root end root$
On squaring both sides,
$straight x squared space equals space 6 plus square root of 6 plus square root of 6 plus square root of 6 plus..... end root end root end root$
$rightwards double arrow space space space straight x squared space equals space 6 space plus space straight x rightwards double arrow space space straight x squared minus straight x minus 6 space equals space 0 rightwards double arrow space space straight x squared minus 3 straight x plus 2 straight x minus 6 space equals space 0 rightwards double arrow space space straight x left parenthesis straight x minus 3 right parenthesis space plus space 2 left parenthesis straight x minus 3 right parenthesis space equals space 0 rightwards double arrow space space left parenthesis straight x space plus space 2 right parenthesis thin space left parenthesis straight x minus 3 right parenthesis space equals space 0$

$rightwards double arrow space space straight x space equals space 3 space space and space space straight x not equal to negative 2 space because space numbers space are space positive.$
Shortcut Method:
Co-Prime factors of 6 are (3, 2) as number is positive, therefore, answer would be highest co-prime factor i.e. 3.

116 Views

25.

open square brackets fraction numerator 1 over denominator 1 space cross times space 2 end fraction space plus space fraction numerator 1 over denominator 2 space cross times 3 end fraction space plus space fraction numerator 1 over denominator 3 space cross times space 4 end fraction space plus.... space plus space fraction numerator 1 over denominator 99 space cross times space 100 end fraction close square brackets

is equal to

$1 over 9900$
$99 over 100$
$100 over 99$
$100 over 99$

146 Views

26.

fraction numerator 0.1 space cross times space 0.1 space cross times space 0.1 space plus space 0.02 space cross times space 0.02 space cross times space 0.02 over denominator 0.2 space cross times space 0.2 space cross times space 0.2 space plus space 0.04 space cross times space 0.04 space cross times space 0.04 end fraction

is equal to

0.125
0.250
0.500
0.500

153 Views

27.

fraction numerator left parenthesis 0.87 right parenthesis cubed space plus space left parenthesis 0.13 right parenthesis cubed over denominator left parenthesis 0.87 right parenthesis squared space plus space left parenthesis 0.13 right parenthesis squared space minus space left parenthesis 0.87 right parenthesis space cross times space left parenthesis 0.13 right parenthesis space end fraction

$1 half$
2
1
1

102 Views

28.

3 over 4 open parentheses 1 plus 1 third close parentheses space open parentheses 1 plus 2 over 3 close parentheses space open parentheses 1 minus 2 over 5 close parentheses space open parentheses 1 plus 6 over 7 close parentheses space open parentheses 1 minus 12 over 13 close parentheses

is equal to

$2 over 13$
$1 over 7$
$1 over 6$
$1 over 6$

95 Views

29.

The value of:
$fraction numerator left parenthesis 0.67 space cross times space 0.67 space cross times space 0.67 right parenthesis space minus space left parenthesis 0.33 space cross times space 0.33 space cross times space 0.33 right parenthesis over denominator left parenthesis 0.67 space cross times space 0.67 right parenthesis space plus space left parenthesis 0.67 space cross times space 0.33 right parenthesis space plus space left parenthesis 0.33 space cross times space 0.33 right parenthesis end fraction$ is

128 Views

30.

The value of :
$4 minus fraction numerator 1 over denominator 1 plus begin display style fraction numerator 1 over denominator 3 plus begin display style fraction numerator 1 over denominator begin display style fraction numerator 8 plus 1 over denominator 4 end fraction end style end fraction end style end fraction end style end fraction$ is