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Algebra

Multiple Choice Questions

101.

If $2 straight x plus 2 over straight x space equals space 1 comma$ then the value of $straight x cubed space plus space 1 over straight x cubed$ is

$13 over 8$
$negative 11 over 8$
$11 over 8$
$11 over 8$

234 Views

102.

If $straight a squared space plus space straight b squared space plus space 1 over straight a squared space plus space 1 over straight b squared space equals space 4 comma$ then the value of $straight a squared space plus space straight b squared$ will be

1
$1 1 half$
2
2

142 Views

103.

If $straight x cubed plus 3 straight x squared plus 3 straight x space equals space 7 comma$ then x is equal to

2
$cube root of 6$
1
1

165 Views

104.

If $2 straight x plus space fraction numerator 1 over denominator 3 straight x end fraction space equals space 6 comma$ then $3 straight x plus fraction numerator 1 over denominator 2 straight x end fraction$ is equal to

123 Views

105.

If $straight x squared space plus straight y squared space minus space 2 straight x space plus space 6 straight y space plus space 10 space equals space 0$ , then the value of (x² + y²) is

104 Views

106.

If a + b + c = 1 and ab + bc + ca = $1 third$ then a : b : c is

1 : 2 : 2
2 : 1 : 2
1 : 1 : 1
1 : 1 : 1

134 Views

107.

If $straight x space equals space left parenthesis square root of 2 space minus 1 right parenthesis to the power of negative 1 half end exponent$ then the value of $open parentheses straight x squared space minus space 1 over straight x squared close parentheses$ is

2
$negative 2 square root of 2$
$2 square root of 2$
$2 square root of 2$

197 Views

108.
If $square root of 7 square root of 7 square root of 7 square root of 7 end root end root end root space equals space left parenthesis 343 right parenthesis to the power of straight y minus 1 end exponent$ , then y is equal to

$2 over 3$

1

$4 over 3$
$4 over 3$

4 over 3

Let $straight x space equals space square root of 7 square root of 7 square root of 7 square root of 7 end root end root end root$
On squaring both sides,
$straight x squared space equals space 7 straight x$
$rightwards double arrow space space space straight x squared space minus space 7 straight x space equals space 0 space space space rightwards double arrow space space space straight x left parenthesis straight x minus 7 right parenthesis space equals space 0 rightwards double arrow space space straight x space equals space 7$

$therefore space space space space space 7 space equals space left parenthesis 7 cubed right parenthesis to the power of straight y to the power of negative 1 end exponent space end exponent equals space 7 to the power of 3 straight y minus 3 end exponent rightwards double arrow space space space 3 straight y space minus space 3 space equals space 1 rightwards double arrow space space space space 3 straight y space equals space 4 rightwards double arrow space space space straight y space equals space 4 over 3$

120 Views

109.

If a² = 2, then (a + 1) is equal to

a - 1
$fraction numerator 2 over denominator straight a minus 1 end fraction$
$fraction numerator straight a plus 1 over denominator 3 minus 2 straight a end fraction$
$fraction numerator straight a plus 1 over denominator 3 minus 2 straight a end fraction$

148 Views

110.

If $straight x to the power of 1 third end exponent space plus space straight y to the power of 1 third end exponent space equals space straight z to the power of 1 third end exponent comma$ then $left parenthesis straight x plus straight y minus straight z right parenthesis cubed space plus space 27 xyz$ is equal to