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If $straight a greater than straight b greater than 0 comma space space AB space equals space straight a minus straight b space cm comma space space space BC space equals space 2 square root of ab space cm comma space space then space angle ABC$ is

$45 degree$
$60 degree$
$90 degree$
$90 degree$

130 Views

32.
If ab = 21 and $fraction numerator left parenthesis straight a plus straight b right parenthesis squared over denominator left parenthesis straight a minus straight b right parenthesis end fraction space equals space 25 over 4$ then value of $straight a squared plus straight b squared plus 3 ab$ is

115

121

125

125

121

ab = 21 ...(i)
$fraction numerator left parenthesis straight a plus straight b right parenthesis squared over denominator left parenthesis straight a minus straight b right parenthesis squared end fraction space equals space 25 over 4$
$rightwards double arrow space space open parentheses fraction numerator straight a plus straight b over denominator straight a minus straight b end fraction close parentheses squared space equals space 25 over 4 rightwards double arrow space space space space space space fraction numerator straight a plus straight b over denominator straight a minus straight b end fraction space equals space 5 over 2 rightwards double arrow space space space space space 2 straight a plus 2 straight b space equals space 5 straight a minus 5 straight b$
$rightwards double arrow$ 3a = 7b
$rightwards double arrow$ $straight a space equals space fraction numerator 7 straight b over denominator 3 end fraction$ ...(ii)
From equation (i),
$fraction numerator 7 straight b cross times straight b over denominator 3 end fraction equals 21$
$straight b squared space equals space 9$
From equation (ii),
$straight a space equals space fraction numerator 7 cross times 3 over denominator 3 end fraction space equals space 7$
$therefore$ $straight a squared plus straight b squared plus 3 ab space equals space left parenthesis 7 right parenthesis squared plus left parenthesis 3 right parenthesis squared plus 3 cross times 7 cross times 3$
= 49 + 9 + 63
= 121

155 Views

33.

Given, $straight a minus straight b space equals space 2$ and $straight a cubed minus straight b cubed space equals space 26$ then $left parenthesis straight a plus straight b right parenthesis squared$ is

130 Views

34.

If x + y + z = 9 then value of $left parenthesis straight x minus 4 right parenthesis cubed plus left parenthesis straight y minus 2 right parenthesis cubed plus left parenthesis straight z minus 3 right parenthesis cubed minus 3 left parenthesis straight x minus straight y right parenthesis left parenthesis straight y minus straight z right parenthesis left parenthesis straight z minus 3 right parenthesis$ is

131 Views

35.

If $straight a over straight b plus straight b over straight a equals negative 1$ , then the value of $straight a squared over straight b squared minus straight b squared over straight a squared$ is

1
-1
0
0

112 Views

36.

Among below expressions which one can be expressed as the difference of two cubic expressions?

$straight x cubed plus straight y cubed plus 3 straight x plus 3 straight y$
$straight x cubed plus 2 straight x squared plus 3 straight x plus straight x squared$
$straight x cubed plus 3 straight x squared plus 3 straight x minus 2$
$straight x cubed plus 3 straight x squared plus 3 straight x minus 2$

105 Views

37.

If $straight a squared plus 1 over straight a squared space equals space 7$ and V₁ and V₂ are the minimum and the maximum values of $straight a cubed plus 1 over straight a cubed comma space$ then $straight V subscript 2 minus straight V subscript 1$ is equal to

107 Views

38.

If $straight x plus fraction numerator 1 over denominator 9 straight x end fraction space equals space 4 comma$ then $9 straight x squared plus fraction numerator 1 over denominator 9 straight x squared end fraction$ is

117 Views

39.

If a = 2, b = -3 then the value of $27 straight a cubed minus 54 straight a squared straight b space plus space 36 ab squared minus 8 straight b cubed$ is

1562
1616
1676
1676

95 Views

40.

If $straight a cubed plus 1 over straight a cubed space equals space 2 comma space$ then value of $fraction numerator straight a squared plus 1 over denominator straight a end fraction$ is (a is a positive number):