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Algebra

Multiple Choice Questions

121.

If x² + y² + 2x + 1 = 0, then the value of x³¹ + y³⁵ is

-1
0
1
1

317 Views

122.

If $open parentheses straight x minus 1 over straight x close parentheses squared space equals space 3 comma$ then the value of $open parentheses straight x to the power of 6 space plus space 1 over straight x to the power of 6 close parentheses$ equals

499 Views

123.

If a³ = 117 + b³ and a = 3 + b, then the value of (a + b) is

$plus-or-minus space 7$
$plus-or-minus space 49$
$plus-or-minus space 13$
$plus-or-minus space 13$

420 Views

124.

If a + b + c = 0 then the value of $fraction numerator 1 over denominator left parenthesis straight a plus straight b right parenthesis thin space left parenthesis straight b plus straight c right parenthesis end fraction space plus space fraction numerator 1 over denominator left parenthesis straight b plus straight c right parenthesis thin space left parenthesis straight c plus straight a right parenthesis end fraction space plus space fraction numerator 1 over denominator left parenthesis straight c plus straight a right parenthesis space left parenthesis straight a plus straight b right parenthesis end fraction$ is

230 Views

125.
If a² + b² + c² = 16, x² + y² + z² = 25 and ax + by + cz = 20, then the value of $fraction numerator straight a plus straight b plus straight c over denominator straight x plus straight y plus straight z end fraction$ is

$3 over 5$
$5 over 3$
$4 over 5$
$4 over 5$

4 over 5

left parenthesis ax plus by plus cz right parenthesis squared space equals space left parenthesis 20 right parenthesis squared space equals space 400 space space space... left parenthesis straight i right parenthesis left parenthesis straight a squared plus straight b squared plus straight c squared right parenthesis thin space left parenthesis straight x squared plus straight y squared plus straight z squared right parenthesis space equals space 25 space cross times space 16 space equals space 400 space... left parenthesis ii right parenthesis

From (i) and (ii)

left parenthesis ax plus by plus cz right parenthesis squared space equals space left parenthesis straight a squared plus straight b squared plus straight c squared right parenthesis space left parenthesis straight x squared space plus space straight y squared space plus space straight z squared right parenthesis

straight a squared straight x squared space plus space straight b squared straight y squared space plus space straight c squared straight z squared space plus space 2 abxy space plus space 2 bcyz space plus space 2 acxz

equals space straight a squared straight x squared space plus space straight a squared straight y squared space plus space straight a squared straight z squared space plus space straight b squared straight x squared space plus space straight b squared straight y squared space plus space straight b squared straight z squared space plus space straight c squared straight x squared space plus space straight c squared straight y squared space plus straight c squared straight z squared

⟹ a²y² + a²z² + b²x² + b²z² + c²x² + c²y² = 2abx + 2bcyz + 2acxz
⟹ a²y² - 2abxy + b²x² + a²z² + c²x² - 2acxz + b²z² + c²y² - 2bcyz = 0
⟹ (ay - bx)² + (az - cx)² + (bz - cy)² = 0
⟹ ay - bx = 0 ⟹ ay = bx ⟹

straight a over straight b space equals space straight x over straight y

az - cx = 0

rightwards double arrow space space space az space equals space cx space space rightwards double arrow space space straight a over straight c space equals space straight x over straight z

therefore space space space straight a space equals space kx semicolon space space straight b space equals space ky semicolon space space straight c space equals space kz therefore space space space straight a squared space plus space straight b squared space plus space straight c squared space equals space 16 rightwards double arrow space space space space space straight k squared left parenthesis straight x squared space plus space straight y squared space plus space straight z squared right parenthesis space equals space 16 rightwards double arrow space space space space space straight k squared space cross times space 25 space equals space 16 rightwards double arrow space space space space space straight k squared space equals space 16 over 25 space rightwards double arrow space space space straight k space equals space 4 over 5

therefore space space space fraction numerator straight a plus straight b plus straight c over denominator straight x plus straight y plus straight z end fraction space equals space straight k space equals 4 over 5

1136 Views

126.

The value of x which satisfies the equation $fraction numerator straight x plus straight a squared plus 2 straight c squared over denominator straight b plus straight c end fraction plus fraction numerator straight x plus straight b squared space plus 2 straight a squared over denominator straight c plus straight a end fraction plus fraction numerator straight x plus straight c squared plus 2 straight b squared over denominator straight a plus straight b end fraction space equals space 0$
is

(a² + b² + c²)
- (a² + b² + c²)
(a² + 2b² + c²)
(a² + 2b² + c²)

394 Views

127.

If $straight x space equals space fraction numerator square root of 5 plus 1 over denominator square root of 5 minus 1 end fraction space and space straight y space equals space fraction numerator square root of 5 minus 1 over denominator square root of 5 plus 1 end fraction comma$ the value of $fraction numerator straight x squared plus xy plus straight y squared over denominator straight x squared minus xy plus straight y squared end fraction$ is

$3 over 4$
$4 over 3$
$3 over 5$
$3 over 5$

389 Views

128.

Let 0 < x < 1. Then the correct inequality is

$straight x space less than space square root of straight x space less than space space straight x squared$
$square root of straight x space less than space straight x space less than space straight x squared$
$straight x squared space less than space straight x space less than space square root of straight x$
$straight x squared space less than space straight x space less than space square root of straight x$