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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

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

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

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

1067 Views

129.
If x⁴ + 2x³ + ax² + bx + 9 is a perfect square, where a and b are positive real numbers, then the values of a and b are

a = 5, b = 6

a = 6, b = 7

a = 7, b = 6

a = 7, b = 6

a = 7, b = 6

(a + b + c)²
= a² + b² + c² + 2ab + 2bc + 2ca
$therefore space space left parenthesis straight x squared plus straight x plus 3 right parenthesis squared$
= x⁴ + x² + 9 + 2x³ + 6x + 6x²
= x⁴ + 2x³ + 7x² + 6x + 9
On comparing with x⁴ + 2x³ + 7x² + 6x + 9
a = 7, b = 6