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Algebra

Multiple Choice Questions

201.

If a and b are two odd positive integers, by which of the following integers is (a⁴ - b⁴) always divisible?

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202.

If x * y = (x + 3)2 (y - 1), then the value of 5 * 4 is

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203.
$fraction numerator left parenthesis 0.05 right parenthesis squared space plus space left parenthesis 0.41 right parenthesis squared space plus space left parenthesis 0.73 right parenthesis squared over denominator left parenthesis 0.005 right parenthesis squared space plus space left parenthesis 0.041 right parenthesis squared space plus space left parenthesis 0.0073 right parenthesis squared end fraction$ is

10

100

1000

None of these

100

Let a = 0.05, b = 0.41 and c = 0.073
$therefore space space space fraction numerator left parenthesis 0.05 right parenthesis squared space plus space left parenthesis 0.41 right parenthesis squared space plus space left parenthesis 0.73 right parenthesis squared over denominator left parenthesis 0.005 right parenthesis squared space plus space left parenthesis 0.041 right parenthesis squared space plus space left parenthesis 0.0073 right parenthesis squared end fraction space space space space equals space fraction numerator straight a squared space plus space straight b squared space plus space straight c squared over denominator open parentheses begin display style straight a over 10 end style close parentheses squared space plus space open parentheses begin display style straight b over 10 end style close parentheses squared space plus space open parentheses begin display style straight c over 10 end style close parentheses squared end fraction space space space equals space fraction numerator straight a squared space plus space straight b squared space plus space straight c squared over denominator begin display style 1 over 100 end style left parenthesis straight a squared space plus space straight b squared space plus space straight c squared right parenthesis end fraction space space space equals space fraction numerator left parenthesis straight a squared space plus space straight b squared plus space straight c squared right parenthesis space cross times space 100 over denominator straight a squared space plus space straight b squared space plus space straight c squared end fraction space equals space space space 100$

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204.

If X * Y = X² + Y² - XY, then 11 * 13 is

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205.

If a and b are odd numbers, then which of the following is even?

a + b + ab
a + b - 1
a + b + 1
a + b + 2ab

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206.

If a^1/3 = 11, then the value of a² - 331 a is

1331331
1331000
1334331
1330030

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207.

If $straight x space equals space 2 space plus space square root of 3 space comma space space space straight y space equals space 2 minus square root of 3 comma$ then the value of $fraction numerator straight x squared plus straight y squared over denominator straight x cubed space plus space straight y cubed end fraction$ is

$7 over 38$
$7 over 40$
$7 over 19$
$7 over 26$

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208.

If $5 straight a space plus space fraction numerator 1 over denominator 3 straight a end fraction space equals space 5 comma$ then the value of $9 straight a squared space plus space fraction numerator 1 over denominator 25 straight a squared end fraction$ is

$34 over 5$
$39 over 5$
$42 over 5$
$52 over 5$

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209.

If $2 straight x space minus space fraction numerator 1 over denominator 2 straight x end fraction space equals space 6 comma$ then the value of $straight x squared space plus space fraction numerator 1 over denominator 16 straight x squared end fraction$ is