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201.
If a and b are two odd positive integers, by which of the following integers is (a⁴ - b⁴) always divisible?

3

6

8

12

a⁴ - b⁴= (a - b) (a + b) (a² + b²), where a and b are odd positive integers.
If two positive integers are odd, then their sum, difference and sum of their squares always even.
∴ (a - b) (a + b) and (a² + b²) are divisible by 2.
Hence (a - b) (a + b) x (a² + b²) = a⁴ - b⁴ is always divisible by 2³ = 8.

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202.

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

37 Views

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

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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

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

30 Views

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