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Question

If $omega$ is a cube root of unity, then $open vertical bar table row cell x plus 1 end cell omega cell omega to the power of 2 end exponent end cell row omega cell x plus omega to the power of 2 end exponent end cell 1 row cell omega to the power of 2 end exponent end cell 1 cell x plus omega end cell end table close vertical bar equals$

$x^{3} + 1$
$x^{3} + ω$
$x^{3} + ω^{2}$
$x^{3}$

The correct answer is: $x to the power of 3 end exponent$

$capital delta equals open vertical bar table row cell x plus 1 end cell omega cell omega to the power of 2 end exponent end cell row omega cell x plus omega to the power of 2 end exponent end cell 1 row cell omega to the power of 2 end exponent end cell 1 cell x plus omega end cell end table close vertical bar$
= $open vertical bar table row cell x plus 1 plus omega plus omega to the power of 2 end exponent end cell omega cell omega to the power of 2 end exponent end cell row cell x plus 1 plus omega plus omega to the power of 2 end exponent end cell cell x plus omega to the power of 2 end exponent end cell 1 row cell x plus 1 plus omega plus omega to the power of 2 end exponent end cell 1 cell x plus omega end cell end table close vertical bar$ , $left parenthesis C subscript 1 end subscript rightwards arrow C subscript 1 end subscript plus C subscript 2 end subscript plus C subscript 3 end subscript right parenthesis$
= $x open vertical bar table row 1 omega cell omega to the power of 2 end exponent end cell row 1 cell x plus omega to the power of 2 end exponent end cell 1 row 1 1 cell x plus omega end cell end table close vertical bar blank open vertical bar table row 1 a cell a to the power of 2 end exponent end cell row 1 b cell b to the power of 2 end exponent end cell row 1 c cell c to the power of 2 end exponent end cell end table close vertical bar not equal to 0$
= $x left square bracket 1 left curly bracket left parenthesis x plus omega to the power of 2 end exponent right parenthesis left parenthesis x plus omega right parenthesis minus 1 right curly bracket plus omega left curly bracket 1 minus left parenthesis x plus omega right parenthesis right curly bracket plus omega to the power of 2 end exponent left curly bracket 1 minus left parenthesis x plus omega to the power of 2 end exponent right parenthesis right curly bracket right square bracket$
= $x left parenthesis x to the power of 2 end exponent plus omega x plus omega to the power of 2 end exponent x plus omega to the power of 3 end exponent minus 1 plus omega minus omega x minus omega to the power of 2 end exponent plus omega to the power of 2 end exponent minus omega to the power of 2 end exponent x minus omega to the power of 4 end exponent right parenthesis$
= $x to the power of 3 end exponent$ , $blank left parenthesis because omega to the power of 3 end exponent equals 1 right parenthesis$

$open vertical bar table row cell b to the power of 2 end exponent plus c to the power of 2 end exponent end cell cell a to the power of 2 end exponent end cell cell a to the power of 2 end exponent end cell row cell b to the power of 2 end exponent end cell cell c to the power of 2 end exponent plus a to the power of 2 end exponent end cell cell b to the power of 2 end exponent end cell row cell c to the power of 2 end exponent end cell cell c to the power of 2 end exponent end cell cell a to the power of 2 end exponent plus b to the power of 2 end exponent end cell end table close vertical bar equals$

Maths-General

General

Maths-

In the expansion of $fraction numerator 1 plus x over denominator 1 factorial end fraction plus fraction numerator left parenthesis 1 plus x right parenthesis to the power of 2 end exponent over denominator 2 factorial end fraction plus fraction numerator left parenthesis 1 plus x right parenthesis to the power of 3 end exponent over denominator 3 factorial end fraction plus..... comma$ the coefficient of $x to the power of n end exponent$ will be

Maths-General

General

Maths-

The value of $log subscript 3 end subscript invisible function application e minus log subscript 9 end subscript invisible function application e plus log subscript 27 end subscript invisible function application e....$ is equal to

Maths-General

General

Maths-

The sum to infinity of the given series $fraction numerator 1 over denominator n end fraction minus fraction numerator 1 over denominator 2 n to the power of 2 end exponent end fraction plus fraction numerator 1 over denominator 3 n to the power of 3 end exponent end fraction minus fraction numerator 1 over denominator 4 n to the power of 4 end exponent end fraction plus....$ is

Maths-General

General

Maths-

$log subscript a end subscript invisible function application x$ is defined for $left parenthesis a greater than 0 right parenthesis$

Maths-General

General

Maths-

The sum of the series $fraction numerator 1 over denominator 2.3 end fraction plus fraction numerator 1 over denominator 4.5 end fraction plus fraction numerator 1 over denominator 6.7 end fraction plus... equals$

Maths-General

General

Maths-

$fraction numerator 1 over denominator 5 end fraction plus fraction numerator 1 over denominator 2 end fraction. fraction numerator 1 over denominator 5 to the power of 2 end exponent end fraction plus fraction numerator 1 over denominator 3 end fraction. fraction numerator 1 over denominator 5 to the power of 3 end exponent end fraction plus..... infinity equals$

Maths-General

General

Physics-

White light is incident normally on a thin film which has n = 1.5 and a thickness of 5000 Å. For what wavelengths in the visible spectrum (4000 – 7000 Å) will the intensity of the reflected light be a maximum?

Physics-General

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Biology

The sum of 730 + 450 using front – end estimation is______.

Front-end estimation means rounding off a number to the nearest place value of the leading digit of the number.

The sum of 730 + 450 using front – end estimation is______.

Maths-General

Front-end estimation means rounding off a number to the nearest place value of the leading digit of the number.

General

Maths-Video

Round the number 5432 to the nearest hundred.

For rounding off to the nearest hundred, we can also look at the number formed by the tens place digit and one place digit. If the number formed is less than 50,we round down and if the number is 50 or more we round up.

Round the number 5432 to the nearest hundred.

Maths-General

General

GeneralVideo

Estimate 275 + 238 to nearest hundred.

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If is a cube root of unity, then

The correct answer is:

=,= = = = ,

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White light is incident normally on a thin film which has n = 1.5 and a thickness of 5000 Å. For what wavelengths in the visible spectrum (4000 – 7000 Å) will the intensity of the reflected light be a maximum?

White light is incident normally on a thin film which has n = 1.5 and a thickness of 5000 Å. For what wavelengths in the visible spectrum (4000 – 7000 Å) will the intensity of the reflected light be a maximum?

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The sum of 730 + 450 using front – end estimation is______.

The sum of 730 + 450 using front – end estimation is______.

Round the number 5432 to the nearest hundred.

Round the number 5432 to the nearest hundred.

Estimate 275 + 238 to nearest hundred.

Estimate 275 + 238 to nearest hundred.

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The correct answer is: $x to the power of 3 end exponent$

The value of $log subscript 3 end subscript invisible function application e minus log subscript 9 end subscript invisible function application e plus log subscript 27 end subscript invisible function application e....$ is equal to

The value of $log subscript 3 end subscript invisible function application e minus log subscript 9 end subscript invisible function application e plus log subscript 27 end subscript invisible function application e....$ is equal to

$log subscript a end subscript invisible function application x$ is defined for $left parenthesis a greater than 0 right parenthesis$

$log subscript a end subscript invisible function application x$ is defined for $left parenthesis a greater than 0 right parenthesis$

The sum of the series $fraction numerator 1 over denominator 2.3 end fraction plus fraction numerator 1 over denominator 4.5 end fraction plus fraction numerator 1 over denominator 6.7 end fraction plus... equals$

The sum of the series $fraction numerator 1 over denominator 2.3 end fraction plus fraction numerator 1 over denominator 4.5 end fraction plus fraction numerator 1 over denominator 6.7 end fraction plus... equals$