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If $a comma b comma c$ are unequal what is the condition that the value of the following determinant is zero $capital delta equals open vertical bar table row a cell a to the power of 2 end exponent end cell cell a to the power of 3 end exponent plus 1 end cell row b cell b to the power of 2 end exponent end cell cell b to the power of 3 end exponent plus 1 end cell row c cell c to the power of 2 end exponent end cell cell c to the power of 3 end exponent plus 1 end cell end table close vertical bar$

$1 + a b c = 0$
$a + b + c + 1 = 0$
$(a - b) (b - c) (c - a) = 0$
None of these

The correct answer is: $1 plus a b c equals 0$

Splitting the determinant into two determinants, we get $capital delta equals open vertical bar table row 1 a cell a to the power of 2 end exponent end cell row 1 b cell b to the power of 2 end exponent end cell row 1 c cell c to the power of 2 end exponent end cell end table close vertical bar plus a b c open vertical bar table row 1 a cell a to the power of 2 end exponent end cell row 1 b cell b to the power of 2 end exponent end cell row 1 c cell c to the power of 2 end exponent end cell end table close vertical bar equals 0$
= $left parenthesis 1 plus a b c right parenthesis left square bracket left parenthesis a minus b right parenthesis left parenthesis b minus c right parenthesis left parenthesis c minus a right parenthesis right square bracket equals 0$
Because a, b, c are different, the second factor cannot be zero. Hence, option (a) , $1 plus a b c equals$ 0, is correct.

If – 9 is a root of the equation $open vertical bar table row x 3 7 row 2 x 2 row 7 6 x end table close vertical bar equals 0$ then the other two roots are

Maths-General

General

Maths-

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

Maths-General

General

Maths-

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

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

General

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.

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$1 + a b c = 0$
$a + b + c + 1 = 0$
$(a - b) (b - c) (c - a) = 0$
None of these

The correct answer is: $1 plus a b c equals 0$

Related Questions to study

If – 9 is a root of the equation $open vertical bar table row x 3 7 row 2 x 2 row 7 6 x end table close vertical bar equals 0$ then the other two roots are

If – 9 is a root of the equation $open vertical bar table row x 3 7 row 2 x 2 row 7 6 x end table close vertical bar equals 0$ then the other two roots are

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 $fraction numerator 1 over denominator 2.3 end fraction plus fraction numerator 1 over denominator 4.5 end fraction plus fraction numerator 1 over denominator 6.7 end fraction plus... equals$

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?

Which of the following is less general in characters as compared to genus?

Which of the following is less general in characters as compared to genus?

For which of the following motions gravity is not responsible?

For which of the following motions gravity is not responsible?

The velocity-time graph of a uniformly decelerating motion is a ____.

The velocity-time graph of a uniformly decelerating motion is a ____.

Sepia is also known as

Sepia is also known as

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

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

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If are unequal what is the condition that the value of the following determinant is zero

None of these

The correct answer is:

Splitting the determinant into two determinants, we get = Because a, b, c are different, the second factor cannot be zero. Hence, option (a) , 0, is correct.

Related Questions to study

If – 9 is a root of the equation then the other two roots are

If – 9 is a root of the equation then the other two roots are

If is a cube root of unity, then

If is a cube root of unity, then

In the expansion of the coefficient of will be

In the expansion of the coefficient of will be

The value of is equal to

The value of is equal to

The sum to infinity of the given series is

The sum to infinity of the given series is

is defined for

is defined for

The sum of the series

The sum of the series

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?

Which of the following is less general in characters as compared to genus?

Which of the following is less general in characters as compared to genus?

For which of the following motions gravity is not responsible?

For which of the following motions gravity is not responsible?

The velocity-time graph of a uniformly decelerating motion is a ____.

The velocity-time graph of a uniformly decelerating motion is a ____.

Sepia is also known as

Sepia is also known as

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

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

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With Turito Foundation.

Get an Expert Advice From Turito.

Turito Academy

With Turito Academy.

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With Turito Foundation.

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$1 + a b c = 0$
$a + b + c + 1 = 0$
$(a - b) (b - c) (c - a) = 0$
None of these

The correct answer is: $1 plus a b c equals 0$

If – 9 is a root of the equation $open vertical bar table row x 3 7 row 2 x 2 row 7 6 x end table close vertical bar equals 0$ then the other two roots are

If – 9 is a root of the equation $open vertical bar table row x 3 7 row 2 x 2 row 7 6 x end table close vertical bar equals 0$ then the other two roots are

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 $fraction numerator 1 over denominator 2.3 end fraction plus fraction numerator 1 over denominator 4.5 end fraction plus fraction numerator 1 over denominator 6.7 end fraction plus... equals$