Maths-
General
Easy
Question
is divisor of
The correct answer is: ![x to the power of 2 end exponent](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAARCAYAAAA/mJfHAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAKtJREFUeNpjYCAd/IfiX0B8FIhVGKgAmIA4C4jPMVAR/KCWQfZAfJAaBklCw0yJUoPUgHgL1ECKXbQNiPnwKUoG4g4s4s1QORgAGaRBjK2gaBZH4icC8RQc6QwZYwUeQNwHZbsA8V5Kw2Q3NMovALEwpYYVQLOKHqUGWQPxGqhXIykxCJT4NgExFxDzAPEZcr0pCo1yZM0+QLyYVIPYgHgdEEtjkVsOjWH6AwCrAB/WUIk6RgAAAGB0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bXN1cD48bWk+eDwvbWk+PG1uPjI8L21uPjwvbXN1cD48L21hdGg+oJ3ZSwAAAABJRU5ErkJggg==)
![open vertical bar table row cell a to the power of 2 end exponent plus x to the power of 2 end exponent end cell cell a b end cell cell c a end cell row cell a b end cell cell b to the power of 2 end exponent plus x to the power of 2 end exponent end cell cell b c end cell row cell c a end cell cell b c end cell cell c to the power of 2 end exponent plus x to the power of 2 end exponent end cell end table close vertical bar](data:image/png;base64,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)
Multiply
by
respectively and hence divide by abc
\ ![capital delta equals fraction numerator 1 over denominator a b c end fraction open vertical bar table row cell a left parenthesis a to the power of 2 end exponent plus x to the power of 2 end exponent right parenthesis end cell cell a b to the power of 2 end exponent end cell cell c to the power of 2 end exponent a end cell row cell a to the power of 2 end exponent b end cell cell b left parenthesis b to the power of 2 end exponent plus x to the power of 2 end exponent right parenthesis end cell cell b c to the power of 2 end exponent end cell row cell c a to the power of 2 end exponent end cell cell b to the power of 2 end exponent c end cell cell c left parenthesis c to the power of 2 end exponent plus x to the power of 2 end exponent right parenthesis end cell end table close vertical bar](data:image/png;base64,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)
Now take out a, b and c common from
and
,
\ ![capital delta equals open vertical bar table row cell a to the power of 2 end exponent plus x to the power of 2 end exponent end cell cell b to the power of 2 end exponent end cell cell c to the power of 2 end exponent end cell row cell a to the power of 2 end exponent end cell cell b to the power of 2 end exponent plus x to the power of 2 end exponent end cell cell c to the power of 2 end exponent end cell row cell a to the power of 2 end exponent end cell cell b to the power of 2 end exponent end cell cell c to the power of 2 end exponent plus x to the power of 2 end exponent end cell end table close vertical bar](data:image/png;base64,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)
Now applying ![C subscript 1 end subscript rightwards arrow C subscript 1 end subscript plus C subscript 2 end subscript plus C subscript 3 end subscript](data:image/png;base64,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)
![capital delta equals left parenthesis a to the power of 2 end exponent plus b to the power of 2 end exponent plus c to the power of 2 end exponent plus x to the power of 2 end exponent right parenthesis open vertical bar table row 1 cell b to the power of 2 end exponent end cell cell c to the power of 2 end exponent end cell row 1 cell b to the power of 2 end exponent plus x to the power of 2 end exponent end cell cell c to the power of 2 end exponent end cell row 1 cell b to the power of 2 end exponent end cell cell c to the power of 2 end exponent plus x to the power of 2 end exponent end cell end table close vertical bar](data:image/png;base64,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)
Þ ![capital delta equals x to the power of 4 end exponent left parenthesis a to the power of 2 end exponent plus b to the power of 2 end exponent plus c to the power of 2 end exponent plus x to the power of 2 end exponent right parenthesis](data:image/png;base64,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)
Hence, it is divisible by ![x to the power of 2 end exponent](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAARCAYAAAA/mJfHAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAKtJREFUeNpjYCAd/IfiX0B8FIhVGKgAmIA4C4jPMVAR/KCWQfZAfJAaBklCw0yJUoPUgHgL1ECKXbQNiPnwKUoG4g4s4s1QORgAGaRBjK2gaBZH4icC8RQc6QwZYwUeQNwHZbsA8V5Kw2Q3NMovALEwpYYVQLOKHqUGWQPxGqhXIykxCJT4NgExFxDzAPEZcr0pCo1yZM0+QLyYVIPYgHgdEEtjkVsOjWH6AwCrAB/WUIk6RgAAAGB0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bXN1cD48bWk+eDwvbWk+PG1uPjI8L21uPjwvbXN1cD48L21hdGg+oJ3ZSwAAAABJRU5ErkJggg==)
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,then the value of k is
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Maths-
If
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](data:image/png;base64,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)
If
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](data:image/png;base64,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)
Maths-General
Maths-
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
Maths-General
Maths-
If
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](data:image/png;base64,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)
If
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](data:image/png;base64,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)
Maths-General
Maths-
Maths-General
Maths-
In the expansion of
the coefficient of
will be
In the expansion of
the coefficient of
will be
Maths-General
Maths-
The value of
is equal to
The value of
is equal to
Maths-General
Maths-
The sum to infinity of the given series
is
The sum to infinity of the given series
is
Maths-General
Maths-
is defined for ![left parenthesis a greater than 0 right parenthesis](data:image/png;base64,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)
is defined for ![left parenthesis a greater than 0 right parenthesis](data:image/png;base64,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)
Maths-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](data:image/png;base64,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)
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](data:image/png;base64,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)
Maths-General
Maths-
Maths-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?
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
Biology
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?
BiologyGeneral