Question
Total number of divisors of 480, that are of the form 4n + 2, n
0, is equal to :
- 2
- 3
- 4
- None of these
Hint:
In order to solve this question, we should know that the number of the divisor of any number
where a, b, c are prime numbers and is given by (m + 1) (n + 1) (p + 1)….. By using this property we can find the solution of this question.
The correct answer is: 4
Detailed Solution
In this question, we have been asked to find the total number of divisors of 480 which are of the form 4n + 2, n
0
In order to solve this question, we should know that the number of the divisor of any number
where a, b, c are prime numbers and is given by (m + 1) (n + 1) (p + 1)…..
We know that 480 can be expressed as ![480 space equals space 2 to the power of 5.3.5](data:image/png;base64,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)
![S o comma space a c c o r d i n g space t o space t h e space f o r m u l a comma space t h e space t o t a l space n u m b e r space o f space d i v i s o r s space o f space 480 space a r e
space left parenthesis 5 space plus space 1 right parenthesis space left parenthesis 1 space plus space 1 right parenthesis space left parenthesis 1 space plus space 1 right parenthesis space equals space 6 cross times 2 cross times 2 equals 24 space.](data:image/png;base64,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)
Now, we have been asked to find the number of divisors which are of the form 4n + 2 = 2 (2n + 1), which means odd divisors cannot be a part of the solution.
![S o comma space t h e space t o t a l space n u m b e r space o f space o d d space d i v i s o r s space t h a t space a r e space p o s s i b l e space a r e space left parenthesis 1 space plus space 1 right parenthesis space left parenthesis 1 space plus space 1 right parenthesis space equals space 2 cross times 2 equals 4 space comma space a c c o r d i n g space t o space t h e space p r o p e r t y.](data:image/png;base64,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)
Now, we can say the total number of even divisors are = all divisors – odd divisor = 24 - 4 = 20
Now, we have been given that the divisor should be of 4n + 2, which means they should not be a multiple of 4 but multiple of 2. For that, we will subtract the multiple of 4 which are divisor of 480 from the even divisors.
And, we know that,
![space S o comma space t h e space n u m b e r space o f space d i v i s o r s space t h a t space a r e space m u l t i p l e s space o f space 4 space a r e space left parenthesis 3 space plus space 1 right parenthesis space left parenthesis 1 space plus space 1 right parenthesis space left parenthesis 1 space plus space 1 right parenthesis space equals space 4 cross times 2 cross times 2 space space equals space 16](data:image/png;base64,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)
Hence, we can say that there are 16 divisors of 480 which are multiple of 4.
![S o comma space t h e space t o t a l space n u m b e r space o f space d i v i s o r s space w h i c h space a r e space e v e n space b u t space n o t space d i v i s i b l e space b y space 2 space c a n space b e space g i v e n space b y space 20 space – space 16 space equals space 4.](data:image/png;base64,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)
Thus, total number of divisors of 480, that are of the form 4n + 2, n
0, is equal to 4.
We can also solve this question by writing 4n + 2 = 2(2n + 1) where 2n + 1 is always an odd number. So, when all odd divisors will be multiplied by 2, we will get the divisors that we require. Hence, we can say a number of divisors of 4n + 2 form is the same as the number of odd divisors for 480.
Related Questions to study
If 9P5 + 5 9P4 =
, then r =
If 9P5 + 5 9P4 =
, then r =
Assertion (A) :If
, then ![A equals 3 comma B equals 2](data:image/png;base64,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)
Reason (R) :![fraction numerator P x plus q over denominator left parenthesis x minus a right parenthesis left parenthesis x minus b right parenthesis end fraction equals fraction numerator P a plus q over denominator left parenthesis x minus a right parenthesis left parenthesis a minus b right parenthesis end fraction plus fraction numerator P b plus q over denominator left parenthesis x minus b right parenthesis left parenthesis b minus a right parenthesis end fraction](data:image/png;base64,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)
Assertion (A) :If
, then ![A equals 3 comma B equals 2](data:image/png;base64,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)
Reason (R) :![fraction numerator P x plus q over denominator left parenthesis x minus a right parenthesis left parenthesis x minus b right parenthesis end fraction equals fraction numerator P a plus q over denominator left parenthesis x minus a right parenthesis left parenthesis a minus b right parenthesis end fraction plus fraction numerator P b plus q over denominator left parenthesis x minus b right parenthesis left parenthesis b minus a right parenthesis end fraction](data:image/png;base64,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)
A particle is released from a height. At certain height its kinetic energy is three times its potential energy. The height and speed of the particle at that instant are respectively
A particle is released from a height. At certain height its kinetic energy is three times its potential energy. The height and speed of the particle at that instant are respectively
If x is real, then maximum value of
is
If x is real, then maximum value of
is
The value of 'c' of Lagrange's mean value theorem for
is
The value of 'c' of Lagrange's mean value theorem for
is
The value of 'c' of Rolle's mean value theorem for
is
The value of 'c' of Rolle's mean value theorem for
is
The value of 'c' of Rolle's theorem for
–
on [–1, 1] is
The value of 'c' of Rolle's theorem for
–
on [–1, 1] is
For
in [5, 7]
For
in [5, 7]
The value of 'c' in Lagrange's mean value theorem for
in [0, 1] is
The value of 'c' in Lagrange's mean value theorem for
in [0, 1] is
The value of 'c' in Lagrange's mean value theorem for
in [0, 2] is
The value of 'c' in Lagrange's mean value theorem for
in [0, 2] is
The equation
represents
The equation
represents
The polar equation of the circle whose end points of the diameter are
and
is
The polar equation of the circle whose end points of the diameter are
and
is
The radius of the circle
is
The radius of the circle
is
The adjoining figure shows the graph of
Then –
![](data:image/png;base64,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)
Here we can see that the graph was given to us and us to take out the conclusion from that since we have the options available so I would suggest you to always start to check from the options because by the use of options we can see how easily we concluded this question.
The adjoining figure shows the graph of
Then –
![](data:image/png;base64,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)
Here we can see that the graph was given to us and us to take out the conclusion from that since we have the options available so I would suggest you to always start to check from the options because by the use of options we can see how easily we concluded this question.
Graph of y = ax2 + bx + c = 0 is given adjacently. What conclusions can be drawn from this graph –
![](data:image/png;base64,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)
Here we can see that the graph was given to us and us to take out the conclusion from that since we have the options available so I would suggest you to always start to check from the options because by the use of options we can see how easily we concluded this question.
Graph of y = ax2 + bx + c = 0 is given adjacently. What conclusions can be drawn from this graph –
![](data:image/png;base64,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)
Here we can see that the graph was given to us and us to take out the conclusion from that since we have the options available so I would suggest you to always start to check from the options because by the use of options we can see how easily we concluded this question.