Question
If 9P5 + 5 9P4 =
, then r =
- 4
- 5
- 9
- 10
Hint:
Here we need to find the value of the given variable. Here we will first apply the formula of the permutation to simplify the equation. Then we will apply the mathematical operations that will be required to simplify the given expression further. After simplifying the terms, we will get the value of the required variable.
Formula used:
![scriptbase P subscript r space equals space fraction numerator n factorial over denominator left parenthesis n minus r right parenthesis factorial end fraction end scriptbase presuperscript n comma space r space i s space t h e space n u m b e r space o f space o b j e c t s space s e l e c t e d space a n d space n space t o t a l space n u m b e r space o f space e l e m e n t s space i n space t h e space s e t.](data:image/png;base64,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)
The correct answer is: 5
Detailed Solution
Here we need to find the value of the given variable.
The given expression is :
![scriptbase P subscript 5 space plus space 5. end scriptbase presuperscript 9 scriptbase P subscript 4 space equals space scriptbase P subscript r end scriptbase presuperscript 10 end scriptbase presuperscript 9](data:image/png;base64,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)
![N o w comma space w e space w i l l space u s e space t h i s space f o r m u l a space o f space p e r m u t a t i o n space
scriptbase P subscript r space equals space fraction numerator n factorial over denominator left parenthesis n minus r right parenthesis factorial end fraction end scriptbase presuperscript n comma space i n space t h e space a b o v e space e q u a t i o n
T h e r e f o r e comma space w e space g e t space
rightwards double arrow fraction numerator 9 factorial over denominator left parenthesis 9 minus 5 right parenthesis factorial end fraction space plus space 5. space fraction numerator 9 factorial over denominator left parenthesis 9 minus 4 right parenthesis factorial end fraction space equals space fraction numerator 10 factorial over denominator left parenthesis 10 minus r right parenthesis factorial end fraction space space space space
rightwards double arrow fraction numerator 9 factorial over denominator left parenthesis 4 right parenthesis factorial end fraction space plus space 5. space fraction numerator 9 factorial over denominator left parenthesis 5 right parenthesis factorial end fraction space equals space fraction numerator 10 factorial over denominator left parenthesis 10 minus r right parenthesis factorial end fraction
D i v i d i n g space b o t h space s i d e s space b y space 9 factorial space w e space g e t
rightwards double arrow fraction numerator 1 over denominator left parenthesis 4 right parenthesis factorial end fraction space plus space 5. space fraction numerator 1 over denominator left parenthesis 5 right parenthesis factorial end fraction space equals space fraction numerator 10 over denominator left parenthesis 9 minus r right parenthesis factorial end fraction............. space space space space space space space space space open parentheses fraction numerator 10 factorial over denominator 9 factorial end fraction space equals space fraction numerator 10 space cross times 9 factorial over denominator 9 factorial end fraction space equals space 10 close parentheses
rightwards double arrow fraction numerator 1 over denominator left parenthesis 4 right parenthesis factorial end fraction space plus space 5. space fraction numerator 1 over denominator 5 space cross times 4 factorial end fraction space equals space fraction numerator 10 over denominator left parenthesis 9 minus r right parenthesis factorial end fraction
rightwards double arrow fraction numerator 1 over denominator left parenthesis 4 right parenthesis factorial end fraction space plus space space fraction numerator 1 over denominator 4 factorial end fraction space equals space fraction numerator 10 over denominator left parenthesis 9 minus r right parenthesis factorial end fraction
rightwards double arrow fraction numerator 2 over denominator 4 factorial end fraction space equals space fraction numerator 10 over denominator left parenthesis 9 minus r right parenthesis factorial end fraction
D i v i d i n g space b y space 2 space o n space b o t h space s i d e s
rightwards double arrow fraction numerator 1 over denominator 4 factorial end fraction space equals space fraction numerator 5 over denominator left parenthesis 9 minus r right parenthesis factorial end fraction
O n space c r o s s space m u l t i p l y i n g
rightwards double arrow left parenthesis 9 minus r right parenthesis factorial space equals space 5 space cross times 4 factorial
rightwards double arrow left parenthesis 9 minus r right parenthesis factorial space equals space 5 factorial
O n space e q u a t i n g space t h e space t w o space f a c t o r i a l s comma space w e space g e t
rightwards double arrow 9 space minus space r space equals space 5
rightwards double arrow r space equals space 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)
Related Questions to study
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,iVBORw0KGgoAAAANSUhEUgAAAVwAAAAlCAYAAAAOTFGRAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAABVNJREFUeNrtnUFIVEEYxwcPEhFBiEh4CKJThxA6hEhE4EEkIrp1iiWQCImIoINIhBfp4CG6dIoQCSQ8hEQQESHiJUQ8dBCiQ0RIIBIisQjbfOwnrMObfTM78+bNvP3/4QP3jbs7M7+ZeW/mzb6/EHHon4wGx56MRRlXBVQ1gTMY78voQTWVp3MyNlpe98oYlfFDxnlUDzhDlWFM6ZuopnJ1Q8ZCxvE7Mh55+o4GqrnynME4fsaU/gacy9UTTYeblTHJsGYz0mc4rQhIJ2Q8l7HLU6S3Ml7IeAxchXGmaeZTGdsy6nyldKbAjgjG4RlT+hRz/s31/lnGaXAOJ1rjua4c65exJaOPX6/LGGhJr3GlFQGphxtBjf8+yQ2lwWdoqBjOy9wxTnG9L1rWNxjHz5jSv/Ngd8h5zvKqF5wdtaWc4S7KWBVHF9rHGAyJ1oQ+FTgNmdac/Sifg+hThXC+xZ2xVa9ljINxpfoypavr9TQI/gXnMKKzzgFX4g7DmdFMMT7KuMJTzT4DKHmh00+ehqj53Ed/KowzXYUMK+/5krOkAMZpMdbV77GcARecPeoSdzYTPRDNtb0LHXyP6VlxiDu6Sz4h+/pTtwrR33tgXCnGuvRhyxkrODuIppKvDP5vRDQXu+f4PUUNuDdlzDvkE+qM858M3utgXCnGuvSHPPUH5wCimyQTOf9zVsY7Gcd5evDVYEmhU0i0kL6YcXzeIJ9Q55x/8dTyUNN8ggXj6jCm9JpyjPbpbopidimAc4aWRPsbI3SH870ywF7TnLl8QKJB/RtPR0i06L/MA8I4+lRhnGmt7yUvJdC67QJzB+PqMKZ0ulk1yq8H+VgNnMNpR7myUc9+SyL7biJtIxkrKE8D/L20Z29NNO+wtssn5Mb5UFN8RTLN/7stitu6A8bhGRPP6zzo0s21DVH81ixwTlA08O+iGoKrH4whcO4+jfNZEgLjMoWftKIvd4Vui+aCPwTGGHDBGepCuWwGh9JlDkEQBGHAhYq4akKEDXDuXsZFvxeRfl+GsKQA4QoXgiAIAy4EQRCEARci3RPZbguxaJbzmGr+TcoAzulz9sG4UXHGXc+ZHoO4lsBJYVVkP7Ixlfy3K0MIgTMYg3MEnOmNQwkUkB5KsRJx/k1soXVlCNVAwBmMY68nXRlis13viPMQFzAVrXBBY8u/jS20WoYQAmcwTqGedGWI1XbdmvMz0XTZTEX3xdG1nVjyb2MLrZYhhMAZjFOoJ10ZfNiuh2inufog43LGcR+W5TYytc5WbTpiyb+NLbSt1YgPVZWzq+U6GMdVT7oy+LBdD9FOc0Wmbr2aNFfLchuZWmf3iqNGdLHk38YWWi1DCFWVs6vlOhjHVU+6MviwXQ/RTnN10CbN1bLcVLbW2fXI8k+ytYWuB+6MVeTsw3IdjOOqpwNPn1lWO3WCRAphWW5rnV2PLP+d2ELH1BlT5RzSch2Mw9TTgafPLKudOk1DSC6W5aaysc62WVIIlX9bW+jYppupcvZhuQ7GcdVTVhl82a6HaKe5orPeiCbN1bLcVDbW2Wolx5B/W1voMm6oVJGzD8t1MI6rnrLK4Mt2PUQ7zZVuG4YPy3JT2VhnT3KeY8q/rS20WoYQqiJnH5brYBxXPWWVwZfteoh2mqusjca+LMtNZWOdbbJROnT+bW2hY9kUnzpnH5brYBxXPWWVwZfteoh2aqS1lnWdsizLTayzdT+lKzv/NrbQZf7ss0qcbT4PjNPqCyrnMmzXXdpprmJ8WESWdTYeXuOmbuDcD8Z4eE3J7dRId0Xcj0OjdZKJhPNvUoYQAmcwBucAnP8DprVKPMDXj7UAAAKcdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1mcmFjPjxtcm93PjxtaT5QPC9taT48bWk+eDwvbWk+PG1vPis8L21vPjxtaT5xPC9taT48L21yb3c+PG1yb3c+PG1vPig8L21vPjxtaT54PC9taT48bW8+JiN4MjIxMjs8L21vPjxtaT5hPC9taT48bW8+KTwvbW8+PG1vPig8L21vPjxtaT54PC9taT48bW8+JiN4MjIxMjs8L21vPjxtaT5iPC9taT48bW8+KTwvbW8+PC9tcm93PjwvbWZyYWM+PG1vPj08L21vPjxtZnJhYz48bXJvdz48bWk+UDwvbWk+PG1pPmE8L21pPjxtbz4rPC9tbz48bWk+cTwvbWk+PC9tcm93Pjxtcm93Pjxtbz4oPC9tbz48bWk+eDwvbWk+PG1vPiYjeDIyMTI7PC9tbz48bWk+YTwvbWk+PG1vPik8L21vPjxtbz4oPC9tbz48bWk+YTwvbWk+PG1vPiYjeDIyMTI7PC9tbz48bWk+YjwvbWk+PG1vPik8L21vPjwvbXJvdz48L21mcmFjPjxtbz4rPC9tbz48bWZyYWM+PG1yb3c+PG1pPlA8L21pPjxtaT5iPC9taT48bW8+KzwvbW8+PG1pPnE8L21pPjwvbXJvdz48bXJvdz48bW8+KDwvbW8+PG1pPng8L21pPjxtbz4mI3gyMjEyOzwvbW8+PG1pPmI8L21pPjxtbz4pPC9tbz48bW8+KDwvbW8+PG1pPmI8L21pPjxtbz4mI3gyMjEyOzwvbW8+PG1pPmE8L21pPjxtbz4pPC9tbz48L21yb3c+PC9tZnJhYz48L21hdGg+0CaBvwAAAABJRU5ErkJggg==)
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.