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Maths-

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Question

If $s i n invisible function application y equals x s i n invisible function application left parenthesis a plus y right parenthesis$ and $fraction numerator d y over denominator d x end fraction equals fraction numerator A over denominator 1 plus x to the power of 2 end exponent minus 2 x c o s invisible function application a end fraction$ then the value of $blank to the power of ´ end exponent A$ ' is

2
$c o s a$
$s i n a$
1

The correct answer is: $s i n invisible function application a$

We are given that $s i n invisible function application y equals x s i n invisible function application left parenthesis a plus y right parenthesis$ then we are asked to find the value of a
siny=xsin(a+y).

∴x=siny/sin(a+y).

Differentiating w.r.t. y, using the Quotient Rule, we have,

dx/dy=[sin(a+y)⋅ddy{siny}−siny⋅ddx{sin(a+y)}]/sin²(a+y),

=[sin(a+y)cosy−sinycos(a+y)⋅ddy(a+y)]/sin ²(a+y),...[The Chain Rule],

=sin(a+y)cosy−sinycos(a+y)/sin ²(a+y),

=sin{(a+y)−y}/sin ²(a+y),

=sina/sin²(a+y).

⇒dy/dx=sin a

Therefore the correct option is choice 3

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2k-mol of an ideal diatomic gas is enclosed in a vertical cylinder fitted with a piston and spring as shown in the figure. Initially the spring is compressed by 5 cm and then the electric heater starts supplying energy to the gas at constant rate of 100 J/S and due to conduction through walls of cylinder and radiation, 20 J/S has been lost to surroundings ( Take K=1000 N/m, $g equals 10 blank m divided by s to the power of 2 end exponent$ atomospheric pressure, $P subscript o end subscript equals 10 to the power of 5 end exponent blank N divided by m to the power of 2 end exponent$ , cross section area of piston $A subscript o end subscript equals 50 blank c m to the power of 2 end exponent$ , mass of piston m=1 kg R=8.3kj mol k) Answer the given question based on this information.

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2k-mol of an ideal diatomic gas is enclosed in a vertical cylinder fitted with a piston and spring as shown in the figure. Initially the spring is compressed by 5 cm and then the electric heater starts supplying energy to the gas at constant rate of 100 J/S and due to conduction through walls of cylinder and radiation, 20 J/S has been lost to surroundings ( Take K=1000 N/m, $g equals 10 blank m divided by s to the power of 2 end exponent$ atomospheric pressure, $P subscript o end subscript equals 10 to the power of 5 end exponent blank N divided by m to the power of 2 end exponent$ , cross section area of piston $A subscript o end subscript equals 50 blank c m to the power of 2 end exponent$ , mass of piston m=1 kg R=8.3kj mol k) Answer the given question based on this information.

The initial pressure of the gas is

Physics-General

parallel

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