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Question

If $cosh to the power of negative 1 end exponent invisible function application left parenthesis p plus i q right parenthesis equals u plus i v comma$ then the equation with roots $cos to the power of 2 end exponent invisible function application u$ and $cos h to the power of 2 end exponent invisible function application v$

$x^{2} - x (p^{2} + q^{2}) + p^{2} = 0$
$x^{2} - x (p^{2} + q^{2} + 1) + 1 = 0$
$x^{2} + x (p^{2} + q^{2} + 1) + 1 = 0$
$x^{2} - x (p^{2} + q^{2} + 1) + p^{2} = 0$

The correct answer is: $x squared minus x open parentheses p squared plus q squared plus 1 close parentheses plus p squared equals 0$

$because$ $cos invisible function application left parenthesis u plus i v right parenthesis equals p plus i q$
Þ $cos invisible function application u cos h invisible function application v minus i sin invisible function application u sin h invisible function application v equals p plus i q$
Þ $p equals cos invisible function application u cosh invisible function application v$ and $q equals negative sin invisible function application u sin h invisible function application v$ and
$p to the power of 2 end exponent plus q to the power of 2 end exponent equals cos to the power of 2 end exponent invisible function application u cos h to the power of 2 end exponent invisible function application blank v plus sin to the power of 2 end exponent invisible function application u sin h to the power of 2 end exponent invisible function application v$
$equals cos to the power of 2 end exponent invisible function application u cos h to the power of 2 end exponent invisible function application v plus left parenthesis 1 minus cos to the power of 2 end exponent invisible function application u right parenthesis left parenthesis cos h to the power of 2 end exponent invisible function application v minus 1 right parenthesis$
\ $p to the power of 2 end exponent plus q to the power of 2 end exponent plus 1 equals cos to the power of 2 end exponent invisible function application u plus cos h to the power of 2 end exponent invisible function application v$
Now equation with roots $cos to the power of 2 end exponent invisible function application u text and end text cos h to the power of 2 end exponent invisible function application v$ is
$x to the power of 2 end exponent minus left parenthesis cos to the power of 2 end exponent invisible function application u plus cos h to the power of 2 end exponent invisible function application v right parenthesis plus cos to the power of 2 end exponent invisible function application u cos h to the power of 2 end exponent invisible function application v equals 0$
\ $x to the power of 2 end exponent minus x left parenthesis p to the power of 2 end exponent plus q to the power of 2 end exponent plus 1 right parenthesis plus p to the power of 2 end exponent equals 0$ .

If $u equals logtan invisible function application open parentheses fraction numerator pi over denominator 4 end fraction plus fraction numerator x over denominator 2 end fraction close parentheses comma$ then $cos h u$ is equal to

maths-General

General

Maths-

If $k less or equal than sin to the power of negative 1 end exponent invisible function application x plus cos to the power of negative 1 end exponent invisible function application x plus tan to the power of negative 1 end exponent invisible function application x less or equal than K$ , then

In this question, we have to find the range of function from k to K. Here we know that sin^-1x + cos^-1x = $straight pi over 2$ and it only defines if -1 ≤ x ≤ 1 . And tan^-1x lines in ( $fraction numerator negative straight pi over denominator 4 end fraction$ ) to ( $straight pi over 4$ ) .

If $k less or equal than sin to the power of negative 1 end exponent invisible function application x plus cos to the power of negative 1 end exponent invisible function application x plus tan to the power of negative 1 end exponent invisible function application x less or equal than K$ , then

Maths-General

General

physics-

In an experiment with a beam balance an unknown mass m is balanced by two known masses of 16 kg and 4 kg as shown in figure. The value of the unknown mass m is :–

physics-General

General

physics-

A particle starts from the point (0m, 8m) and moves with uniform velocity of $3 stack i with tilde on top$ m/s After 5 seconds, the angular velocity of the particle about the origin will be

physics-General

General

physics-

A particle of mass M is at a distance a from surface of a thin spherical shell of equal mass and having radius a

physics-General

General

physics-

There is a concentric hole of radius R in a solid sphere of radius 2R. Mass of the remaining portion is M. What is the gravitational potential at centre ?

physics-General

General

physics-

A thin rod of mass M and length L is struck at one end by a ball of clay of mass m, moving with speed v as shown in figure. The ball sticks to the rod. After the collision, the angular momentum of the clay-rod system about A, the midpoint of the rod, is

physics-General

General

physics-

A non uniform rod OA of liner mass density $lambda equals lambda subscript 0 end subscript x$ ( $lambda subscript 0 end subscript$ = const.) is suspended from ceiling with hinge joint O & light string as shown in figure. Find the angular acceleration of rod just after the string is cut

physics-General

General

physics-

A particle of mass m moves with a constant velocity. Which of the following statements is not correct about its angular momentum:

physics-General

General

physics-

In the figure (A) half of the meter scale is made of wood while the other half of steel. The wooden part is pivoted at O. A force F is applied at the end of steel part. In figure (B) the steel part is pivoted at O and the same force is applied at the wooden end:–

physics-General

General

physics-

A person supports a book between finger and thumb as shown (the point of grip is assumed to be at the corner of the book). If the book has a weight of W then the person is producing a torque on the book of

physics-General

General

physics-

A string is wrapped around the rim of a wheel of moment of inertia 0.20 kg- $m to the power of 2 end exponent$ and radius 20 cm. The wheel is free to rotate about its axis and initially the wheel is rest. The string is now pulled by a force of 20N. The angular velocity of the string after 5 seconds will be:–

physics-General

General

physics-

In figure, the winch is mounted on an axle, and the 6-sided nut is welded to the winch. By turning the nut with a wrench, a person can rotate the winch. For instance, turning the nut clockwise lifts the block off the ground, because more and more rope gets wrapped around the winch. Three students agree that using a longer wrench makes it easier to turn the winch. But they disagree about why. All three students are talking about the case where the winch is used, over a 10 s time interval, to lift the block one metre off the ground.
Student 1 By using a longer wrench, the person decreases the average force he must exert on the wrench, in order to lift the block one metre in 10s.
Student 2 : Using a longer wrench reduces the work done by the person as he uses the winch to lift the block 1m in 10s.
Student 3 : Using a longer wrench reduces the power that the person must exert to lift the block 1m in 10s.Which of the following is true about student 2 and 3 :-

physics-General

General

physics-

A pendulum beating seconds is taken from the earth to a planet having both the mass and radius half as compared to the earth The time period of the pendulum will be

physics-General

General

physics-

the dimensions of (force constant / mass) $blank to the power of 1 divided by 2 end exponent$ are the same as that

physics-General

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If then the equation with roots and

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Þ Þ and and\ Now equation with roots is\.

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In an experiment with a beam balance an unknown mass m is balanced by two known masses of 16 kg and 4 kg as shown in figure. The value of the unknown mass m is :–

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A particle starts from the point (0m, 8m) and moves with uniform velocity of m/s After 5 seconds, the angular velocity of the particle about the origin will be

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A non uniform rod OA of liner mass density (= const.) is suspended from ceiling with hinge joint O & light string as shown in figure. Find the angular acceleration of rod just after the string is cut

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A particle of mass m moves with a constant velocity. Which of the following statements is not correct about its angular momentum:

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In the figure (A) half of the meter scale is made of wood while the other half of steel. The wooden part is pivoted at O. A force F is applied at the end of steel part. In figure (B) the steel part is pivoted at O and the same force is applied at the wooden end:–

In the figure (A) half of the meter scale is made of wood while the other half of steel. The wooden part is pivoted at O. A force F is applied at the end of steel part. In figure (B) the steel part is pivoted at O and the same force is applied at the wooden end:–

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A person supports a book between finger and thumb as shown (the point of grip is assumed to be at the corner of the book). If the book has a weight of W then the person is producing a torque on the book of

A string is wrapped around the rim of a wheel of moment of inertia 0.20 kg- and radius 20 cm. The wheel is free to rotate about its axis and initially the wheel is rest. The string is now pulled by a force of 20N. The angular velocity of the string after 5 seconds will be:–

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The correct answer is: $x squared minus x open parentheses p squared plus q squared plus 1 close parentheses plus p squared equals 0$

If $u equals logtan invisible function application open parentheses fraction numerator pi over denominator 4 end fraction plus fraction numerator x over denominator 2 end fraction close parentheses comma$ then $cos h u$ is equal to

If $u equals logtan invisible function application open parentheses fraction numerator pi over denominator 4 end fraction plus fraction numerator x over denominator 2 end fraction close parentheses comma$ then $cos h u$ is equal to

If $k less or equal than sin to the power of negative 1 end exponent invisible function application x plus cos to the power of negative 1 end exponent invisible function application x plus tan to the power of negative 1 end exponent invisible function application x less or equal than K$ , then

If $k less or equal than sin to the power of negative 1 end exponent invisible function application x plus cos to the power of negative 1 end exponent invisible function application x plus tan to the power of negative 1 end exponent invisible function application x less or equal than K$ , then

A particle starts from the point (0m, 8m) and moves with uniform velocity of $3 stack i with tilde on top$ m/s After 5 seconds, the angular velocity of the particle about the origin will be

A particle starts from the point (0m, 8m) and moves with uniform velocity of $3 stack i with tilde on top$ m/s After 5 seconds, the angular velocity of the particle about the origin will be

A non uniform rod OA of liner mass density $lambda equals lambda subscript 0 end subscript x$ ( $lambda subscript 0 end subscript$ = const.) is suspended from ceiling with hinge joint O & light string as shown in figure. Find the angular acceleration of rod just after the string is cut

A non uniform rod OA of liner mass density $lambda equals lambda subscript 0 end subscript x$ ( $lambda subscript 0 end subscript$ = const.) is suspended from ceiling with hinge joint O & light string as shown in figure. Find the angular acceleration of rod just after the string is cut

the dimensions of (force constant / mass) $blank to the power of 1 divided by 2 end exponent$ are the same as that

the dimensions of (force constant / mass) $blank to the power of 1 divided by 2 end exponent$ are the same as that