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Question

The values of theta satisfying Sin space 5 theta equals Sin space 3 theta minus Sin space theta and 0 less than theta less than pi over 2 are

  1. pi over 6 comma pi over 3
  2. pi over 6 comma pi over 4
  3. pi over 4 comma pi over 3
  4. pi over 4 comma pi over 2

The correct answer is: pi over 6 comma pi over 3

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Related Questions to study

General
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A body of mass m is resting on a wedge of angle theta as shown in figure. The wedge is given at acceleration alpha. What is the value of a son that the mass m just falls freely?

The horizontal acceleration a of the wedge should be such that in time the wedge moves the horizontal distance B C. The body must fall through a vertical distance A B under gravity. Hence,
B C equals fraction numerator 1 over denominator 2 end fraction a t to the power of 2 end exponent and A B equals fraction numerator 1 over denominator 2 end fraction g t to the power of 2 end exponent
tantheta equals fraction numerator A B over denominator B C end fraction equals fraction numerator g over denominator a end fractionor a equals fraction numerator g over denominator t a n theta end fraction equals g blank c o t theta

A body of mass m is resting on a wedge of angle theta as shown in figure. The wedge is given at acceleration alpha. What is the value of a son that the mass m just falls freely?

physics-General
The horizontal acceleration a of the wedge should be such that in time the wedge moves the horizontal distance B C. The body must fall through a vertical distance A B under gravity. Hence,
B C equals fraction numerator 1 over denominator 2 end fraction a t to the power of 2 end exponent and A B equals fraction numerator 1 over denominator 2 end fraction g t to the power of 2 end exponent
tantheta equals fraction numerator A B over denominator B C end fraction equals fraction numerator g over denominator a end fractionor a equals fraction numerator g over denominator t a n theta end fraction equals g blank c o t theta
General
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A cyclist starts from the centre O of a circular park of radius one kilometre, reaches the edge P of the park, then cycles along the circumference and returns to the centre along Q O as shown in figure. If the round trip takes ten minutes, the net displacement and average speed of the cyclist (in metre and kilometre per hour) is

Net displacement equals 0 and total distance equals O P plus P Q plus Q O
equals 1 plus fraction numerator 2 pi cross times 1 over denominator 4 end fraction plus 1 equals fraction numerator 14.28 over denominator 4 end fraction blank k m
Average speedblank equals fraction numerator 14.28 over denominator 4 cross times 10 divided by 60 end fraction
equals fraction numerator 6 cross times 14.28 over denominator 4 end fraction equals 21.42 blank k m divided by h

A cyclist starts from the centre O of a circular park of radius one kilometre, reaches the edge P of the park, then cycles along the circumference and returns to the centre along Q O as shown in figure. If the round trip takes ten minutes, the net displacement and average speed of the cyclist (in metre and kilometre per hour) is

physics-General
Net displacement equals 0 and total distance equals O P plus P Q plus Q O
equals 1 plus fraction numerator 2 pi cross times 1 over denominator 4 end fraction plus 1 equals fraction numerator 14.28 over denominator 4 end fraction blank k m
Average speedblank equals fraction numerator 14.28 over denominator 4 cross times 10 divided by 60 end fraction
equals fraction numerator 6 cross times 14.28 over denominator 4 end fraction equals 21.42 blank k m divided by h
General
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A ball is thrown vertically upwards. Which of the following graph/graphs represent velocity-time graph of the ball during its flight (air resistance is neglected)

In the positive region the velocity decreases linearly (during rise) and in the negative region velocity increases linearly (during fall) and the direction is opposite to each other during rise and fall, hence fall is shown in the negative region

A ball is thrown vertically upwards. Which of the following graph/graphs represent velocity-time graph of the ball during its flight (air resistance is neglected)

physics-General
In the positive region the velocity decreases linearly (during rise) and in the negative region velocity increases linearly (during fall) and the direction is opposite to each other during rise and fall, hence fall is shown in the negative region
General
physics-

Which of the following graphs cannot possibly represent one dimensional motion of a particle

I is not possible because total distance covered by a particle increases with time
II is not possible because at a particular time, position cannot have two values
III is not possible because at a particular time, velocity cannot have two values
IV is not possible because speed can never be negative

Which of the following graphs cannot possibly represent one dimensional motion of a particle

physics-General
I is not possible because total distance covered by a particle increases with time
II is not possible because at a particular time, position cannot have two values
III is not possible because at a particular time, velocity cannot have two values
IV is not possible because speed can never be negative
General
physics-

Which of the following graphs cannot possibly represent one dimensional motion of a particle

I is not possible because total distance covered by a particle increases with time
II is not possible because at a particular time, position cannot have two values
III is not possible because at a particular time, velocity cannot have two values
IV is not possible because speed can never be negative

Which of the following graphs cannot possibly represent one dimensional motion of a particle

physics-General
I is not possible because total distance covered by a particle increases with time
II is not possible because at a particular time, position cannot have two values
III is not possible because at a particular time, velocity cannot have two values
IV is not possible because speed can never be negative
General
maths-

The solution of left parenthesis sin space x minus 2 right parenthesis squared plus left parenthesis cos space x minus 3 divided by 2 right parenthesis squared equals 0 is

The solution of left parenthesis sin space x minus 2 right parenthesis squared plus left parenthesis cos space x minus 3 divided by 2 right parenthesis squared equals 0 is

maths-General
General
maths-

If Sin space x plus Cos space x equals square root of 2 cos space alpha not stretchy rightwards double arrow x equals midline horizontal ellipsis

If Sin space x plus Cos space x equals square root of 2 cos space alpha not stretchy rightwards double arrow x equals midline horizontal ellipsis

maths-General
General
physics-

Acceleration velocity graph of a particle moving in a straight line is as shown in figure. The slope of velocity-displacement graph

From acceleration-velocity graph, we have a equals k blank v blankwhere k is a constant which represents the slope of the given line.
As, a equals v fraction numerator d v over denominator d s end fraction comma so v equals fraction numerator d v over denominator d s end fraction equals k v
or fraction numerator d v over denominator d s end fraction equals k equals a constant
Thus, the slope of velocity-displacement graphs is same as that of acceleration velocity. Which is constant.

Acceleration velocity graph of a particle moving in a straight line is as shown in figure. The slope of velocity-displacement graph

physics-General
From acceleration-velocity graph, we have a equals k blank v blankwhere k is a constant which represents the slope of the given line.
As, a equals v fraction numerator d v over denominator d s end fraction comma so v equals fraction numerator d v over denominator d s end fraction equals k v
or fraction numerator d v over denominator d s end fraction equals k equals a constant
Thus, the slope of velocity-displacement graphs is same as that of acceleration velocity. Which is constant.
General
maths-

If Tanp space theta equals Cotq space theta then solutions of theta are in -

If Tanp space theta equals Cotq space theta then solutions of theta are in -

maths-General
General
maths-

In capital delta A B C comma I f a comma b, care in H.P., then Sin invisible function application 2 A over 2 , Sin2 fraction numerator B over denominator 2 end fraction , Sin2 fraction numerator C over denominator 2 end fraction are in

a comma b comma c are in H. P comma fraction numerator 1 over denominator a end fraction comma fraction numerator 1 over denominator b end fraction comma fraction numerator 1 over denominator c end fraction are in A. P fraction numerator s minus a over denominator a end fraction comma fraction numerator s minus b over denominator b end fraction comma fraction numerator s minus c over denominator c end fraction are in A. P

In capital delta A B C comma I f a comma b, care in H.P., then Sin invisible function application 2 A over 2 , Sin2 fraction numerator B over denominator 2 end fraction , Sin2 fraction numerator C over denominator 2 end fraction are in

maths-General
a comma b comma c are in H. P comma fraction numerator 1 over denominator a end fraction comma fraction numerator 1 over denominator b end fraction comma fraction numerator 1 over denominator c end fraction are in A. P fraction numerator s minus a over denominator a end fraction comma fraction numerator s minus b over denominator b end fraction comma fraction numerator s minus c over denominator c end fraction are in A. P
General
maths-

Solution of Tan space x plus Tan space open parentheses 120 to the power of 6 plus x close parentheses plus Tan space open parentheses x minus 120 to the power of ring operator close parentheses equals 0 is

Solution of Tan space x plus Tan space open parentheses 120 to the power of 6 plus x close parentheses plus Tan space open parentheses x minus 120 to the power of ring operator close parentheses equals 0 is

maths-General
General
maths-

If Tan space bold A plus Tan space 2 bold A plus square root of 3 Tan space bold ATan 2 bold A equals square root of 3 then the general solution of A over 2 equals

If Tan space bold A plus Tan space 2 bold A plus square root of 3 Tan space bold ATan 2 bold A equals square root of 3 then the general solution of A over 2 equals

maths-General
General
physics-

The graph between the displacement x and t for a particle moving in a straight line is shown in figure. During the interval O A comma A B comma B C and C D comma the acceleration of the particle is

O A comma blank A B comma blank B C, C D

Region O A shows that graph bending toward time axis i. e. acceleration is negative.
Region A B shows that graph is parallel to time axisi. e. blankvelocity is zero. Hence acceleration is zero.
Region B C shows that graph is bending towards displacement axis i. e. acceleration is positive.
Region C D blankshows that graph having constant slope i. e. velocity is constant. Hence acceleration is zero

The graph between the displacement x and t for a particle moving in a straight line is shown in figure. During the interval O A comma A B comma B C and C D comma the acceleration of the particle is

O A comma blank A B comma blank B C, C D

physics-General
Region O A shows that graph bending toward time axis i. e. acceleration is negative.
Region A B shows that graph is parallel to time axisi. e. blankvelocity is zero. Hence acceleration is zero.
Region B C shows that graph is bending towards displacement axis i. e. acceleration is positive.
Region C D blankshows that graph having constant slope i. e. velocity is constant. Hence acceleration is zero
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maths-

tan space open parentheses pi over 4 plus x over 2 close parentheses minus tan space open parentheses pi over 4 minus x over 2 close parentheses equals 2 then the general solution of x =

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maths-General
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Velocity-time left parenthesis v-t right parenthesis graph for a moving object is shown in the figure. Total displacement of the object during the same interval when there is non-zero acceleration and retardation is

Between time interval 20 blank s e c to 40 blank s e c, there is non-zero acceleration and retardation. Hence distance travelled during this interval
equals Area between time interval 20 blank s e c to 40 blank s e c
equals fraction numerator 1 over denominator 2 end fraction cross times 20 cross times 3 plus 20 cross times 1 equals 30 plus 20 equals 50 blank m

Velocity-time left parenthesis v-t right parenthesis graph for a moving object is shown in the figure. Total displacement of the object during the same interval when there is non-zero acceleration and retardation is

physics-General
Between time interval 20 blank s e c to 40 blank s e c, there is non-zero acceleration and retardation. Hence distance travelled during this interval
equals Area between time interval 20 blank s e c to 40 blank s e c
equals fraction numerator 1 over denominator 2 end fraction cross times 20 cross times 3 plus 20 cross times 1 equals 30 plus 20 equals 50 blank m