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General
Easy

Question

left parenthesis sin space x plus cos space x right parenthesis squared plus cos squared space open parentheses pi over 4 plus x close parentheses element of

  1. left square bracket 0 comma 1 right square bracket
  2. left square bracket 0 comma 2 right square bracket
  3. left square bracket 1 comma 2 right square bracket
  4. left square bracket 0 comma 3 right square bracket

The correct answer is: left square bracket 1 comma 2 right square bracket

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Related Questions to study

General
Maths-

The minimum and maximum values of cos space x plus 3 square root of 2 sin space open parentheses x plus pi over 4 close parentheses plus 6 are

The minimum and maximum values of cos space x plus 3 square root of 2 sin space open parentheses x plus pi over 4 close parentheses plus 6 are

Maths-General
General
Maths-

The minimum and maximum values of sin space open parentheses x plus pi over 4 close parentheses sin space open parentheses x minus pi over 4 close parentheses are

sin space open parentheses x plus pi over 4 close parentheses sin space open parentheses x minus pi over 4 close parentheses
equals sin squared x minus sin squared straight pi over 4
equals fraction numerator 1 minus cos 2 x over denominator 2 end fraction minus open parentheses fraction numerator 1 over denominator square root of 2 end fraction close parentheses squared
equals 1 half minus fraction numerator cos 2 x over denominator 2 end fraction minus 1 half
equals negative 1 half cos 2 x
F o r space m i n i m u m space v a l u e space o f space f left parenthesis x right parenthesis comma space cos 2 x equals 1
f left parenthesis x right parenthesis equals negative 1 half cross times 1 equals fraction numerator negative 1 over denominator 2 end fraction
F o r space m a x i m u m space v a l u e space o f space f left parenthesis x right parenthesis comma space cos 2 x equals negative 1
f left parenthesis x right parenthesis equals negative 1 half cross times negative 1 equals 1 half
S o comma space sin space open parentheses x plus pi over 4 close parentheses sin space open parentheses x minus pi over 4 close parentheses element of open square brackets fraction numerator negative 1 over denominator 2 end fraction comma 1 half close square brackets

The minimum and maximum values of sin space open parentheses x plus pi over 4 close parentheses sin space open parentheses x minus pi over 4 close parentheses are

Maths-General
sin space open parentheses x plus pi over 4 close parentheses sin space open parentheses x minus pi over 4 close parentheses
equals sin squared x minus sin squared straight pi over 4
equals fraction numerator 1 minus cos 2 x over denominator 2 end fraction minus open parentheses fraction numerator 1 over denominator square root of 2 end fraction close parentheses squared
equals 1 half minus fraction numerator cos 2 x over denominator 2 end fraction minus 1 half
equals negative 1 half cos 2 x
F o r space m i n i m u m space v a l u e space o f space f left parenthesis x right parenthesis comma space cos 2 x equals 1
f left parenthesis x right parenthesis equals negative 1 half cross times 1 equals fraction numerator negative 1 over denominator 2 end fraction
F o r space m a x i m u m space v a l u e space o f space f left parenthesis x right parenthesis comma space cos 2 x equals negative 1
f left parenthesis x right parenthesis equals negative 1 half cross times negative 1 equals 1 half
S o comma space sin space open parentheses x plus pi over 4 close parentheses sin space open parentheses x minus pi over 4 close parentheses element of open square brackets fraction numerator negative 1 over denominator 2 end fraction comma 1 half close square brackets
General
Maths-

sin squared space x plus cos to the power of 4 space x element of

sin squared space x plus cos to the power of 4 space x element of

Maths-General
General
physics-

A piston fitted in cylindrical pipe is pulled as shown in the figure. A tuning fork is sounded at open end and loudest sound is heard at open length 13cm, 41 cm and 69 cm, the frequency of tuning fork if velocity of sound is 350 m s to the power of negative 1 end exponent is

In a closed organ pipe in which length of air-column can be increased or decreased, the first resonance occurs at lambda divided by 4 and second resonance occurs at 3 lambda divided by 4.
Thus, at first resonance
fraction numerator lambda over denominator 4 end fraction equals 13 blank horizontal ellipsis open parentheses i close parentheses
And a second resonance
fraction numerator 3 lambda over denominator 4 end fraction equals 41 blank horizontal ellipsis open parentheses i i close parentheses


Subtracting Eq.(i) from Eq.(ii), we have
fraction numerator 3 lambda over denominator 4 end fraction minus fraction numerator lambda over denominator 4 end fraction equals 41 minus 13
⟹ fraction numerator lambda over denominator 2 end fraction equals 28
therefore blank lambda equals 56 blank c m
Hence, frequency of tuning fork
v equals fraction numerator v over denominator lambda end fraction equals fraction numerator 350 over denominator 56 cross times 10 to the power of negative 2 end exponent end fraction equals 365 blank H z

A piston fitted in cylindrical pipe is pulled as shown in the figure. A tuning fork is sounded at open end and loudest sound is heard at open length 13cm, 41 cm and 69 cm, the frequency of tuning fork if velocity of sound is 350 m s to the power of negative 1 end exponent is

physics-General
In a closed organ pipe in which length of air-column can be increased or decreased, the first resonance occurs at lambda divided by 4 and second resonance occurs at 3 lambda divided by 4.
Thus, at first resonance
fraction numerator lambda over denominator 4 end fraction equals 13 blank horizontal ellipsis open parentheses i close parentheses
And a second resonance
fraction numerator 3 lambda over denominator 4 end fraction equals 41 blank horizontal ellipsis open parentheses i i close parentheses


Subtracting Eq.(i) from Eq.(ii), we have
fraction numerator 3 lambda over denominator 4 end fraction minus fraction numerator lambda over denominator 4 end fraction equals 41 minus 13
⟹ fraction numerator lambda over denominator 2 end fraction equals 28
therefore blank lambda equals 56 blank c m
Hence, frequency of tuning fork
v equals fraction numerator v over denominator lambda end fraction equals fraction numerator 350 over denominator 56 cross times 10 to the power of negative 2 end exponent end fraction equals 365 blank H z
General
physics-

In a sine wave, position of different particles at time t equals 0 is shown in figure. The equation for this wave travelling along positive x minus a x i s can be

As is clear from figure, att equals 0 comma x equals 0, displacementy equals 0. Therefore, option (a)or (d)may be correct.
In case of (d);y equals A sin invisible function application left parenthesis k x minus omega t right parenthesis
fraction numerator d y over denominator d t end fraction equals A cos invisible function application left parenthesis k x minus omega t right parenthesis open square brackets negative omega close square brackets
fraction numerator d y over denominator d x end fraction equals A cos invisible function application left parenthesis k x minus omega t right parenthesis open square brackets k close square brackets
fraction numerator fraction numerator d y over denominator d t end fraction over denominator d y divided by d x end fraction equals fraction numerator negative omega A cos invisible function application left parenthesis k x minus omega t right parenthesis over denominator k A cos invisible function application left parenthesis k x minus omega t right parenthesis end fraction equals negative fraction numerator omega over denominator k end fraction equals negative v
fraction numerator d y over denominator d t end fraction equals negative v open parentheses fraction numerator d y over denominator d x end fraction close parentheses
i e blank p a r t i c l e blank v e l o c i t y equals negative left parenthesis w a v e blank s p e e d right parenthesis cross times s l o p e.
And slope at x equals 0 and t equals 0is positive, in figure. Therefore, particle velocity is in negative y-direction.

In a sine wave, position of different particles at time t equals 0 is shown in figure. The equation for this wave travelling along positive x minus a x i s can be

physics-General
As is clear from figure, att equals 0 comma x equals 0, displacementy equals 0. Therefore, option (a)or (d)may be correct.
In case of (d);y equals A sin invisible function application left parenthesis k x minus omega t right parenthesis
fraction numerator d y over denominator d t end fraction equals A cos invisible function application left parenthesis k x minus omega t right parenthesis open square brackets negative omega close square brackets
fraction numerator d y over denominator d x end fraction equals A cos invisible function application left parenthesis k x minus omega t right parenthesis open square brackets k close square brackets
fraction numerator fraction numerator d y over denominator d t end fraction over denominator d y divided by d x end fraction equals fraction numerator negative omega A cos invisible function application left parenthesis k x minus omega t right parenthesis over denominator k A cos invisible function application left parenthesis k x minus omega t right parenthesis end fraction equals negative fraction numerator omega over denominator k end fraction equals negative v
fraction numerator d y over denominator d t end fraction equals negative v open parentheses fraction numerator d y over denominator d x end fraction close parentheses
i e blank p a r t i c l e blank v e l o c i t y equals negative left parenthesis w a v e blank s p e e d right parenthesis cross times s l o p e.
And slope at x equals 0 and t equals 0is positive, in figure. Therefore, particle velocity is in negative y-direction.
General
Maths-

The function sin space open parentheses x squared close parentheses plus cosplus cos space square root of x is

The function sin space open parentheses x squared close parentheses plus cosplus cos space square root of x is

Maths-General
General
Maths-

The period of the function f left parenthesis x right parenthesis equals left square bracket 6 x plus 7 right square bracket plus cos space pi x minus 6 x where [.] de-notes the greatest integer function, is

The period of the function f left parenthesis x right parenthesis equals left square bracket 6 x plus 7 right square bracket plus cos space pi x minus 6 x where [.] de-notes the greatest integer function, is

Maths-General
General
Maths-

The period of the function open vertical bar sin cubed space x over 2 close vertical bar plus open vertical bar cos to the power of 5 space x over 5 close vertical bar is

The period of the function open vertical bar sin cubed space x over 2 close vertical bar plus open vertical bar cos to the power of 5 space x over 5 close vertical bar is

Maths-General
General
Maths-

In any straight triangle A B C fraction numerator left parenthesis a plus b plus c right parenthesis left parenthesis b plus c minus a right parenthesis left parenthesis c plus a minus b right parenthesis left parenthesis a plus b minus c right parenthesis over denominator 4 b squared c squared end fraction =

In any straight triangle A B C fraction numerator left parenthesis a plus b plus c right parenthesis left parenthesis b plus c minus a right parenthesis left parenthesis c plus a minus b right parenthesis left parenthesis a plus b minus c right parenthesis over denominator 4 b squared c squared end fraction =

Maths-General
General
Maths-

In straight triangle A B C sum a cubed Sin space left parenthesis B minus C right parenthesis =

In straight triangle A B C sum a cubed Sin space left parenthesis B minus C right parenthesis =

Maths-General
General
Maths-

In straight triangle A B C comma sum a left parenthesis sin space B minus sin space C right parenthesis equals

In straight triangle A B C comma sum a left parenthesis sin space B minus sin space C right parenthesis equals

Maths-General
General
Maths-

If the period of fraction numerator cos space left parenthesis sin space left parenthesis n x right parenthesis right parenthesis over denominator tan space left parenthesis x divided by n right parenthesis end fraction comma n element of N is 6 pi then n=

If the period of fraction numerator cos space left parenthesis sin space left parenthesis n x right parenthesis right parenthesis over denominator tan space left parenthesis x divided by n right parenthesis end fraction comma n element of N is 6 pi then n=

Maths-General
General
Maths-

Let f left parenthesis x right parenthesis equals cos space square root of p x where p equals left square bracket a right square bracket where  is the integral part of x. If the period of f(x) is pi, then a element of

Let f left parenthesis x right parenthesis equals cos space square root of p x where p equals left square bracket a right square bracket where  is the integral part of x. If the period of f(x) is pi, then a element of

Maths-General
General
physics-

Which of the following options is correct for the object having a straight line motion represented by the following graph

From given figure, it is clear that the net displacement is zero. So average velocity will be zero

Which of the following options is correct for the object having a straight line motion represented by the following graph

physics-General
From given figure, it is clear that the net displacement is zero. So average velocity will be zero
General
physics-

A body begins to walk eastward along a street in front of his house and the graph of his position from home is shown in the following figure. His average speed for the whole time interval is equal to

Average speed is the ratio of distance to time taken
Distance travelled from 0 to 5 s equals 40 blank m
Distance travelled from 5 to 10 s equals 0 blank m
Distance travelled from 10 to 15 s equals 60 blank m
Distance travelled from 15to 20 s equals 20
So, total distance equals 40 plus 0 plus 60 plus 20 equals 120 blank m
Total time taken equals 20 blank m i n u t e s
Hence, average speed
equals fraction numerator d i s t a n c e blank t r a v e l l e d blank left parenthesis m right parenthesis over denominator t i m e blank left parenthesis m i n right parenthesis end fraction equals fraction numerator 120 over denominator 20 end fraction equals 6 blank m divided by m i n

A body begins to walk eastward along a street in front of his house and the graph of his position from home is shown in the following figure. His average speed for the whole time interval is equal to

physics-General
Average speed is the ratio of distance to time taken
Distance travelled from 0 to 5 s equals 40 blank m
Distance travelled from 5 to 10 s equals 0 blank m
Distance travelled from 10 to 15 s equals 60 blank m
Distance travelled from 15to 20 s equals 20
So, total distance equals 40 plus 0 plus 60 plus 20 equals 120 blank m
Total time taken equals 20 blank m i n u t e s
Hence, average speed
equals fraction numerator d i s t a n c e blank t r a v e l l e d blank left parenthesis m right parenthesis over denominator t i m e blank left parenthesis m i n right parenthesis end fraction equals fraction numerator 120 over denominator 20 end fraction equals 6 blank m divided by m i n