Maths-

General

Easy

Question

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

Periodic with period $π$
Periodic with period 2 $π$
Periodic with period 0
Not a Periodic function Extreme Values:

Hint:

In this question we have to find the correct option. As we know sin x and cos x are periodic functions only when x varies from $open parentheses negative infinity comma infinity close parentheses$ .

The correct answer is: Not a Periodic function Extreme Values:

$f left parenthesis x right parenthesis equals sin left parenthesis x squared right parenthesis plus cos square root of x sin x space i s space p e r i o d i c space f u n c t i o n space w h e n space x space v a r i e s space f r o m space minus infinity space t o space infinity. S o comma space f left parenthesis x right parenthesis equals sin left parenthesis x squared right parenthesis comma space x squared greater or equal than 0 H e r e comma space x squared space v a r i e s space f r o m space 0 space t o space infinity S o comma space sin left parenthesis x squared right parenthesis space i s space n o t space a space p e r i o d space f u n c t i o n. S i m i l a r l y comma space f left parenthesis x right parenthesis equals cos open parentheses square root of x close parentheses comma square root of x greater or equal than 0 comma space x greater or equal than 0 H e r e square root of x space v a r i e s space f r o m space 0 space t o space infinity. S o comma space cos square root of x space i s space n o t space a space p e r i o d i c space f u n c t i o n. l e t space g left parenthesis x right parenthesis equals sin left parenthesis x squared right parenthesis plus cos square root of x d o m a i n space o f space g left parenthesis x right parenthesis equals x element of left square bracket 0 comma infinity right parenthesis f o r space p e r i c space f u n c t i o n comma space d o m a i n space o f space f u n c t i o n space s h o u l d space b e space i n space left parenthesis negative infinity comma infinity right parenthesis t h i s space i m p l i e s space t h a t space g left parenthesis x right parenthesis space i s space n o t space a space p e r i o d i c space f u n c t i o n.$

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

Maths-General

General

Maths-

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

Maths-General

General

Maths-

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

Maths-General

General

Maths-

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

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=

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 $a element of$

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

5 s equals 40 blank m

Distance travelled from

5

10 s equals 0 blank m

Distance travelled from

10

15 s equals 60 blank m

Distance travelled from

15

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

5 s equals 40 blank m

Distance travelled from

5

10 s equals 0 blank m

Distance travelled from

10

15 s equals 60 blank m

Distance travelled from

15

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

General

physics-

A particle is moving with uniform acceleration along a straight line. The average velocity of the particle from $P$ to $Q$ is $8 m s to the power of negative 1 end exponent$ and that from $Q$ to $S$ is $12 m s to the power of negative 1 end exponent$ . If $Q S minus P Q$ , then the average velocity from $P$ to $S$ is

Average velocity

equals fraction numerator 2 cross times 8 cross times 12 over denominator 8 plus 12 end fraction m s to the power of negative 1 end exponent equals 9.6 m s to the power of negative 1 end exponent

A particle is moving with uniform acceleration along a straight line. The average velocity of the particle from $P$ to $Q$ is $8 m s to the power of negative 1 end exponent$ and that from $Q$ to $S$ is $12 m s to the power of negative 1 end exponent$ . If $Q S minus P Q$ , then the average velocity from $P$ to $S$ is

physics-General

Average velocity

equals fraction numerator 2 cross times 8 cross times 12 over denominator 8 plus 12 end fraction m s to the power of negative 1 end exponent equals 9.6 m s to the power of negative 1 end exponent

General

chemistry-

i)
ii)
iii)
iv) $Me minus identical to negative straight H rightwards arrow with text dil.H end text subscript 2 SO subscript 4 plus Hg to the power of 2 plus end exponent on top$
Which of the statements are correct?

chemistry-General

General

physics-

A body is travelling in a straight line with a uniformly increasing speed. Which one of the plot represents the changes in distance (s) travelled with time ( $t$ )

s equals u t plus fraction numerator 1 over denominator 2 end fraction a t to the power of 2 end exponent

s equals fraction numerator 1 over denominator 2 end fraction a t to the power of 2 end exponent

[

because u equals 0

]
It is an equation of parabola

A body is travelling in a straight line with a uniformly increasing speed. Which one of the plot represents the changes in distance (s) travelled with time ( $t$ )

physics-General

s equals u t plus fraction numerator 1 over denominator 2 end fraction a t to the power of 2 end exponent

s equals fraction numerator 1 over denominator 2 end fraction a t to the power of 2 end exponent

[

because u equals 0

]
It is an equation of parabola

General

Maths-

The value of integer n for which the function $f left parenthesis x right parenthesis equals fraction numerator sin begin display style space end style n x over denominator sin begin display style space end style left parenthesis x divided by n right parenthesis end fraction$ has $4 pi$ as its period is

f left parenthesis x right parenthesis equals fraction numerator sin begin display style space end style n x over denominator sin begin display style space end style left parenthesis x divided by n right parenthesis end fraction

Given, period =

4 straight pi

s o comma space fraction numerator sin space n straight pi over denominator sin begin display style x over n end style end fraction equals fraction numerator sin open square brackets n open parentheses x plus 4 straight pi close parentheses close square brackets over denominator sin open parentheses begin display style fraction numerator x plus 4 straight pi over denominator n end fraction end style close parentheses end fraction rightwards double arrow fraction numerator sin space n straight pi over denominator sin begin display style x over n end style end fraction equals fraction numerator sin open parentheses n x plus 4 n straight pi close parentheses over denominator sin open parentheses begin display style x over n end style plus begin display style fraction numerator 4 straight pi over denominator n end fraction end style close parentheses end fraction f r o m space o p t i o n s space i t space i s space o n l y space t r u e space f o r space space n equals 2

The value of integer n for which the function $f left parenthesis x right parenthesis equals fraction numerator sin begin display style space end style n x over denominator sin begin display style space end style left parenthesis x divided by n right parenthesis end fraction$ has $4 pi$ as its period is

Maths-General

f left parenthesis x right parenthesis equals fraction numerator sin begin display style space end style n x over denominator sin begin display style space end style left parenthesis x divided by n right parenthesis end fraction

Given, period =

4 straight pi

s o comma space fraction numerator sin space n straight pi over denominator sin begin display style x over n end style end fraction equals fraction numerator sin open square brackets n open parentheses x plus 4 straight pi close parentheses close square brackets over denominator sin open parentheses begin display style fraction numerator x plus 4 straight pi over denominator n end fraction end style close parentheses end fraction rightwards double arrow fraction numerator sin space n straight pi over denominator sin begin display style x over n end style end fraction equals fraction numerator sin open parentheses n x plus 4 n straight pi close parentheses over denominator sin open parentheses begin display style x over n end style plus begin display style fraction numerator 4 straight pi over denominator n end fraction end style close parentheses end fraction f r o m space o p t i o n s space i t space i s space o n l y space t r u e space f o r space space n equals 2

General

Maths-

$cos squared space open parentheses 60 to the power of ring operator plus x close parentheses minus cos squared space open parentheses 60 to the power of ring operator minus x close parentheses element of open square brackets negative m over 2 comma m over 2 close square brackets not stretchy rightwards double arrow straight m equals$

space space space space cos squared open parentheses 60 plus x close parentheses minus cos squared open parentheses 60 minus x close parentheses equals open square brackets cos open parentheses 60 plus x close parentheses plus cos space open parentheses 60 minus x close parentheses close square brackets open square brackets cos space open parentheses 60 plus x close parentheses minus cos open parentheses 60 minus x close parentheses close square brackets equals open parentheses 2. cos space 60. cos space x close parentheses open parentheses negative 2. sin 60. sin space x close parentheses equals open parentheses 2.1 half. cos space x close parentheses open parentheses negative 2. fraction numerator square root of 3 over denominator 2 end fraction. sin space x close parentheses equals negative square root of 3. cos space x. sin space x equals negative fraction numerator square root of 3 over denominator 2 end fraction. sin space 2 x space 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 sin space 2 x equals 1 f left parenthesis x right parenthesis equals fraction numerator negative square root of 3 over denominator 2 end fraction cross times 1 equals fraction numerator negative square root of 3 over denominator 2 end fraction F o r space m i n i m u m space v a l u e space o f space f space left parenthesis x right parenthesis comma space sin space 2 x space equals negative 1 f left parenthesis x right parenthesis equals fraction numerator negative square root of 3 over denominator 2 end fraction cross times negative 1 equals fraction numerator square root of 3 over denominator 2 end fraction A s space space cos squared open parentheses 60 plus x close parentheses minus cos squared open parentheses 60 minus x close parentheses element of open square brackets fraction numerator negative square root of 3 over denominator 2 end fraction comma fraction numerator square root of 3 over denominator 2 end fraction close square brackets S o comma space m equals square root of 3

$cos squared space open parentheses 60 to the power of ring operator plus x close parentheses minus cos squared space open parentheses 60 to the power of ring operator minus x close parentheses element of open square brackets negative m over 2 comma m over 2 close square brackets not stretchy rightwards double arrow straight m equals$

Maths-General

space space space space cos squared open parentheses 60 plus x close parentheses minus cos squared open parentheses 60 minus x close parentheses equals open square brackets cos open parentheses 60 plus x close parentheses plus cos space open parentheses 60 minus x close parentheses close square brackets open square brackets cos space open parentheses 60 plus x close parentheses minus cos open parentheses 60 minus x close parentheses close square brackets equals open parentheses 2. cos space 60. cos space x close parentheses open parentheses negative 2. sin 60. sin space x close parentheses equals open parentheses 2.1 half. cos space x close parentheses open parentheses negative 2. fraction numerator square root of 3 over denominator 2 end fraction. sin space x close parentheses equals negative square root of 3. cos space x. sin space x equals negative fraction numerator square root of 3 over denominator 2 end fraction. sin space 2 x space 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 sin space 2 x equals 1 f left parenthesis x right parenthesis equals fraction numerator negative square root of 3 over denominator 2 end fraction cross times 1 equals fraction numerator negative square root of 3 over denominator 2 end fraction F o r space m i n i m u m space v a l u e space o f space f space left parenthesis x right parenthesis comma space sin space 2 x space equals negative 1 f left parenthesis x right parenthesis equals fraction numerator negative square root of 3 over denominator 2 end fraction cross times negative 1 equals fraction numerator square root of 3 over denominator 2 end fraction A s space space cos squared open parentheses 60 plus x close parentheses minus cos squared open parentheses 60 minus x close parentheses element of open square brackets fraction numerator negative square root of 3 over denominator 2 end fraction comma fraction numerator square root of 3 over denominator 2 end fraction close square brackets S o comma space m equals square root of 3

General

Maths-

$cos squared space open parentheses 60 to the power of ring operator minus x close parentheses plus cos squared space open parentheses 60 to the power of ring operator plus x close parentheses element of$

space space space space cos squared space open parentheses 60 to the power of ring operator minus x close parentheses plus cos squared space open parentheses 60 to the power of ring operator plus x close parentheses equals open parentheses cos space open parentheses 60 plus x close parentheses plus cos open parentheses 60 minus x close parentheses close parentheses squared minus 2 cos space open parentheses 60 minus x close parentheses. cos space open parentheses 60 plus x close parentheses equals open parentheses 2. cos space 60. cos space x close parentheses squared minus open parentheses cos space 2 x space plus cos space 120 space close parentheses equals 4 cross times 1 fourth cross times cos squared x minus cos space 2 x space minus open parentheses fraction numerator negative 1 over denominator 2 end fraction close parentheses equals cos squared x minus cos space 2 x plus 1 half equals cos squared x minus 2 cos squared x plus 1 plus 1 half equals 3 over 2 minus cos squared x

For maximum value of f (x),

cos squared x equals 0

f (x)=

3 over 2 minus 0 equals 3 over 2

For minimum value of f (x),

cos squared x equals 1

f (x)=

3 over 2 minus 1 equals 1 half

So,

cos squared space open parentheses 60 to the power of ring operator minus x close parentheses plus cos squared space open parentheses 60 to the power of ring operator plus x close parentheses element of open square brackets 1 half comma 3 over 2 close square brackets

$cos squared space open parentheses 60 to the power of ring operator minus x close parentheses plus cos squared space open parentheses 60 to the power of ring operator plus x close parentheses element of$

Maths-General

space space space space cos squared space open parentheses 60 to the power of ring operator minus x close parentheses plus cos squared space open parentheses 60 to the power of ring operator plus x close parentheses equals open parentheses cos space open parentheses 60 plus x close parentheses plus cos open parentheses 60 minus x close parentheses close parentheses squared minus 2 cos space open parentheses 60 minus x close parentheses. cos space open parentheses 60 plus x close parentheses equals open parentheses 2. cos space 60. cos space x close parentheses squared minus open parentheses cos space 2 x space plus cos space 120 space close parentheses equals 4 cross times 1 fourth cross times cos squared x minus cos space 2 x space minus open parentheses fraction numerator negative 1 over denominator 2 end fraction close parentheses equals cos squared x minus cos space 2 x plus 1 half equals cos squared x minus 2 cos squared x plus 1 plus 1 half equals 3 over 2 minus cos squared x

For maximum value of f (x),

cos squared x equals 0

f (x)=

3 over 2 minus 0 equals 3 over 2

For minimum value of f (x),

cos squared x equals 1

f (x)=

3 over 2 minus 1 equals 1 half

So,

cos squared space open parentheses 60 to the power of ring operator minus x close parentheses plus cos squared space open parentheses 60 to the power of ring operator plus x close parentheses element of open square brackets 1 half comma 3 over 2 close square brackets

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The function is

Periodic with period Periodic with period 2Periodic with period 0Not a Periodic function Extreme Values:

In this question we have to find the correct option. As we know sin x and cos x are periodic functions only when x varies from.

The correct answer is: Not a Periodic function Extreme Values:

Related Questions to study

The period of the function where [.] de-notes the greatest integer function, is

The period of the function where [.] de-notes the greatest integer function, is

The period of the function is

The period of the function is

In any =

In any =

In =

In =

In

In

If the period of is then n=

If the period of is then n=

Let where where is the integral part of x. If the period of f(x) is , then

Let where where is the integral part of x. If the period of f(x) is , then

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

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

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

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

A particle is moving with uniform acceleration along a straight line. The average velocity of the particle from to is and that from to is . If , then the average velocity from to is

A particle is moving with uniform acceleration along a straight line. The average velocity of the particle from to is and that from to is . If , then the average velocity from to is

i) ii) iii) iv) Which of the statements are correct?

i) ii) iii) iv) Which of the statements are correct?

A body is travelling in a straight line with a uniformly increasing speed. Which one of the plot represents the changes in distance (s) travelled with time ()

A body is travelling in a straight line with a uniformly increasing speed. Which one of the plot represents the changes in distance (s) travelled with time ()

The value of integer n for which the function has as its period is

The value of integer n for which the function has as its period is

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

Periodic with period $π$
Periodic with period 2 $π$
Periodic with period 0
Not a Periodic function Extreme Values:

In this question we have to find the correct option. As we know sin x and cos x are periodic functions only when x varies from $open parentheses negative infinity comma infinity close parentheses$ .

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

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

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

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

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

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

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=

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 $a element of$

i)
ii)
iii)
iv) $Me minus identical to negative straight H rightwards arrow with text dil.H end text subscript 2 SO subscript 4 plus Hg to the power of 2 plus end exponent on top$
Which of the statements are correct?

i)
ii)
iii)
iv) $Me minus identical to negative straight H rightwards arrow with text dil.H end text subscript 2 SO subscript 4 plus Hg to the power of 2 plus end exponent on top$
Which of the statements are correct?

A body is travelling in a straight line with a uniformly increasing speed. Which one of the plot represents the changes in distance (s) travelled with time ( $t$ )

A body is travelling in a straight line with a uniformly increasing speed. Which one of the plot represents the changes in distance (s) travelled with time ( $t$ )