Maths-
General
Easy

Question

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

  1. 2 pi
  2. 10 pi
  3. 8 pi
  4. 5 pi

The correct answer is: 10 pi

Book A Free Demo

+91

Grade*

Related Questions to study

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
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 Sis 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 Sis 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?

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.
General
physics-

The effective capacitance between points X and Y shown in figure. Assuming C subscript 2 end subscript equals 10 blank muF and that outer capacitors are all 4 blank muF is

The arrangement shows a Wheatstone bridge.
As fraction numerator C subscript 1 end subscript over denominator C subscript 3 end subscript end fraction equals fraction numerator C subscript 4 end subscript over denominator C subscript 5 end subscript end fraction equals 1 comma blanktherefore the bridge is balanced.
fraction numerator 1 over denominator C subscript s subscript 1 end subscript end subscript end fraction equals fraction numerator 1 over denominator 4 end fraction plus fraction numerator 1 over denominator 4 end fraction equals fraction numerator 2 over denominator 4 end fraction equals fraction numerator 1 over denominator 2 end fraction comma C subscript s subscript 1 end subscript end subscript equals 2 mu blank F
Similarly, C subscript s end subscript subscript 2 end subscript equals 2 mu blank F
therefore effective capacitance
equals C subscript p end subscript equals C subscript s end subscript subscript 1 end subscript plus C subscript s end subscript subscript 2 end subscript equals 2 plus 2 plus equals 4 mu blank F

The effective capacitance between points X and Y shown in figure. Assuming C subscript 2 end subscript equals 10 blank muF and that outer capacitors are all 4 blank muF is

physics-General
The arrangement shows a Wheatstone bridge.
As fraction numerator C subscript 1 end subscript over denominator C subscript 3 end subscript end fraction equals fraction numerator C subscript 4 end subscript over denominator C subscript 5 end subscript end fraction equals 1 comma blanktherefore the bridge is balanced.
fraction numerator 1 over denominator C subscript s subscript 1 end subscript end subscript end fraction equals fraction numerator 1 over denominator 4 end fraction plus fraction numerator 1 over denominator 4 end fraction equals fraction numerator 2 over denominator 4 end fraction equals fraction numerator 1 over denominator 2 end fraction comma C subscript s subscript 1 end subscript end subscript equals 2 mu blank F
Similarly, C subscript s end subscript subscript 2 end subscript equals 2 mu blank F
therefore effective capacitance
equals C subscript p end subscript equals C subscript s end subscript subscript 1 end subscript plus C subscript s end subscript subscript 2 end subscript equals 2 plus 2 plus equals 4 mu blank F
General
physics-

The four capacitors, each of 25 muF are connected as shown in figure. The DC voltmeter reads 200 V. the change on each plate of capacitor is

Charge on each plate of each capacitor
Q equals plus-or-minus C V equals plus-or-minus 25 cross times 10 to the power of negative 6 end exponent cross times 200
equals plus-or-minus 5 cross times 10 to the power of negative 3 end exponent C

The four capacitors, each of 25 muF are connected as shown in figure. The DC voltmeter reads 200 V. the change on each plate of capacitor is

physics-General
Charge on each plate of each capacitor
Q equals plus-or-minus C V equals plus-or-minus 25 cross times 10 to the power of negative 6 end exponent cross times 200
equals plus-or-minus 5 cross times 10 to the power of negative 3 end exponent C