Maths-
General
Easy

Question

Period of fraction numerator 2 sin space 2 x minus 5 cos space 2 x over denominator 7 cos space x minus 8 sin space x end fraction is

  1. pi
  2. 2 pi
  3. pi over 2
  4. pi over 3

The correct answer is: 2 pi

Book A Free Demo

+91

Grade*

Related Questions to study

General
physics-

The current I drawn from the 5V source will be

The given circuit can be redrawn as

The current I drawn from the 5V source will be

physics-General
The given circuit can be redrawn as
General
physics-

In the circuit given E=0.6V, R subscript 1 end subscript=100capital omega,R subscript 2 end subscript equals R subscript 3 end subscript equals 50 capital omega comma blank R subscript 4 end subscript equals 75 capital omega. The equivalent resistance of the circuit, in ohm is

R subscript 2 end subscript comma blank R subscript 3 end subscript a n d R subscript 4 end subscript are in parallel order, so their equivalent resistance
fraction numerator 1 over denominator R to the power of ´ end exponent end fraction equals fraction numerator 1 over denominator R to the power of 2 end exponent end fraction plus fraction numerator 1 over denominator R to the power of 3 end exponent end fraction plus fraction numerator 1 over denominator R to the power of 4 end exponent end fraction
equals fraction numerator 1 over denominator 50 end fraction plus fraction numerator 1 over denominator 50 end fraction plus fraction numerator 1 over denominator 75 end fraction
equals fraction numerator 30 plus 30 plus 20 over denominator 1500 end fraction
equals fraction numerator 80 over denominator 1500 end fraction equals fraction numerator 4 over denominator 75 end fraction
therefore blank R to the power of ´ end exponent equals fraction numerator 75 over denominator 4 end fraction capital omega
R equals R subscript 1 end subscript plus R to the power of ´ end exponent equals 100 plus fraction numerator 75 over denominator 4 end fraction
equals fraction numerator 475 over denominator 4 end fraction capital omega equals 118.75 capital omega

In the circuit given E=0.6V, R subscript 1 end subscript=100capital omega,R subscript 2 end subscript equals R subscript 3 end subscript equals 50 capital omega comma blank R subscript 4 end subscript equals 75 capital omega. The equivalent resistance of the circuit, in ohm is

physics-General
R subscript 2 end subscript comma blank R subscript 3 end subscript a n d R subscript 4 end subscript are in parallel order, so their equivalent resistance
fraction numerator 1 over denominator R to the power of ´ end exponent end fraction equals fraction numerator 1 over denominator R to the power of 2 end exponent end fraction plus fraction numerator 1 over denominator R to the power of 3 end exponent end fraction plus fraction numerator 1 over denominator R to the power of 4 end exponent end fraction
equals fraction numerator 1 over denominator 50 end fraction plus fraction numerator 1 over denominator 50 end fraction plus fraction numerator 1 over denominator 75 end fraction
equals fraction numerator 30 plus 30 plus 20 over denominator 1500 end fraction
equals fraction numerator 80 over denominator 1500 end fraction equals fraction numerator 4 over denominator 75 end fraction
therefore blank R to the power of ´ end exponent equals fraction numerator 75 over denominator 4 end fraction capital omega
R equals R subscript 1 end subscript plus R to the power of ´ end exponent equals 100 plus fraction numerator 75 over denominator 4 end fraction
equals fraction numerator 475 over denominator 4 end fraction capital omega equals 118.75 capital omega
General
physics-

Six equal resistances are connected between points P, Q and R as shown in the figure. Then the net resistance will be maximum between

R subscript P Q end subscript equals fraction numerator 5 over denominator 11 end fraction r comma blank R subscript Q R end subscript equals fraction numerator 4 over denominator 11 end fraction r a n d R subscript P R end subscript equals fraction numerator 3 over denominator 11 end fraction r
therefore R subscript P Q end subscriptis maximum.

Six equal resistances are connected between points P, Q and R as shown in the figure. Then the net resistance will be maximum between

physics-General
R subscript P Q end subscript equals fraction numerator 5 over denominator 11 end fraction r comma blank R subscript Q R end subscript equals fraction numerator 4 over denominator 11 end fraction r a n d R subscript P R end subscript equals fraction numerator 3 over denominator 11 end fraction r
therefore R subscript P Q end subscriptis maximum.
General
physics-

In the circuit shown the equivalent resistance between A and B is

The three resistances between A and B are parallel,
fraction numerator 1 over denominator R subscript c o m b end subscript end fraction equals fraction numerator 1 over denominator R subscript 1 end subscript end fraction plus fraction numerator 1 over denominator R subscript 2 end subscript end fraction plus fraction numerator 1 over denominator R subscript 3 end subscript end fraction
equals fraction numerator 1 over denominator 9 end fraction plus fraction numerator 1 over denominator 9 end fraction plus fraction numerator 1 over denominator 9 end fraction
fraction numerator 1 over denominator R subscript c o m b end subscript end fraction equals fraction numerator 3 over denominator 9 end fraction
⟹ R subscript c o m b end subscript equals 3 capital omega

In the circuit shown the equivalent resistance between A and B is

physics-General
The three resistances between A and B are parallel,
fraction numerator 1 over denominator R subscript c o m b end subscript end fraction equals fraction numerator 1 over denominator R subscript 1 end subscript end fraction plus fraction numerator 1 over denominator R subscript 2 end subscript end fraction plus fraction numerator 1 over denominator R subscript 3 end subscript end fraction
equals fraction numerator 1 over denominator 9 end fraction plus fraction numerator 1 over denominator 9 end fraction plus fraction numerator 1 over denominator 9 end fraction
fraction numerator 1 over denominator R subscript c o m b end subscript end fraction equals fraction numerator 3 over denominator 9 end fraction
⟹ R subscript c o m b end subscript equals 3 capital omega
General
physics-

In the circuit shown, the currents i subscript 1 end subscript blank a n d blank i subscript 2 end subscriptare

R equals fraction numerator 12 cross times 4 over denominator 12 plus 4 end fraction plus 2 equals 5 capital omega
I equals fraction numerator E over denominator R plus r end fraction equals fraction numerator 12 over denominator 6 end fraction equals 2 A
I subscript 1 end subscript plus I subscript 1 end subscript equals 2 A
I proportional to fraction numerator 1 over denominator R end fraction
therefore I subscript 1 end subscript equals 0.5 A comma blank I subscript 2 end subscript equals 1.5 A

In the circuit shown, the currents i subscript 1 end subscript blank a n d blank i subscript 2 end subscriptare

physics-General
R equals fraction numerator 12 cross times 4 over denominator 12 plus 4 end fraction plus 2 equals 5 capital omega
I equals fraction numerator E over denominator R plus r end fraction equals fraction numerator 12 over denominator 6 end fraction equals 2 A
I subscript 1 end subscript plus I subscript 1 end subscript equals 2 A
I proportional to fraction numerator 1 over denominator R end fraction
therefore I subscript 1 end subscript equals 0.5 A comma blank I subscript 2 end subscript equals 1.5 A
General
physics-

The resistance is connected as shown in the figure below. Find the equivalent resistance between the points A and B.

) 3blank capital omega
R’=3+7=10capital omega
R’ and 10capital omega are in parallel, so
R to the power of ´ end exponent equals fraction numerator 10 cross times 10 over denominator 10 plus 10 end fraction equals 5 capital omega
R to the power of ´ end exponent a n d blank 5 capital omega blankare in series, so
R’=5+5=10capital omega
Now, R’ and 10capital omega are in parallel, so
R equals fraction numerator 10 cross times 10 over denominator 10 plus 10 end fraction equals 5 capital omega

The resistance is connected as shown in the figure below. Find the equivalent resistance between the points A and B.

physics-General
) 3blank capital omega
R’=3+7=10capital omega
R’ and 10capital omega are in parallel, so
R to the power of ´ end exponent equals fraction numerator 10 cross times 10 over denominator 10 plus 10 end fraction equals 5 capital omega
R to the power of ´ end exponent a n d blank 5 capital omega blankare in series, so
R’=5+5=10capital omega
Now, R’ and 10capital omega are in parallel, so
R equals fraction numerator 10 cross times 10 over denominator 10 plus 10 end fraction equals 5 capital omega
General
Maths-

The cosecant function whose period is 4 is

f(x)=cosecx
period of f(x)=4
We know that period of cosec open vertical bar k close vertical bar=fraction numerator 2 straight pi over denominator open vertical bar k close vertical bar end fraction
rightwards double arrow fraction numerator 2 straight pi over denominator open vertical bar k close vertical bar end fraction equals 4
rightwards double arrow open vertical bar k close vertical bar equals straight pi over 2
So, cosecant function whose period is 4 is cosecopen parentheses πx over 2 close parentheses.

The cosecant function whose period is 4 is

Maths-General
f(x)=cosecx
period of f(x)=4
We know that period of cosec open vertical bar k close vertical bar=fraction numerator 2 straight pi over denominator open vertical bar k close vertical bar end fraction
rightwards double arrow fraction numerator 2 straight pi over denominator open vertical bar k close vertical bar end fraction equals 4
rightwards double arrow open vertical bar k close vertical bar equals straight pi over 2
So, cosecant function whose period is 4 is cosecopen parentheses πx over 2 close parentheses.
General
Maths-

Sine functions whose period is 6 is

f(x)=sinx
period of f(x)=6
We know that period of sin ax =fraction numerator 2 straight pi over denominator a end fraction
rightwards double arrow fraction numerator 2 straight pi over denominator a end fraction equals 6
rightwards double arrow 2 straight pi equals 6 straight a
rightwards double arrow straight a equals straight pi over 3
So comma space sine space function space whose space period space is space 6 space is space sin open parentheses πx over 3 close parentheses.

Sine functions whose period is 6 is

Maths-General
f(x)=sinx
period of f(x)=6
We know that period of sin ax =fraction numerator 2 straight pi over denominator a end fraction
rightwards double arrow fraction numerator 2 straight pi over denominator a end fraction equals 6
rightwards double arrow 2 straight pi equals 6 straight a
rightwards double arrow straight a equals straight pi over 3
So comma space sine space function space whose space period space is space 6 space is space sin open parentheses πx over 3 close parentheses.
General
physics-

Which graph represents the uniform acceleration

Since slope of graph remains constant for velocity-time graph

Which graph represents the uniform acceleration

physics-General
Since slope of graph remains constant for velocity-time graph
General
physics-

An object is dropped from rest. Its v-t graph is

Using
V equals u plus a t
V equals g t(i)
Comparing with y equals m x plus c
Equation (i) represents a straight line passing through origin inclined x-axis (slope -g)

An object is dropped from rest. Its v-t graph is

physics-General
Using
V equals u plus a t
V equals g t(i)
Comparing with y equals m x plus c
Equation (i) represents a straight line passing through origin inclined x-axis (slope -g)
General
physics-

In circuit shown below, the resistances are given in ohm and the battery is assumed ideal with emf equal to 3V. The voltage across the resistance R subscript 4 end subscript is

Equivalent resistance of the given network
R subscript e q end subscript equals 75 capital omega
∴ Total current through battery,
i equals fraction numerator 3 over denominator 75 end fraction
i subscript 1 end subscript equals i subscript 2 end subscript equals fraction numerator 3 over denominator 75 cross times 2 end fraction equals fraction numerator 3 over denominator 150 end fraction

Current through resistance
R subscript 4 end subscript equals fraction numerator 3 over denominator 150 end fraction cross times fraction numerator 60 over denominator open parentheses 30 plus 60 close parentheses end fraction
equals fraction numerator 3 over denominator 150 end fraction cross times fraction numerator 60 over denominator 90 end fraction
equals fraction numerator 2 over denominator 150 end fraction A
V subscript 4 end subscript equals i subscript 4 end subscript cross times R subscript 4 end subscript
equals fraction numerator 2 over denominator 150 end fraction cross times 30
equals fraction numerator 2 over denominator 5 end fraction equals 0.4 blank v o l t

In circuit shown below, the resistances are given in ohm and the battery is assumed ideal with emf equal to 3V. The voltage across the resistance R subscript 4 end subscript is

physics-General
Equivalent resistance of the given network
R subscript e q end subscript equals 75 capital omega
∴ Total current through battery,
i equals fraction numerator 3 over denominator 75 end fraction
i subscript 1 end subscript equals i subscript 2 end subscript equals fraction numerator 3 over denominator 75 cross times 2 end fraction equals fraction numerator 3 over denominator 150 end fraction

Current through resistance
R subscript 4 end subscript equals fraction numerator 3 over denominator 150 end fraction cross times fraction numerator 60 over denominator open parentheses 30 plus 60 close parentheses end fraction
equals fraction numerator 3 over denominator 150 end fraction cross times fraction numerator 60 over denominator 90 end fraction
equals fraction numerator 2 over denominator 150 end fraction A
V subscript 4 end subscript equals i subscript 4 end subscript cross times R subscript 4 end subscript
equals fraction numerator 2 over denominator 150 end fraction cross times 30
equals fraction numerator 2 over denominator 5 end fraction equals 0.4 blank v o l t
General
physics-

The resistance across A blank a n d blank Bin the figure below will be

Resistance are in parallel
therefore blank R subscript e q end subscript equals fraction numerator R over denominator 3 end fraction

The resistance across A blank a n d blank Bin the figure below will be

physics-General
Resistance are in parallel
therefore blank R subscript e q end subscript equals fraction numerator R over denominator 3 end fraction
General
physics-

Five equal resistances, each of resistance R commaare connected as shown in figure below. A bettery of V volt is connected between A blank a n d blank B.The current flowing in F C will be

I equals fraction numerator V over denominator R end fraction

therefore blank C u r r e n t blank i n blank F C equals fraction numerator 1 over denominator 2 end fraction equals fraction numerator V over denominator 2 R end fraction

Five equal resistances, each of resistance R commaare connected as shown in figure below. A bettery of V volt is connected between A blank a n d blank B.The current flowing in F C will be

physics-General
I equals fraction numerator V over denominator R end fraction

therefore blank C u r r e n t blank i n blank F C equals fraction numerator 1 over denominator 2 end fraction equals fraction numerator V over denominator 2 R end fraction
General
Maths-

If f left parenthesis x right parenthesis equals sin squared space open parentheses pi over 8 plus x over 2 close parentheses minus sin squared space open parentheses pi over 8 minus x over 2 close parentheses, then the period of f(x) is

f left parenthesis x right parenthesis equals sin squared space open parentheses pi over 8 plus x over 2 close parentheses minus sin squared space open parentheses straight pi over 8 minus x over 2 close parentheses
equals 1 half open square brackets 1 minus cos 2 open parentheses straight pi over 8 plus x over 2 close parentheses space close square brackets minus 1 half open square brackets 1 minus cos 2 open parentheses straight pi over 8 minus x over 2 close parentheses close square brackets
equals 1 half open square brackets 1 minus cos open parentheses straight pi over 4 plus x close parentheses space close square brackets minus 1 half open square brackets 1 minus cos open parentheses straight pi over 4 minus x close parentheses close square brackets
equals 1 half open square brackets cos open parentheses straight pi over 4 minus x close parentheses minus cos open parentheses straight pi over 4 plus x close parentheses close square brackets
equals 1 half open square brackets cos straight pi over 4. cos x space plus sin straight pi over 4 sin x space minus cos straight pi over 4 cos x plus sin straight pi over 4 sin x close square brackets
equals 1 half open square brackets 2 sin straight pi over 4 sin x close square brackets
equals fraction numerator 1 over denominator square root of 2 end fraction sin x space
f u n d a m e n t a l space p e r i o d space o f space sin a x space i s space fraction numerator 2 straight pi over denominator a end fraction.
S o comma space p e r i o d space o f space fraction numerator 1 over denominator square root of 2 end fraction sin x equals 2 straight pi

If f left parenthesis x right parenthesis equals sin squared space open parentheses pi over 8 plus x over 2 close parentheses minus sin squared space open parentheses pi over 8 minus x over 2 close parentheses, then the period of f(x) is

Maths-General
f left parenthesis x right parenthesis equals sin squared space open parentheses pi over 8 plus x over 2 close parentheses minus sin squared space open parentheses straight pi over 8 minus x over 2 close parentheses
equals 1 half open square brackets 1 minus cos 2 open parentheses straight pi over 8 plus x over 2 close parentheses space close square brackets minus 1 half open square brackets 1 minus cos 2 open parentheses straight pi over 8 minus x over 2 close parentheses close square brackets
equals 1 half open square brackets 1 minus cos open parentheses straight pi over 4 plus x close parentheses space close square brackets minus 1 half open square brackets 1 minus cos open parentheses straight pi over 4 minus x close parentheses close square brackets
equals 1 half open square brackets cos open parentheses straight pi over 4 minus x close parentheses minus cos open parentheses straight pi over 4 plus x close parentheses close square brackets
equals 1 half open square brackets cos straight pi over 4. cos x space plus sin straight pi over 4 sin x space minus cos straight pi over 4 cos x plus sin straight pi over 4 sin x close square brackets
equals 1 half open square brackets 2 sin straight pi over 4 sin x close square brackets
equals fraction numerator 1 over denominator square root of 2 end fraction sin x space
f u n d a m e n t a l space p e r i o d space o f space sin a x space i s space fraction numerator 2 straight pi over denominator a end fraction.
S o comma space p e r i o d space o f space fraction numerator 1 over denominator square root of 2 end fraction sin x equals 2 straight pi
General
physics-

The plot represents the flow of current through a wire at three different times.

The ratio of charges flowing through the wire at different times is

) 2 : 3 : 3
Therefore, charge is equal to area under the curve.
∴ Ist rectangle =q=lb=2
IInd rectangle =q=lb=2
I I I r d blank t r i a n g l e equals q equals fraction numerator 1 over denominator 2 end fraction l b equals 2
Hence, ratio is 1:1:1.

The plot represents the flow of current through a wire at three different times.

The ratio of charges flowing through the wire at different times is

physics-General
) 2 : 3 : 3
Therefore, charge is equal to area under the curve.
∴ Ist rectangle =q=lb=2
IInd rectangle =q=lb=2
I I I r d blank t r i a n g l e equals q equals fraction numerator 1 over denominator 2 end fraction l b equals 2
Hence, ratio is 1:1:1.