Maths-
General
Easy
Question
The period of 
is
Hint:
In this question we have to find the period of . Also, we know if the period of f(x) is T then the period of g(f(x)) is also T, so, we can find the period.
The correct answer is:
Period of sin
As we know, if the period of f(x) is T then the period of g(f(x)) is also T.
So, period of sin(sin
) =2
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Maths-
The period of 
is
f(x)=
Period of sin kx =
In numerator,
period of sin (
)=
In denominator,
period of sin (
)=
So, the period of f(x) is 1.
Period of sin kx =
In numerator,
period of sin (
)=In denominator,
period of sin (
)=So, the period of f(x) is 1.
The period of is
Maths-General
f(x)=
Period of sin kx =
In numerator,
period of sin ()=
In denominator,
period of sin ()=
So, the period of f(x) is 1.
Period of sin kx =
In numerator,
period of sin (
)=In denominator,
period of sin (
)=So, the period of f(x) is 1.
Maths-
Period of tan 4x+sec 4x is
f(x)= tan 4x + sec 4x
Period of tan 4x =
Period of sec 4x=
So, period of f(x)=LCM of
Period of tan 4x =
Period of sec 4x=
So, period of f(x)=LCM of
Period of tan 4x+sec 4x is
Maths-General
f(x)= tan 4x + sec 4x
Period of tan 4x =
Period of sec 4x=
So, period of f(x)=LCM of
Period of tan 4x =
Period of sec 4x=
So, period of f(x)=LCM of
Maths-
The cotangent function whose period 
is
Period of cot (k x) = 
given,
So, cotangent function whose period is
.
given,
So, cotangent function whose period is
.The cotangent function whose period is
Maths-General
Period of cot (k x) =
given,
So, cotangent function whose period is.
given,
So, cotangent function whose period is
.physics-
Thirteen resistances each of resistance R
are connected in the circuit as shown in the figure. The effective resistance between points A and B is
Resistance R bisecting the circuit can be neglected due to the symmetry of the circuit.
Now, there are four triangles
Effective resistance of each triangle
Now the given circuit reduced to
Therefore, effective resistance between A and B,
Now, there are four triangles
Effective resistance of each triangle
Now the given circuit reduced to
Therefore, effective resistance between A and B,
Thirteen resistances each of resistance R are connected in the circuit as shown in the figure. The effective resistance between points A and B is
physics-General
Resistance R bisecting the circuit can be neglected due to the symmetry of the circuit.
Now, there are four triangles
Effective resistance of each triangle
Now the given circuit reduced to
Therefore, effective resistance between A and B,
Now, there are four triangles
Effective resistance of each triangle
Now the given circuit reduced to
Therefore, effective resistance between A and B,
physics-
Six resistors, each of value 3
are connected as shown in the figure. A cell of emf 3V is connected across 
The effective resistance across 
and the current through the arm will be
The equivalent circuit is shown as
We can emit the resistance in the arm DF as balance condition is satisfied.
Therefore, the 3 resistances in arm CD and DE are in series.
Similarly, for arms CF and FE, R’’=6
are in parallel
R’’’=3
Now, R’’’ and 3 resistances are in parallel
Moreover, V across AB=3V and resistance in the arm=3
∴ Current through the arm will be
We can emit the resistance in the arm DF as balance condition is satisfied.
Therefore, the 3
resistances in arm CD and DE are in series.Similarly, for arms CF and FE, R’’=6
are in parallelR’’’=3
Now, R’’’ and 3
resistances are in parallelMoreover, V across AB=3V and resistance in the arm=3
∴ Current through the arm will be
Six resistors, each of value 3 are connected as shown in the figure. A cell of emf 3V is connected across The effective resistance across and the current through the arm will be
physics-General
The equivalent circuit is shown as
We can emit the resistance in the arm DF as balance condition is satisfied.
Therefore, the 3 resistances in arm CD and DE are in series.
Similarly, for arms CF and FE, R’’=6
are in parallel
R’’’=3
Now, R’’’ and 3 resistances are in parallel
Moreover, V across AB=3V and resistance in the arm=3
∴ Current through the arm will be
We can emit the resistance in the arm DF as balance condition is satisfied.
Therefore, the 3
resistances in arm CD and DE are in series.Similarly, for arms CF and FE, R’’=6
are in parallelR’’’=3
Now, R’’’ and 3
resistances are in parallelMoreover, V across AB=3V and resistance in the arm=3
∴ Current through the arm will be
physics-
In the circuit shown the value of I in ampere is
We can simplify the network as shown
So, net resistance,
R=2.4+1.6=4.0
Therefore, current from the battery.
Now, from the circuit (b),
4I’ =6I
But
=I+I’
So, net resistance,
R=2.4+1.6=4.0
Therefore, current from the battery.
Now, from the circuit (b),
4I’ =6I
But
=I+I’In the circuit shown the value of I in ampere is
physics-General
We can simplify the network as shown
So, net resistance,
R=2.4+1.6=4.0
Therefore, current from the battery.
Now, from the circuit (b),
4I’ =6I
But=I+I’
So, net resistance,
R=2.4+1.6=4.0
Therefore, current from the battery.
Now, from the circuit (b),
4I’ =6I
But
=I+I’physics-
The given graph shows the variation of velocity with displacement. Which one of the graph given below correctly represents the variation of acceleration with displacement?
The 
equation from the given graph can be written as,
Substituting
from Eq. (i), we get
Thus,
graph is a straight line with positive slope and negative intercept.
equation from the given graph can be written as,Substituting
from Eq. (i), we getThus,
graph is a straight line with positive slope and negative intercept.The given graph shows the variation of velocity with displacement. Which one of the graph given below correctly represents the variation of acceleration with displacement?
physics-General
The equation from the given graph can be written as,
Substituting from Eq. (i), we get
Thus, graph is a straight line with positive slope and negative intercept.
equation from the given graph can be written as,Substituting
from Eq. (i), we getThus,
graph is a straight line with positive slope and negative intercept.physics-
The displacement-time graphs of two moving particles make angles of 
with the 
axis. The ratio of their velocities is
Slope of displacement time-graph is velocity
The displacement-time graphs of two moving particles make angles of with the axis. The ratio of their velocities is
physics-General
Slope of displacement time-graph is velocity
Maths-
The minimum and maximum values of 
3x are
As we know, if f(x)=a sin x+ b cos x
Then, range of f(x)
As f(x)= 8 cos 3x - 15 sin 3x
So, range of f(x)
Then, range of f(x)
As f(x)= 8 cos 3x - 15 sin 3x
So, range of f(x)
The minimum and maximum values of 3x are
Maths-General
As we know, if f(x)=a sin x+ b cos x
Then, range of f(x)
As f(x)= 8 cos 3x - 15 sin 3x
So, range of f(x)
Then, range of f(x)
As f(x)= 8 cos 3x - 15 sin 3x
So, range of f(x)
Maths-
Extreme Values:The range of 
Extreme Values:The range of
Maths-General
physics-
What is the equivalent resistance between 
in the given circuit?
and 
are in series
are in parallel
and 
are in series
and 
are in parallel
and 
are in series
Now,
and 
are in parallel
What is the equivalent resistance between in the given circuit?
physics-General
and are in series are in paralleland are in series and are in parallel and are in seriesNow,
and are in parallelphysics-
The current in the 1 resistor shown in the circuit is
In the given circuit 4 resistors are connected in parallel, this combination is connected in series with 1 resistance.
Also, R’’=2 +1 =3
From Ohm’s law,
resistors are connected in parallel, this combination is connected in series with 1 resistance.Also, R’’=2
+1 =3From Ohm’s law,
The current in the 1 resistor shown in the circuit is
physics-General
In the given circuit 4 resistors are connected in parallel, this combination is connected in series with 1 resistance.
Also, R’’=2 +1 =3
From Ohm’s law,
resistors are connected in parallel, this combination is connected in series with 1 resistance.Also, R’’=2
+1 =3From Ohm’s law,
physics-
The current in the 1 resistor shown in the circuit is
In the given circuit 4 resistors are connected in parallel, this combination is connected in series with 1 resistance.
Also, R’’=2 +1 =3
From Ohm’s law,
resistors are connected in parallel, this combination is connected in series with 1 resistance.Also, R’’=2
+1 =3From Ohm’s law,
The current in the 1 resistor shown in the circuit is
physics-General
In the given circuit 4 resistors are connected in parallel, this combination is connected in series with 1 resistance.
Also, R’’=2 +1 =3
From Ohm’s law,
resistors are connected in parallel, this combination is connected in series with 1 resistance.Also, R’’=2
+1 =3From Ohm’s law,
physics-
The total current supplied to the given circuit by the battery is
The equivalent circuit of the given circuit is as shown
Resistances 6 and 2 are in parallel
Resistances
Resistances 3 and 3 are in parallel
The current,
Resistances 6
and 2 are in parallelResistances
Resistances 3
and 3 are in parallelThe current,
The total current supplied to the given circuit by the battery is
physics-General
The equivalent circuit of the given circuit is as shown
Resistances 6 and 2 are in parallel
Resistances
Resistances 3 and 3 are in parallel
The current,
Resistances 6
and 2 are in parallelResistances
Resistances 3
and 3 are in parallelThe current,
physics-
A current of 2A flows in an electric circuit as shown in figure. The potential difference
, in volts( 
are potentials at R and S respectively) is
Current through each arm
PRQ and PSQ=1A
From Eqs. (i) and (ii), we get
PRQ and PSQ=1A
From Eqs. (i) and (ii), we get
A current of 2A flows in an electric circuit as shown in figure. The potential difference, in volts( are potentials at R and S respectively) is
physics-General
Current through each arm
PRQ and PSQ=1A
From Eqs. (i) and (ii), we get
PRQ and PSQ=1A
From Eqs. (i) and (ii), we get