Maths-
General
Easy
Question
Period of
is
Hint:
In this question we have to find the fundamental period oof f(x). As we know, by fundamental property of f(x) periodic function with period T, f(x+T) will be equal to f(x). Now, we will look at the options and check which one will satisfies the statement.
The correct answer is: 
By fundamental property of f(x) periodic function with period T.
f (x+T) =f(x)
let f (x) =
assuming from the options smallest period of f(x) to be
.

Related Questions to study
physics-
Two inclined planes are located as shown in figure. A particle is projected from the foot of one frictionless plane along its line with a velocity just sufficient to carry it to top after which the particle slides down the other frictionless inclined plane. The total time it will take to reach the point
is

The time of ascent = time of descent 
total time of flight 





or




or
Two inclined planes are located as shown in figure. A particle is projected from the foot of one frictionless plane along its line with a velocity just sufficient to carry it to top after which the particle slides down the other frictionless inclined plane. The total time it will take to reach the point
is

physics-General
The time of ascent = time of descent 
total time of flight 





or




or
physics-
characteristic of a copper wire of length
and area of cross-section
is shown in figure. The slope of the curve becomes

Slope of graph

If experiment is performed at higher temperature then resistance increase and hence slope decrease, choice (a) is wrong.
Similarly in choice (b) and (c) resistance increase.
But for choice (d) resistance R increases, so slope decreases
If experiment is performed at higher temperature then resistance increase and hence slope decrease, choice (a) is wrong.
Similarly in choice (b) and (c) resistance increase.
But for choice (d) resistance R increases, so slope decreases
characteristic of a copper wire of length
and area of cross-section
is shown in figure. The slope of the curve becomes

physics-General
Slope of graph

If experiment is performed at higher temperature then resistance increase and hence slope decrease, choice (a) is wrong.
Similarly in choice (b) and (c) resistance increase.
But for choice (d) resistance R increases, so slope decreases
If experiment is performed at higher temperature then resistance increase and hence slope decrease, choice (a) is wrong.
Similarly in choice (b) and (c) resistance increase.
But for choice (d) resistance R increases, so slope decreases
physics-
Four concurrent coplanar forces in newton are acting at a point and keep it in equilibrium figure. Then values of
and
are

In equilibrium position along
-direction
2 sin 60
or
or 
As
or 
Along
-direction, 

N
2 sin 60
or
As
Along
Four concurrent coplanar forces in newton are acting at a point and keep it in equilibrium figure. Then values of
and
are

physics-General
In equilibrium position along
-direction
2 sin 60
or
or 
As
or 
Along
-direction, 

N
2 sin 60
or
As
Along
physics-
The effective capacitance between points
and
shown in figure. Assuming
F and that outer capacitors are all
F is

The arrangement shows a Wheatstone bridge.
As
therefore the bridge is balanced.

Similarly,
effective capacitance

As
Similarly,
The effective capacitance between points
and
shown in figure. Assuming
F and that outer capacitors are all
F is

physics-General
The arrangement shows a Wheatstone bridge.
As
therefore the bridge is balanced.

Similarly,
effective capacitance

As
Similarly,
physics-
The four capacitors, each of 25
F 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


The four capacitors, each of 25
F 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


physics-
For the circuit shown in figure the charge on 4
F capacitor is

Combined capacity of
and
= 1 + 5=
Now,
and
are in series.


Charge in the arm containing
capacitor is

Now,
Charge in the arm containing
For the circuit shown in figure the charge on 4
F capacitor is

physics-General
Combined capacity of
and
= 1 + 5=
Now,
and
are in series.


Charge in the arm containing
capacitor is

Now,
Charge in the arm containing
physics-
The variation of electric potential with distance from a fixed point is shown in figure. What is the value of electric field at
=2 m.

The variation of electric potential with distance from a fixed point is shown in figure. What is the value of electric field at
=2 m.

physics-General
Maths-
The integrating factor of the differential equation
is given by
The integrating factor of the differential equation
is given by
Maths-General
physics-
As shown in figure, if the point
is earthed and the point
is given a potential of 2000 V, then the potential at point
will be

Equivalent capacitance between points
is

Now equivalent capacitance between points
is

Charge on capacitor of capacity 5
is

(Since, potential at the point
will be zero)
Now, potential difference across capacitor of 5
is
=1500volt
As,
volt
Hence,
volt.
Now equivalent capacitance between points
Charge on capacitor of capacity 5
(Since, potential at the point
Now, potential difference across capacitor of 5
As,
Hence,
As shown in figure, if the point
is earthed and the point
is given a potential of 2000 V, then the potential at point
will be

physics-General
Equivalent capacitance between points
is

Now equivalent capacitance between points
is

Charge on capacitor of capacity 5
is

(Since, potential at the point
will be zero)
Now, potential difference across capacitor of 5
is
=1500volt
As,
volt
Hence,
volt.
Now equivalent capacitance between points
Charge on capacitor of capacity 5
(Since, potential at the point
Now, potential difference across capacitor of 5
As,
Hence,
physics-
The equivalent capacitance between points
for the combination of capacitors shown in figure, where all capacitances are in microfarad is

all the three capacitors are connected in parallel. Therefore, equivalent capacitance between points
is
.


As
are in series,


Similarly,
are in parallel

are in series


Now,
are in parallel.


As
Similarly,
Now,
The equivalent capacitance between points
for the combination of capacitors shown in figure, where all capacitances are in microfarad is

physics-General
all the three capacitors are connected in parallel. Therefore, equivalent capacitance between points
is
.


As
are in series,


Similarly,
are in parallel

are in series


Now,
are in parallel.


As
Similarly,
Now,
physics-
The effective capacitance between points
is


The effective capacitance between points
is

physics-General

physics-
A gang capacitor is formed by interlocking a number of plates as shown in figure. The distance between the consecutive plates is 0.885 cm and the overlapping area of the plates is
The capacity of the unit is

The given arrangement of nine plates is equivalent to the parallel combination of 8 capacitors.
The capacity of each capacitor,


Hence, the capacity of 8 capacitors

The capacity of each capacitor,
Hence, the capacity of 8 capacitors
A gang capacitor is formed by interlocking a number of plates as shown in figure. The distance between the consecutive plates is 0.885 cm and the overlapping area of the plates is
The capacity of the unit is

physics-General
The given arrangement of nine plates is equivalent to the parallel combination of 8 capacitors.
The capacity of each capacitor,


Hence, the capacity of 8 capacitors

The capacity of each capacitor,
Hence, the capacity of 8 capacitors
physics-
A parallel plate capacitor with air as the dielectric has capacitance
A slab of dielectric constant
and having the same thickness as the separation between the plates is introduced so as to fill one-fourth of the capacitor as shown in the figure. The new capacitance will be

The capacitor with air as the dielectric has capacitance

Similarly, the capacitor with
as the dielectric constant has capacitance 
Since,
are in parallel




Similarly, the capacitor with
Since,
A parallel plate capacitor with air as the dielectric has capacitance
A slab of dielectric constant
and having the same thickness as the separation between the plates is introduced so as to fill one-fourth of the capacitor as shown in the figure. The new capacitance will be

physics-General
The capacitor with air as the dielectric has capacitance

Similarly, the capacitor with
as the dielectric constant has capacitance 
Since,
are in parallel




Similarly, the capacitor with
Since,
physics-
Four capacitors are connected in a circuit as shown in the following figure. Calculate the effective capacitance between the points
.

Effective capacitance of 


Now,
are in parallel, therefore effective capacitance 

Now,
are in series, therefore,
effective capacitance between points


Now,
Now,
effective capacitance between points
Four capacitors are connected in a circuit as shown in the following figure. Calculate the effective capacitance between the points
.

physics-General
Effective capacitance of 


Now,
are in parallel, therefore effective capacitance 

Now,
are in series, therefore,
effective capacitance between points


Now,
Now,
effective capacitance between points
physics-
Equivalent capacitance between
is


The capacitors 2
So, equivalent capacitance now is 2
This capacitance is now in series with 2
So, final effective capacitance=2
Equivalent capacitance between
is

physics-General

The capacitors 2
So, equivalent capacitance now is 2
This capacitance is now in series with 2
So, final effective capacitance=2