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
total time of flight 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
total time of flight 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
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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
-direction2 sin 60
or
or As
or Along
-direction, NFour 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
-direction2 sin 60
or
or As
or Along
-direction, N
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
therefore the bridge is balanced.Similarly,
effective capacitanceThe 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.
Astherefore the bridge is balanced.
Similarly,
effective capacitance
As
therefore the bridge is balanced.Similarly,
effective capacitancephysics-
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
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physics-
For the circuit shown in figure the charge on 4F capacitor is
Combined capacity of 
and 
= 1 + 5=
Now,
and 
are in series.
Charge in the arm containingcapacitor is
and = 1 + 5=Now,
and are in series.Charge in the arm containing
capacitor isFor the circuit shown in figure the charge on 4F capacitor is
physics-General
Combined capacity of and = 1 + 5=
Now,and are in series.
Charge in the arm containingcapacitor is
and = 1 + 5=Now,
and are in series.Charge in the arm containing
capacitor is
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.
isNow equivalent capacitance between points
isCharge on capacitor of capacity 5
is(Since, potential at the point
will be zero)Now, potential difference across capacitor of 5
is=1500voltAs,
voltHence,
volt.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.
isNow equivalent capacitance between points
isCharge on capacitor of capacity 5
is(Since, potential at the point
will be zero)Now, potential difference across capacitor of 5
is=1500voltAs,
voltHence,
volt.
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.
is.As
are in series,Similarly,
are in parallel are in seriesNow,
are in parallel.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
.
Asare in series,
Similarly, are in parallel
are in series
Now, are in parallel.
is.As
are in series,Similarly,
are in parallel are in seriesNow,
are in parallel.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
as the dielectric constant has capacitance Since,
are in parallelA 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
as the dielectric constant has capacitance Since,
are in parallelphysics-
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,
are in parallel, therefore effective capacitance Now,
are in series, therefore,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,
are in parallel, therefore effective capacitance Now,
are in series, therefore,effective capacitance between points
physics-
Equivalent capacitance between is
The capacitors 2
and 2 of arm 
are in series. So, their equivalent capacitance is 1 which is in parallel with capacitor of 1 of arm 
.So, equivalent capacitance now is 2
.This capacitance is now in series with 2
capacitance of arm 
which equivalents to 1 is in parallel with 1 capacitance of arm 
So, final effective capacitance=2
.Equivalent capacitance between is
physics-General
The capacitors 2
and 2 of arm are in series. So, their equivalent capacitance is 1 which is in parallel with capacitor of 1 of arm .So, equivalent capacitance now is 2
.This capacitance is now in series with 2
capacitance of arm which equivalents to 1 is in parallel with 1 capacitance of arm So, final effective capacitance=2
.
