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 .

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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

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.

As are in series,

Similarly, are in parallel

are in series

Now, are in parallel.

.

As are in series,

Similarly, are in parallel

are in series

Now, are in parallel.

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

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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.

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As are in series,

Similarly, are in parallel

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The capacity of each capacitor,

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The capacity of each capacitor,

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### 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

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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 .

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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

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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

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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.