The function f x = sin π x n ! − cos π x n + 1 ! is

periodic, with period 2 n + 1 !

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The period of $f(x)=\sin 2 \sqrt{x+1}$ is:-

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Important Questions on Relation and Function

EASY

Mathematics>Algebra>Relation and Function>Periodic Functions

Consider the function

f (x) = \cos x^{2}

. Then

EASY

Mathematics>Algebra>Relation and Function>Periodic Functions

In the wave equation

y = 0.5 \sin \frac{2 π}{λ} (400 t - x) m

the velocity of the wave will be :

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Mathematics>Algebra>Relation and Function>Periodic Functions

The function $f (x) = |sin 4 x| + |cos 2 x|,$ is a periodic function with a fundamental period

HARD

Mathematics>Algebra>Relation and Function>Periodic Functions

A particle performing S.H.M. starts from the equilibrium position and its time period is

16 s

. After

2 s

its velocity is

π m s^{- 1} .

Amplitude of oscillation is

(\cos 45^{o} = \frac{1}{\sqrt 2})

HARD

Mathematics>Algebra>Relation and Function>Periodic Functions

a, b

be two fixed positive integers such that

f (a + x) = b + {[b^{3} + 1 - 3 b^{2} f (x) + 3 b {\{f (x)\}}^{2} - {\{f (x)\}}^{3}]}^{1 / 3}

for all real

x

then

f (x)

is a periodic function with period

EASY

Mathematics>Algebra>Relation and Function>Periodic Functions

The period of the function

f (x) = \cos 4 x + \tan 3 x

EASY

Mathematics>Algebra>Relation and Function>Periodic Functions

A travelling wave is described by the equation $y (x, t) = [0.05 \sin (8 x - 4 t)] m$ . The velocity of the wave is:

[All the quantities are in SI unit]

EASY

Mathematics>Algebra>Relation and Function>Periodic Functions

The period of the function

g (x) = 5 \cot (\frac{π}{3} x + \frac{π}{6}) + 2

is equal to

EASY

Mathematics>Algebra>Relation and Function>Periodic Functions

f : R \to R

is a function satisfying

f (2 x + 3) + f (2 x + 7) = 2 \forall x \in R

, then the period of

f (x)

EASY

Mathematics>Algebra>Relation and Function>Periodic Functions

A wave is represented by the equation

y = (0.02 m) \sin (5 π x - 20 t) .

The minimum distance between the two particles always having the same speed is. (Assume

x

and

t

are in SI units)

EASY

Mathematics>Algebra>Relation and Function>Periodic Functions

f (a + x) = f (x)

, then

\int_{0}^{n a} f (x) d x

, where

n \in N

, is equal to

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Mathematics>Algebra>Relation and Function>Periodic Functions

For a transvers wave travelling, along a straight line, the distance between two peaks (crests) is

5 m

, while the distance between one crest and one trough is

1.5 m

. The possible wavelengths (in

m

) of the waves are:

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Mathematics>Algebra>Relation and Function>Periodic Functions

The period of

\sin^{2} θ

EASY

Mathematics>Algebra>Relation and Function>Periodic Functions

The function

f (x) = \tan π x - x + [x]

has period, where

[.]

denotes greatest integer function

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Mathematics>Algebra>Relation and Function>Periodic Functions

The function

f (x) = \sin (\frac{π x}{n!}) - \cos (\frac{π x}{(n + 1)!})

EASY

Mathematics>Algebra>Relation and Function>Periodic Functions

Let $f (x) = \sin x + \cos a x$ be a periodic function. Then,

HARD

Mathematics>Algebra>Relation and Function>Periodic Functions

Two vectors

\vec{A}

and

\vec{B}

are defined as

\vec{A} = a \hat{i}

and

\vec{B} = a (\cos ω t \hat{i} + \sin ω t \hat{j})

, where a is a constant and

ω = \frac{π}{6} rad s^{- 1} .

|\vec{A} + \vec{B}| = \sqrt{3} |\vec{A} - \vec{B}|

at time

t = τ

for the first time, the value of

τ

in seconds, is_______

MEDIUM

Mathematics>Algebra>Relation and Function>Periodic Functions

A wave travelling along the x-axis is described by the equation

y (x, t) = 0.005 \cos (α x - β t)

. If the wavelength and the time period of the wave are

0.08 m and 2.0 s

, respectively, than

α

and

β

in appropriate unit are

MEDIUM

Mathematics>Algebra>Relation and Function>Periodic Functions

A transverse wave is described by the equation,

y = y_{0} \sin 2 π (f t - \frac{x}{λ})

. The maximum particle velocity is equal to four times the wave velocity if

EASY

Mathematics>Algebra>Relation and Function>Periodic Functions

Y = 5 \sin \frac{π}{2} (100 t - 2 x),

what is time period?

The period of $f(x)=\sin 2 \sqrt{x+1}$ is:-

Important Questions on Relation and Function

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