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

periodic, with period 2 n + 1 !

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

periodic, with period 2 n + 1 !

A wave pulse in a string is described by the equation y 1 = 5 3 x - 4 t 2 + 2 and another wave pulse in the same string is described by y 2 = - 5 3 x + 4 t - 6 2 + 2 . The values of y 1 , y 2 and x are in metres and t is in seconds. Which of the following statement is correct?

At x = 1 m , y 1 and y 2 always cancel

y 1 travels along - x -direction and y 2 along + x -direction

Both y 1 and y 2 travel along + x -direction

At time t = 1 s , y 1 and y 2 exactly cancel everywhere

At time t = 3 s , y 1 and y 2 exactly cancel everywhere

MEDIUM

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

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Important Questions on Functions

HARD

Mathematics>Differential Calculus>Functions>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_______

EASY

Mathematics>Differential Calculus>Functions>Periodic Functions

f (a + x) = f (x)

, then

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

, where

n \in N

, is equal to

MEDIUM

Mathematics>Differential Calculus>Functions>Periodic Functions

The period of

\sin^{2} θ

EASY

Mathematics>Differential Calculus>Functions>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)

HARD

Mathematics>Differential Calculus>Functions>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

MEDIUM

Mathematics>Differential Calculus>Functions>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:

EASY

Mathematics>Differential Calculus>Functions>Periodic Functions

The period of the function

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

is equal to

EASY

Mathematics>Differential Calculus>Functions>Periodic Functions

The maximum transverse velocity and maximum transverse acceleration of a harmonic wave in a

o n e - d i m e n s i o n a l

string are

1 m s^{- 1}

and

1 m s^{- 2}

respectively. The phase velocity of the wave is

1 m s^{- 1}

. The waveform is

EASY

Mathematics>Differential Calculus>Functions>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>Differential Calculus>Functions>Periodic Functions

The function

f (x) = \tan π x - x + [x]

has period, where

[.]

denotes greatest integer function

EASY

Mathematics>Differential Calculus>Functions>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 :

EASY

Mathematics>Differential Calculus>Functions>Periodic Functions

Consider the function

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

. Then

EASY

Mathematics>Differential Calculus>Functions>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]

HARD

Mathematics>Differential Calculus>Functions>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})

MEDIUM

Mathematics>Differential Calculus>Functions>Periodic Functions

A simple harmonic motion is represented by:

y = 5 (\sin 3 π t + \sqrt{3} \cos 3 π t) cm

The amplitude and time period of the motion are:

MEDIUM

Mathematics>Differential Calculus>Functions>Periodic Functions

A wave pulse in a string is described by the equation

y_{1} = \frac{5}{{(3 x - 4 t)}^{2} + 2}

and another wave pulse in the same string is described by

y_{2} = \frac{- 5}{{(3 x + 4 t - 6)}^{2} + 2}

. The values of

y_{1}, y_{2}

and

x

are in metres and

t

is in seconds. Which of the following statement is correct?

EASY

Mathematics>Differential Calculus>Functions>Periodic Functions

Consider a wire with density

(d)

and stress

(σ) .

For the same density, if the stress increases

2

times, the speed of the transverse waves along the wire changes by

EASY

Mathematics>Differential Calculus>Functions>Periodic Functions

The period of the function

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

EASY

Mathematics>Differential Calculus>Functions>Periodic Functions

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

MEDIUM

Mathematics>Differential Calculus>Functions>Periodic Functions

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

The function fx=sinπxn!−cosπxn+1! is

Important Questions on Functions

Learn and Prepare for any exam you want !

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