If f x = x - x 4 , x ∈ R , where x denotes the greatest integer function, then:

l i m x → 4 + f x exists but l i m x → 4 - f x does not exist

l i m x → 4 - f x exists but l i m x → 4 + f x does not exist

Both l i m x → 4 - f x and l i m x → 4 + f x exist but are not equal

Check the continuity of the function f x = 2 x + 3 at x = 1 .

Given, f x = 2 x + 3 Here the function f x is said to be continuous at x = 1 if lim x → 1 f x = f 1 Now The function is defined at the given point x = 1 And its value is f 1 = 2 × 1 + 3 = 5 Now, limit of the function at x = 1 lim x → 1 f x = lim x → 1 2 x + 3 = 2 1 + 3 = 5 Thus lim x → 1 f x = 5 = f 1 Hence, f is continuous at x = 1 .

The function f x = e x is

continuous everywhere but not differentiable at x = 0

continuous and differentiable everywhere

Match List - I with List - II. List-I List-II (a) Source of microwave frequency (i) Radioactive decay of nucleus (b) Source of infrared frequency (ii) Magnetron (c) Source of Gamma Rays (iii) Inner shell electrons (d) Source of X -rays (iv) Vibration of atoms and molecules (v) LASER (vi) RC circuit Choose the correct answer from the options given below:

(a)-(ii), (b)-(iv), (c)-(i), (d)-(iii)

(a)-(ii), (b)-(iv), (c)-(vi), (d)-(iii)

(a)-(vi), (b)-(iv), (c)-(i), (d)-(v)

(a)-(vi), (b)-(v), (c)-(i), (d)-(iv)

The function f x = x + x - 1 is

continuous at x = 0 as well as at x = 1

continuous at x = 1 b ut not at x = 0

discontinuous at x = 0 as well as at x = 1

continuous at x = 0 b ut not at x = 1

Let f : R → R be a function defined as f x = 5 , i f x ≤ 1 a + b x , i f 1 < x < 3 b + 5 x , i f 3 ≤ x < 5 30 , i f x ≥ 5 Then f is:

not continuous for any values of a and b

continuous if a = - 5 and b = 10

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Important Questions on Electromagnetic Waves

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f (x) = [x] - [\frac{x}{4}], x \in R,

where

[x]

denotes the greatest integer function, then:

HARD

Physics>Modern Physics>Electromagnetic Waves>Sources of Electromagnetic Waves

Let

[x]

be the greatest integer less than or equals to

x

. Then, at which of the following point(s) the function

f (x) = x \cos (π (x + [x]))

is discontinuous?

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If the function

f

defined on

(\frac{π}{6}, \frac{π}{3})

f (x) = \{\begin{matrix} \frac{\sqrt{2} c o s x - 1}{c o t x - 1}, x \neq \frac{π}{4} \\ k, x = \frac{π}{4} \end{matrix}

is continuous, then

k

is equal to

EASY

Physics>Modern Physics>Electromagnetic Waves>Sources of Electromagnetic Waves

The function

f (x) = \tan x

is discontinuous on the set

EASY

Physics>Modern Physics>Electromagnetic Waves>Sources of Electromagnetic Waves

Long distance short- wave radio broadcasting uses

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Physics>Modern Physics>Electromagnetic Waves>Sources of Electromagnetic Waves

f (x) = \{\begin{matrix} \frac{s i n (p + 1) x + s i n x}{x} & , & x < 0 \\ q & , & x = 0 \\ \frac{\sqrt{x + x^{2}} - \sqrt{x}}{x^{3 / 2}} & , & x > 0 \end{matrix}

is continuous at

x = 0

, then the ordered pair

(p, q)

is equal to:

EASY

Physics>Modern Physics>Electromagnetic Waves>Sources of Electromagnetic Waves

Let

f : [- 1,3] \to R

be defined as

f (x) = \{\begin{matrix} |x| + [x], \\ x + |x|, \\ x + [x], \end{matrix} \begin{matrix} - 1 \leq x < 1 \\ 1 \leq x < 2 \\ 2 \leq x \leq 3, \end{matrix}

Where

[t]

denotes the greatest integer less than or equal to

t

. Then,

f

is discontinuous at:

EASY

Physics>Modern Physics>Electromagnetic Waves>Sources of Electromagnetic Waves

Check the continuity of the function

f (x) = 2 x + 3

x = 1

EASY

Physics>Modern Physics>Electromagnetic Waves>Sources of Electromagnetic Waves

Equation for wave vector is:

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Physics>Modern Physics>Electromagnetic Waves>Sources of Electromagnetic Waves

If the function

f

defined as

f (x) = \frac{1}{x} - \frac{k - 1}{e^{2 x} - 1}, x \neq 0

is continuous at

x = 0

, then ordered pair

(k, f (0))

is equal to

HARD

Physics>Modern Physics>Electromagnetic Waves>Sources of Electromagnetic Waves

The function

f (x) = e^{|x|}

EASY

Physics>Modern Physics>Electromagnetic Waves>Sources of Electromagnetic Waves

Match List - I with List - II.

List-I		List-II
(a)	Source of microwave frequency	(i)	Radioactive decay of nucleus
(b)	Source of infrared frequency	(ii)	Magnetron
(c)	Source of Gamma Rays	(iii)	Inner shell electrons
(d)	Source of $X$ -rays	(iv)	Vibration of atoms and molecules
		(v)	LASER
		(vi)	RC circuit

Choose the correct answer from the options given below:

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The function

f (x) = |x| + |x - 1|

EASY

Physics>Modern Physics>Electromagnetic Waves>Sources of Electromagnetic Waves

If the function

f (x) = \{\begin{matrix} a |π - x| + 1, x \leq 5 \\ b |x - π| + 3, x > 5 \end{matrix}

is continuous at

x = 5,

then the value of

a - b

is:

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Show that the function

f (x) = 2 x - |x|

is continuous at

x = 0

but not differentiable at

x = 0

EASY

Physics>Modern Physics>Electromagnetic Waves>Sources of Electromagnetic Waves

A donor impurity results in

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Physics>Modern Physics>Electromagnetic Waves>Sources of Electromagnetic Waves

Let

f : R \to R

be a function defined as

f (x) = \{\begin{matrix} 5, i f x \leq 1 \\ a + b x, i f 1 < x < 3 \\ b + 5 x, i f 3 \leq x < 5 \\ 30, i f x \geq 5 \end{matrix}

Then

f

is:

EASY

Physics>Modern Physics>Electromagnetic Waves>Sources of Electromagnetic Waves

The value of

k

which the function

f (x) = \{\begin{matrix} {(\frac{4}{5})}^{\frac{\tan 4 x}{\tan 5 x}}, & 0 < x < \frac{π}{2} \\ k + \frac{2}{5}, & x = \frac{π}{2} \end{matrix}

is continuous at

x = \frac{π}{2},

EASY

Physics>Modern Physics>Electromagnetic Waves>Sources of Electromagnetic Waves

The source of electromagnetic wave can be a charge.

EASY

Physics>Modern Physics>Electromagnetic Waves>Sources of Electromagnetic Waves

Out of the following options which one can be used to produce a propagating electromagnetic wave?

What is the primary medium of communication in quaternary activities?

Important Questions on Electromagnetic Waves

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