The equation of the circle touching the initial line at pole an-Turito

Maths-

General

Easy

Question

The equation of the circle touching the initial line at pole and radius 2 is

$r = 2 s i n θ$
$r = 4 s i n θ$
$r = 2 C o s θ$
$r = 4 C o s θ$

The correct answer is: $r equals 4 s i n space theta$

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A small source of sound moves on a circle as shown in the figure and an observer is standing on $O.$ Let $n subscript 1 end subscript comma n subscript 2 end subscript$ and $n subscript 3 end subscript$ be the frequencies heard when the source is at $A comma blank B blank$ and $C$ respectively. Then

At point

A comma

source is moving away from observer so apparent frequency

n subscript 1 end subscript less than n

(actual frequency) At point

B

source is coming towards observer so apparent frequency

n subscript 2 end subscript greater than n

and point

C

source is moving perpendicular to observer so

n subscript 3 end subscript equals n

Hence

n subscript 2 end subscript greater than n subscript 3 end subscript greater than n subscript 1 end subscript

A small source of sound moves on a circle as shown in the figure and an observer is standing on $O.$ Let $n subscript 1 end subscript comma n subscript 2 end subscript$ and $n subscript 3 end subscript$ be the frequencies heard when the source is at $A comma blank B blank$ and $C$ respectively. Then

physics-General

At point

A comma

source is moving away from observer so apparent frequency

n subscript 1 end subscript less than n

(actual frequency) At point

B

source is coming towards observer so apparent frequency

n subscript 2 end subscript greater than n

and point

C

source is moving perpendicular to observer so

n subscript 3 end subscript equals n

Hence

n subscript 2 end subscript greater than n subscript 3 end subscript greater than n subscript 1 end subscript

General

maths-

In a triangle ABC, if a : b : c = 7 : 8 : 9, then cos A : cos B equals to

maths-General

General

physics-

Which of the following curves represents correctly the oscillation given by $y equals y subscript 0 end subscript sin invisible function application open parentheses omega t minus ϕ close parentheses comma blank w h e r e blank 0 less than ϕ less than 90$

Given equation

y equals y subscript 0 end subscript sin invisible function application left parenthesis omega t minus ϕ right parenthesis

t equals 0 comma blank y equals negative y subscript 0 end subscript sin invisible function application ϕ

This is case with curve marked

D

Which of the following curves represents correctly the oscillation given by $y equals y subscript 0 end subscript sin invisible function application open parentheses omega t minus ϕ close parentheses comma blank w h e r e blank 0 less than ϕ less than 90$

physics-General

Given equation

y equals y subscript 0 end subscript sin invisible function application left parenthesis omega t minus ϕ right parenthesis

t equals 0 comma blank y equals negative y subscript 0 end subscript sin invisible function application ϕ

This is case with curve marked

D

General

maths-

A is a set containing n elements. A subset P₁ is chosen, and A is reconstructed by replacing the elements of P₁. The same process is repeated for subsets P₁, P₂, … , P_m, with m > 1. The Number of ways of choosing P₁, P₂, …, P_m so that P₁ $union$ P₂ $union$ … $union$ P_m= A is -

Let A = {a₁, a₂,…..a_n}.
For each a_i (1

less or equal than

less or equal than

n), either a_i

element of

P_j or a_i

not an element of

P_j (1

less or equal than

less or equal than

m) . Thus, there are 2^m choices in which a_i (1

less or equal than

less or equal than

n) may belong to the P_j

apostrophe

s.
Also there is exactly one choice, viz., a_i

not an element of

P_j for j = 1, 2, …, m, for which a_i

not an element of

P₁

union

P₂

union

...

union

P_m.
Therefore, a_i

not an element of

P₁

union

P₂

union

….

union

P_m in (2^m – 1) ways . Since there are n elements in the set A, the number of ways of constructing subsets
P₁, P₂, ….. , P_m is (2^m – 1)ⁿ

A is a set containing n elements. A subset P₁ is chosen, and A is reconstructed by replacing the elements of P₁. The same process is repeated for subsets P₁, P₂, … , P_m, with m > 1. The Number of ways of choosing P₁, P₂, …, P_m so that P₁ $union$ P₂ $union$ … $union$ P_m= A is -

maths-General

Let A = {a₁, a₂,…..a_n}.
For each a_i (1

less or equal than

less or equal than

n), either a_i

element of

P_j or a_i

not an element of

P_j (1

less or equal than

less or equal than

m) . Thus, there are 2^m choices in which a_i (1

less or equal than

less or equal than

n) may belong to the P_j

apostrophe

s.
Also there is exactly one choice, viz., a_i

not an element of

P_j for j = 1, 2, …, m, for which a_i

not an element of

P₁

union

P₂

union

...

union

P_m.
Therefore, a_i

not an element of

P₁

union

P₂

union

….

union

P_m in (2^m – 1) ways . Since there are n elements in the set A, the number of ways of constructing subsets
P₁, P₂, ….. , P_m is (2^m – 1)ⁿ

General

maths-

The number of points in the Cartesian plane with integral co-ordinates satisfying the inequalities |x| $less or equal than$ k, |y| $less or equal than$ k, |x – y| $less or equal than$ k ; is-

|x|

less or equal than

rightwards double arrow

–k

less or equal than

less or equal than

k ….(1)
& |y|

less or equal than

rightwards double arrow

–k

less or equal than

less or equal than

k ….(2)

& |x – y|

less or equal than

rightwards double arrow

|y – x|

less or equal than

rightwards double arrow

–k

less or equal than

y – x

less or equal than

rightwards double arrow

x – k

less or equal than

less or equal than

x + k ….(3)

therefore

Number of points having integral coordinates
= (2k + 1)² – 2
= (3k² + 3k + 1).

The number of points in the Cartesian plane with integral co-ordinates satisfying the inequalities |x| $less or equal than$ k, |y| $less or equal than$ k, |x – y| $less or equal than$ k ; is-

maths-General

|x|

less or equal than

rightwards double arrow

–k

less or equal than

less or equal than

k ….(1)
& |y|

less or equal than

rightwards double arrow

–k

less or equal than

less or equal than

k ….(2)

& |x – y|

less or equal than

rightwards double arrow

|y – x|

less or equal than

rightwards double arrow

–k

less or equal than

y – x

less or equal than

rightwards double arrow

x – k

less or equal than

less or equal than

x + k ….(3)

therefore

Number of points having integral coordinates
= (2k + 1)² – 2
= (3k² + 3k + 1).

General

maths-

The angle between the lines $r left square bracket 2 C o s space theta plus 5 S i n space theta right square bracket equals 3$ and $r left square bracket 2 s i n space theta minus 5 C o s space theta right square bracket plus 4 equals 0$ is

maths-General

General

maths-

The polar equation of the straight line passing through $open parentheses 6 comma fraction numerator pi over denominator 3 end fraction close parentheses$ and perpendicular to the initial line is

maths-General

General

maths-

The polar equation of the straight line passing through $open parentheses 2 comma fraction numerator pi over denominator 6 end fraction close parentheses$ and parallel to the initial line is

maths-General

General

maths-

The equation of the line passing through pole and $open parentheses 2 comma fraction numerator pi over denominator 3 end fraction close parentheses$ is

maths-General

General

maths-

The polar equation of $y to the power of 2 end exponent equals 4 x$ is

maths-General

General

maths-

The cartesian equation of $r equals a s i n space 2 theta$ is

maths-General

General

physics-

Two tuning forks $P$ and $Q$ are vibrated together. The number of beats produced are represented by the straight line $O A$ in the following graph. After loading $Q$ with wax again these are vibrated together and the beats produced are represented by the line $O B.$ If the frequency of $P$ is $341 H z comma$ the frequency of $Q$ will be

n subscript Q end subscript equals 341 plus-or-minus 3 equals 344 H z

338 H z

On waxing

Q comma

the number of beats decreases hence

n subscript Q end subscript equals 344 H z

Two tuning forks $P$ and $Q$ are vibrated together. The number of beats produced are represented by the straight line $O A$ in the following graph. After loading $Q$ with wax again these are vibrated together and the beats produced are represented by the line $O B.$ If the frequency of $P$ is $341 H z comma$ the frequency of $Q$ will be

physics-General

n subscript Q end subscript equals 341 plus-or-minus 3 equals 344 H z

338 H z

On waxing

Q comma

the number of beats decreases hence

n subscript Q end subscript equals 344 H z

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The equation of the circle touching the initial line at pole and radius 2 is

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The correct answer is:

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A is a set containing n elements. A subset P1 is chosen, and A is reconstructed by replacing the elements of P1. The same process is repeated for subsets P1, P2, … , Pm, with m > 1. The Number of ways of choosing P1, P2, …, Pm so that P1 P2 … Pm= A is -

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Two tuning forks and are vibrated together. The number of beats produced are represented by the straight line in the following graph. After loading with wax again these are vibrated together and the beats produced are represented by the line If the frequency of is the frequency of will be

Two tuning forks and are vibrated together. The number of beats produced are represented by the straight line in the following graph. After loading with wax again these are vibrated together and the beats produced are represented by the line If the frequency of is the frequency of will be

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The correct answer is: $r equals 4 s i n space theta$

(Area of $increment$ GPL) to (Area of $increment$ ALD) is equal to

(Area of $increment$ GPL) to (Area of $increment$ ALD) is equal to

Which of the following curves represents correctly the oscillation given by $y equals y subscript 0 end subscript sin invisible function application open parentheses omega t minus ϕ close parentheses comma blank w h e r e blank 0 less than ϕ less than 90$

Which of the following curves represents correctly the oscillation given by $y equals y subscript 0 end subscript sin invisible function application open parentheses omega t minus ϕ close parentheses comma blank w h e r e blank 0 less than ϕ less than 90$

The number of points in the Cartesian plane with integral co-ordinates satisfying the inequalities |x| $less or equal than$ k, |y| $less or equal than$ k, |x – y| $less or equal than$ k ; is-

The number of points in the Cartesian plane with integral co-ordinates satisfying the inequalities |x| $less or equal than$ k, |y| $less or equal than$ k, |x – y| $less or equal than$ k ; is-

The angle between the lines $r left square bracket 2 C o s space theta plus 5 S i n space theta right square bracket equals 3$ and $r left square bracket 2 s i n space theta minus 5 C o s space theta right square bracket plus 4 equals 0$ is

The angle between the lines $r left square bracket 2 C o s space theta plus 5 S i n space theta right square bracket equals 3$ and $r left square bracket 2 s i n space theta minus 5 C o s space theta right square bracket plus 4 equals 0$ is

The polar equation of the straight line passing through $open parentheses 6 comma fraction numerator pi over denominator 3 end fraction close parentheses$ and perpendicular to the initial line is

The polar equation of the straight line passing through $open parentheses 6 comma fraction numerator pi over denominator 3 end fraction close parentheses$ and perpendicular to the initial line is

The polar equation of the straight line passing through $open parentheses 2 comma fraction numerator pi over denominator 6 end fraction close parentheses$ and parallel to the initial line is

The polar equation of the straight line passing through $open parentheses 2 comma fraction numerator pi over denominator 6 end fraction close parentheses$ and parallel to the initial line is

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The equation of the line passing through pole and $open parentheses 2 comma fraction numerator pi over denominator 3 end fraction close parentheses$ is

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The polar equation of $y to the power of 2 end exponent equals 4 x$ is

The cartesian equation of $r equals a s i n space 2 theta$ is

The cartesian equation of $r equals a s i n space 2 theta$ is