Maths-
General
Easy

Question

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

  1. r equals 2 s i n space theta    
  2. r equals 4 s i n space theta    
  3. r equals 2 C o s space theta    
  4. r equals 4 C o s space theta    

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

Book A Free Demo

+91

Grade*

Related Questions to study

General
maths-

The equation of the circle passing through pole and centre at (4,0) is

The equation of the circle passing through pole and centre at (4,0) is

maths-General
General
maths-

The polar equation of the circle with pole as centre and radius 3 is

The polar equation of the circle with pole as centre and radius 3 is

maths-General
General
maths-

(Area of incrementGPL) to (Area of incrementALD) is equal to

(Area of incrementGPL) to (Area of incrementALD) is equal to

maths-General
General
physics-

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 blankand 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 blankand 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

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
At 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
At 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, … , Pm, with m > 1. The Number of ways of choosing P1, P2, …, Pm so that P1 union P2 union … union Pm= A is -

Let A = {a1, a2,…..an}.
For each ai (1 less or equal thanless or equal than n), either ai element of Pj or ai not an element of Pj (1 less or equal thanless or equal than m) . Thus, there are 2m choices in which ai (1 less or equal thanless or equal than  n) may belong to the Pj apostrophes.
Also there is exactly one choice, viz., ai not an element of Pj for j = 1, 2, …, m, for which ai not an element of P1 union P2 union...union Pm.
Therefore, ai not an element of P1 union P2 union …. union Pm in (2m – 1) ways . Since there are n elements in the set A, the number of ways of constructing subsets
P1, P2, ….. , Pm is (2m – 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, … , Pm, with m > 1. The Number of ways of choosing P1, P2, …, Pm so that P1 union P2 union … union Pm= A is -

maths-General
Let A = {a1, a2,…..an}.
For each ai (1 less or equal thanless or equal than n), either ai element of Pj or ai not an element of Pj (1 less or equal thanless or equal than m) . Thus, there are 2m choices in which ai (1 less or equal thanless or equal than  n) may belong to the Pj apostrophes.
Also there is exactly one choice, viz., ai not an element of Pj for j = 1, 2, …, m, for which ai not an element of P1 union P2 union...union Pm.
Therefore, ai not an element of P1 union P2 union …. union Pm in (2m – 1) ways . Since there are n elements in the set A, the number of ways of constructing subsets
P1, P2, ….. , Pm is (2m – 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 k rightwards double arrow –k less or equal thanless or equal than k ….(1)
& |y| less or equal thanrightwards double arrow –k less or equal thanless or equal than k ….(2)

& |x – y| less or equal thanrightwards double arrow |y – x| less or equal thanrightwards double arrow –k less or equal than y – x less or equal thanrightwards double arrow x – k less or equal thanless 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 k rightwards double arrow –k less or equal thanless or equal than k ….(1)
& |y| less or equal thanrightwards double arrow –k less or equal thanless or equal than k ….(2)

& |x – y| less or equal thanrightwards double arrow |y – x| less or equal thanrightwards double arrow –k less or equal than y – x less or equal thanrightwards double arrow x – k less or equal thanless 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

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

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

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

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

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

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 or 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 or 338 H z
On waxing Q comma the number of beats decreases hence
n subscript Q end subscript equals 344 H z