Maths-
General
Easy

Question

The centre of the circle r squared minus 2 r left parenthesis 3 c o s space theta plus 4 s i n space theta right parenthesis minus 24 is

  1. open square brackets 5 comma t a n to the power of negative 1 end exponent invisible function application left parenthesis 4 divided by 3 right parenthesis close square brackets    
  2. open square brackets 13 comma t a n to the power of negative 1 end exponent invisible function application left parenthesis 5 divided by 12 right parenthesis close square brackets    
  3. open square brackets 15 comma t a n to the power of negative 1 end exponent invisible function application left parenthesis 5 divided by 3 right parenthesis close square brackets    
  4. open square brackets 9 comma t a n to the power of negative 1 end exponent invisible function application left parenthesis 6 divided by 5 right parenthesis close square brackets    

The correct answer is: open square brackets 5 comma t a n to the power of negative 1 end exponent invisible function application left parenthesis 4 divided by 3 right parenthesis close square brackets

Related Questions to study

General
maths-

The equation of the circle with centre at open parentheses 1 comma 0 to the power of 0 end exponent close parentheses, which passes through the point open parentheses 0 comma fraction numerator pi over denominator 2 end fraction close parentheses is

The equation of the circle with centre at open parentheses 1 comma 0 to the power of 0 end exponent close parentheses, which passes through the point open parentheses 0 comma fraction numerator pi over denominator 2 end fraction close parentheses is

maths-General
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maths-

The foot of the perpendicular from left parenthesis negative 1 comma pi divided by 6 right parenthesis on the line r left parenthesis 3 s i n space theta plus square root of 3 c o s space theta right parenthesis equals 3 is

The foot of the perpendicular from left parenthesis negative 1 comma pi divided by 6 right parenthesis on the line r left parenthesis 3 s i n space theta plus square root of 3 c o s space theta right parenthesis equals 3 is

maths-General
General
maths-

The foot of the perpendicular from the pole on the line r left parenthesis c o s space theta plus square root of 3 s i n space theta right parenthesis equals 2 is

The foot of the perpendicular from the pole on the line r left parenthesis c o s space theta plus square root of 3 s i n space theta right parenthesis equals 2 is

maths-General
parallel
General
maths-

The equation of the line parallel to r left square bracket 3 C o s space theta plus 2 S i n space theta right square bracket equals 5 and passing through open parentheses 2 comma fraction numerator pi over denominator 2 end fraction close parentheses is

The equation of the line parallel to r left square bracket 3 C o s space theta plus 2 S i n space theta right square bracket equals 5 and passing through open parentheses 2 comma fraction numerator pi over denominator 2 end fraction close parentheses is

maths-General
General
Maths-

The line passing through the points open parentheses 2 comma fraction numerator pi over denominator 2 end fraction close parentheses, (3,0) is

The line passing through the points open parentheses 2 comma fraction numerator pi over denominator 2 end fraction close parentheses, (3,0) is

Maths-General
General
Maths-

Statement-I : If fraction numerator 3 x plus 4 over denominator left parenthesis x plus 1 right parenthesis squared left parenthesis x minus 1 right parenthesis end fraction equals fraction numerator A over denominator x minus 1 end fraction plus fraction numerator B over denominator x plus 1 end fraction plus fraction numerator C over denominator left parenthesis x plus 1 right parenthesis squared end fraction then A=7 over 4
Statement-II : If fraction numerator p x plus q over denominator left parenthesis 2 x minus 3 right parenthesis squared end fraction equals fraction numerator 1 over denominator 2 x minus 3 end fraction plus fraction numerator 3 over denominator left parenthesis 2 x minus 3 right parenthesis squared end fraction then p equals 2 comma q equals 3

Which of the above statements is true

Statement-I : If fraction numerator 3 x plus 4 over denominator left parenthesis x plus 1 right parenthesis squared left parenthesis x minus 1 right parenthesis end fraction equals fraction numerator A over denominator x minus 1 end fraction plus fraction numerator B over denominator x plus 1 end fraction plus fraction numerator C over denominator left parenthesis x plus 1 right parenthesis squared end fraction then A=7 over 4
fraction numerator 3 x plus 4 over denominator left parenthesis x plus 1 right parenthesis squared left parenthesis x minus 1 right parenthesis end fraction equals fraction numerator A over denominator x minus 1 end fraction plus fraction numerator B over denominator x plus 1 end fraction plus fraction numerator C over denominator left parenthesis x plus 1 right parenthesis squared end fraction
space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator A left parenthesis x plus 1 right parenthesis squared plus B left parenthesis x minus 1 right parenthesis left parenthesis x plus 1 right parenthesis plus C left parenthesis x minus 1 right parenthesis over denominator left parenthesis x plus 1 right parenthesis squared left parenthesis x minus 1 right parenthesis end fraction
space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator A left parenthesis x squared plus 2 x plus 1 right parenthesis plus B left parenthesis x squared minus 1 right parenthesis plus C x minus C over denominator left parenthesis x plus 1 right parenthesis squared left parenthesis x minus 1 right parenthesis end fraction
space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator A x squared plus A 2 x plus A plus B x squared minus B plus C x minus C over denominator left parenthesis x plus 1 right parenthesis squared left parenthesis x minus 1 right parenthesis end fraction
space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator x squared left parenthesis A plus B right parenthesis plus x left parenthesis 2 A plus C right parenthesis plus 1 left parenthesis A minus B minus C right parenthesis over denominator left parenthesis x plus 1 right parenthesis squared left parenthesis x minus 1 right parenthesis end fraction
N o w comma space o n space c o m p a r i n g space b o t h space s i d e s space comma space
A plus B equals 0 comma space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space 2 A plus C equals 3 comma space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space A minus B minus C equals 4
rightwards double arrow A equals negative B space space space space space space space space space space space space space space space space space space space space space space space space space rightwards double arrow negative 2 B plus C equals 3 space space space space space space space space space space space space space space space space space space space space space space space space space rightwards double arrow negative B minus B minus C equals 4
p u t t i n g space B equals fraction numerator negative 7 over denominator 4 end fraction space space space space space space space space space space space space space space space space rightwards double arrow space minus 2 B equals 3 minus C space space space space space space space space space space space space space space space space space space space space space space space space rightwards double arrow negative 2 B minus C equals 4
rightwards double arrow A equals 7 over 4 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space p u t t i n g C equals fraction numerator negative 1 over denominator 2 end fraction space space space space space space space space space space space space space space space space space space space rightwards double arrow space space space 3 minus C minus C equals 4
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space rightwards double arrow negative 2 B equals 3 plus 1 half space space space space space space space space space space space space space space space space space space space space space space space rightwards double arrow space space space 3 minus 2 C equals 4
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space rightwards double arrow B equals fraction numerator negative 7 over denominator 4 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space rightwards double arrow space C equals fraction numerator negative 1 over denominator 2 end fraction space space space space space space space space
statement 1 is true.
Statement-II : If fraction numerator p x plus q over denominator left parenthesis 2 x minus 3 right parenthesis squared end fraction equals fraction numerator 1 over denominator 2 x minus 3 end fraction plus fraction numerator 3 over denominator left parenthesis 2 x minus 3 right parenthesis squared end fraction then p equals 2 comma q equals 3  
fraction numerator p x plus q over denominator left parenthesis 2 x minus 3 right parenthesis squared end fraction equals fraction numerator 1 over denominator 2 x minus 3 end fraction plus fraction numerator 3 over denominator left parenthesis 2 x minus 3 right parenthesis squared end fraction
space space space space space space space space space space space space space space space space equals fraction numerator left parenthesis 2 x minus 3 right parenthesis plus 3 over denominator left parenthesis 2 x minus 3 right parenthesis squared end fraction
space space space space space space space space space space space space space space space space equals fraction numerator 2 x over denominator left parenthesis 2 x minus 3 right parenthesis squared end fraction
N o w comma space o n space c o m p a r i n g space b o t h space s i d e s space comma space
p equals 2 space a n d space q equals 0
statement 2 is false.

Statement-I : If fraction numerator 3 x plus 4 over denominator left parenthesis x plus 1 right parenthesis squared left parenthesis x minus 1 right parenthesis end fraction equals fraction numerator A over denominator x minus 1 end fraction plus fraction numerator B over denominator x plus 1 end fraction plus fraction numerator C over denominator left parenthesis x plus 1 right parenthesis squared end fraction then A=7 over 4
Statement-II : If fraction numerator p x plus q over denominator left parenthesis 2 x minus 3 right parenthesis squared end fraction equals fraction numerator 1 over denominator 2 x minus 3 end fraction plus fraction numerator 3 over denominator left parenthesis 2 x minus 3 right parenthesis squared end fraction then p equals 2 comma q equals 3

Which of the above statements is true

Maths-General
Statement-I : If fraction numerator 3 x plus 4 over denominator left parenthesis x plus 1 right parenthesis squared left parenthesis x minus 1 right parenthesis end fraction equals fraction numerator A over denominator x minus 1 end fraction plus fraction numerator B over denominator x plus 1 end fraction plus fraction numerator C over denominator left parenthesis x plus 1 right parenthesis squared end fraction then A=7 over 4
fraction numerator 3 x plus 4 over denominator left parenthesis x plus 1 right parenthesis squared left parenthesis x minus 1 right parenthesis end fraction equals fraction numerator A over denominator x minus 1 end fraction plus fraction numerator B over denominator x plus 1 end fraction plus fraction numerator C over denominator left parenthesis x plus 1 right parenthesis squared end fraction
space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator A left parenthesis x plus 1 right parenthesis squared plus B left parenthesis x minus 1 right parenthesis left parenthesis x plus 1 right parenthesis plus C left parenthesis x minus 1 right parenthesis over denominator left parenthesis x plus 1 right parenthesis squared left parenthesis x minus 1 right parenthesis end fraction
space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator A left parenthesis x squared plus 2 x plus 1 right parenthesis plus B left parenthesis x squared minus 1 right parenthesis plus C x minus C over denominator left parenthesis x plus 1 right parenthesis squared left parenthesis x minus 1 right parenthesis end fraction
space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator A x squared plus A 2 x plus A plus B x squared minus B plus C x minus C over denominator left parenthesis x plus 1 right parenthesis squared left parenthesis x minus 1 right parenthesis end fraction
space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator x squared left parenthesis A plus B right parenthesis plus x left parenthesis 2 A plus C right parenthesis plus 1 left parenthesis A minus B minus C right parenthesis over denominator left parenthesis x plus 1 right parenthesis squared left parenthesis x minus 1 right parenthesis end fraction
N o w comma space o n space c o m p a r i n g space b o t h space s i d e s space comma space
A plus B equals 0 comma space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space 2 A plus C equals 3 comma space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space A minus B minus C equals 4
rightwards double arrow A equals negative B space space space space space space space space space space space space space space space space space space space space space space space space space rightwards double arrow negative 2 B plus C equals 3 space space space space space space space space space space space space space space space space space space space space space space space space space rightwards double arrow negative B minus B minus C equals 4
p u t t i n g space B equals fraction numerator negative 7 over denominator 4 end fraction space space space space space space space space space space space space space space space space rightwards double arrow space minus 2 B equals 3 minus C space space space space space space space space space space space space space space space space space space space space space space space space rightwards double arrow negative 2 B minus C equals 4
rightwards double arrow A equals 7 over 4 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space p u t t i n g C equals fraction numerator negative 1 over denominator 2 end fraction space space space space space space space space space space space space space space space space space space space rightwards double arrow space space space 3 minus C minus C equals 4
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space rightwards double arrow negative 2 B equals 3 plus 1 half space space space space space space space space space space space space space space space space space space space space space space space rightwards double arrow space space space 3 minus 2 C equals 4
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space rightwards double arrow B equals fraction numerator negative 7 over denominator 4 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space rightwards double arrow space C equals fraction numerator negative 1 over denominator 2 end fraction space space space space space space space space
statement 1 is true.
Statement-II : If fraction numerator p x plus q over denominator left parenthesis 2 x minus 3 right parenthesis squared end fraction equals fraction numerator 1 over denominator 2 x minus 3 end fraction plus fraction numerator 3 over denominator left parenthesis 2 x minus 3 right parenthesis squared end fraction then p equals 2 comma q equals 3  
fraction numerator p x plus q over denominator left parenthesis 2 x minus 3 right parenthesis squared end fraction equals fraction numerator 1 over denominator 2 x minus 3 end fraction plus fraction numerator 3 over denominator left parenthesis 2 x minus 3 right parenthesis squared end fraction
space space space space space space space space space space space space space space space space equals fraction numerator left parenthesis 2 x minus 3 right parenthesis plus 3 over denominator left parenthesis 2 x minus 3 right parenthesis squared end fraction
space space space space space space space space space space space space space space space space equals fraction numerator 2 x over denominator left parenthesis 2 x minus 3 right parenthesis squared end fraction
N o w comma space o n space c o m p a r i n g space b o t h space s i d e s space comma space
p equals 2 space a n d space q equals 0
statement 2 is false.
parallel
General
Maths-

If b > a , then the equation, (x - a) (x - b) - 1 = 0, has:

If b > a , then the equation, (x - a) (x - b) - 1 = 0, has:

Maths-General
General
Maths-

If alpha comma beta be that roots 4 x squared minus 16 x plus lambda equals 0 where lambda element of R,  such that 1 less than alpha less than 2 and 2 less than beta less than 3 then the number of integral solutions of λ is

If alpha comma beta be that roots 4 x squared minus 16 x plus lambda equals 0 where lambda element of R,  such that 1 less than alpha less than 2 and 2 less than beta less than 3 then the number of integral solutions of λ is

Maths-General
General
Maths-

If α,β then the equationx squared minus 3 x plus 1 equals 0 with roots fraction numerator 1 over denominator alpha minus 2 end fraction comma fraction numerator 1 over denominator beta minus 2 end fraction will be

If α,β then the equationx squared minus 3 x plus 1 equals 0 with roots fraction numerator 1 over denominator alpha minus 2 end fraction comma fraction numerator 1 over denominator beta minus 2 end fraction will be

Maths-General
parallel
General
maths-

The equation of the directrix of the conic 2 equals r left parenthesis 3 plus C o s invisible function application theta right parenthesis is

The equation of the directrix of the conic 2 equals r left parenthesis 3 plus C o s invisible function application theta right parenthesis is

maths-General
General
maths-

The conic with length of latus rectum 6 and eccentricity is

The conic with length of latus rectum 6 and eccentricity is

maths-General
General
maths-

For the circle r equals 6 C o s space theta centre and radius are

For the circle r equals 6 C o s space theta centre and radius are

maths-General
parallel
General
Maths-

The polar equation of the circle of radius 5 and touching the initial line at the pole is

The polar equation of the circle of radius 5 and touching the initial line at the pole is

Maths-General
General
maths-

The circle with centre at and radius 2 is

The circle with centre at and radius 2 is

maths-General
General
Maths-

Statement-I : If fraction numerator x squared plus 3 x plus 1 over denominator x squared plus 2 x plus 1 end fraction equals A plus fraction numerator B over denominator x plus 1 end fraction plus fraction numerator C over denominator left parenthesis x plus 1 right parenthesis squared end fraction text  then  end text bold italic A plus bold italic B plus bold italic C equals bold 0
Statement-II :If fraction numerator x squared plus 2 x plus 3 over denominator x cubed end fraction equals A over x plus B over x squared plus C over x cubed text  then  end text A plus B minus C equals 0

Which of the above statements is true

Statement-I: If fraction numerator x squared plus 3 x plus 1 over denominator x squared plus 2 x plus 1 end fraction equals A plus fraction numerator B over denominator x plus 1 end fraction plus fraction numerator C over denominator left parenthesis x plus 1 right parenthesis squared end fraction text  then  end text bold italic A plus bold italic B plus bold italic C equals bold 0
equals fraction numerator A left parenthesis x plus 1 right parenthesis squared plus B left parenthesis x plus 1 right parenthesis plus C over denominator left parenthesis x plus 1 right parenthesis squared end fraction
equals fraction numerator A left parenthesis x squared plus 2 x plus 1 right parenthesis plus B left parenthesis x plus 1 right parenthesis plus C over denominator left parenthesis x plus 1 right parenthesis squared end fraction
equals fraction numerator A x squared plus A 2 x plus A plus B x plus B plus C over denominator left parenthesis x plus 1 right parenthesis squared end fraction
equals fraction numerator A x squared plus x open parentheses 2 A plus B close parentheses plus A plus B plus C over denominator left parenthesis x plus 1 right parenthesis squared end fraction
Now, A=1         2A+B=3              A+B+C=1
rightwards double arrow 2 plus B equals 3
rightwards double arrow B equals 1         rightwards double arrow 1 plus 1 plus C equals 1
rightwards double arrow C equals 1 minus 2
rightwards double arrow C equals negative 1
A+B+C=1+1-1=-1
Statement 1 is not true.
Statement-II :If
fraction numerator x squared plus 2 x plus 3 over denominator x cubed end fraction equals A over x plus B over x squared plus C over x cubed text  then  end text A plus B minus C equals 0
space space space space space space space space space space space space space space space space space space space space equals fraction numerator A x squared plus B x plus C over denominator x cubed end fraction
Now, A=1, B=2, C=3
A+B-C=0
1+2-3=0
So, statement 2 is true.

Statement-I : If fraction numerator x squared plus 3 x plus 1 over denominator x squared plus 2 x plus 1 end fraction equals A plus fraction numerator B over denominator x plus 1 end fraction plus fraction numerator C over denominator left parenthesis x plus 1 right parenthesis squared end fraction text  then  end text bold italic A plus bold italic B plus bold italic C equals bold 0
Statement-II :If fraction numerator x squared plus 2 x plus 3 over denominator x cubed end fraction equals A over x plus B over x squared plus C over x cubed text  then  end text A plus B minus C equals 0

Which of the above statements is true

Maths-General
Statement-I: If fraction numerator x squared plus 3 x plus 1 over denominator x squared plus 2 x plus 1 end fraction equals A plus fraction numerator B over denominator x plus 1 end fraction plus fraction numerator C over denominator left parenthesis x plus 1 right parenthesis squared end fraction text  then  end text bold italic A plus bold italic B plus bold italic C equals bold 0
equals fraction numerator A left parenthesis x plus 1 right parenthesis squared plus B left parenthesis x plus 1 right parenthesis plus C over denominator left parenthesis x plus 1 right parenthesis squared end fraction
equals fraction numerator A left parenthesis x squared plus 2 x plus 1 right parenthesis plus B left parenthesis x plus 1 right parenthesis plus C over denominator left parenthesis x plus 1 right parenthesis squared end fraction
equals fraction numerator A x squared plus A 2 x plus A plus B x plus B plus C over denominator left parenthesis x plus 1 right parenthesis squared end fraction
equals fraction numerator A x squared plus x open parentheses 2 A plus B close parentheses plus A plus B plus C over denominator left parenthesis x plus 1 right parenthesis squared end fraction
Now, A=1         2A+B=3              A+B+C=1
rightwards double arrow 2 plus B equals 3
rightwards double arrow B equals 1         rightwards double arrow 1 plus 1 plus C equals 1
rightwards double arrow C equals 1 minus 2
rightwards double arrow C equals negative 1
A+B+C=1+1-1=-1
Statement 1 is not true.
Statement-II :If
fraction numerator x squared plus 2 x plus 3 over denominator x cubed end fraction equals A over x plus B over x squared plus C over x cubed text  then  end text A plus B minus C equals 0
space space space space space space space space space space space space space space space space space space space space equals fraction numerator A x squared plus B x plus C over denominator x cubed end fraction
Now, A=1, B=2, C=3
A+B-C=0
1+2-3=0
So, statement 2 is true.
parallel

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