Maths-
General
Easy

Question

If fraction numerator 1 over denominator left parenthesis 1 plus 2 x right parenthesis open parentheses 1 minus x squared close parentheses end fraction equals fraction numerator A over denominator 1 plus 2 x end fraction plus fraction numerator B over denominator 1 plus x end fraction plus fraction numerator C over denominator 1 minus x end fraction then ascending order of A, B, C.

  1. A,B,C
  2. B,C,A
  3. C,A,B
  4. B,A,C

hintHint:

In this question using the equation we will find the value of A, B and C. After finding the values we will arrange the values in ascending order to find the required sequence.

The correct answer is: B,C,A


    space space space fraction numerator 1 over denominator left parenthesis 1 plus 2 x right parenthesis open parentheses 1 minus x squared close parentheses end fraction equals fraction numerator A over denominator 1 plus 2 x end fraction plus fraction numerator B over denominator 1 plus x end fraction plus fraction numerator C over denominator 1 minus x end fraction
rightwards double arrow A left parenthesis 1 minus x squared right parenthesis plus B left parenthesis 1 plus 2 x right parenthesis left parenthesis 1 minus x right parenthesis plus C left parenthesis 1 plus 2 x right parenthesis left parenthesis 1 plus x right parenthesis equals 1
rightwards double arrow A minus A x squared plus B plus B x minus 2 x squared B plus C plus 3 x C plus 2 x squared C equals 1
rightwards double arrow x squared left parenthesis 2 C minus 2 B minus A right parenthesis plus x open parentheses B plus 3 C close parentheses plus open parentheses A plus B plus C close parentheses equals 1
rightwards double arrow A plus B plus C equals 1 space o r space 2 C minus 2 B minus A equals 0 space o r space B plus 3 C equals 0

space space space space space B plus 3 C equals 0
rightwards double arrow B equals negative 3 C

space space space space A plus B plus C equals 1
rightwards double arrow A minus 3 C plus C equals 1
rightwards double arrow A minus 2 C equals 1
rightwards double arrow A equals 1 plus 2 C

space space space space space 2 C minus 2 B minus A equals 0
rightwards double arrow 2 C minus 2 left parenthesis negative 3 C right parenthesis minus left parenthesis 1 plus 2 C right parenthesis equals 0
rightwards double arrow 2 C plus 6 C minus 1 minus 2 C equals 0
rightwards double arrow 6 C equals 1
rightwards double arrow C equals 1 over 6

A equals 1 plus 2 cross times 1 over 6 equals 1 plus 1 third equals 4 over 3

B equals negative 3 C equals negative 3 cross times 1 over 6 equals fraction numerator negative 1 over denominator 2 end fraction

S o comma space v a l u e s space i n space a s s c e n d i n g space o r d e r space i s space B comma space C comma space A.

    Related Questions to study

    General
    Maths-

    The number of different seven digit numbers that can be written using only the three digits 1, 2 and 3 with the condition that the digit 2 occurs twice in each number is-

    We know that there is not much difference between permutation and combination. Permutation is the way or method of arranging numbers from a given set of numbers such that the order of arrangement matters. Whereas combination is the way of selecting items from a given set of items where order of selection doesn’t matter. Both the word combination and permutation is the way of arrangement. Here, we will not use permutation because the order of toys is not necessary.

    The number of different seven digit numbers that can be written using only the three digits 1, 2 and 3 with the condition that the digit 2 occurs twice in each number is-

    Maths-General

    We know that there is not much difference between permutation and combination. Permutation is the way or method of arranging numbers from a given set of numbers such that the order of arrangement matters. Whereas combination is the way of selecting items from a given set of items where order of selection doesn’t matter. Both the word combination and permutation is the way of arrangement. Here, we will not use permutation because the order of toys is not necessary.

    General
    Maths-

    The centre and radius of the circle r equals c o s space theta minus s i n space theta are respectively

    The centre and radius of the circle r equals c o s space theta minus s i n space theta are respectively

    Maths-General
    General
    maths-

    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

    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

    maths-General
    parallel
    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
    General
    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

    So here we used the concept of the equation of the line passing through two points. Here we also used the trigonometric terms to find the answer using the formulas. So the final solution is r left square bracket 3 s i n space theta plus 2 C o s space theta right square bracket equals negative 6.

    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

    So here we used the concept of the equation of the line passing through two points. Here we also used the trigonometric terms to find the answer using the formulas. So the final solution is r left square bracket 3 s i n space theta plus 2 C o s space theta right square bracket equals negative 6.

    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
    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
    parallel
    General
    Maths-

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

    Here we used the concept of quadratic equations and solved the problem. We also understood the concept of discriminant and used it in the solution to find the intervals. Therefore, one of the roots will be in the interval of (α,a) and the other root will be in the interval (b,α).

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

    Maths-General

    Here we used the concept of quadratic equations and solved the problem. We also understood the concept of discriminant and used it in the solution to find the intervals. Therefore, one of the roots will be in the interval of (α,a) and the other root will be in the interval (b,α).

    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

    Here we used the concept of quadratic equations and solved the problem. We also understood the concept of discriminant and used it in the solution to find the intervals. Therefore, the number of integral solutions of λ is in between 8 less than lambda less than 16

    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

    Here we used the concept of quadratic equations and solved the problem. We also understood the concept of discriminant and used it in the solution to find the intervals. Therefore, the number of integral solutions of λ is in between 8 less than lambda less than 16

    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

    Here we used the concept of quadratic equations and solved the problem. We found the sum and product of the roots first and then proceeded for the final answer. Therefore, x to the power of 2 end exponent minus x minus 1 equals 0 will be the equation for the roots fraction numerator 1 over denominator alpha minus 2 end fraction comma fraction numerator 1 over denominator beta minus 2 end fraction .

    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

    Here we used the concept of quadratic equations and solved the problem. We found the sum and product of the roots first and then proceeded for the final answer. Therefore, x to the power of 2 end exponent minus x minus 1 equals 0 will be the equation for the roots fraction numerator 1 over denominator alpha minus 2 end fraction comma fraction numerator 1 over denominator beta minus 2 end fraction .

    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

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.