Maths-
General
Easy

Question

If x, y are rational number such that x plus y plus left parenthesis x minus 2 y right parenthesis square root of 2 equals 2 x minus y plus left parenthesis x minus y minus 1 right parenthesis square root of 6 Then

  1. x and y cannot be determined
  2. x = 2, y =1
  3. x = 5, y = 1
  4. none of these

hintHint:

In this question we have to find the value of x and y. Firstly, we know that as square root of 2 space a n d space square root of 6 are linearly independent so its coefficient will be zero. Further we will have two equations, then we will subtract the equation to get the value of y and later substitute in any equation to find the value of a and b.

The correct answer is: x = 2, y =1


    A s space t h e y space a r e space r a t i o n a l space n u m b e r comma space c o f f i c i e n t s space o f space square root of 2 comma square root of 6 s h o u l d space b e space 0.
t h u s comma space x minus 2 y equals 0 space space _ _ _ _ space left parenthesis i right parenthesis space a n d space x minus y minus 1 equals 0 space _ _ _ _ _ _ _ left parenthesis i i right parenthesis
S u b t r a c t i n g space left parenthesis i right parenthesis space a n d space left parenthesis i i right parenthesis comma space w e space g e t colon
rightwards double arrow negative y plus 1 equals 0
rightwards double arrow y equals 1
S u b s t i t u t i n g space v a l u e space o f space y space i n space r q u a t i o n space left parenthesis i right parenthesis comma
rightwards double arrow x minus 2 cross times 1 equals 0
rightwards double arrow x equals 2
S o comma space x equals 2 space a n d space y space equals 1.

    Related Questions to study

    General
    maths-

    A class contains 4 boys and g girls. Every Sunday five students, including at least three boys go for a picnic to Appu Ghar, a different group being sent every week. During, the picnic, the class teacher gives each girl in the group a doll. If the total number of dolls distributed was 85, then value of g is -

    A class contains 4 boys and g girls. Every Sunday five students, including at least three boys go for a picnic to Appu Ghar, a different group being sent every week. During, the picnic, the class teacher gives each girl in the group a doll. If the total number of dolls distributed was 85, then value of g is -

    maths-General
    General
    maths-

    There are three piles of identical yellow, black and green balls and each pile contains at least 20 balls. The number of ways of selecting 20 balls if the number of black balls to be selected is twice the number of yellow balls, is -

    There are three piles of identical yellow, black and green balls and each pile contains at least 20 balls. The number of ways of selecting 20 balls if the number of black balls to be selected is twice the number of yellow balls, is -

    maths-General
    General
    maths-

    If a, b, c are the three natural numbers such that a + b + c is divisible by 6, then a3 + b3 + c3 must be divisible by -

    If a, b, c are the three natural numbers such that a + b + c is divisible by 6, then a3 + b3 + c3 must be divisible by -

    maths-General
    parallel
    General
    maths-

    For x element of R, let [x] denote the greatest integer less or equal than x, then value ofopen square brackets negative fraction numerator 1 over denominator 3 end fraction close square brackets+open square brackets negative fraction numerator 1 over denominator 3 end fraction minus fraction numerator 1 over denominator 100 end fraction close square brackets+ open square brackets negative fraction numerator 1 over denominator 3 end fraction minus fraction numerator 2 over denominator 100 end fraction close square brackets+…+open square brackets negative fraction numerator 1 over denominator 3 end fraction minus fraction numerator 99 over denominator 100 end fraction close square bracketsis -

    For x element of R, let [x] denote the greatest integer less or equal than x, then value ofopen square brackets negative fraction numerator 1 over denominator 3 end fraction close square brackets+open square brackets negative fraction numerator 1 over denominator 3 end fraction minus fraction numerator 1 over denominator 100 end fraction close square brackets+ open square brackets negative fraction numerator 1 over denominator 3 end fraction minus fraction numerator 2 over denominator 100 end fraction close square brackets+…+open square brackets negative fraction numerator 1 over denominator 3 end fraction minus fraction numerator 99 over denominator 100 end fraction close square bracketsis -

    maths-General
    General
    maths-

    The number of integral solutions of the equation x + y + z = 24 subjected to conditions that 1 less or equal thanless or equal than 5, 12 less or equal thanless or equal than 18, z less or equal than –1

    The number of integral solutions of the equation x + y + z = 24 subjected to conditions that 1 less or equal thanless or equal than 5, 12 less or equal thanless or equal than 18, z less or equal than –1

    maths-General
    General
    maths-

    Ravish write letters to his five friends and address the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that at least two of them are in the wrong envelopes -

    Ravish write letters to his five friends and address the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that at least two of them are in the wrong envelopes -

    maths-General
    parallel
    General
    maths-

    In how many ways can we get a sum of at most 17 by throwing six distinct dice -

    In how many ways can we get a sum of at most 17 by throwing six distinct dice -

    maths-General
    General
    maths-

    The number of non negative integral solutions of equation 3x + y + z = 24

    The number of non negative integral solutions of equation 3x + y + z = 24

    maths-General
    General
    maths-

    Sum of divisors of 25 ·37 ·53 · 72 is –

    Sum of divisors of 25 ·37 ·53 · 72 is –

    maths-General
    parallel
    General
    maths-

    The length of the perpendicular from the pole to the straight line fraction numerator 6 square root of 2 over denominator r end fraction equals C o s space theta plus S i n space theta is

    The length of the perpendicular from the pole to the straight line fraction numerator 6 square root of 2 over denominator r end fraction equals C o s space theta plus S i n space theta is

    maths-General
    General
    maths-

    The condition for the lines c subscript 1 over r equals a subscript 1 c o s space theta plus b subscript 1 s i n space theta and c subscript 2 over r equals a subscript 2 c o s space theta plus b subscript 2 s i n space theta to be perpendicular is

    The condition for the lines c subscript 1 over r equals a subscript 1 c o s space theta plus b subscript 1 s i n space theta and c subscript 2 over r equals a subscript 2 c o s space theta plus b subscript 2 s i n space theta to be perpendicular is

    maths-General
    General
    Maths-

    If f : R →R; f(x) = sin x + x, then the value of not stretchy integral subscript 0 end subscript superscript pi end superscript blank (f-1 (x)) dx, is equal to

    Here we used the concept of integration and the inverse functions to solve the question. Finding an antiderivative of a function is the procedure known as integration. The process of adding the slices to complete it is comparable. The process of integration is the opposite of that of differentiation. So the final answer is straight pi squared over 2 minus 2.

    If f : R →R; f(x) = sin x + x, then the value of not stretchy integral subscript 0 end subscript superscript pi end superscript blank (f-1 (x)) dx, is equal to

    Maths-General

    Here we used the concept of integration and the inverse functions to solve the question. Finding an antiderivative of a function is the procedure known as integration. The process of adding the slices to complete it is comparable. The process of integration is the opposite of that of differentiation. So the final answer is straight pi squared over 2 minus 2.

    parallel
    General
    maths-

    The polar equation of the straight line with intercepts 'a' and 'b' on the rays theta equals 0 and theta equals fraction numerator pi over denominator 2 end fraction respectively is

    The polar equation of the straight line with intercepts 'a' and 'b' on the rays theta equals 0 and theta equals fraction numerator pi over denominator 2 end fraction respectively is

    maths-General
    General
    maths-

    The polar equation of the straight line parallel to the initial line and at a distance of 4 units above the initial line is

    The polar equation of the straight line parallel to the initial line and at a distance of 4 units above the initial line is

    maths-General
    General
    maths-

    The polar equation of x to the power of 3 end exponent plus y to the power of 3 end exponent equals 3 axy is

    The polar equation of x to the power of 3 end exponent plus y to the power of 3 end exponent equals 3 axy is

    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.