Maths-
General
Easy

Question

Let p, q, r element of R+ and 27 pqr ≥ (p + q + r)3 and 3p + 4q + 5r = 12 then p3 + q4 + r5 is equal to -

  1. 2    
  2. 6    
  3. 3    
  4. none of these    

hintHint:

apply the property of AM GM and solve

The correct answer is: 3



    Given, p,q.r > 0
    Therefore, we can use the property of AM>=GM
    => (p+q+r)/3 >= (pqr)^(1/3)
    Cubing both sides we get
    (p+q+r)3  /27>=pqr
    (p+q+r)3 >=27pqr
    Given, (p+q+r)3  <=27pqr
    Therefore, (p+q+r)3  = 27pqr
    This is only possible when p=q=r=1.
    Therefore, p3+q4+r5=1+1+1
    = 3

    for real and positive numbers, we can use the property AM>=GM

    Related Questions to study

    General
    chemistry-

    For the chemical reaction 3 straight O subscript 2 not stretchy rightwards arrow 2 straight O subscript 3, the rate of formation of straight O subscript 3 is 0.04 mole lit-1sec-1. Determine the rate of disappearance of straight O subscript 2

    For the chemical reaction 3 straight O subscript 2 not stretchy rightwards arrow 2 straight O subscript 3, the rate of formation of straight O subscript 3 is 0.04 mole lit-1sec-1. Determine the rate of disappearance of straight O subscript 2

    chemistry-General
    General
    chemistry-

    If a homogenous catalytic reaction follows three alternative paths A comma B and C comma then which of the following indicates the relative ease with which the reaction moves?

    If a homogenous catalytic reaction follows three alternative paths A comma B and C comma then which of the following indicates the relative ease with which the reaction moves?

    chemistry-General
    General
    chemistry-

    For the reaction 2 N O left parenthesis g right parenthesis plus H subscript 2 end subscript left parenthesis text end text g right parenthesis ⟶ N subscript 2 end subscript O left parenthesis g right parenthesis plus H subscript 2 end subscript O(g), at 900 K. following data are observed.

    Find out the rate law and order of reaction -

    For the reaction 2 N O left parenthesis g right parenthesis plus H subscript 2 end subscript left parenthesis text end text g right parenthesis ⟶ N subscript 2 end subscript O left parenthesis g right parenthesis plus H subscript 2 end subscript O(g), at 900 K. following data are observed.

    Find out the rate law and order of reaction -

    chemistry-General
    parallel
    General
    chemistry-

    During the transformation of blank subscript c end subscript superscript a end superscript X t o subscript d end subscript superscript b end superscript Y comma the number of beta minus p a r t i c l e emitted is

    During the transformation of blank subscript c end subscript superscript a end superscript X t o subscript d end subscript superscript b end superscript Y comma the number of beta minus p a r t i c l e emitted is

    chemistry-General
    General
    Maths-

    For which positive integers n is the ratio, fraction numerator stretchy sum from k equals 1 to n of   k to the power of 2 end exponent over denominator stretchy sum from k equals 1 to n of   k end fraction an integer?

    an A.P is a sequence of mathematical terms which have a common difference with their adjacent elements. the variable n is generalized using an AP as well.

    For which positive integers n is the ratio, fraction numerator stretchy sum from k equals 1 to n of   k to the power of 2 end exponent over denominator stretchy sum from k equals 1 to n of   k end fraction an integer?

    Maths-General

    an A.P is a sequence of mathematical terms which have a common difference with their adjacent elements. the variable n is generalized using an AP as well.

    General
    Maths-

    A particle begins at the origin and moves successively in the following manner as shown, 1 unit to the right, 1 halfunit up, 1 fourth unit to the right, 1 over 8 unit down, 1 over 16 unit to the right etc. The length of each move is half the length of the previous move and movement continues in the ‘zigzag’ manner indefinitely. The co-ordinates of the point to which the ‘zigzag’ converges is

    the problem states that the particle’s movement follows a geometric progression with the first term being 1 and the ratio being ½ and the particle moves infinitely.
    The ratio in the x direction is ¼ . The ratio in the y direction is -1/4

    A particle begins at the origin and moves successively in the following manner as shown, 1 unit to the right, 1 halfunit up, 1 fourth unit to the right, 1 over 8 unit down, 1 over 16 unit to the right etc. The length of each move is half the length of the previous move and movement continues in the ‘zigzag’ manner indefinitely. The co-ordinates of the point to which the ‘zigzag’ converges is

    Maths-General

    the problem states that the particle’s movement follows a geometric progression with the first term being 1 and the ratio being ½ and the particle moves infinitely.
    The ratio in the x direction is ¼ . The ratio in the y direction is -1/4

    parallel
    General
    Maths-

    If a1, a2, a3, ........., an are positive real numbers whose product is a fixed number c, then the minimum value of a1 + a2 + a3 + .... + an – 1 + 2an is

    the Am- Gm relation is a handy tool for solving sequence related problems. it is applicable to any sequence of numbers.

    If a1, a2, a3, ........., an are positive real numbers whose product is a fixed number c, then the minimum value of a1 + a2 + a3 + .... + an – 1 + 2an is

    Maths-General

    the Am- Gm relation is a handy tool for solving sequence related problems. it is applicable to any sequence of numbers.

    General
    Maths-

    Let s subscript 1 comma s subscript 2 comma s subscript 3 horizontal ellipsis horizontal ellipsis and t subscript 1 end subscript comma t subscript 2 end subscript comma t subscript 3 end subscript horizontal ellipsis horizontal ellipsis are two arithmetic sequences such that s subscript 1 end subscript equals t subscript 1 end subscript not equal to 0 semicolon s subscript 2 end subscript equals 2 t subscript 2 end subscript and stretchy sum from i equals 1 to 10 of   s subscript i end subscript equals stretchy sum from i equals 1 to 15 of   t subscript i end subscript then the value of fraction numerator s subscript 2 end subscript minus s subscript 1 end subscript over denominator t subscript 2 end subscript minus t subscript 1 end subscript end fraction is

    an A.P is a sequence of mathematical terms which have a common difference with their adjacent elements

    Let s subscript 1 comma s subscript 2 comma s subscript 3 horizontal ellipsis horizontal ellipsis and t subscript 1 end subscript comma t subscript 2 end subscript comma t subscript 3 end subscript horizontal ellipsis horizontal ellipsis are two arithmetic sequences such that s subscript 1 end subscript equals t subscript 1 end subscript not equal to 0 semicolon s subscript 2 end subscript equals 2 t subscript 2 end subscript and stretchy sum from i equals 1 to 10 of   s subscript i end subscript equals stretchy sum from i equals 1 to 15 of   t subscript i end subscript then the value of fraction numerator s subscript 2 end subscript minus s subscript 1 end subscript over denominator t subscript 2 end subscript minus t subscript 1 end subscript end fraction is

    Maths-General

    an A.P is a sequence of mathematical terms which have a common difference with their adjacent elements

    General
    Maths-

    If a, b and c are three consecutive positive terms of a G.P. then the graph of y = ax2 + bx + c is

    Nature of graph of a quadratic equation is given by its discriminant.
    Here, a = a, b= ar, c = ar2 , where r is the common ratio of the GP
    Given, a,b,c>0

    If a, b and c are three consecutive positive terms of a G.P. then the graph of y = ax2 + bx + c is

    Maths-General

    Nature of graph of a quadratic equation is given by its discriminant.
    Here, a = a, b= ar, c = ar2 , where r is the common ratio of the GP
    Given, a,b,c>0

    parallel
    General
    Maths-

    If ln (a + c) , ln (c – a), ln (a – 2b + c) are in A.P., then :

    an A.P is a sequence of mathematical terms which have a common difference with their adjacent elements
    An = A1+(n-1)x d
    A2= A1 + d
    A3 = A1 + 2d
    A3 = A2+d
    A3-A2=A2-A1

    If ln (a + c) , ln (c – a), ln (a – 2b + c) are in A.P., then :

    Maths-General

    an A.P is a sequence of mathematical terms which have a common difference with their adjacent elements
    An = A1+(n-1)x d
    A2= A1 + d
    A3 = A1 + 2d
    A3 = A2+d
    A3-A2=A2-A1

    General
    chemistry-

    Which of the following is a natural polymer

    Which of the following is a natural polymer

    chemistry-General
    General
    chemistry-

    Which of the following is an example of condensation polymer

    Which of the following is an example of condensation polymer

    chemistry-General
    parallel
    General
    chemistry-

    Which of the following is thermoplastic

    Which of the following is thermoplastic

    chemistry-General
    General
    chemistry-

    Among the following a natural polymer is

    Among the following a natural polymer is

    chemistry-General
    General
    chemistry-

    Melmoware are

    Melmoware are

    chemistry-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.