Here are the solutions to your math MCQs.

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•      If (x+y)=3 and xy=2 then the value of (x³-y³) is 

Ans:         now,    (x-y)² = (x+y)²-4xy

                      or,   (x-y)²  =  (3)² - 4×2    [ since, (x+y)=3 and xy=2 ]

                      or,   (x-y)² = 9-8

                      or,   (x-y)² = 1

                      or,  (x-y) = 1.....(ii)

 

 now,       x+y = 3....(i)

                  x-y = 1....(ii)

now, add the two equations,  

                                    (x+y)+(x-y)=4

                              or,    2x  =  4

                              or,     x  =  2

                  As (x=2),  y = 3-x

                               or,   y = 3-2

                               or,    y = 1

     now,  x³-y³   =    (2)³ – (1)³  =   8 – 1 =  7  

•     The value of  (4096)^5/6  is

Ans:        (4096)^5/6

       =        {(16)³}^5/6

       =         (16)^5/2

       =         {(16)^1/2}⁵

       =         (4)⁵

       =        1024 

 

•       If 4 women or 3 men earn Rs. 960 in a day then the earning of 11 women and 7 men in a day will be-

Ans:      4 women earn Rs. 960 in a day.

    Or,  1  woman earn Rs.( 960/4 ) in a day.

       Or,   1 woman earn Rs. 240 in a day.

 

Now,     3 men earn Rs. 960 in a day.

           Or, 1 man earn Rs. (960/3) in a day.

          Or,  1 man earn Rs. 320 in a day.

 

        11 women will earn in a day-   (11×240) = 2640/-

           7 women will earn in a day-  (7×320) = 2240/-

 

        Now, 11 women and 7 men will earn (2640+2240) =  4480/- in a day.

 

•         x is directly proportional to y when x=24,  y=40. Find x when y=130.

Ans:     x ∝ y

        or,  x = k.y   [ where k is a constant ]

       or,   24 = k.40  [ As, x=24,  y=40 ]

       or,   k = 24/40

      or,    k = 3/5

 

Again,      x = k.y

           or,   x = 3/5 × 130   [ As, k = 3/5, y = 130 ]

           or,    x = 78 

 

•        Three numbers are in the ratio of 2:3:4. The sum of their cubes is 33957. Find the largest number.

Ans:       I guess the three numbers will be 2x, 3x, 4x

              As the question’s condition,

              (2x)³+(3x)³+(4x)³  =  33957

            or,   8x³+27x³+64x³  =  33957

                          or,   99x³   =   33957

                             or,    x³   =    343

                               or,    x   =    7

  now, the largest number is (7×4) =  28 

  

•        What is the value of x in (3x-8) (3x+2) – (4x-11) (2x+1) = (x-3) (x+7) 

Ans:      (3x-8) (3x+2) – (4x-11) (2x+1) = (x-3) (x+7)

       or,   9x²+6x-24x-16-(8x²+4x-22x-11)  =  x²+7x-3x-21

       or,   9x²+6x-24x-16-8x²-4x+22x+11  =  x²+4x-21

       or,   x²-5  =  x²+4x-21

       or,    4x = 21-5

       or,     x  =  4 

 

•         {3^(-7) ÷ 3^(-10)} × 3^(-4)

Ans:     =   3³ × 3^(-4)

                    ^{=     1/3} 

•    If x:y = 3:5 then (2x+5y) : (2x+7y) is

Ans:      x:y =3:5

      or,    x/y  =  3/5

      or,    x/3  = y/5 = k    [ where k is a constant ]

    now,   x = 4k     and     y = 5k

              now,  2x+5y = (2×4k)+(5×5k) = 31k

                         2x+7y = (2×4k)+(7×5k) = 41k

 

               Now,      (2x+5y) : (2x+7x)

                          =    (2x+5y) / (2x+7x)

                          =     31k/41k

                          =    31/41

                          =    31 : 41 

•   Which one of the following is a perfect cube?

Ans:      Here  1728  is the perfect cube because,

                         (1728)^1/3

                   =   ( 2³ × 2³ × 3³ )^1/3

                   =   2 × 2 × 3

•      (y^2-8xy-7y+56x) ÷ (y-7) = ?

  Ans:           (y-7)  (y-8x) = (y²-8xy-7y+56x)....✅

                    (y-7) (x+8y) = (8y²+xy-7x-56y)....❌

                    (y-7) (y+8x) = (y²+8xy-7y-56x)....❌

                    (y-7) (x-8y) = (xy-8y²-7x+56y).....❌