EXERCISE 4 (OBJECTIVE TYPE QUESTIONS SOLUTION IN 111 120)

111.       2 a + b/ a + 4b = 3    2a + b = 3 ( a + 4b)   a = -11b.

                                 A + b / a + 2b = -11b + b /-11b + 2b = -10b / -9b = 10 /9.

112.       ( 2 a + 3b) (2 c – 3 d ) = (2 a – 3b) (2c + 3 d)

= (2 a + 3b) /(2 a – 3b) = (2 c + 3d ) /( 2 c -3 d)  = 2 (a / b)+ 1/ (2 ( a/b ) -1= ( 2 (c/d) +1   / 2 (c/d) – 1   a / b = c/d.

113.       ( a + b + 2c + 3d) ( a – b – 2c + 3d ) = ( a – b+ 2 c – 3 d ) a + b – 2 c – 3 d)

              [(a + b) + (2c + 3d)] [(a – b ) –(2 c – 3 d)]

                      = [( a – b ) + (2c – 3d )] [( a +b) –(2 c + 3 d)]

              (a + b ) ( a – b ) – (a + b ) (2 c – 3d ) + ( a – b ) ( 2c + 3 d ) –(2c + 3d ) (2c – 3d)

                  =(a – b ) (a + b) – (a –b) *2c + 3d ) +( a + b) (2c =3d) –(2 c + 3 d) (2 c – 3d)

             ( a =) (2 c – 3d ) =3bd = 2ac + 3 ad – 2bc – 3bd

              4bc = 6ad  2 b c =3ad.

114.       X = y   1 – q = 2q + 1 3 q = 0    q -0.

115.       X/5 – X /6 = 4.  6 X – 5X /30  = 4   X =120.

116.       2 X – 2y = 21 / 22 X/y = (21 / 22 x 2/3) =7/11  X = 7/11 y.

4 X + 5y = 83   4 x 7/11  y + 5y = 83    28 /11 y + 5y = 83  83 y = 83 x 11    y = 11.