EXERCISE 4 (OBJECTIVE TYPE QUESTIONS SOLUTION IN 201 210)

201.       X² -1 /X + 1 = 4        (X + 1 ) (X -1) /X + 1 = 4         - 1 = 4       X = 5.

202.       If a = 3 2/3,b = 2 ½,  C = 4 ¾,  D = 3 1/3, then

Given exp. = (a² - b²) / (c² -d²) + (a – c) / (c – d) = (a² -  b²)  / (c² -d²) x (c – d) /(a – b) = (a + b) / (c + d)

= 3 2/3 + 2 ½

 4 3/4 + 3 1/3 = 11/3 + 5/2 / 19/4 + 10/3 = 37 / 6 x 12 / 97 = 74 / 97.

203.       . Given exp. = a² - b² / a + b = a – b = (1 + 1 / 1 _ 1/100 ) – (1 -  1/ 1 + 100)

= 2 x 1/ (101 / 100) = 2 x 100 / 101 = 2 x 100 / 101 = 200 /101.

204.       (a + b +c) ²= a² + b² + c² + 2 (a b + b c + ca)

2 (a b + b c + ca) =(a + b + c)²= 169 – 69 = 100.

A b + b c + ca = 50.

205.       Given : X²  + y² + z² - 64 = -2 ( x y  - y z – z x )

  Now, [X + y + (-z)] ²= X ² + y² + z² + 2 (x y – y z – z x)

  (3z – z)²  = x² + y² + z²) – + 2  (x y – y z – z x)

- 2 (x y – y z – z x) = (X² + y² = z²) – (2z)²

From (I) and (II), we get: (2z)² = 64      4z² = 64    z² = 16     Z = 4.

206.       Given exp. = (a³ + b³/ a² -b² - a b) = (a +b), where a = 785, b = 435

= (785 + 435) = 1220.

207.       Given exp. = (a² + a b + b²/ a³ -b³) = (a/a- b), where a = 147, b = 143

            = (1/147 – 143) = 1/4

208.       Let 13³ + 7³ / 13³ + 7²-X= 20. Then,

       13² + 7² -X     13² + 7² - 13 x 7 = 13² + 7² - x X = 13 x 7 = 91.

209.       Given exp. = a³ - b³ / a² - b² = (a – b ) (a² + a b + b²) / (a – b) *a + b) = (a² + a b + b²) . ( a +  b)

        = (3/5)² + (3/5 x 2/5 ) +( 2/5)²/ (3/6 + 2/5) = 9/25 + 6/25 + 4/25 = 19/25.

210.   Given exp. = a³ + b³ + c³ - 3abc / a² + b² + c² - a b – b c – ca =a + b + c = (38 + 34 + 28 )=   100.