EXERCISE 7A (OBJECTIVE TYPE QUESTIONS IN 21 25 SOLUTION )

21.       Find a positive number which when increased by 17 is equal to 50 times the reciprocal of the number.

a)      3

b)      5

c)       7

d)      9

22.       The sum of a positive number and its reciprocal is thrice the difference of the number and its reciprocal. The number is:

a)     

b)     

c)      

d)     

23.       The product of two natural numbers is 17. Then, the sum of the reciprocals of their squares is:

a)      1/289

b)      289 / 290

c)       290 / 289

d)      289

24.       If 2 ½ is added to a number and the sum multiplied by 4 ½ and 3 is added to the product and then dividing the sum by 1 1/15, the quotient becomes 25. What is the number?

a)      2 1/2

b)      3 ½

c)       4 ½

d)      5 ½

25.       Three numbers are in the ration 4:5:6f and their average is 25. The largest number is:

a)      30

b)      32

c)       36

d)      42

ANSWERS

21.C

22.A

23.C

24.B

25.A

SOLUTION 

21.       Let the number be x.

Then, x – 4 = 21 /X 21 /X     X² - 4x – 21 = 0  ( X – 7 ) (X + 3) = 0     X = 7.

22.       Let the number be X. then, x + 1/X = (3 ( X – 1/x )   x² + 1 / x = 3 ( x² - 1 / X )

X² + 1 = 3X² - 3  2X² = 4   x² = 2   x = 2

23.       Let the numbers be a and b. then, ab = 17   a = 1 and b = 17.

So, 1 / a² + 1 /b² = a² + b² / a² b² = 1² + (17)² / (1 x 17)² = 290 / 289.

24.       Let the number be x. then,

4 ½ ( X + 2 ½ ) + 3 / 1  1/5 = 25       9/2 ( X + 5/2 ) + 3 / 6/5 = 25

9x / 2 + 45 / 4 + (3 = 25 x 6 / 5 = 30       9X / 2 =30 – 57 / 4      9x / 2 = 63 / 4

X =(63 / 4 x 2/9 ) = 7/ 2 = 3 1/2

25.       Let the numbers be 4X, 5x and 6x. Then, 4x + 5X + 6x / 3      9x / 2   = 63 / 4.

Largest number = 6x = 30.