Exercise Problem and Solution Part: 1 (Equation, Solving Equations, Systems of liner equations, Quadratic equations, Inequalities)

Question: 1 If X+Y = 9 and X/Y =  2, then X equals to ....?Option: (a) 3 (b) 4 (c) 5 (d) 6 (e) 7
Explore:
x+y = 9 => y = 9-x
x/ = 2
=> x/(9-x) = 2
=> x = 18 -2x
=> x+ 2x =18
=> 3x = 18
=> x = 18/3
=> x = 8
Answer: (d)
Question: 2 If  1/3 + 1/2 + 1/X = 4 then X = ?Option: (a) 18/5 (b) 19/6 (c) 24/11 (d) 6/19 (e) 5/18

Explore:
1/3 + 1/2 + 1/X = 4
=> 1/X = 4 - 1/3 - 1/2
            = (24 - 2 - 3)/6
            = 19/9
=> X = 6/19
Answer: (d)   

Question: 3 If a+b = √5 and a - b = √3, then a 2 + b 2 =  ?Option: (a) √8 (b) 6 (c) 4 (d) 4√2 (e) 8 Explore: (a + b) 2 = 5 Or, a 2 + 2ab + b 2 = 5  .................................(1) And (a - b) 2 = 3 Or, a 2 - 2ab + b 2 = 3....................................(2) (1) + (2)  => 2 (a 2 + b 2 ) = 8 => a 2 + b 2= 4 Answer: (c)

Question: 4 In the expression of (x - y) 3 , the coefficient of y 2 is....?Option: (a) 1 (b) 3 (c) 3a (d) -3a 2  (e)  None

Explore:
The co-efficient to a term is the constant that is multiplied to the variable part. So, since
(x - y) 3 = x 2- 3x 2y + 3xy 2- y 3, So, the co-efficient is 3.
Answer: (b)

Question: 5 When number 6 is added to 1/3 of a number, the result is 28. What is that number?
Option: (a) 44 (b) 66 (c) 42 (d) 84 (e) 88

Explore:
Let, the number be x.
According to the question,
x/3 + 6 = 28
=> x/3 = 28 - 6 = 22
X = 22 x 3 = 66
Answer: (b)

Question: 6 If 5/X  = 3 and Y/6 = 2, then (3+Y)/(X+6) = ?
Explore:
5/X = 3 :. X = 5/3
Y/6 = 2 :. Y = 2 x 6 = 12
:. (3 + Y)/(X + 6) = (3 + 12)/((5/3) + 6) = (15)/((5 + 18)/ 3)
= 15/23/3
= 15x(3/23)
= 45/3
Answer: 45/3

Question: 7 X/2 + 3 = X/3 + 4. In this equation what is the value of X?
Option: (a) 7 (b) 6 (c) 5(d) 4
Explore:
X/2 + 3 = X/3 + 4
=> X/2 - X/3 = 4 - 3
=> (3X - 3X)/6 = 1
=> X = 6
Answer: (b)

Posted in: Equation & Inequality, Exercise Problem, Solutions to Problems