Algebra Formula

Algebra Questions and Answers

Question : Kobe Bryant wants to know that If a \times b = 2a – 3b + ab , then 3 \times 5 + 5\times 3 is equal to :

(1) 22
(2) 24
(3) 26
(4) 28

Solution : a \times* b = 2a – 3b + ab
=> 3\times 5 = 2 \times 3 – 3 \times 5 + 3 \times 5 = 6
5 \times 3 = 2 \times 5 – 3 \times 3 + 3 \times 5
= 10 – 9 + 15 = 16
Therefore, 3 \times 5 + 5 \times 3
= 6 + 16 = 22

Question : Kareena Kapoor wants to know that if p \times q = p + q +\frac{p}{q}  , then the value of   8 \times 2 is :

 (1) 6

 (2) 10

 (3) 14 

(4) 16

Solution :   p \times q= p +q + \frac{p}{q}  

\therefore  8 \times 2 = 8 + 2 + \frac{8}{2}  

 =10 + 4 = 14

Question : Varun Dhawan wants to know that if two numbers x and y (x > y) are such that their sum is equal to three times their difference. Then value of \frac{3xy}{2(x^{2} -y^{2}) } will be: 

(1) 2/ 3

 (2) 1 

(3) 1 1 /2 

(4) 1 2 /3

Solution : (x + y) = 3 (x – y) = 3x – 3y

=> 3y + y = 3x – x

=> 2x = 4y

=> x = 2y

=> \frac{x}{y} = \frac{2}{1}

\therefore x = 2, y = 1

\frac{3xy}{2(x^{2} -y^{2}) }

= \frac{3*2*1}{2x *(4-1) }

= \frac{6}{6} =1

Question : Siddharth Malhotra wants to know the value of  expression: (1 + \frac{1}{x})(1 + \frac{1}{(x+1)})(1 + \frac{1}{(x+2)})(1 + \frac{1}{(x+3)})

(1) (1 + 1/(x+4))

(2) x+4 

(3) 1/ x 

(4)  x + 4/x

Solution :  (1 + \frac{1}{x})(1 + \frac{1}{(x+1)})(1 + \frac{1}{(x+2)})(1 + \frac{1}{(x+3)})

=  x+\frac{1}{x}* x+\frac{2}{x+1} * x+\frac{3}{x+2} * x+\frac{4}{x+3}

= x+\frac{4}{x}

Question : Ranveer Singh wants to know that If a * b = 2 (a + b), then 5 * 2 is equal to : 

(1) 3

 (2) 10

(3) 14

 (4) 20

Solution : a * b = 2 (a + b)

\therefore 5 * 2 = 2 (5 + 2)

= 2 *7 = 14