What is the value of 6x2 - 5y26x2&# | Simplification Questions & Answers

Q:

In a group of buffaloes and ducks, the number of legs are 24 more than twice the number of heads. What is the number of buffaloes in the group ?

A) 6	B) 10
C) 8	D) 12

Answer & Explanation Answer: D) 12

Explanation:

Let the number of buffaoes be x and number of ducks be y.

Then 4x + 2y = 2(x + y) + 24

=> 2x = 24

=> x = 12.

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Q:

If $3 x + 7 = x^{2} + p = 7 x + 5$ , what is the value of P ?

A) 17/2	B) 25/3
C) 33/4	D) 41/5

Answer & Explanation Answer: A) 17/2

Explanation:

$3 x + 7 = 7 x + 5 = > 7 x - 3 x = 2 = > 4 x = 2 = > x = 2$

Now, $3 x + 7 = x^{2} + p = \frac{3}{2} + 7 = \frac{1}{4} + p = > p = \frac{17}{2}$

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Q:

If 2 tables and 3 chairs cost Rs, 3500 and 3 tables and 2 chairs cost Rs. 4000, then how much does a table cost ?

A) 500	B) 1000
C) 1500	D) 2000

Answer & Explanation Answer: B) 1000

Explanation:

Let the cost of a table and that of a chair be Rs. x and Rs, y respectively.

Then, 2x + 3y = 3500 ...(i)

and 3x + 2y = 4000 .....(ii)

solving (i) and (ii) we get x = 1000, y = 500

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A) 2	B) 3
C) 4	D) 5

What is the value of $(6 x^{2} - 5 y^{2}) (6 x^{2} + 5 y^{2}), if x = \frac{1}{\sqrt{3}} and y = \frac{1}{\sqrt{5}}$ ?