Directions: In the following questions, two equations numbered I and II are given. You have to solve both the equations and give an answer.
I. 12/√x – 23/√x = 5√x
II. √y/12 – 5√y/12 = 1/√y
Solving equation I
⇒ 12 – 23 = 5√x × √x
⇒ – 11 = 5x
⇒ x = – 11/5
Solving equation II
⇒ (√y – 5√y)/12 = 1/√y
⇒ – 4√y × √y = 12
⇒ – 4y = 12
⇒ y = – 3
when x = – 11/5, y = – 3
This condition satisfies x > y
∴ x > y
1. If x = (√2 - 1)1/3, then the value of x3 – 1/x3 is:
5. If $\frac{sin+cos}{sin-cos}$=3 then the value of $sin^{4}-cos^{4}$ is
7. If a + b + c = 0 , then the value of $a^{3}+b^{3}+c^{3}$ is
8. .If a = 2 , b = 3 then the value of $27a^{3}-54a^{2}b+36ab^{2}-8b^{3}$ is
9. If the unit digit of 2a is 8 where 17 > a > 13. Find the value of a.
10. If 2 + 4x < 5 - x/2 and 3x + 3 > -5 - 3x; then x can take which of the following values?