1. Evaluate: (1-aˣ⁻ʸ)⁻¹ -(1-aʸ⁻ˣ)⁻¹

2. The mean of 6 numbers is 20. If one is delected, their mean30 is 15. Find the delected number.

3. Solve: 1/3√2x-3 =2

4. Simplify: 5ˣ⁺³-15*5ˣ⁻¹/61*5ˣ

5. Find the HCF of (ax⁴+a²x³+a³x²) and (x⁴+a²x²+a⁴)

6. What will be the sum of the roots of quadratic equation: 6x²-x-12=0?

7. Two numbers are in the ratio of 3:5. If their sum is 40, find the greater number.

8. What is the area of an equilateral triangle of perimeter 30cm²?

9. The top of tree, which is broken by the wind, makes an angle of 30° with the group at a distance of 18m from the foot of the tree. Find the length of the broken part of tree.

10. Solve: (√5)ˣ⁻¹=25

11. A cone has radius of the base 7 cm and its slant height is 25cm. Find the volume of the cone.

12. What is the total surface area of a hemisphere?

13. Which is the formula of curved surface area of hemisphere?

14. Among 100 students of a school 85 like Arthmetic, 65 like Geometry and 10 students not like both subjects. Find how many like Geometry only.

15. A cylindrical tank with radius 3.5 meter contains 4,62,000 litres of water. What is its height?

16. The sum of three consective numbers is 54, then the first two numbers.

17. What is HCF of x²-y², x²+2xy+y² and x³+y³?

18. Which is the formula of a²+b²?

19. If 6 is added to the square of a number, the result is 31. Find the number.

20. Simplify: 3³ᵃ⁺²-m³ᵃ⁺¹/6*27ᵃ

21. 1,5,7,2x-4. x+7, 2x+1 and 3x+2 are in ascending iorde. If the third quartile (Q₃) is 15, what will be the value of x?

22. If 4 is subtracted from the square of a number the result is 21. Find the number.

23. In how many years will Rs.8000 amount to Rs.13824 at 20% per annum interest compounded annually?

24. Which are the factors of (2√3x²-7x+2√3)?

25. The total surface area of hemisphere is 48 π cm². Find its volume.

26. A number card is drawn at random from the group of number card, numbered from 2 to 13. Find the probability of getting prime numbered or even numbered card.