1. ABCD is a cyclic trapezium, where AD \(\parallel\) BC. If \(\angle\)ABC = 70°, then the measure of \(\angle\)BCD will be—?

(a) 110° (b) 80° (c) 70° (d) 120°

2. ABCD is a cyclic quadrilateral where AB is the diameter of the circle. If \(\angle\)ADC = 120°, then the measure of \(\angle\)BAC will be 40°.

3. If PORS is a cyclic parallelogram (i.e., inscribed in a circle), then the measure of \(\angle P\) will be:

(a) \(45^\circ\) (b) \(60^\circ\) (c) \(90^\circ\) (d) \(50^\circ\)

4. ABCD is a cyclic quadrilateral. If \(\angle ADB = x^\circ\) and \(\angle ABD = y^\circ\), then the measure of \(\angle BCD\) will be \((x + y)^\circ\).

5. If ABCD is a cyclic quadrilateral and ∠A = 100°, then the measure of ∠C is—?

(a) 50° (b) 200° (c) 80° (d) 180°

6. If ABCD is a cyclic parallelogram, what is the measure of ∠B?

(a) 90° (b) 60° (c) 45° (d) 50°

7. PQRS is a cyclic quadrilateral in which side QR is extended up to point T. If the measures of angles ∠SRQ and ∠SRT are in the ratio 4:5, then find the measures of ∠SPQ and ∠SRQ.

8. In the cyclic quadrilateral ABCD, side AB is extended to point X. If ∠XBC = 82° and ∠ADB = 47°, then find the measure of ∠BAC.

9. ABCD is a cyclic quadrilateral. The sides AB and DC are extended to meet at point P, and the sides AD and BC are extended to meet at point Q. If ∠ADC = 85° and ∠BPC = 40°, then find the measures of ∠BAD and ∠CQD.

10. If the current population of a village is \(P\) and the annual population growth rate is \(2r\%\), then after \(n\) years the population will be ———.

11. If the radius of a circle is 7 cm, then what will be the radian measure of the central angle subtended by an arc of length 5.5 cm?

12. In the cyclic quadrilateral ABCD, side AB is extended up to point P. If ∠CAB = 35° and ∠CBP = 82°, then what is the measure of ∠ADB?

(a) 47° (b) 55° (c) 35° (d) 60°

13. ABCD is a cyclic trapezium in which sides AD and BC are parallel. If ∠ABC = 85°, then what is the measure of ∠BCD?

(a) 85° (b) 95° (c) 90° (d) 80°

14. If the three consecutive angles of a cyclic quadrilateral are in the ratio \(1:2:5\), then the measure of the fourth angle will be _____.

15. If three consecutive angles of a cyclic quadrilateral are in the ratio \(1:3:4\), then the measure of the fourth angle will be _____.

16. In the given figure, O is the center of the circle and AB is the diameter. ABCD is a cyclic quadrilateral. If ∠ADC = 120°, then find the measure of ∠BAC.

(a) 50° (b) 60° (c) 30° (d) 40°

17. In the given figure, O is the center of the circle and AB is the diameter. ABCD is a cyclic quadrilateral. If ∠ABC = 65° and ∠DAC = 40°, then find the measure of ∠BCD.

(a) 75° (b) 105° (c) 115° (d) 80°

18. “In the adjacent figure, O is the center of the circle and AC is the diameter. If ∠AOB = 80° and ∠ACE = 10°, then find the measure of ∠BED.”

19. “In the adjacent figure, O is the center of the circle and AB is the diameter. If ∠AOD = 140° and ∠CAB = 50°, then find the measure of ∠BED.”

20. In a circle centered at point O, AB is a diameter. If chord AC creates a 60° angle at the center, then the measure of \(\angle\)OCB will be:

(a) 20° (b) 30° (c) 40° (d) 50°

21. For the quadratic equation \(x^2 - bkx + 5 = 0\), if one of the roots is 5, then the value of \(k\) will be.

(a) \(-\cfrac{1}{2}\) (b) -1 (c) 1 (d) 0

22. The volumes of two perpendicular circular rings are equal. The ratio of their heights is 4:9, then what will be the ratio of their radii?

(a) 3:2 (b) 2:3 (c) 4:9 (d) 8:9

23. If the base radius of a right circular cone is 3 cm and the height is 4 cm, then the lateral surface area of the cone will be.

(a) \(10\pi \, cm^2\) (b) \(15\pi \, cm^2\) (c) \(12\pi \, cm^2\) (d) \(18\pi \, cm^2\)

24. The current price of a machine is rupees 2P, and if its price decreases by 2r% each year, then after 2n years, the price of the machine will be:

(a) \(P\left(1-\cfrac{r}{100}\right)^n\) (b) \(2P\left(1-\cfrac{r}{50}\right)^n\) (c) \(P\left(1-\cfrac{r}{50}\right)^{2n}\) (d) \(2P\left(1-\cfrac{r}{50}\right)^{2n}\)

25. If the ratio of the capital investments of A, B, and C is \(\cfrac{1}{2} : \cfrac{1}{3} : \cfrac{1}{4}\) and the total profit is ₹520, then C's share of the profit will be

(a) ₹120 (b) ₹160 (c) ₹180 (d) ₹140

26. If the ratio of the radii of two vertical solid circular cylinders is 2:3, and the ratio of their heights is 5:3, then the ratio of their curved surface areas will be –

(a) 2:5 (b) 8:7 (c) 10:9 (d) 16:9

27. If the interest on a principal for 5 years is \(\cfrac{1}{4}\) of the principal, then the annual interest rate will be –

(a) 5% (b) 10% (c) 15% (d) 20%

28. If the annual simple interest on a principal is \(\cfrac{1}{9}\) of it, then what will be the accumulated amount in 4 years if the total sum becomes 1326 rupees?

(a) ₹ 1080 (b) ₹ 1120 (c) ₹ 918 (d) ₹ 750

29. The center of a circle is O, and AB is its diameter. ABCD is a cyclic quadrilateral. If \(\angle\)ABC = 65° and \(\angle\)DAC = 40°, then the measure of \(\angle\)BCD is—?

(a) 75° (b) 105° (c) 115° (d) 80°

30. If the average of the quantities \(x_1, x_2, x_3,.......,x_{10}\) is 20, then the average of \(x_1+4, x_2+4, x_3+4,...., x_{10}+4\) will be—?

(a) 20 (b) 24 (c) 40 (d) 10