Gagan Pratap Advance Maths Complete Class Notes Exclusive 【5000+ COMPLETE】

13. In a $\triangle ABC$, if $\angle A = 90^\circ$ and $AD \perp BC$. If $BD = 4$ cm and $CD = 9$ cm, find the length of $AD$. (A) 5 cm (B) 6 cm (C) 7 cm (D) 8 cm

14. The ratio of the areas of two circles is $4:9$. What is the ratio of their circumferences? (A) 2:3 (B) 3:2 (C) 4:9 (D) 16:81

15. In $\triangle ABC$, $I$ is the incenter. If $\angle BAC = 60^\circ$, find $\angle BIC$. (A) $100^\circ$ (B) $110^\circ$ (C) $120^\circ$ (D) $130^\circ$

16. Two circles touch externally. The sum of their areas is $130\pi$ sq. cm and the distance between their centers is 14 cm. Find the radius of the smaller circle. (A) 3 cm (B) 4 cm (C) 5 cm (D) 6 cm

17. In a cyclic quadrilateral $ABCD$, $\angle A = 75^\circ$. Find $\angle C$. (A) $75^\circ$ (B) $105^\circ$ (C) $115^\circ$ (D) $125^\circ$ gagan pratap advance maths complete class notes exclusive

18. The diagonals of a rhombus are 24 cm and 10 cm. Find the perimeter of the rhombus. (A) 26 cm (B) 52 cm (C) 48 cm (D) 68 cm

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When juxtaposed with competitors (e.g., Rakesh Yadav’s 7300+ or Kiran’s SSC Mathematics), Gagan Pratap’s notes hold a distinct position: | Source | Details | |--------|---------| | Gagan

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Total Questions: 25 Maximum Marks: 50 Time: 30 Minutes

Most students carry a separate formula book. After studying these notes, you won’t need one. Gagan Pratap integrates formulas into solved examples. By the time you finish 50 questions on circles, you will have memorized all 30 circle theorems subconsciously.

At the end of every chapter, there is a section called "Yahan galati hoti hai" (Mistakes happen here). For example: ⚠️ Avoid illegal PDF selling websites — they

19. The curved surface area of a right circular cylinder is $440 \text cm^2$. If its height is 10 cm, find its volume. (A) $1386 \text cm^3$ (B) $1540 \text cm^3$ (C) $1690 \text cm^3$ (D) $1760 \text cm^3$

20. A cone and a cylinder have the same base and height. What is the ratio of their volumes? (A) 1:2 (B) 1:3 (C) 2:3 (D) 3:4

21. The area of a trapezium is $105 \text cm^2$. If the lengths of the parallel sides are 12 cm and 8 cm, find the distance between them (height). (A) 10.5 cm (B) 10 cm (C) 8.5 cm (D) 12 cm