Trigonometry: Class 10 Previous Year Questions

Trigonometry questions asked in CBSE board exams

Repeated questions first. Open the free app to see each question as it appeared in the paper, with its marking scheme.

1. In a quadrilateral ABCD, diagonals AC and BD intersect each other at O such that = as shown in the given figure. Prove that ABCD is a trapezium.
   Board 20255 markslong answerRepeated: 2023,2025
2. (a)In the given figure, DE II AC and DF II AE 31. Prove that BF BE FE EC OR Page 15 (b) AO. CO BO=OD ABCD 32. (b) I l I n 14··13 3425 () 100 - 150 150 - 200 200-250 250 - 300 300 - 350 12 3+2 Page 16 (b) The diagonals of a quadrilateral ABCD intersect each oth…
   Board 20233 marksshort answerRepeated: 2023,2025
3. | P a g e 21. Solve the following system of equations for x and y : + = 1 and x = 3 14| P a g e 22. , PQ RS , POQ SOR. , OSR OQP, ROQ = 125 ORS = 70 . OSR OQP 23. 6 cm 10 cm , , 24. A B (0 A < 90 , 0 B < 90 ) , tan (A + B) = 1 tan (A B) = tan 45 = 1. 25. 20 cm…
   Board 20252 marksshort answer
4. The value of (sin2 A + cos2 A) + (sec2 A tan2 A) (cot2 A cosec2 A) is : (A) 1 (B) 1 (C) 3 (D)
   Board 20251 markMCQ
5. | P a g e 9. In two concentric circles, a tangent to the smaller circle will intersect the larger circle at : (A) zero point (B) one point (C) two points (D) three points 6| P a g e 10. : (A) 3 (B) (C) (D) 11. (sin2 A + cos2 A) + (sec2 A tan2 A) (cot2 A cosec2…
   Board 20251 markMCQ
6. The total number of outcomes in the experiment of simultaneous throw of three dice is : (A) 6 (B) 18 (C) 36 (D) 216 Questions number 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled as Assertion (A) and the other is la…
   Board 20251 markAssertion-Reason
7. | P a g e 36. An injured bird was found on the roof of a building. The building is 15 m high. A fireman was called to rescue the bird. The fireman used an adjustable ladder to reach the roof. He placed the ladder in such a way that the ladder makes an angle of…
   Board 20254 marksshort answer
8. | P a g e 36. Kite festival is a popular festival in India which takes place during Makar Sankranti. The festival is celebrated by people flying kites from their rooftops. Reena and Ravi are also flying kites to enjoy the festival. to the kite is temporarily t…
   Board 20254 marksshort answer
9. | P a g e 30. Prove the following trigonometric identity : 14| P a g e 31. (chance) (i) 2 ? (ii) 9 ? (iii) 4 ? 4 - (LA) , 5 4 5=20 32. ( ) 2650 cm2 280 cm ( ) (x 0 2) , 33. SAS OA . OC = OB . OD. SAS AD||CB.
   Board 20253 marksshort answer
10. | P a g e 37. A woman borrowed 10,00,000 from her friend and promised to return the borrowed money in monthly instalments beginning from the next month. After one month, she returned 10,000, the next month she returned 15,000, the third month she returned 20,0…
    Board 20254 marksshort answer
11. (a) Find the values of A and B (0 A < 90 , 0 B < 90 ), if tan (A + B) = 1 and tan (A B) = . OR (b) Prove that tan 45 = 1 geometrically.
    Board 20252 marksshort answer
12. | P a g e 8. From the figures given below, which of the following is true about the measure of P ? (A) P = 60 (B) P = 80 (C) P = 40 (D) The measure of P cannot be determined 6| P a g e 9. , O PA - OP = 10 cm , AP (A) 10 cm (B) 20 cm (C) 5 cm (D) 5 cm 10. - ? (…
    Board 20251 markMCQ
13. Which of the following statements is false ? (A) tan 45 = cot 45 (B) sin 90 = tan 45 (C) sin 30 = cos 30 (D) sin 45 = cos 45
    Board 20251 markMCQ
14. The HCF of smallest 2 – digit number and the smallest composite number is : 1 (A) 2 (B) 20 (C) 40 (D)
    Board 20241 markMCQ
15. Page 5 6. If sin A = 5 3 , then value of cot A is : 1 (A) 4 3 (B) 3 4 (C) 5 4 (D) 4 5 Page 6 7. A cot 1 A tan 1 2 2 + +    1 (A) sec2 A (B) –1 (C) cot2 A (D) tan2 A 8. 2 tan 30° 1 – tan230°    1 (A) cos 60° (B) sin 60° (C) tan 60° (D) sin 30° 9…
    Board 20241 markMCQ
16. Page 13 ( ) 27. (a) In two concentric circles, a chord of length 24 cm of larger circle touches the smaller circle, whose radius is 5 cm. Find the radius of the larger circle. 3 OR (b) Prove that the angle between the two tangents drawn from an external point …
    Board 20243 marksshort answer
17. D is a point on the side BC of ·ABC such that ZADC = ZBAC. Show that AC2 = BC × DC. C3ABD/1 /31 Page 7 22.·A· x + 2= 9 -2x= 2 (B)·4, 3),= [ =x 23.·A·64 (B) 11 × 19 × 233×11 24. A = 30° B= 45°, sin A cos B+ cos A sin B l 26.2025 2718 28.·2, 2)(7,4) 29A)· 9 =0 =…
    Board 20242 marksshort answer
18. A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was ` 750. Find the total number of t…
    Board 20245 markslong answer
19. Page 9 18. If a pole 6 m high casts a shadow 2 3 m long on the ground, then the sun’s elevation is 1 (A) 30° (B) 45° (C) 60° (D) 90° Page 10   19  20    (A)     (R)            : (A) (A)…
    Board 20241 markAssertion-Reason
20. In the given figure, BC and BD are tangents to the circle with centre O and radius 9 cm. If OB = 15 cm, then the length (BC + BD) is : 9 cm 15 cm (a) 18 cm (b) 12 cm 24 cm (c) (d) 36 cm (Assertion - Reason based questions) Directions for Q.19 & Q.20 : In quest…
    Board 20231 markAssertion-Reason

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