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. The probability for a randomly selected number out of 1, 2, 3, 4, .., 25 to be a composite number is : 15 (A) 25 10 (B) 25 11 (C) 25 (D) 25 Questions number 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled as Assertion…
   Board 20261 markAssertion-ReasonRepeated: 2023,2026
2. The value of k for which the system of equations 3x – y + 8 = 0 and 6x – ky + 16 = 0 has infinitely many solutions, is 1 (A) –2 (B) 2 (C) 1 2 (D) – 1
   Board 20241 markMCQRepeated: 2023,2024
3. For any natural number n, 6" ends with the digit : (b) 6 (c) 3 (a) (d)
   Board 20261 markMCQ
4. The common difference of the AP : 2, 2/2, 3/2, 4/2, .... is : (c) 2/2 (a) (b) (d) - ~2 Page 3 of 16 7. ABC DEF 2 AB=DE BC=8cm, EF (b) 8cm (c) 12 cm (a) 4 cm (d) 16 cm 8. (5,4)(6,4)· (b) - (c· sin =f, cos : 9. b- (b) (c) (a) (d) Vb2 - ·2 Vb2 - ·2 f cos A 10. si…
   Board 20261 markMCQ
5. (A) In · ABC, DE I BC. If AD = x, DB = x - 2, AE = x + 2 and EC = x - 1, then find the value of x. OR (B) 4cm 6cm 6 cm 7.2 cm In the figure given above, · ABC · XYZ, then find the values of x and y. Page 7 of 16 23. 24 (A) tan = sin cos 24. (1 + sin 0) (1 - si…
   Board 20262 marksshort answer
6. (A) If tan = then find the value of sin + cos 0. OR then find the value of (1 + sin 0) (1- sin0) If cot : (B) (1 + cos 0) (1 -cos 0)
   Board 20262 marksshort answer
7. (A) If x = h + a cos , y = k + b sin ·, then prove that : OR tan A tan A = 2 cosec A
   Board 20263 marksshort answer
8. The distance of the point A(4a, 3a) from x-axis is : (A) 3a (B) - 3a (C) (D) 4a - 4a 10. f cos A = 3- (A) (B) (C) (D) 11. f 2 sin A = 1 , tan A + cot A : (A) (B) (C) (D) 12. 10 /3 (A) (B) 30 /3 (C) 60 (D) 30 13. ABOAB=15 Z APB T H : (B) (A) 30° 15° (C) 45° (D)…
   Board 20261 markMCQ
9. (a) In the given figure, · AHK · · ABC. If AK = 10 cm, BC = 3-5 cm and HK = 7 cm, find the length of AC. OR PQ ,XY QR, (·) PR=63cmYR XQ 23. A(4, 5), B(m, 6), C(4, 3) D(1, n) ABCD , : 2·,tan2 - f tan + 24. (·) tan · 1-sin · (·) : sec - tan 0 V1+ sin · 25. PQ (b…
   Board 20262 marksshort answer
10. (a) If tan · + 2, find the value of tan2 e + tan · tan? OR 1-sin 0 (b) Prove that : sec 0 - tan 0 1+ sin
    Board 20262 marksshort answer
11. In the given figure, O is the centre of the circle. PQ and PR are tangents. Show that the quadrilateral PQOR is cyclic. 6x3=18 26. 27. A(1, 4) B(3,2)(oints of trisection)i 28. (·) cosec : sec ·. cosec (sec · + cosec 0) sec?0-1 cosec2 0-1 sec · tan · (·) q,(p22…
    Board 20262 marksshort answer
12. (a) Prove that : Sec3 cosec sec 0. cosec · (sec + cosec 0) OR tan · (b) pand = q, then prove that (p2 - q2) sec2 · = p². cosec · cosec ·
    Board 20263 marksshort answer
13. (a) Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio. OR (b) As shown in the given figure, a girl of height 90 cm is walking away from t…
    Board 20265 markslong answer
14. In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato. The other potatoes are arranged 3 m apart in a straight line, with a total of 10 potatoes, as shown in the figure : 5m 3m 3m 3m 3m 3m 3m 3m 3m 3m A competitor start…
    Board 20264 marksshort answer
15. Your elder brother wants to buy a car and plans to take a loan from a bank for his car. He repays his total loan of 1,18,000 by paying every month, starting with the first instalment of 1,000 and he increases the instalment by 100 every month. Based on the inf…
    Board 20264 markscase-based
16. | P a g e 1. If and are the zeroes of polynomial 3x2 + 6x + k such that + + = , then the value of k is : (A) 8 (B) 8 (C) 4 (D) 4 4| P a g e 2. x = 1 y = 2, 2x 3y + a = 0 2x + 3y b = 0 , (A) a = 2b (B) 2a = b (C) a + 2b = 0 (D) 2a + b = 0 3. P( 4, 5) Q(4, 6) - …
    Board 20251 markMCQ
17. A piece of wire 20 cm long is bent into the form of an arc of a circle of radius cm. The angle subtended by the arc at the centre of the circle is : (A) 30 (B) 60 (C) 90 (D) 50 Questions number 19 and 20 are Assertion and Reason based questions. Two statements…
    Board 20251 markAssertion-Reason
18. (a) If x cos 60 + y cos 0 + sin 30 cot 45 = 5, then find the value of x + 2y. OR (b) Evaluate :
    Board 20252 marksshort answer
19. | P a g e 26. (a) In the given figure, O is the centre of the circle and BCD is tangent to it at C. Prove that BAC + ACD = 90 . OR (b) Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle…
    Board 20253 marksshort answer
20. If tan A = ; where A is an acute angle, then find the value of .
    Board 20252 marksshort answer

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