Important CBSE Question of Math Class 10 (Arithmetic progression, coordinate geometry, Surface area Volume, Trigonometry)

 

1. Find the 9th term from the end  of the A.P. 5, 9, 13, ....., 185. (1 Marks)
2. Find the ratio in which y-axis divides the line segment joining the points A(5, - 6) and B( -1, -4).  Also find the coordinates of the point of division. (2 Marks)
3. How many terms of the A.P. 18, 16, 14, .... be taken so that their sum is zero? ( 2 Marks)
4. A decorative block, made up of two solids – a cube and a hemisphere. The base of the block is a cube of side 6 cm and the hemisphere fixed on the top has a diameter of 3.5 cm. Find the total surface area of the block. (3 Marks)
5. Find the distance of a point P(x, y) from the origin. ( 1 Marks)
6. Find volume of cone of hight 7 cm and radius 4 cm. (1 Marks)
7. In 4tan A = 3 Evaluate (4sinA – Cos A + 1) / (4sinA +Cos A - 1)                 (3Marks)
8. Prove that (sin A – 2 sin³ A)/ (2cos³ A – cos A) = tan A                               (4Marks)
9.  (sinA + 1 + cos A) (sin A – 1 + cos A) . sec A cosec A = 2                           (3Marks)      
10. If Sin A = 3/4, Calculate cos A and tan A.                                                   (3Marks)
11. If tan(A+B)=√3 and tan(A-B)=1/√3, 0 <(A+B)                                           (2Marks)
12. If secA + tanA = m, Show that ( m²-1) / (m²+1) = sinA                              (4Marks)
13. The value of cos 0°. cos 1°. cos 2°. cos 3°… cos 89° cos 90° is    (1Marks)
14. If x tan 45° sin 30° = cos 30° tan 30°, then x is equal to                (1Marks)
15. (Sin 30°+cos 60°)-(sin 60° + cos 30°) is equal to:                         (1 Marks)
16. The value of tan 60°/cot 30° is equal to                                         (1 Marks)
17. If cos X = ⅔ then tan X is equal to:                                               (1 Marks)
18. sin 2A = 2 sin A is true when A = (a)30° (b)45° (c)0° (d)60°        (1 Marks)
19. If sin θ + sin² θ = 1, then cos² θ + cos4 θ =                                    (1 Marks)
20. 5 tan² A – 5 sec² A + 1 is equal to (a) 6 (b) -5 (c) 1 (d) -4              (1 Marks)
21. If x = a cosƟ and y = b sinƟ, then b²x² + a²y² = (a) ab  (b) b² + a² (c) a²b² (d) a⁴b⁴ (1 Marks)
22. What is the minimum value of cos θ, 0 ≤ θ ≤ 90°   (a) -1 (b) 0 (c) 1 (d) 1/2            (1 Marks)
23.  If in ΔABC, ∠C = 90°, then sin (A + B) = (a) 0 (b) ½  (c) 1/√2 (d) 1                 ( 1 Marks)