Samacheer Kalvi class 11 Math Assignment 2024

Assignment covering important concept based sums 

1. Differentiate f(x) = x – 3 sin x

2. Find the magnitude of a x b if a =2i+j+3k and b=3i+5j-2k

3. Find the unit vector parallel to the resultant of the vectors î + ĵ – k̂ and î – 2ĵ + k̂ is

4. Write the following in roster form.

(i) {x ∈ N : x2 < 121 and x is a prime}

5. Prove that the relation ‘friendship’ is not an equivalence relation on the set of all people in Chennai.

6. Find the range of the function 1/(2Cosx-1)
 

7. Prove that √3 is an irrational number.

8. Solve for x
(i) |3 – x| < 7

9. If n (A ∩ B ) = 3 and n(A ∪ B ) = 10 , then find n(P(A ∆ B)).

10. If a and b are the roots of x^2+√2x+3=0, form a quadratic polynomial with roots 1/a and 1/b 

11. Solve x2 + 3x – 2 ≥ 0

12. Find the zeros of the polynomial function f(x) = 4x2 – 25

13. Solve 23x < 100 when
(i) x is a natural number,
(ii) x is an integer.

14. If x4 + x + 1 is a factor of the polynomial 3x3 + 8x2 + 8x + a, then find the value of a.

15. Resolve into partial fractions

(x+12)/(x-2)(x+1)²

16. Simplify and hence find the value of n:

= 27 

17. Convert 330° to radians

18. Compute log9 27 – log27 9

19. Find the values of the other five trigonometric functions of the following
(i) cos θ = -3/5, θ lies in the III quadrant

20. Find all the angles between 0° and 360° which satisfy the equation sin2θ = 

34
 

21. If sin x = 1517  and cos y =  1213, 0 < x < π2, 0 < y <π2, find the value of
(i) sin(x + y)
(ii) cos(x – y)
(iii) tan(x + y)

22. Show that cot 75° + tan 75° = 4

23. Express sin 50° + sin 40°    as a product 

24. In a ∆ ABC, if Cos C = Sin A/2SinB show that the triangle is isosceles.

25. If the sides of a ∆ ABC are a = 4, b = 6 and C = 8, then show that 4 cos B + 3 cos C = 2. 

26. If (n – 1)P3 : nP4 = 1 : 10 find n.

27. A mobile phone has a passcode of 6 distinct digits. What is the maximum number of attempts one makes to retrieve the passcode?

28. If nPr = 720, If nCr = 120, find n, r = ?

29. Compute

(i) 1024
(ii) 99^5

30. Prove that 15C3 + 2 × 15C4 + 15C5 = 17C5

31. Prove that

32. Find the area of the triangle whose vertices are (0, 0), (1, 2) and (4, 3)

33. If (k, 2), (2, 4) and (3, 2) are vertices of the triangle of area 4 square units then determine the value of k.

 
34. Find the value λ for which the vectors  and b⃗   are perpendicular, where
(i) a⃗  a = 2î + λĵ – k̂ and bb⃗  = î – 2ĵ + 3k̂

35. Find the direction cosines of a vector whose direction ratios are
(i) 1, 2, 3

36. Differentiate sin^3 x + cos^ 2 x

37. Find dy/dx if y= x tanx / logx

38. Find dy/dx if x= at^3 and y= 2at

39. Integrate sin^2 x 

40. Integrate logx / x

41. Integrate sin^2 x / cosx

42. Find the second differential if y = x^3 + 2x^2 - 6x

43. If A and B are two events associated with a random experiment for which P (A) = 0.35, P (A or B ) = 0.85 , and P (A and B) = 0.15 find (i) P (only B) (ii) P (B) (iii) P (only A)

44. The probability of an event A occurring is 0.5 and B occurring is 0.3. If A and B are mutually exclusive events, then find the probability of

(i) P(A∪B)

(ii) P(A ∩ B̅)

(iii) P(A̅ ∩ B)

45. If A and B are two events such that

P ( A ∪ B ) = 0.7 , P (A ∩ B) = 0.2 , and P (B) = 0.5 , then show that A and B are independent.