CLASS 10 SAMACHEER KALVI RELATIONS AND FUNCTIONS, NUMBERS AND SEQUENCES

 SAMACHEER KALVI CLASS 10

IMPORTANT CONCEPT BASED QUESTIONS

 RELATIONS AND FUNCTIONS

NUMBERS AND SEQUENCES

TOTAL NUMBER OF QUESTIONS: 32

1. Find A × B, A × A and B × A
(i) A = {2, -2, 3} and B = {1, -4}

 2. Given the function f: x → x2 – 5x + 6, evaluate

(i) f(-1)
(ii) f(2a)
(iii) f(2)
(iv) f(x – 1)

3. A function f is defined by f(x) = 3 – 2x. Find x such that f(x2) = (f (x))2.

4. Represent the function f = {(1,2), (2,2), (3,2), (4,3),(5,4)} through (i) an arrow diagram (it) a table form (iii) a graph.

5. Let A= {-1,1}and B = {0,2}.

If the function f: A → B defined by

f(x) = ax + b is an onto function? Find a and b.

6. If the function f is defined by

find the value of
(i) f(3)
(ii) f(0)
(iii) f(1. 5)

(iv) f(2) + f(-2) 

7. Find the value of k, such that fog = gof

(i) f(x) = 3x + 2, g(x) = 6x – k
(ii) f(x) = 2x – k, g(x) = 4x + 5

8. Consider the functions f(x), g(x), h(x) as given below. Show that (fog)oh = fo(goh)    f(x) = x – 1, g(x) = 3x + 1 and h(x) = x2

9. Use Euclid’s Division Algorithm to find the Highest Common Factor (H.C.F) of

(i) 340 and 412
(ii) 867 and 255

 10.  Find the H.C.F. of 252525 and 363636.

11. If 13824 = 2a × 3b then find a and b?

12. Find the first four terms of the sequences whose nth terms are given by  an = n3 – 2.

13. Find the indicated terms:   an = – (n2 – 4); a4 and a11    

14. Find the 19th term of an A.P. -11, -15, -19,…

15. If 3 + k, 18 – k, 5k + 1 are in A.P. then find k?

16. Find x, y and z, given that the numbers x, 10, y, 24, z are in A.P.

17. The sum of three consecutive terms that are in A.P. is 27 and their product is 288. Find the three terms.

18. In a G.P. 729, 243, 81,… find t7.

19. Find x so that x + 6, x + 12 and x + 15 are consecutive terms of a Geometric Progression

20. Find the number of terms in the following G.P.

 4,8,16,…,8192?

21. In a G.P. the 9th term is 32805 and 6th term is 1215. Find the 12th term.

22. Find the 10th term of a G.P. whose 8th term is 768 and the common ratio is 2.
 

23. In a G.P. the product of three consecutive terms is 27 and the sum of the product of two terms taken at a time is 572. Find the three terms.

24. Find the sum of first six terms of the G.P. 5,15,45,…

25. Find the sum to infinity of (i) 9 + 3 + 1 + ….

(ii) 21 + 14 + 283 ……

26. If the first term of an infinite G.P. is 8 and its sum to infinity is 323 then find the common ratio.

27. Find the sum to n terms of the series

3 + 33 + 333 + ………… to n terms

28. Find the sum

(i) 62 + 72 + 82 + …….. + 212

(ii) 103 + 113 + 123 + …….. + 203

(iii) 1 + 3 + 5 + …… + 71

29. If 1 + 2 + 3 + …. + k = 325 , then find 13 + 23 + 33 + …………. + k3

 

30. If 13 + 23 + 33 + ………… + K3 = 44100 then find 1 + 2 + 3 + ……. + k

31. Rekha has 15 square colour papers of sizes 10 cm, 11 cm, 12 cm, …, 24 cm. How much area can be decorated with these colour papers?

32. How many terms of the series 13 + 23 + 33 + …………… should be taken to get the sum 14400?