Page 1
( jiyg;gpw;F fPNo cs;s ypq;if fpspf; nra;J FOtpy; ,izaTk;! )
Padasalai's NEWS - Group
https://t.me/joinchat/NIfCqVRBNj9hhV4wu6_NqA
Padasalai's Channel - Group
https://t.me/padasalaichannel
Lesson Plan - Group
https://t.me/joinchat/NIfCqVWwo5iL-21gpzrXLw
12th Standard - Group
https://t.me/Padasalai_12th
11th Standard - Group
https://t.me/Padasalai_11th
10th Standard - Group
https://t.me/Padasalai_10th
9th Standard - Group
https://t.me/Padasalai_9th
6th to 8th Standard - Group
https://t.me/Padasalai_6to8
1st to 5th Standard - Group
https://t.me/Padasalai_1to5
TET - Group
https://t.me/Padasalai_TET
PGTRB - Group
https://t.me/Padasalai_PGTRB
TNPSC - Group
https://t.me/Padasalai_TNPSC
Page 2
Padasalai
A.BALAIAH TIRUNELVELI 9750493961 1 | P a g e
SSLC MATHS MINIMUM MATERIAL (50% MARK) by A.BALAIAH (9750493961)
RELATIONS and FUNCTIONS
1. Let A={ x ∈N / 1 < x < 4}, B ={ x ∈W | 0 x < 2} and C={ x ∈N | x < 3}. Then verify that
(i) A x (B U C) = (A x B ) U ( A x C ) (ii) A x ( B ∩ C ) = ( A x B ) ∩ ( A x C ).
2. Given that ሺݔሻ = ቐටݔ– 1; ݔ 14; ݔ ൏ 1 � Find (i) ሺ0ሻ (ii) ሺ3ሻ (iii) ሺ 1ሻ in terms of . (given that ≥0).
3. If A={5,6}, B={4,5,6}, C={5,6,7}, Show that AxA=(BxB)∩(CxC).
4. If A = {1,3,5} and B = {2,3}, then (i) find AxB and BxA. (ii) Is AxB = BxA? If not why?
(iii) Show that n(AxB) = n(BxA) = n(A) ൈn(B).
5. If A x B = {(3,2), (3,4), (5,2), (5,4)}, then find A and B.
6. Let A = {x ∈W / x < 2},B = { x ∈N / 1 < x 4 } and C = { 3, 5}. Verify that
(i) Ax(BUC) = (AxB)U(AxC) (ii) Ax(B∩C) = (AxB)∩(AxC) (iii) (AUB)xC=(AxC)U(BxC)
7. Find A x B, A x A and B x A (i) A = {2,െ2,3} and B = {1,െ4} (ii) A = B = {p, q}
(iii) A = {m, n}; B = ∅.
8. Let A = {1,2,3} and B = { x/ x is a prime number less than 10}. Find A x B and B x A.
9. If B×A = {(െ2,3), (െ2,4), (0,3), (0,4), (3,3), (3,4)} find A and B.
10. If the function :→is defined by ሺݔሻൌቐ 2x 7ifx ൏ െ2x²– 2if– 2 x ൏ 33x– 2ifx 3 � then the values of (i) ሺ4) (ii)ሺെ2ሻ (iii) ሺ4ሻ 2ሺ1ሻ (iv) ሺଵሻଷሺସሻሺଷሻ 11. Let A = The set of all natural numbers less than 8, B=The set of all prime numbers less than 8,
C = The set of even prime number. Verify that (i) (A∩B)Xc = (AxC)∩(BxC)
(ii) Ax(BെC) = (AxB) െ (AxC)
12. A function :ሾെ5,9ሿ→is defined as follows: ሺݔሻൌቐ6ݔ 1if– 5 ݔ ൏ –²ݔ25 1if2 ݔ ൏ ݔ36 െ 4if6 ݔ 9�Find
(iሻሺെ3ሻ ሺ2ሻ (ii) ሺ7ሻ െ ሺ1ሻ (iii)2ሺ4ሻ ሺ8ሻ ሺݒሻ2ሺെ2ሻെሺ6ሻሺ4ሻሺെ2ሻ .13. Let :ܣ→ܤbe a function defined by ሺݔሻൌ௫ଶെ1, where ܣൌሼ2,4,6,10,12ሽ,ܤൌሼ0,1,2,4,5,9ሽ.
Represent by (i) set of ordered pairs (ii) a table (iii) an arrow diagram (iv) a graph.
14. The function ‘ݐ’which maps temperature in Celsius ሺܥሻinto temperature in Fahrenheit ሺܨሻis
defined by ݐሺܥሻ ൌ = where F ܨଽହC+32. Find (i) t(0) (ii) t(28) (iii) t(െ10) (iv) the value of ܥ
when ݐሺܥሻൌ212(v) the temperature when the Celsius value is equal to the Fahrenheit value.
15. A function is defined by ሺݔሻൌ2ݔെ3. (i) Find ሺሻାሺଵሻଶ . (ii) Find x such that f(x) = 0.
(iii) Find x such that f(x) = x. (iv) Find x such that f(x) = f (1െ x).
16. Given the function :ݔ→2ݔെ5ݔ6,evaluate (i) f(-1) (ii) f(2a) (iii)f(2) (iv) f(x-1)
17. The distance (in km) travelled by a particle in time ݐhours is given by Sሺݐሻൌ௧²ା௧ଶ . Find the
distance travelled by the particle after (i) three and half hrs. (ii) eight hrs and fifteen min.
18. Forensic scientists can determine the height (in cm) of a person based on the length of their thigh
bone. They usually do so using the function ሺሻൌ2.4754.10where is the length of the
thigh bone. (i) Check if the function is one-one. (ii) Also find the height of a person if the
length of his thigh bone is 50 cm. (iii) Find the length of the thigh bone if the height of a
person is 147.96 cm.
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
www.Padasalai.Net www.TrbTnpsc.com
Send Your Questions and Answers to Our Email Id - [email protected]
Page 3
Padasalai
A.BALAIAH TIRUNELVELI 9750493961 2 | P a g e
19. Let be a function :→be defined by ሺݔሻൌ3ݔ2,ݔ∈(i) Find the images of 1,2,3
(ii) Find the pre-images of 29, 53 (iii) Identify the type of function. 20. Given fሺݔሻൌ2ݔെ2ݔ, find (i) f(1) ሺሻሺݔ1ሻሺሻሺݔሻሺ1ሻ.21. If =ሼെ5,1,3,4ሽand =ሼ,,ሽ, then which of the following relations are functions from to . (i) R1={(െ5,a), (1,a), (3,b)} (ii) R2={(െ5,b), (1,b), (3,a), (4,c)}
(iii) R3={(െ5,a), (1,a), (3,b), (4,c), (1,b)}
22. Represent each of the given relations by (a) an arrow diagram, (b) a graph and (c) a set in roster
form, wherever possible. (i) {(x, y) / x=2y, x∈{2,3,4,5},y∈{1,2,3,4}
(ii) {(x, y) / y = x+3, x, y are natural numbers < 10}
23. Let A = {9,10,11,12,13,14,15,16,17} and let f: A N be defined by ሺሻ ൌ the highest prime
factor of n ∈A. Write f as a set of ordered pairs and find the range of f.
24. The Cartesian product AxA has 9 elements among which (െ1,0) and (0,1) are found. Find the set
A and the remaining elements of AxA.
25. If the ordered pairs (x2 െ 3x, y
2+4y) and (െ2,5) are equal, then find ݔ and ݕ.
26. In electrical circuit theory, a circuit Cሺݐሻis called a linear circuit if it satisfies the superposition
principle given by Cሺ1ݐ2ݐሻൌܥሺ1ݐሻܥሺ2ݐሻ, where ,are constants. Show that the
circuit Cሺݐሻൌ3ݐis linear.
27. Let A={1,2,3,4,…,45} and R be the relation defined as “is a square of” on ܣ. Write R as a
subset of AൈA. Also, find the domain and range of R. 28. A relation is defined by fሺݔሻൌ2ݔ–2where, ݔ∈ሼെ2,െ1,0,1,3ሽ(i) List the elements of (ii) Is a function?
29. Let ൌሼሺ,ݔݕሻ/,ݔݕ∋ݕൌ2ݔሽbe a relation on N. Find the domain, co-domain and range.
Is this relation a function?
30. Let ൌሼ3,4,6,8ሽ. Determine whether the relation R = {(x, f(x))/ x∈X, f(x) = x2+1} is a
function from X to N?
31. Let ሺݔሻൌ2ݔ5. If ݔ0then find ሺ௫ାଶሻሺଶሻ௫ .
32. A function is defined by fሺݔሻൌ3െ2ݔ. Find ݔsuch that ሺ2ݔሻൌሺሺݔሻሻ2.33. A plane is flying at a speed of 500 km per hour. Express the distance travelled by the plane as
function of time ݐin hours.
34. Let ܣൌሼ1,2,3ሽ,ܤൌሼ4,5,6,7ሽand ൌሼሺ1,4ሻ,ሺ2,5ሻ,ሺ3,6ሻሽbe a function from ܣto ܤ. Show
that is one-one but not onto function.
35. If ܣൌሼെ2,െ1,0,1,2ሽand :ܣ→ܤis an onto function defined by ሺݔሻൌ2ݔݔ1then
find ܤ.
36. Let be a function from to defined by ሺݔሻൌ3ݔെ5. Find the values of and given
that ሺ,4ሻand ሺ1,ሻbelong to . 37. Show that the function :→defined by ሺݔሻൌ2ݔെ1is one-one but not onto.38. Show that the function :→defined by ሺሻൌ23is one-one function.39. Let ܣൌሼ1,2,3,4ሽܤൌ. Let :ܣ→ܤbe defined by ሺݔሻൌ3ݔthen, (i) find the range of (ii) identify the type of function.
40. In each of the following cases state whether the function is bijective or not. Justify your answer.
(i) :→defined by fሺݔሻൌ2ݔ1 (ii) :→defined by f(x) = 3െ4x2
41. Let ܣൌሼെ1,1ሽ,ܤൌሼ0,2ሽ. If the function :ܣ→ܤdefined by ሺݔሻൌݔis an onto
function? Find a and .
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
www.Padasalai.Net www.TrbTnpsc.com
Send Your Questions and Answers to Our Email Id - [email protected]
Page 4
Padasalai
A.BALAIAH TIRUNELVELI 9750493961 3 | P a g e
42. The distance an object travels under the influence of gravity in time ݐseconds is given by
Sሺݐሻൌଵଶ2ݐݐwhere, ( g is the acceleration due to gravity), , are constants. Check if
the function Sሺݐሻis one-one.
43. If ሺݔሻ ൌ ݔ3 െ 2, ሺݔሻ ൌ ݔ2 and if ൌ .then find the value of k ,
44. Find if ሺሻ ൌ 5, where ሺሻ ൌ 2 െ 1. 45. Represent the function f(x) = √2²ݔ െ ݔ5 3 as a composition of two functions.
46. If fሺݔሻൌ2ݔെ1,gሺݔሻൌ௫ାଵଶ , show that ൌൌݔ.
47. (i) If f(ݔ) = x2െ 1 , ሺݔሻ ൌ ݔ െ 2 find a, if ሺሻ ൌ 1. (ii)Find k, if ሺሻ ൌ 2 െ 1 and ሺሻ ൌ 5.
48. Let fሺݔሻൌ2ݔെ1. Find ሺሻo ሺሻ
49. If f(x) = ௫ଵ௫ାଵ , x1 show that f(f(x)) =
ଵ௫ , provided x0.
50. Consider the functions ሺݔሻ,gሺݔሻ,ሺݔሻare given below. Show that ሺሻൌoሺሻin each
case. (iሻሺݔሻ ൌ ݔ െ 1, ሺݔሻ ൌ ݔ3 1 and ሺݔሻ =2 ݔ
51. If :→and :→are defined by ሺݔሻൌ5ݔand gሺݔሻൌ4ݔthen check if ,are one-one
and is one-one?
52. The functions and are defined by ሺݔሻ ൌ ݔ6 8; ሺݔሻ= ௫ଶଷ (i) Calculate the value of
ሺ12ሻ(ii) Write an expression for ሺݔሻ in its simplest form.
SQUARE ROOT :
1. Find the square root of 64x4 – 16x
3+17x
2 – 2x+1
2. Find the square root of the expression 4௫మ௬మ20௫௬13–30௬௫9௬మ
௫మ
3. If 9x4+12x
3+28x
2+ax+b is a perfect square, find the values of a and b.
4. Find the square root of the following polynomials by division method (i) x4 – 12x
3+42x
2 – 36x+9
(ii) 289x4 – 612x
3+970x
2 – 684x+361 (iii) 16x
4+8x
2+1 (iv) 121x
4 – 198x
3 – 183x
2+216x+144
5. Find the square root of the expression ௫మ௬మെ10௫௬27െ10௬௫௬మ
௫మ6. Find the values of a and b if the following polynomials are perfect squares
( i) 4x4 – 12x
3+37x
2+bx+a (ii) ax
4+bx
3+361x
2+220x+100
(iii) ଵ௫ర– ௫యଵଷ௫మ௫b (iv) x4 – 8x
3 + ax
2 + bx +16
AREA OF QUADRILATERAL:
1. Find the area of the quadrilateral formed by the points (8,6), (5,11), (െ5,12) and (െ4,3).
2. Find the value of ‘a’ for which the given points are collinear. (2,3), (4,a) and (6,െ3)
3. Find k, if the area of a quadrilateral is 28 sq. units, whose vertices are (െ4,െ2), (െ3,k), (3,െ2) and (2,3).
4. Let P(11,7), Q(13.5, 4) and R(9.5, 4) be the midpoints of the sides AB, BC and AC respectively of
ΔABC. Find the coordinates of the vertices A, B and C. Hence find the area of ΔABC and compare
this with area of ΔPQR.
5. A triangular shaped glass with vertices at A(െ5,െ 4), B(1,6) and
C(7,െ4) has to be painted. If one bucket of paint covers 6 sq. ft., how
many buckets of paint will be required to paint the whole glass,
if only one coat of paint is applied.
6. In the figure, find the area of (i) ΔAGF (ii) ΔFED
(iii) quadrilateral BCEG.
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
www.Padasalai.Net www.TrbTnpsc.com
Send Your Questions and Answers to Our Email Id - [email protected]
Page 5
Padasalai
A.BALAIAH TIRUNELVELI 9750493961 4 | P a g e
MATRIX:
1. If A=ቀ ቁand I = ቀ1 00 1ቁ show that A2 െ (a+d)A = (bc – ad) I2.
2. A= ቀ3 04 5ቁ, B=ቀ6 38 5ቁ, C=ቀ3 61 1ቁ find the matrix D, such that CD – AB = 0.
3. A = ൭1 8 33 5 08 7 6൱, B = ൭8 െ6 െ42 11 െ30 1 5 ൱ compute ଵଶA –
ଷହ B .
4. If A = ቌ5 4 െ2ଵଶ ଷସ √21 9 4 ቍ, B = ቌെ7 4 െ3ଵସ ଶ 35 െ6 9 ቍ,find 4A – 3B.
5. Solve for x, y: ൬ݔଶݕଶ൰ + 2൬െ2ݔെݕ ൰ = ቀ58ቁ
6. If A=(1 −1 2), B= ൭1 െ12 11 3 ൱ and C = ቀ1 22 െ1ቁ show that (AB)C = A(BC).
7. If A=ቀ5 2 91 2 8ቁ, B= ൭1 71 25 െ1൱ verify that (AB)T = B
TA
T.
8. If A= ቀ 3 1െ1 2ቁ show that A2 – 5A +7I2 = 0
9. If cos ߠ ቀ ߠݏ ߠݏെߠݏ ቀ ߠ ቁ × sinߠݏ ݔ െߠݏߠݏ ݔ ቁ = I2 , find x.
10. Given A=ቀ 00 2ቁ B=ቀ0 െ1ݍ 2 ቁ, C= ቀ2 െ22 2 ቁ and if BA=C2, find p and q.
11. If A = ቀcos ߠ 00 ߠቁ, B= ቀsinߠݏ 00 ቁ then show that Aߠݏ2+B
2 = I
12. Let A = ቀ1 21 3ቁ, B = ቀ4 01 5ቁ, (A – B)T = A
T – B
T.
13. Find X and Y if X+Y=ቀ7 03 5ቁ and X – Y =ቀ3 00 4ቁ.
14. Find x and y if xቀ 4െ3ቁ+yቀെ23 ቁ= ቀ46ቁ
15. If A=൬ 2 െ2√2√2 2 ൰ and B=൬ 2 2√2െ√2 2 ൰, show that A and B satisfy commutative property with respect
to matrix multiplication.
16. Solve ቀ2 11 2ቁ ቀݕݔቁ= ቀ45ቁ
17. Find x ,y ,z if (i) ൬ ݔ െ 3 ݔ3 െ ݔݖ ݕ 7 ݔ ݕ = ቀ1൰ݖ 01 6ቁ (ii) (3+ݖ ݖ−ݕ ݔ) + (3 4 ݕ)=(16 8 4)
18. A has ‘a’ rows and ‘a+3’ columns. B has ‘b’ rows and ’17 – b ’ columns and if both products AB and BA
exist, find a,b?
19. i) Verify that A2=I when A = ቀ5 െ46 െ5ቁ. ii) If A=ቀ cos ߠ ߠݏെߠݏ ቁ prove that AAߠݏ
T=I
20. If A is of order p x q and B is of order q x r what is the order of AB and BA?
21. A = ൭1 93 48 െ3൱, B = ൭5 73 31 0൱ then verify that (i) A+B = B+A (ii) A + (−A ) = (−A ) + A = O
22. Construct a 3 × 3 matrix whose elements are given by (i) =|iെ2j| (ii) = ሺାሻయ
ଷ iii) =ଶଶ.
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
www.Padasalai.Net www.TrbTnpsc.com
Send Your Questions and Answers to Our Email Id - [email protected]
Page 6
Padasalai
A.BALAIAH TIRUNELVELI 9750493961 5 | P a g e
PROBABILITY:
1. Abagcontains5blueballsand4greenballs.Aballisdrawnatrandomfromthebag.Find
theprobabilitythattheballdrawnis(i)blue(ii)notblue.
2. Abagcontains6greenballs,someblackandredballs.Numberofblackballsisastwiceas
thenumberofredballs.Probabilityofgettingagreenballisthricetheprobabilityofgettinga
redball.Find(i)numberofblackballs(ii)totalnumberofballs.
3. Abagcontains12blueballsandxredballs.Ifoneballisdrawnatrandom(i)whatisthe
probabilitythatitwillbearedball?(ii)If8moreredballsareputinthebag,andiftheprobability
ofdrawingaredballwillbetwicethatoftheprobabilityin(i),thenfindx.
4. Abagcontains5redballs,6whiteballs,7greenballs,8blackballs.Oneballisdrawnat
randomfromthebag.Findtheprobabilitythattheballdrawnis(i)white(ii)blackorred(iii)not
white(iv)neitherwhitenorblack.
5. Abagcontains5whiteandsomeblackballs.Iftheprobabilityofdrawingablackballfromthe
bagistwicetheprobabilityofdrawingawhiteballthenfindthenumberofblackballs.
6. Twodicearerolled.Findtheprobabilitythatthesumofoutcomesis(i)equalto4(ii)greater
than10(iii)lessthan13.
7. Twounbiaseddicearerolledonce.Findtheprobabilityofgetting(i)thedoublet(equalnumberson
bothdice)(ii)theproductasaprimenumber(iii)thesumasaprimenumber(iv)thesumas1.
8. Twodicearenumbered1,2,3,4,5,6and1,1,2,2,3,3respectively.Theyarerolledandthe sum
ofthenumbersonthemisnoted.Findtheprobabilityofgettingeachsumfrom2to9 separately.
9. Twodicearerolledtogether.Findtheprobabilityofgettingadoubletorsumoffacesas4.
10. Twodicearerolledonce.Findtheprobabilityofgettinganevennumberonthefirstdieortotalof
facesum8.
11. Iftwodicearerolled,thenfindtheprobabilityofgettingtheproductoffacevalue6orthe
differenceoffacevalue5.
12. Threefaircoinsaretossedtogether.Findtheprobabilityofgetting(i)allheads(ii)atleastonetail
(iii)atmostonehead(iii)atmosttwotails.
13. Threecoinsaretossedonce.Findtheprobabilityofgettingatmost2tailsoratleast2heads.
14. Acoinistossedthrice.Findtheprobabilityofgettingexactlytwoheadsoratleastonetailor
consecutivetwoheads
15. Fromawellshuffledpackof52cards,onecardisdrawnatrandom.Findtheprobabilityof
getting(i)redcard(ii)heartcard(iii)redking(iv)facecard(v)numbercard.
16. Thekingandqueenofdiamonds,queenandjackofhearts,jackandkingofspadesareremoved
fromadeckof52playingcardsandthenwellshuffled.Nowonecardisdrawnatrandomfromthe
remainingcards.Determinetheprobabilitythatthecardis(i)aclavor(ii)aqueenofredcard
(iii)akingofblackcard.
17. Acardisdrawnapackof52cards.Findtheprobabilityofgettingakingoraheartoraredcard.
18. Fromawellshuffledpackof52cards,acardisdrawnatrandom.Findtheprobabilityofitbeing
eitheraredkingorablackqueen.
19. Theking,Queenandjackofthesuitspadeareremovedfromadeckof52cards.Onecardis
selectedfromtheremainingcards.Findtheprobabilityofgetting(i)adiamond(ii)aqueen
(iii)aspade(iv)aheartcardbearingthenumber5.
20. Agameofchanceconsistsofspinninganarrowwhichisequallylikelytocometorest
pointingtooneofthenumbers1,2,3,…,12.Whatistheprobabilitythatitwillpointto
(i)7(ii)aprimenumber(iii)acompositenumber?
21. Atafete,cardsbearingnumbers1to1000,onenumberononecardareputinabox.Eachplayer
selectsonecardatrandomandthatcardisnotreplaced.Iftheselectedcardhasaperfectsquare
numbergreaterthan500,theplayerwinsaprize.Whatistheprobabilitythat(i)thefirstplayer
winsaprize(ii)thesecondplayerwinsaprize,ifthefirsthaswon?
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
www.Padasalai.Net www.TrbTnpsc.com
Send Your Questions and Answers to Our Email Id - [email protected]
Page 7
Padasalai
A.BALAIAH TIRUNELVELI 9750493961 6 | P a g e
22. Inaboxthereare20non-defectiveandsomedefectivebulbs.Iftheprobabilitythatabulbselected
atrandomfromtheboxfoundtobedefectiveisଷthen,findthenumberofdefectivebulbs.
23. TwocustomersPriyaandAmuthanarevisitingaparticularshopinthesameweek(Mondayto
Saturday).Eachisequallylikelytovisittheshoponanyonedayasonanotherday.Whatisthe
probabilitythatbothwillvisittheshopon(i)thesameday(ii)differentdays(iii)consecutivedays?
24. Inagame,theentryfeeisRs.150.Thegameconsistsoftossingacoin3times.Dhanaboughta
ticketforentry.Ifoneortwoheadsshow,shegetsherentryfeeback.Ifshethrows3heads,she
receivesdoubletheentryfees.Otherwiseshewilllose.Findtheprobabilitythatshe(i)getsdouble
entryfee(ii)justgetsherentryfee(iii)losestheentryfee.
25. IfAandBaretwoeventssuchthatP(A)=ଵସ,P(B)=ଵଶandP(AandB)=ଵ,find(i)P(AorB)
(ii)P(notAandnotB).
26. Inaclassof50students,28optedforNCC,30optedforNSSand18optedbothNCCand
NSS.Oneofthestudentsisselectedatarandom.Findtheprobabilitythat(i)Thestudentopted
forNCCbutnotNSS.(ii)ThestudentoptedforNSSbutnotNCC.(iii)Thestudentoptedfor
exactlyoneofthem.
27. AandBaretwocandidatesseekingadmissiontoIIT.TheprobabilitythatAgettingselected
is0.5andtheprobabilitythatbothAandBgettingselectedis0.3.Provethattheprobabilityof
Bbeingselectedisatmost0.8.
28. TheprobabilitythatatleastoneofAandBoccuris0.6.IfAandBoccursimultaneouslywith
probability0.2,thenfindP(ܣ)+P(ܤ).29. TheprobabilityofhappeningofaneventAis0.5andthatofBis0.3.IfAandBaremutually
exclusiveevents,thenfindtheprobabilitythatneitherAnorBhappen.
30. Aboxcontainscardsnumbered3,5,7,9,…,35,37.Acardisdrawnatrandomfromthebox.Find
theprobabilitythatthedrawncardhaveeithermultiplesof7oraprimenumber.
31. Theprobabilitythatapersonwillgetanelectrificationcontractisଷହandtheprobabilitythathe
willnotgetplumbingcontractisହ.Theprobabilityofgettingatleastonecontractis
ହ.Whatis theprobabilitythathewillgetboth?
32. Inatownof8000people,1300areover50yearsand3000arefemale.Itisknownthat30%ofthe
femaleareover50years.Whatistheprobabilitythatachosenindividualfromthetowniseithera
femaleorover50years?
33. IfA,B,CareanythreeeventssuchthatprobabilityofBistwiceasthatofprobabilityofAand
probabilityofCisthriceasthatofprobabilityofAandifP(A∩B)=ଵ,P(B∩C)=ଵସ,
P(A∩C)=ଵ,P(AUBUC)=
ଽଵ,P(A∩B∩C)= ଵଵହ,thenfindP(A),P(B)andP(C)?34. Inaclassof35,studentsarenumberedfrom1to35.Theratioofboystogirlsis4:3.Theroll
numbersofstudentsbeginwithboysandendwithgirls.Findtheprobabilitythatastudentselected
iseitheraboywithprimerollnumberoragirlwithcompositerollnumberoraneven rollnumber.
35. TheprobabilitythatastudentwillpassthefinalexaminationinbothEnglishandTamilis0.5 and
theprobabilityfpassingneitheris0.1.IftheprobabilityofpassingtheEnglishexaminationis0.75.
WhatistheprobabilityofpassingtheTamilexamination?
36. Writethesamplespaceforselectingtwoballsfromabagcontaining6ballsnumbered1to6
37. IfAisaneventofarandomexperimentsuchthatP(A):P(ܣ)=17:15andn(S)=640, thenfind(i)P(ܣ) (ii)n(A).38. Acoinistossedthrice.Whatistheprobabilityofgettingtwoconsecutivetails?
39. IfP(A)=0.37,P(B)=0.42,P(A∩B)=0.09,thenϐindP(AUB).
40. Whatistheprobabilityofdrawingeitherakingoraqueeninasingledrawfromawell
shuffledpackof52cards?
41. IfP(A)=ଶଷ,P(B)=ଶହ,P(AUB)=ଵଷ,thenfindP(A∩B).
42. AandBaretwoeventssuchthat,P(A)=0.42,P(B)=0.48andP(A∩B)=0.16.Find(i)P(notA)(ii)
P(notB)(iii)P(AorB).
43. IfAandBaretwomutuallyexclusiveeventsofarandomexperimentandP(notA)=0.45,
P(AUB)=0.65,thenfindP(B).
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
www.Padasalai.Net www.TrbTnpsc.com
Send Your Questions and Answers to Our Email Id - [email protected]
Page 8
Padasalai
A.BALAIAH TIRUNELVELI 9750493961 7 | P a g e
STATISTICS
1. Findthemeanandvarianceofthefirstnnaturalnumbers.2. For a group of 100 candidates the mean and standard deviation of their marks were found to be 60 and 15 respectively. Later on it was found that the scores 45 and 72 were wrongly entered as 40 and
27. Find the correct mean and standard deviation.
3. The mean and variance of seven observations are 8 and 16 respectively. If five of these are
2, 4, 10, 12 and 14, then find the remaining two observations.
4. The mean and standard deviation of 15 observations are found to be 10 and 5 respectively. On
rechecking it was found that one of the observation with value 8 was incorrect. Calculate the
correct mean and standard deviation if the correct observation value was 23?
5. If for a distribution, Σሺݔെ5ሻൌ3,Σሺݔെ5ሻ2ൌ43,and total number of observations is 18, find the mean
and standard deviation.
6. The mean of the following frequency distribution is 62.8 and the sum of all frequencies is 50.
Compute the missing frequencies ଵ and ଶ.
7. The frequency distribution is given. In the table, k is a positive integer, has a variance of 160.
Determine the value of k.
8. If the range and coefficient of range of the data are 20 and 0.2 respectively, then find the largest and
smallest values of the data.
9. The standard deviation of some temperature data in degree Celsius (°C) is 5. If the data were
converted into degree Fahrenheit (°F) then what is the variance?
10. The measurement of the diameters (in cm) of the plates prepared in a factory is given below.
Find its standard deviation.
11. The marks scored by the students in a slip test are given below. Find the standard deviation of
their marks.
12. The marks scored by 10 students in a class test are 25, 29, 30, 33, 35, 37, 38, 40, 44, 48. Find
the standard deviation.
13. The amount of rainfall in a particular season for 6 days are given as 17.8 cm, 19.2cm,
16.3cm, 12.5cm, 12.8cm and 11.4cm. Find its standard deviation.
14. Find the variance and standard deviation of the wages of 9 workers given below: Rs.310, Rs.290, Rs.320,
Rs.280, Rs.300, Rs.290, Rs.320, Rs.310, Rs.280.
15. A wall clock strikes the bell once at 1 o’clock, 2 times at 2 o’clock, 3 times at 3 o’clock and so on. How
many times will it strike in a particular day. Find the standard deviation of the number of strikes the bell
make a day.
16. The temperature of two cities A and B in a winter season are given below. Find which city is more
consistent in temperature changes?
17. The mean and standard deviation of marks obtained by 40 students of a
class in three subjects Mathematics, Science and Social science are given.
Which of the three subjects shows highest variation and which shows
lowest variation in marks?
18. If ൌ 5, ݔ ൌ 6, ଶݔߑ ൌ 765, then calculate the coefficient of variation.
19. The s.d and coefficient of variation of a data are 1.2 and 25.6 respectively. Find the value of mean.
20. Find the standard deviation of first 21 natural numbers.
21. If the standard deviation of a data is 3.6 and each value of the data is divided by 3, then find the new
variance and new standard deviation.
22. Find the range and coefficient of range of the following data.
(i) 63, 89, 98, 125, 79, 108, 117, 68 (ii) 43.5, 13.6, 18.9, 38.4, 61.4, 29.8
23. If the range and the smallest value of a set of data are 36.8 and 13.4 respectively, then find the
largest value.
24. If the standard deviation of a data is 4.5 and if each value of the data is decreased by 5, then find the new
standard deviation.
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
www.Padasalai.Net www.TrbTnpsc.com
Send Your Questions and Answers to Our Email Id - [email protected]
Page 9
Padasalai
A.BALAIAH TIRUNELVELI 9750493961 8 | P a g e
GRAPH:
1. Draw the graph of y = x2
– 4 and hence solve x2
– x – 12=0
2. Draw the graph of y = x2+x and hence solve x
2+1=0.
3. Draw the graph of y=x2+x – 2 and hence solve x
2+x – 2 = 0.
4. Draw the graph of y = 2x2
– 3x – 5 and hence solve 2x2
– 4x – 6 =0.
5. Draw the graph of y = x2+3x+2 and use it to solve x
2+2x+1=0.
6. Draw the graph of y = x2+3x – 4 and hence use it to solve x
2+3x – 4 = 0.
7. Draw the graph of y = x2
– 5x – 6 and hence solve x2
– 5x – 14=0.
8. Draw the graph of y = ( x – 1 )( x + 3 ) and hence solve x2
– x – 6 =0.
9. Draw the graph of y=x2
– 4x+3 and use it to solve x2
– 6x + 9 = 0.
10. Draw the graph of y=x2+4x+3 and hence find the roots of x
2+x+1=0.
11. Draw the Graph and state their nature of solutions.
(i) x2
– 9x +20 = 0 (ii) x2
– 4x+4=0 (iii) x2+x+7=0
(iv) x2
– 9 =0 (v) x2
– 6x+9 = 0 (vi) (2x – 3)(x+2)=0
(vii) x2+x – 12=0 (viii) x
2 – 8x+16=0 (ix) x
2+2x+5=0
PRACTICAL GEOMETRY:
1. Draw a triangle ABC of base BC=8cm, ∠A=60° and the bisector of ∠A meets BC at D such that
BD=6cm.
2. Construct a triangle similar to a given triangle PQR with its sides equal to ସof the
corresponding sides of the triangle PQR
3. Draw a circle of radius 4.5cm. Take a point on the circle. Draw the tangent at that point using
the alternative segment theorem.
4. Construct a ΔABC such that AB=5.5cm, ∟C=25° and the alƟtude from C to AB is 4cm.
5. Construct a triangle similar to a given triangle LMN with its sides equal to ସହ of the
corresponding sides of the triangle LMN.
6. Draw a tangent to the circle from the point P having radius 3.6cm, and centre at O. Point P is
at a distance 7.2cm from the centre and measure their lengths.
7. Construct a ΔPQR which the base PQ=4.5cm, ∟R=35° and the median from R to RG is 6cm.
8. Draw a tangent at any point R on the circle of radius 3.4cm and centre at P?
1. Tossing an unbiased coin twice S =
2. Tossing an unbiased coin thrice S =
3. Rolling an unbiased die once S =
4. Rolling an unbiased die twice S =
5. The probability of an event A lies between ____________
6. The probability of the sure event P(S) = _________
7. The probability of an impossible event p(ø) = _______
8. The probability that the event A will not occur p(ܣ) = ________
9. If A and B are mutually exclusive events, Then P(A∩B) = _________
10. P(AUB) =
11. P(AUBUC) =
12. Only one =
13. Prime numbers = 18. S.D (group)= ________
14. Neither A nor B = 19. S.D (ungroup)=________
15. Range = 20. S.D (word problem) =
16. Co – range = 21. Mean =
17. C.V =
No of cards -
Black card -
Red card -
Red king -
Black Queen -
Red diamond -
Red spade -
Face cards -
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
Padasalai
www.Padasalai.Net www.TrbTnpsc.com
Send Your Questions and Answers to Our Email Id - [email protected]
