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7/27/2019 Algebra Home Work
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OMTEX CLASSESHOME WORK ASSIGNMENT
1. Find the first four terms of the sequence whose nthterm is 3n+1. (Ans. 4, 7, 10, 13)
2. Find the first three terms of the sequence whose nthterm is 12 + 1. (Ans. 2, 54, 109 )
3. If = +1for a sequence then find the first three terms. . 12 , 16 , 1124. Write the next three terms of the A.P. whose first term is 11 and the common difference
is 1.5. (Ans. 12.5, 14, 15.5)
5. State whether the following sequence is an A.P. or not. 13, 23 , 33 , 43, .. . (Not an A.P.)6. The sum of the measures of angles of a triangle is 1800, of a quadrilateral is 3600, of a
pentagon is 5400, of a hexagon is 7200 , and so on. Then find the sum of measures of angles
of a dodecagon (i.e. polygon with 12 sides). (Ans. 18000).
7. Find tn and hence t15of the following A.P. 3, 8, 13, 18, .... (Ans. tn = 5n 2 , t15= 73)8. Show that the nth odd natural number is 2n 1 .9. Find n if the sequence is 5, 8, 11, 14 ....68. (Ans. n=22)
10 . If the 10thterm and the 18thterm of an A.P. are 25 and 41 respectively then find the
following. (i) the 1stterm and the common difference. (ii) the 38thterm. (iii) n such that the
nthterm is 99. (Ans. (i) a = 7 , d = 2 (ii) t38= 81, (iii) n = 47)
11. How many terms are there in the A.P. 187, 194, 201, 439? (Ans. 37)12. Find the sum of 7, 11, 15, 19, , up to 60 terms. (Ans. S60 = 7500)13.If for an A.P., the first term is 3 and the common difference is 6 then find Snand hence
find S10.(Ans. Sn= 3n2, S10 = 300)
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OMTEX CLASSESHOME WORK ASSIGNMENT
14. You wish to buy a pencil, a notebook and a pen. The prices of these are in A.P. such that
the sum of prices of these three things is 27 and sum of the square of their prices is 341.
Find the price of each thing. (Ans. 2, 9, 16 OR 16, 9, 2)
15. Find four consecutive terms in an A.P. such that the sum of the middle two terms is 18
and product of the two end terms is 45. (Ans. 3, 7, 11, 15 OR 15, 11, 7, 3)
16. Find three consecutive terms in an A.P. whose sum is 27 and their product is 504. (Ans.
4,9, 14 OR 14, 9, 4)
17. A man repays a loan of Rs. 3250 by paying Rs. 305 in the first month and then decreases
the payment by Rs. 15 every month. How long will it take to clear his loan? (Ans. n= 20
MONTHS)
18. A farmer borrows Rs. 1000 and agrees to repay with a total interest of Rs. 140 in 12
instalments, each instalment being less than the preceding instalment by Rs. 10. What
should be his first instalment? (Ans. Rs. 150)
19. Solve the following quadratic equations by factorization method.
(i). 2 13 + 30 = 0 (Ans. 10 , 3) (ii) 2 5 36 = 0 (Ans. 9, -4) (iii) 32 14 + 8 =0 (Ans. 4,
2
3) (iv) 642 625 = 0. (Ans. = 25
8 ,
25
8) (v) + 35 = 12 (Ans. 7,5)
20. Solve by completing square: 2 + 8 + 15 = 0 (Ans. -3, -5)21. Solve by completing square: 2 + 3 + 1 = 0 (Ans. 3+52 , 352 .22. Solve by formula: (i) 2 + 2 7 = 0 (ii) 3x2 + 8x + 3 = 0 (iii) 52 + 5 = 1 (iv)2 + 4 1 = 0 (Ans. (i) 1 22 (ii) 47
3 (iii)
53510
(iv) 2 5)
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OMTEX CLASSESHOME WORK ASSIGNMENT
23. Find the value of discriminant for each of the following equation.
(i) 2 + 4 + 1 = 0 (Ans. = 12) (ii) 32 + 2 + 1 = 0 (. = 8)25. Determine the nature of roots of the following equations from their discriminating.
(i) 2 2 + 94
= 0 (Ans. Not real) (ii) 2 = 0 (Ans. Real and equal)26. Find the value of if the given equation 42 3 + 1 = 0 has real and equal roots.(Ans. = 4
3 or = 4
3)
27. Find , if the root of the equation 52 + 6 + = 0 is 5 times the other. (Ans. = 1)28. Find , if the roots of the equation 2 + + 48 = 0 are in the ratio 3:4. (Ans. = 14)29. If and are the roots of the equation 2 4 + 1 = 0, find (i) 2 + 2(ii) + (Ans. (i) = 14 (ii) = 14)
30. If one root of the quadratic equation 2 8 + = 0 is 4 + 3 , find . (Ans. = 13. )31. If the roots of the quadratic equation are 6 and 7 find the quadratic equation. (Ans.
2 13 + 42 = 0)32. If one of the root of the quadratic equation is 2 5. Find the quadratic equation.(Ans. 2 4 1 = 0)33. If
+
= 5 and
2 +
2 = 53. Find a quadratic equation whose roots are
and
.
(Ans. 2 5 14 = 0)34. If + = 5 and 3 + 3 = 35. Find a quadratic equation whose roots are and .(Ans. 2 5 + 6 = 0)
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OMTEX CLASSESHOME WORK ASSIGNMENT
35. Solve: 54 222 + 8 = 0 (Ans. 2 , 25 )
36. 42 + 6 2 = 11 (Ans. 2 , 32 )37. (2 + )(2 + 2) = 24 (Ans. -3, 2, Not real roots)38. 2 + 1 2 7 + 1 = 14 (Ans. 352 , 2 3)
39. 12 2 + 1 2 28 1 9 = 0. (Ans. 2, 12 , 32 , 23)40. Without actually solving the simultaneous equations given below, examine which
simultaneous equations have unique solution, no solution or infinitely many solutions.
(i) + 3 + 4 = 0; 2x+ 6 y 3 = 0 (No solution) (ii) 4x y 6 = 0; 2 2
= 3 (Infinitely
many solutions) (iii) y = 2x + 14 ; 7x = 2y + 5 (unique solution)
41. Find the value of k for which the given simultaneous equations have infinitely many
solutions: k y + 3 y = 8 ; 6 x + 9 y = 24 . (Ans. = 2)
42 . Find the value of k for which the given simultaneous equations have infinitely many
solutions. k x + 2 y = k 2 ; 8 x + k y = k (Ans. k = 4 which satisfies both the conditions.)43. Find the value of m for which the given simultaneous equations have unique solution:
+ 5 11 = 0, 14 = 15 7) ( Ans. 10. Therefore, the simultaneous equationswill have a unique solution for all the values of m, except 10)
44. Solve the following simultaneous equations:4
+3
= 1;8
9 = 7 (Ans. x = 2 and y = -3)
45. Solve:1
3 14 + 1 = 0; 15 + 12 = 415 (Ans. = 12 and = 34)
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OMTEX CLASSESHOME WORK ASSIGNMENT
46.7
2+1 +13
+2 = 27;13
2+1 +7
+2 = 33. Ans. = 14and = 1.47. Two coins are tossed simultaneously. Write the sample space 'S' and the number of
sample points n(S). Write the following events using set notation and mention the total
number of elements in each of them.
A is the event of getting at least one head.
B is the event of getting exactly one head.
C is the event of getting at most one tail.
D is the event of getting at most one tail.
D is the event of getting no head.
Find the events among the events defined above which are complementary events,
mutually exclusive events.
Ans. n(S) = 4, n(A) = 3, n(B) = 2, n(C) = 3, n(D) = 1
Events A and D are complementary events and mutually exclusive also.
Events C and D are complementary events and also mutually exclusive.
Events B and D are mutually exclusive events but not complementary events.
48. In a bag, there are fifty cards bearing number from 1 to 50, one card is drawn at
random. Write the sample space S. Write the events A and B using set and mention number
of sample points in them, where A is the event that the number on the card is divisible by 5.
B is the event that the number on the card is a prime number. Also examine whether events
A and B are complementary events or mutually exclusive events or both.
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OMTEX CLASSESHOME WORK ASSIGNMENT
Ans. n(S) = 50, n(A) = 10, n(B) = 15. A and B are not complementary events and also not
mutually exclusive.
49. There are three boys and three girls. An environment committee of two is to be formed.
Write the sample space S, the number of sample points n(S).
A is the event that the committee should contain atleast two girls.
B is the event that the committee should contain both boys.
C is the event that there is only one girl in the committee.
D is the event that there is atmost one boy in the committee.
Find the events among the events defined above which are:
Complementary events, mutually exclusive events and exhaustive events.
Ans. n(S) = 15, n(A) = 5, n(B) = 3, n(D) =12,
A and B are mutually exclusive events.
B and C are mutually exclusive events.
B and D are mutually exclusive events.
B and D are complementary events and exhaustive events.
50. A coin is tossed. Find the probability of the events. (i) Getting a head (ii) Getting a tail.
(Ans. (i) (ii) )
51. A card is drawn at random from a pack of well shuffled 52 cards. Find the probability
that the card drawn is (i) a king (ii) an ace. (Ans. (i) 1/13 , (ii) 1/13.
52. If a card is drawn from a pack of 52 cards then find the probability of getting (i) a red
card (ii) a face card. Ans. (i) (ii) 3/13