Roll No. :
Date :
Time MM - 67
1. If m times the mth term of an A.P. is equal to n times its nth term, show that the (m + n)th term of
the A.P. is zero.
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2.
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Find the value of n, so that
may be geometric mean between a and b.
3. Solve the equation for ‘x’ : 2 + 5 + 8 + 11 + .......... + x = 345
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4. If a, b, c and d are in G.P. Prove that, (an + bn), (bn + cn), (cn + dn) are in G.P.
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5. The pth, qth and rth terms of an A.P. are a, b, c respectively. Show that (q – r) a + (r – p) b + (p –
q) c = 0
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6. Find the sum of first 24 terms of the A.P. a1, a2, a3 ............ if it is known that a1 + a5 + a10 + a15
+ a20 + a24 = 225.
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7. Find the sum the following series up to n terms : 7 + 77 + 777 + .......
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8. How many terms of the series
+ ...... will make the sum 39 + 13
?
9. The first term of a G.P. exceeds the second term by 2 and the sum to infinity is 50. Find the G.P.
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10. If x = 1 + a + a2 + ........ ∞, | a | < 1 and y = 1 + b + b2 + ..... ∞, | b | < 1, show that 1 + ab + a2b2 + 4
a3b3 + ..... =
.
11. In a survey of 25 students, it was found that 15 had taken Mathematics, 12 had taken Physics
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and 11 had taken Chemistry, 5 had taken Mathematics and Chemistry, 9 had taken Mathematics
and Physics, 4 had taken Physics and Chemistry and 3 had taken all the three subjects. Find the
number of students that had taken,
(i) Only Chemistry
(ii) Only Mathematics
(iii) Only Physics
(iv) Physics and Chemistry but not Mathematics.
(v) Mathematics and Physics but not Chemistry.
(vi) Only one of the subject
(vii) At least one of the three subjects
(viii) None of the subjects.
12. The product of three terms in G.P. is 1000. If 6 and 7 are added to second and third terms
respectively, the terms form an A.P., find the G.P.
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13. If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers 6
are A ±
.
14. If S = {x|x is a positive multiple of 3 less than 100} P = {x|x is a prime number less than 20}.
Then n(S) + n(P) is
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(a) 34 (b) 31 (c) 33 (d) 41
15. In a group of 40 students, 26 take tea, 18 take coffee and 8 take neither of the two, then number of persons taking both the tea
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and coffee is
(a)
32
(b)
18
(c)
12
(d)
8
16. Find the value of k so that 2k + 1, k2 + k + 1, 3k2 – 3k + 3 are in AP.
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17. Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. find (i) A′ (ii) 2
(A ∩ C)′ (iii) (A′)′ (iv) (B – C)′
18. If A = {1, 3, 5, 7, 9, 11, 13, 15, 17}, B = {2, 4, 6, ....., 18} and N is the universal set, then find A′ ∪
{(A ∪ B) ∩ B′}.
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19. Find the sum of infinity for each of the following G.P.'s : 10, – 9, 8.1, .......
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