1.Algebra Booster

8.26 Algebra Booster
5, 6, 7. A card is drawn from each of the boxes. Let x i
be the number on the card drawn from the ith box, i =1,
2, 3.
(i) The probability that x 1
+ x 2
+ x 3
is odd, is
(a)
29
105
(b)
53
105
(c)
57
105
(d)
1
2
(ii) The probability that x 1
.x 2
.x 3
are in an arithmetic
progression, is
(a)
9
105
(b)
10
105
(c)
11 7
(d)
105 105
[IIT-JEE, 2014]
ANSWERS
LEVEL I
1. (i) 1/4 (ii) 1/2 (iii) 1/4
2. (i) 3/8 (ii) 1/2 (iii) 3/8
3. (i) 1/12 (ii) 5/18 (iii) 1/2
(iv) 1/2 (v) 5/36 (vi) 1/6
4. (i) 1/216 (ii) 1/72 (iii) 1/36
(iv) 1/18 (v) 5/72 (vi) 5/54
(vii) 5/108
5. (i) 1/2 (ii) 1/2 (iii) 1/13
(iv) 1/26 (v) 1/52 (vi) 3/13
6. (i) 25/102 (ii) 1/221
(iii) 4/221 (iv) 32/663
(v) 4/13 (vi) 13/102
7. (i)
(ii)
(v)
(vii)
(ix)
26 2
C2 ¥ C2
52
C4
13
4 ¥ C
52
C
12
52
C
C
4
4
4
4
4 48
C2 ¥ C2
52
C4
36
52
C
C
4
4
(iv)
(vi)
(x)
12
52
C
C
4
4
(ii)
16 36
C3 ¥ C1
52
C4
(viii)
4
C4
¥
52
C4
9
(13)
52
C
4
4
12 40
C2 ¥ C2
52
C4
8. (i) 1/2 (ii) 1/2 (iii) 6/25
(iv) 1/50 (v) 1/25 (vi) 3/10
(vii) 1/10 (viii) 3/100
(ix) 1/50 (x) 1/50
9. (i) 1/165 (ii) 7/2475
(iii) 1/825 (iv) 1/330
(v) 10/99 (vi) 2/275
(vii) 2/2375 (viii) 1/4950
(ix) 1/2475
10. (i) 2/15 (ii) 1/3 (iii) 8/15
(iv) 7/15
11. (i) 1/20 (ii) 37/100 (iii) 3/50
12.
48 4
C9¥
C4
52
C4
13. 35/36
14. 1/6
7! ¥ 6!
15.
(12)!
16. 119/120
17. 2/3
18. 3/10
19. 1/3
5! ¥ 10! ¥ 8! ¥ 3!
20.
(23)!
21.
22. 2/3
23. 6/7
24.
25.
26.
7! ¥ 4!
(10)!
7
6! ¥ P4
(10)!
10! ¥ 9!
(19)!
2¥ 5! ¥ 5!
(10)!
27. 551/15134
28. 1/5
341
29.
5
(12)
Ê
365
C ˆ
n
30. Á1 -
(365)
n ˜
Ë ¯
31. 3/8
32. 9/4
33. 2/7
34. 1/7
35. 5/28
36. 9/50
37. 3/10
38. (i) 1/25 (ii) 67/100
(iii) 1/25 (iv) 21/25
(v) 1/2
39. 1/18
40. 53/54