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Guess paper proof
A
14 – 03 – 2015
Part – III
MATHEMATICS, Paper – II (A)
(Algebra and Probability)
Time: 3 hours
Max. Marks: 75
Section – A
Very short answer types questions.
i)
Answer all questions
ii)
Each questions carries two marks
1. Find the real and imaginary parts of the complex number
.(concept problem,p.no:8)
2. Represent the complex number 2 + 3i in argand plane.
(out of problem)
3. If
.(Q.NO:28,29,39
are the cube roots of unity then that
Method)
4. Find the values of m, if the equation x2 – 15 – m(2x – 8) = 0have equal roots.
(Q.NO:38 direct problem)
5. Find the polynomial equation whose roots are the reciprocals of the roots of x4- 3x3
+ 7x2 + 5x - 2 =0.
6. If
= 42,
(Q.NO:63 direct problem)
, find n
(Q.NO:67 direct problem)
7. Find the number of ways of selecting 4 boys and 3 girls from a group of boys and 5
girls. (P.NO:186 , concept problem)
Sol:
= 70
10
= 700
8. If the coefficients of
term and
term in the expansion of
are equal, then find r.
(Q.NO: 82, 83 - Method)
9. Find the mean deviation about the median for the following data: 4, 6, 9, 3, 10, 13, 2
(Q.NO:102 ( C ) , Direct problem)
10. The mean and variance of a binomial distribution are 4 and 3 respectively. Fix the
distribution and find P(X 1).
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(Q.NO:111 , Direct problem)
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Section – B
Short answer types questions.
(i) Attempt any five questions
(ii) Each questions carries four marks
, show that 4x2 – 1 = 0.
11. If
12. Solve 2x4 + x3 – 11x2 + x + 2 = 0.
(Q.NO:116 , Direct problem)
(P.NO:69, II(3) )
13. Find the sum of all 4 digit numbers that can be formed using the digits 0, 2, 4, 7, 8
without repetition.
(Q.NO:168 , Direct problem)
14. Find the number of ways of forming a committee of 5 numbers out of 6 Indians and
5 Americans so that always the Indians will be in majority in the committee.
(Q.NO:162 , Direct problem)
15. Resolve
into partial fractions.
(Q.NO:186 , 2nd Method)
16. If A, B are two events with
, then find the value
of P(Ac) + P(Bc). (P.NO:338(13) , 2M Method )
Sol:
= P(A) + P(B) –
P(A) + P(B)
=
= 0.65 + 0.15
= 0.8
1Mark
P(Ac) + P(Bc) = 1- P(A) + 1 – P(B)
= 2 – [P(A) + P(B)]
1 Mark
=2 – 0.8
= 1.2
17. Find the probability of drawing an ace or a spade from a well shuffled pack of 52
playing cards.
(4th example , P.NO:323 ) – 2M
Sol: A pack of cards contains a total of 52 cards. These 52 cards are divided into 4 sets namely
Hearts, Diamonds, Spades and Clubs. Each set consists of 13 cards, namely.
A, 2, 3, 4, 5, 6, 7, 8, 10, J, Q, K
(Here : A: Ace, K : King, Q:Queen, J:Jack)
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Section – C
Long answer types questions.
(i) Attempt any five questions
(ii) Each questions carries seven marks
18. If
show that
+
(Q.NO:203 , Direct problem)
19. Solve 3x3 – 26x2 + 52x – 24 = 0, given that the roots are in geometric progression.
(Q.NO:214, Method)
20. For r = 0, 1, 2,………n prove that C0 . Cr + C1 . Cr+1 + C2 . Cr+2 + ……. + Cn-r . Cn =
(Q.NO:233 , Direct problem)
And hence deduce that
(i)
C02 + C12 + C22 + …………………+Cn2 =
(ii)
C0 . C1 + C1 . C2 + C2 . C3 +………………….. +Cn-1 . Cn =
21. Find the sum of the infinite series
…………
(Q.NO:244, Direct problem)
22. Find the variance and standard deviation of the following frequency distribution: (P.
NO:11th example, p. no:291, Method – example 12 - 295)
xi
4
8
11
17
20
24
32
fi
3
5
9
5
4
3
1
23. If A, B, C are three independent evens of an experiment such that, P(A Bc Cc) = ,
P(Ac Bc Cc) = , then find P(A), P(B), P(C).
(P. NO:337)
24. The range of a random variable X is {0, 1, 2}. Given that P(X=0)= 3c3, P(X=1)=4c10c2, P(X=2)=5c=1
(Q.NO: 355, II(1))
(i) Find the value of c.
(ii) P(X<1), P(1<X
3).
Note: P.NO
Telugu Akademi text book page number
Direct problems total scoring
: 43
Method problems total scoring
: 30
Total Scoring: 43 + 30 = 73
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Senior Intermediate
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2A IPE 2015 Question paper
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