Download OU Intermediate 2018 Core Subjects 0266 Mathematics Question Paper

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Total No. of Questions - 24 Regd

Total No. of Printed Pages - 4

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Part - III

MATHEMATICS, Paper - II (A)

(Algebra and Probability)

(English Version)

Time : 3 Hours Max. Marks : 75

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Note : This question paper consists of three Sections A, B and C:

SECTION A 10x2=20

I. Very Short Answer Type Questions

i) Answer all questions.

ii) Each question carries two marks.

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1. If z = 2 - 3i, then show that, z² - 4z + 13 = 0.
2. If z₁ = -1 and z₂ = i, then find Arg(z₁/z₂).
3. If x = Cis θ, then find the value of (x⁶ + 1/x⁶).
4. Form a quadratic equation whose roots are 7 + 2√5.
5. If -1, 2, and α are the roots of 2x³ + bx² - 7x - 6 = 0, then find b.

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6. Find the number of ways of arranging the letters of the word MATHEMATICS.
7. If ⁿC₇ = ⁿC₉, then find ⁿC₂.
8. Prove that C₀ + 2.C₁ + 4.C₂ + 8.C₃ +...+ 2ⁿ.C_n = 3ⁿ.
9. Find the mean deviation about the median for the following data: 4, 6, 9, 3, 10, 18, 2.
10. A Poisson variable satisfies P(X=1) = P(X=2). Find P(X=5).

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SECTION B 5x4 = 20

II. Short Answer Type Questions.

i) Attempt any five questions.

ii) Each question carries four marks.

1. Show that the points in the Argand diagram represented by the complex numbers 2 + 2i, -2 - 2i, -2√3 + 2√3i are the vertices of an equilateral triangle.

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2. Prove that (3x+1)/(x+1) does not lie between 1 and 4, if x is real.
3. Find the sum of all 4 digit numbers that can be formed using the digits 1, 3, 5, 7, 9.
4. Find the number of ways of forming a team of 11 players from 7 batsmen and 6 bowlers, such that there will be at least 5 bowlers in the team.
5. Resolve (x²+5x+4)/(x-1)(x-2)(x-3) into partial fraction.
6. Suppose A and B are independent events with P(A) = 0.6, P(B) = 0.7. Then compute (i) P(A∩B), (ii) P(A∪B), (iii) P(B/A), (iv) P(A^c∩B^c).

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7. A, B, C are three horses in a race. The probability of A to win the race is twice that of B and probability of B is twice that of C. What are the probabilities of A, B and C to win the race?

SECTION C 5x7=35

III. Long Answer Type Questions.

i) Attempt any five questions.

ii) Each question carries seven marks.

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1. If Cosα + Cosβ + Cosγ = 0 = Sinα + Sinβ + Sinγ, then prove that Cos²α + Cos²β + Cos²γ = 3/2 = Sin²α + Sin²β + Sin²γ.
2. Solve the equation x⁴ - 10x³ + 26x² - 10x + 1 = 0.
3. If the coefficients of r^th, (r + 1)^th and (r + 2)^th terms in the expansion of (1+x)ⁿ are in A.P. Then show that n² - (4r+1)n + 4r² - 2 = 0.
4. If X = 5/(3.6) + (5.7)/(3.6.9) + (5.7.9)/(3.6.9.12) + ... ∞, then prove that 9x² + 24x = 11.
5. Find the mean deviation about the mean for the following data:

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19. State and prove the addition theorem on probability.
20. A random variable X has the following probability distribution.

Find (i) k (ii) Mean (iii) P(0 < X < 5)

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