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TGBIE · 2nd Year · MPC

Maths IIA — Important Questions

Chapter-wise important questions for TS Intermediate 2nd Year Mathematics IIA — organised by question type (VSAQ · SAQ · LAQ) as per the TGBIE exam pattern. Paper: 75 marks · 3 hours.

VSAQ(2 marks each)

Answer in 2–3 lines. Expect 10 questions — attempt all.

  1. 1.
    [Complex Numbers]Find the multiplicative inverse of 2 + 3i.
  2. 2.
    [Complex Numbers]If z = (√3 + i)³, find the modulus and amplitude of z.
  3. 3.
    [De Moivre's]Find the cube roots of unity. Show that they form vertices of an equilateral triangle.
  4. 4.
    [De Moivre's]If 1, ω, ω² are cube roots of unity, find the value of (1 + ω − ω²)⁸.
  5. 5.
    [Quadratic Expressions]For what values of x is x² − 3x + 2 > 0?
  6. 6.
    [Permutations]How many 5-digit numbers can be formed using 1, 2, 3, 4, 5 without repetition?
  7. 7.
    [Permutations]Find the number of ways of arranging 7 men and 3 women in a row if all women sit together.
  8. 8.
    [Combinations]Find ¹⁰C₃ + ¹⁰C₄ using Pascal's identity.
  9. 9.
    [Partial Fractions]Resolve x/(x² − 1) into partial fractions.
  10. 10.
    [Dispersion]If the mean of a dataset is 20 and variance is 25, find the coefficient of variation.
SAQ(4 marks each)

Answer in 5–7 lines with working. Choose 5 from 7 questions.

  1. 1.
    [Complex Numbers]If z₁ = 2 + 5i and z₂ = 1 − 3i, find z₁/z₂ in the form a + ib. Find its modulus and amplitude.
  2. 2.
    [Quadratic Expressions]Find the range of values of x for which (x − 1)(x + 2)/(x − 3) < 0.
  3. 3.
    [Theory of Equations]If α, β, γ are the roots of x³ − 5x² + 8x − 6 = 0, find α² + β² + γ².
  4. 4.
    [Theory of Equations]Solve: x⁴ − 5x³ + 5x² + 5x − 6 = 0 given one root is 1.
  5. 5.
    [Binomial Theorem]Find the general term and middle term of (2x − 3/x)⁸.
  6. 6.
    [Measures of Dispersion]Find the variance and standard deviation of the numbers 3, 6, 10, 12, 14.
  7. 7.
    [Probability]Two dice are thrown simultaneously. Find the probability that the sum is 7 or 11.
LAQ(7 marks each)

Full working required. Choose 5 from 7. Each carries 7 marks.

  1. 1.
    [Binomial Theorem]State and prove the Binomial theorem for a positive integer n. Find the sum of all coefficients and sum of coefficients of odd powers of x in (1+x)ⁿ.
  2. 2.
    [Binomial Theorem (Rational Index)]Find the first four terms of (1 + 2x)^(1/2) and hence approximate √(1.04).
  3. 3.
    [Theory of Equations]Solve x⁴ − 10x³ + 26x² − 10x + 1 = 0 (reciprocal equation).
  4. 4.
    [Permutations]Prove that the number of circular permutations of n distinct objects is (n−1)!. In how many ways can 6 people sit at a round table if two particular persons always sit together?
  5. 5.
    [Probability]State and prove Bayes' theorem. Apply it to solve: A bag has 4 white and 3 red balls. Another bag has 3 white and 5 red balls. One bag is chosen at random and one ball is drawn. If it is red, find the probability it came from the second bag.
  6. 6.
    [Random Variables]For a binomial distribution with n = 10 and p = 1/3, find P(X = 2), mean, and variance.
  7. 7.
    [Measures of Dispersion]Calculate the mean, variance, and coefficient of variation from a frequency distribution table.
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