TS Inter 2nd Year Maths 2A Question Paper March 2023

Thoroughly analyzing TS Inter 2nd Year Maths 2A Model Papers and TS Inter 2nd Year Maths 2A Question Paper March 2023 helps students identify their strengths and weaknesses.

TS Inter 2nd Year Maths 2A Question Paper March 2023

Time: 3 Hours
Maximum Marks: 75

Section – A
(10 × 2 = 20 Marks)

I. Very Short Answer Type Questions.

• Answer ALL questions.
• Each question carries TWO marks.

Question 1.
If z₁ = (2, -1), z₂ = (6, 3), find z₁ – z₂.

Question 2.
Write the conjugate of the complex number (3 + 4i).

Question 3.
If x = cis θ, then find the value of \(\left(x^6+\frac{1}{x^6}\right)\).

Question 4.
Find the roots of the equation x² – 7x + 12 = 0.

Question 5.
If 1, -2, and 3 are the roots of x³ – 2x² – ax + 6 = 0, then find a.

Question 6.
Find the number of ways of arranging the letters of the word INDEPENDENCE.

Question 7.
If ⁿC₄ = ⁿC₆, find n.

Question 8.
Find the middle term of the (3a – 5b)⁶.

Question 9.
Find the variance for the discrete data: 6, 7, 10, 12, 13, 4, 8, 12

Question 10.
A Poisson variable satisfies P(x = 1) = P(x = 2), Find P(x = 5).

Section – B
(5 × 4 = 20 Marks)

II. Short Answer Type Questions.

• Attempt ANY FIVE questions.
• Each question carries FOUR marks.

Question 11.
If z = 3 – 5i, then show that z³ – 10z² + 58z – 136 = 0.

Question 12.
Prove that \(\frac{1}{3 x+1}+\frac{1}{x+1}-\frac{1}{(3 x+1)(x+1)}\) does not lie between 1 and 4, if x is real.

Question 13.
Find the number of ways of selecting a cricket team of 11 players from 7 batsmen and 6 bowlers such that there will be at least 5 bowlers in the team.

Question 14.
If the letters of the word MASTER are permuted in all possible ways and the words thus formed are arranged in the dictionary order, then find the rank of the word REMAST.

Question 15.
Resolve \(\frac{5 x+1}{(x+2)(x-1)}\) into partial fractions.

Question 16.
A, B, C are three horses in a race. The probability of A winning the race is twice that of B, and the probability of B is twice that of C. What are the probabilities of A, B, and C to win the race?

Question 17.
A and B are events with P(A) = 0.5, P(B) = 0.4 and P (A ∩ B) = 0.3. Find the probability that
(i) A does not occur
(ii) neither A nor B occurs.

Section – C
(5 × 7 = 35 Marks)

III. Long Answer Type Questions.

• Answer ANY FIVE questions.
• Each question carries SEVEN marks.

Question 18.
If n is an integer, then show that (1 + cos θ + i sin θ)ⁿ + (1 + cos θ – i sin θ)ⁿ = \(2^{n+1} \cos ^n\left(\frac{\theta}{2}\right) \cdot \cos \left(\frac{\mathrm{n} \theta}{2}\right)\)

Question 19.
Solve the equation 3x³ – 26x² + 52x – 24 = 0 given that the roots are in G.P.

Question 20.
Find the sum of the infinite series \(1+\frac{1}{3}+\frac{1.3}{3.6}+\frac{1.3 .5}{3.6 .9}+\ldots \ldots \ldots .\)

Question 21.
If the coefficients of x⁹, x¹⁰, x¹¹ in the expansion of (1 + x)ⁿ are in A.P., then prove that n² – 41n + 398 = 0.

Question 22.
Find the mean deviation about the mean for the following data:

xi	2	5	7	8	10	35
fi	6	8	10	6	8	2

Question 23.
Suppose that an urn B₁ contains 2 white and 3 black balls and another urn B₂ contains 3 white and 4 black balls. One urn is selected at random and a ball is drawn from it. If the ball drawn is found black, find the probability that the urn chosen was B₁.

Question 24.
The range of a random variable x is (0, 1, 2). Given that P(x = 0) = 3c³, P(x = 1) = 4c – 10c², P(x = 2) = 5c – 1.
(i) Find the value of c.
(ii) P(x < 1), P(1 < x ≤ 2) and P(0 < x ≤ 3).