Part-I Secondary and Senior Secondary Standard: is a Maths Part-I Secondary/Sr.Sec (Senior Teacher) topic in the RAS/RPSC syllabus. This page gathers exam-style Part-I Secondary and Senior Secondary Standard: multiple-choice questions with correct answers and explanations, so aspirants can test recall and revise frequently examined concepts.
Practice 294 Part-I Secondary and Senior Secondary Standard: multiple-choice questions with detailed answers and explanations. Ideal for RAS/RPSC exam preparation.
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Q1. For the parametric curve x = t^2, y = t^3 - 3t with t != 0, the value of d^2y/dx^2 is
Explanation
Here dy/dt = 3t^2 - 3 and dx/dt = 2t, so dy/dx = 3(t^2-1)/(2t) = (3/2)(t - 1/t). Differentiating with respect to t gives (3/2)(1 + 1/t^2), and division by dx/dt = 2t gives d^2y/dx^2 = 3(t^2+1)/(4t^3).
Q2. If A = tan^(-1)(1/2) + tan^(-1)(1/3), where tan^(-1) denotes principal value, then A is equal to:
Explanation
For u = 1/2 and v = 1/3, tan(D) = (u + v)/(1 - uv) = (5/6)/(5/6) = 1. Since both terms are principal positive acute angles, A lies in (0, pi/2), so A = pi/4.
Q3. If |[[x, 2], [3, x + 1]]| = 4, then the sum of all real values of x is
Explanation
The determinant is x(x + 1) - 2·3 = x^2 + x - 6. Equating it to 4 gives x^2 + x - 10 = 0. For ax^2 + bx + c = 0, the sum of roots is -b/a; here it is -1. But because the equation is x^2 + x - 10 = 0, the sum of all real values is -1.
Q4. For the matrix A = [[1, 2, 3], [0, -1, 4], [2, 1, 0]], what is det(A)?
Explanation
Expand along the first row: det(A) = 1((-1)(0) - 4(1)) - 2(0(0) - 4(2)) + 3(0(1) - (-1)(2)). This equals -4 - 2(-8) + 3(2) = -4 + 16 + 6 = 18.
Q5. A discrete random variable X takes values 0, 1, 2 and 3 with probabilities k, 2k, 3k and 4k respectively. Which statement is correct?
Explanation
For a probability distribution, the probabilities must sum to 1; hence k + 2k + 3k + 4k = 10k = 1. So k = 1/10 and P(X >= 2) = 3k + 4k = 7/10. Also E(X) = 2 and E(X^2) = 5, giving Var(X) = 5 - 2^2 = 1.
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