SOLVED PAPER 2022 (CDS) (I) (Elementary Mathematics)Total Questions: 10041. Consider a question and two statements:Question Is 3x + 2y positive?Statements I. x³ = - 29.8 II. y³ = 3xWhich one of the following is correct in respect of the question and the statements?(a) Statement I alone is sufficient to answer the question(b) Statement II alone is sufficient to answer the question(c) Both Statement I and Statement II are together sufficient to answer the question(d) Both Statement I and Statement II are not sufficient to answer the questionCorrect Answer: (c) Both Statement I and Statement II are together sufficient to answer the question42. Consider a question and two statements:Question Does the equation ax² + bx + c = 0 have real roots of opposite sign ?Statements I. The discriminant D > 0 II. (c/a) > 0Which one of the following is correct in respect of the question and the statements?(a) Statement I alone is sufficient to answer the question(b) Statement II alone is sufficient to answer the question(c) Both Statement I and Statement II are together sufficient to answer the question(d) Both Statement I and Statement II are not sufficient to answer the questionCorrect Answer: (b) Statement II alone is sufficient to answer the question43. Consider a question and two statements:Question Is a² + b² + c² - ab - bc - ca (a, b, c are distinct real numbers) always positive?(a) Statement I alone is required to answer the question(b) Statement II alone is required to answer the question(c) Both Statement I and Statement II are required to answer the question(d) Neither Statement I nor Statement II is required to answer the questionCorrect Answer: (d) Neither Statement I nor Statement II is required to answer the question44. Solved (a) Statement I alone is required to answer the question(b) Statement II alone is required to answer the question(c) Both Statement I and Statement II are required to answer the question(d) Neither Statement I nor Statement II is required to answer the questionCorrect Answer: (d) Neither Statement I nor Statement II is required to answer the question45. How many quadratic equations have the sum of their roots equal to the product of their roots?(a) Zero(b) One(c) Two(d) Infinitely manyCorrect Answer: (d) Infinitely many46. Solved(a)(b)(c)(d)Correct Answer: (b)47. Solved(a)(b)(c)(d)Correct Answer: (a)48. What is the minimum value ofsin⁴θ + cos⁴θ - 2sin²θ cos²θ ?(a) 0(b) 1(c) 2(d) Minimum value does not existCorrect Answer: (a) 049. If cosθ + secθ - 2 = 0, where0 ≤ θ < π/2, then what is the value of cos⁴θ + sec⁴θ - 2(a) -2(b) -1(c) 0(d) 2Correct Answer: (c) 050. If y = cos² x + sec² x where0 ≤ θ ≤ π/2, then which one of the following is correct?(a) 0 0.5(b) 0.5 ≤ y < 1(c) 1 ≤ y < 2(d) y ≥ 2Correct Answer: (d) y ≥ 2Submit Quiz« Previous12345678910Next »
