JEE Advanced Mathematics Question Paper 2022 Download Free PDF
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JEE Advanced Mathematics Question Paper 2022 Download
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SAMPLE QUESTIONS
Q1. Let πΌ, π½, πΎ, πΏ be real numbers such that πΌ 2 + π½ 2 + πΎ 2 β 0 and πΌ + πΎ = 1. Suppose the point (3, 2, β1) is the mirror image of the point (1, 0, β1) with respect to the plane πΌπ₯ + π½π¦ + πΎπ§ = πΏ. Then which of the following statements is/are TRUE?
(A) πΌ + π½ = 2
(B) πΏ β πΎ = 3
(C) πΏ + π½ = 4
(D) πΌ + π½ + πΎ = πΏ
Q2. Suppose π, π denote the distinct real roots of the quadratic polynomial π₯2 + 20π₯ β 2020 and suppose π, π denote the distinct complex roots of the quadratic polynomial π₯2 β 20π₯ + 2020. Then the value of
ππ(π β π) + ππ(π β π) + ππ(π β π) + ππ(π β π) is
(A) 0
(B) 8000
(C) 8080
(D) 16000
Q3. If the function π: β βΆ β is defined by π(π₯) = |π₯|(π₯ β sin π₯), then which of the following statements is TRUE?
(A) π is one-one, but NOT onto
(B) π is onto, but NOT one-one
(C) π is BOTH one-one and onto
(D) π is NEITHER one-one NOR onto
Q4. Let the function π: β β β be defined by π(π₯) = π₯3 β π₯2 + (π₯ β 1) sin π₯ and let π: β β β be an arbitrary function. Let ππ: β β β be the product function defined by (ππ)(π₯) = π(π₯)π(π₯). Then which of the following statements is/are TRUE?
(A) If π is continuous at π₯ = 1, then ππ is differentiable at π₯ = 1
(B) If ππ is differentiable at π₯ = 1, then π is continuous at π₯ = 1
(C) If π is differentiable at π₯ = 1, then ππ is differentiable at π₯ = 1
(D) If ππ is differentiable at π₯ = 1, then π is differentiable at π₯ = 1
Q5. Let π be a 3 Γ 3 invertible matrix with real entries and let πΌ denote the 3 Γ 3 identity matrix. If πβ1 = adj (adj π), then which of the following statements is/are ALWAYS TRUE?
(A) π = πΌ
(B) det π = 1
(C) π2 = πΌ
(D) (adj π)2 = πΌ
See Alsoβ¦.