# JEE Advanced Mathematics Question Paper 2022

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SAMPLE QUESTIONS

Q1. Let πΌ, π½, πΎ, πΏ be real numbers such that πΌ 2 + π½ 2 + πΎ 2 β  0 and πΌ + πΎ = 1. Suppose the point (3, 2, β1) is the mirror image of the point (1, 0, β1) with respect to the plane πΌπ₯ + π½π¦ + πΎπ§ = πΏ. Then which of the following statements is/are TRUE?

(A) πΌ + π½ = 2

(B) πΏ β πΎ = 3

(C) πΏ + π½ = 4

(D) πΌ + π½ + πΎ = πΏ

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

ππ(π β π) + ππ(π β π) + ππ(π β π) + ππ(π β π) is

(A) 0

(B) 8000

(C) 8080

(D) 16000

Q3. If the function π: β βΆ 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 ππ: β β β be the product function defined by (ππ)(π₯) = π(π₯)π(π₯). Then which of the following statements is/are TRUE?

(A) If π is continuous at π₯ = 1, then ππ is differentiable at π₯ = 1

(B) If ππ is differentiable at π₯ = 1, then π is continuous at π₯ = 1

(C) If π is differentiable at π₯ = 1, then ππ is differentiable at π₯ = 1

(D) If ππ 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 πΌ denote the 3 Γ 3 identity matrix. If πβ1 = adj (adj π), then which of the following statements is/are ALWAYS TRUE?

(A) π = πΌ

(B) det π = 1

(C) π2 = πΌ