*JEE Advanced Mathematics Question Paper 2022 Download Free PDF*

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*JEE Advanced Mathematics Question Paper 2022 Download*

*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} + 20**

**π₯ β 2020 and suppose**

**π,**

**π denote the distinct complex roots of the quadratic polynomial**

**π₯**

^{2}β 20**π₯ + 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 ****π ^{β1} = adj (adj **

**π), then which of the following statements is/are ALWAYS TRUE?**

(A) π = πΌ

(B) det π = 1

(C) π^{2} = πΌ

(D) (adj π)^{2} = πΌ

**See Alsoβ¦.**