Engineering Entrance

JEE Advanced 2023 — Set 1

English

Practice the official JEE Advanced 2023 previous year question paper

Questions

3.0

Marks/Question

180 min

Duration

English

Language

About This Paper

This is the official JEE Advanced 2023 examination paper, Set 1. The paper contains 54 multiple-choice questions.

The exam duration is 180 minutes.

Each correct answer carries 3.0 mark with a deduction of 1.0 for wrong answers.

Joint Entrance Examination (Advanced) — the gateway to IITs. Two papers (Physics, Chemistry, Mathematics), 3 hours each. Multiple question types: MCQ single/multiple, integer, matrix match.

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Sample Questions

Q1Section 1 – Single Correct Answer

Let (0,1) (1,2) (3,4) S = ∪ ∪ and {0,1,2,3} T = . Then which of the following statements is(are) true?

A.There are infinitely many functions from S to T

B.There are infinitely many strictly increasing functions from S to T

C.The number of continuous functions from S to T is at most 120

D.Every continuous function from S to T is differentiable

Q2Section 1 – Single Correct Answer

Let 1T and 2T be two distinct common tangents to the ellipse 2 2 : 1 6 3 x y E + = and the parabola 2 : 12 P y x = . Suppose that the tangent 1T touches P and E at the points 1A and 2 A , respectively and the tangent 2T touches P and E at the points 4 A and 3A , respectively. Then which of the following statements is(are) true?

A.The area of the quadrilateral 1 2 3 4 A A A A is 35 square units

B.The area of the quadrilateral 1 2 3 4 A A A A is 36 square units

C.The tangents 1T and 2T meet the x -axis at the point ( 3,0) −

D.The tangents 1T and 2T meet the x -axis at the point ( 6,0) −

Q3Section 1 – Single Correct Answer

Let :[0,1] [0,1] f → be the function defined by 3 2 5 17 ( ) 3 9 36 x f x x x = − + + . Consider the square region [0,1] [0,1] S = × . Let {( , ) : ( )} G x y S y f x = ∈ > be called the green region and {( , ) : ( )} R x y S y f x = ∈ < be called the red region. Let {( , ) : [0,1]} h L x h S x = ∈ ∈ be the horizontal line drawn at a height [0,1] h∈ . Then which of the following statements is(are) true?

A.There exists an 1 2 , 4 3 h ⎡ ⎤ ∈⎢ ⎥ ⎣ ⎦ such that the area of the green region above the line hL equals the area of the green region below the line hL

B.There exists an 1 2 , 4 3 h ⎡ ⎤ ∈⎢ ⎥ ⎣ ⎦ such that the area of the red region above the line hL equals the area of the red region below the line hL

C.There exists an 1 2 , 4 3 h ⎡ ⎤ ∈⎢ ⎥ ⎣ ⎦ such that the area of the green region above the line hL equals the area of the red region below the line hL

D.There exists an 1 2 , 4 3 h ⎡ ⎤ ∈⎢ ⎥ ⎣ ⎦ such that the area of the red region above the line hL equals the area of the green region below the line hL