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JEE Mathematics 2023 previous year questions with solutions

752 JEE Mathematics questions from 2023 in the Quantrex bank. Featured questions below open unique solution pages. Browse by chapter on JEE Mathematics.

752 questions2023

Let S be the set of all twice differentiable functions f from ℝ to ℝ such that d 2 f d x 2 x > 0 for all x ∈ - 1 , 1 . For f ∈ S , l

JEE Advanced 2023 Application of Derivatives Solution View → 2

max 0 ≤ x ≤ π x - 2 sin x cos x + 1 3 sin 3 x =

JEE Main 2023 Application of Derivatives Solution View → 3

The set of all a ∈ ℝ for which the equation x | x - 1 | + | x + 2 | + a = 0 has exactly one real root, is

JEE Main 2023 Application of Derivatives Solution View → 4

If the total maximum value of the function f x = 3 e 2 sin x sin 2 x , x ∈ 0 , π 2 , is k e , then k e 8 + k 8 e 5 + k 8 is equal to

JEE Main 2023 Application of Derivatives Solution View → 5

Let f : 2 , 4 → ℝ be a differentiable function such that x log e x f ' x + log e x f x + f x ≥ 1 , x ∈ 2 , 4 with f 2 = 1 2 and f 4

JEE Main 2023 Application of Derivatives Solution View → 6

Let g x = f x + f 1 - x and f " x > 0 , x ∈ 0 , 1 . If g is decreasing in the interval 0 , α and increasing in the interval α , 1 , then

JEE Main 2023 Application of Derivatives Solution View → 7

In the figure, θ 1 + θ 2 = π 2 and 3 BE = 4 AB . If the area of ∆ CAB is 2 3 - 3 unit 2 , when θ 2 θ 1 is the largest, then the p

JEE Main 2023 Application of Derivatives Solution View → 8

Let the quadratic curve passing through the point - 1 , 0 and touching the line y = x at 1 , 1 be y = f x . Then the x -intercept of the normal to the curve at

JEE Main 2023 Application of Derivatives Solution View → 9

A square piece of tin of side 30 cm is to be made into a box without top by cutting a square from each corner and folding up the flaps to form a box. If the vol

JEE Main 2023 Application of Derivatives Solution View → 10

If a α is the greatest term in the sequence a n = n 3 n 4 + 147 , n = 1 , 2 , 3 . . . . , then α is equal to _ _ _ _ _ _

JEE Main 2023 Application of Derivatives Solution View → 11

Let a curve y = f x , x ∈ 0 , ∞ pass through the points P 1 , 3 2 and Q a , 1 2 . If the tangent at any point R ( b , f ( b ) ) to the given curve c

JEE Main 2023 Application of Derivatives Solution View → 12

The number of points, where the curve y = x 5 - 20 x 3 + 50 x + 2 crosses the x -axis, is _____.

JEE Main 2023 Application of Derivatives Solution View → 13

Let the tangent to the curve x 2 + 2 x - 4 y + 9 = 0 at the point P 1 , 3 on it meet the y - axis at A . Let the line passing through P and parallel to the line

JEE Main 2023 Application of Derivatives Solution View → 14

The sum of the abosolute maximum and minimum values of the function f x = x 2 - 5 x + 6 - 3 x + 2 in the interval - 1 , 3 is equal to :

JEE Main 2023 Application of Derivatives Solution View → 15

Let f x = 2 x + tan - 1 x and g x = log e 1 + x 2 + x , x ∈ 0 , 3 . Then

JEE Main 2023 Application of Derivatives Solution View → 16

Let f x = 1 + sin 2 x cos 2 x sin 2 x sin 2 x 1 + cos 2 x sin 2 x sin 2 x cos 2 x 1 + sin 2 x , x ∈ π 6 , π 3 . If α and β respectivel

JEE Main 2023 Application of Derivatives Solution View → 17

If f x = x 2 + g ' 1 x + g " 2 and g x = f 1 x 2 + x f ' x + f " x , then the value of f 4 - g 4 is equal to _____ .

JEE Main 2023 Application of Derivatives Solution View → 18

The absolute minimum value, of the function f x = x 2 - x + 1 + x 2 - x + 1 , where t denotes the greatest integer function, in the interval - 1 , 2 , is

JEE Main 2023 Application of Derivatives Solution View → 19

A wire of length 20 m is to be cut into two pieces. A piece of length ℓ 1 is bent to make a square of area A 1 and the other piece of length ℓ 2 is

JEE Main 2023 Application of Derivatives Solution View → 20

If the functions f x = x 3 3 + 2 b x + a x 2 2 and g x = x 3 3 + a x + b x 2 , a ≠ 2 b have a common extreme point, then a + 2 b + 7 is equal to

JEE Main 2023 Application of Derivatives Solution View → 21

The number of points on the curve y = 54 x 5 - 135 x 4 - 70 x 3 + 180 x 2 + 210 x at which the normal lines are parallel to x + 90 y + 2 = 0 is:

JEE Main 2023 Application of Derivatives Solution View → 22

If the equation of the normal to the curve y = x - a x + b x - 2 at the point 1 , - 3 is x - 4 y = 13 then the value of a + b is equal to ______

JEE Main 2023 Application of Derivatives Solution View → 23

Let the function f ( x ) = 2 x 3 + ( 2 p - 7 ) x 2 + 3 ( 2 p - 9 ) x - 6 have a maxima for some value of x < 0 and a minima for some value of x > 0 . Th

JEE Main 2023 Application of Derivatives Solution View → 24

Let x = 2 be a local minima of the function f x = 2 x 4 - 18 x 2 + 8 x + 12 , x ∈ - 4 , 4 . If M is local maximum value of the function f in - 4 , 4 , the

JEE Main 2023 Application of Derivatives Solution View →

Other years

2014 · 118 2015 · 87 2016 · 88 2017 · 88 2018 · 130 2019 · 349 2020 · 1,141 2021 · 663 2022 · 650 2024 · 634 2025 · 507 2026 · 509

All JEE Maths chapters →

JEE Mathematics 2023 previous year questions with solutions

Let S be the set of all twice differentiable functions f from &#8477; to &#8477; such that d 2 f d x 2 x &#62; 0 for all x &#8712; - 1 , 1 . For f &#8712; S , l

max 0 &#8804; x &#8804; &#960; x - 2 sin x cos x + 1 3 sin 3 x =

The set of all a &#8712; &#8477; for which the equation x | x - 1 | + | x + 2 | + a = 0 has exactly one real root, is

If the total maximum value of the function f x = 3 e 2 sin x sin 2 x , x &#8712; 0 , &#960; 2 , is k e , then k e 8 + k 8 e 5 + k 8 is equal to

Let f : 2 , 4 &#8594; &#8477; be a differentiable function such that x log e x f &#39; x + log e x f x + f x &#8805; 1 , x &#8712; 2 , 4 with f 2 = 1 2 and f 4

Let g x = f x + f 1 - x and f &#34; x &#62; 0 , x &#8712; 0 , 1 . If g is decreasing in the interval 0 , &#945; and increasing in the interval &#945; , 1 , then

In the figure, &#952; 1 + &#952; 2 = &#960; 2 and 3 BE = 4 AB . If the area of &#8710; CAB is 2 3 - 3 unit 2 , when &#952; 2 &#952; 1 is the largest, then the p

Let the quadratic curve passing through the point - 1 , 0 and touching the line y = x at 1 , 1 be y = f x . Then the x -intercept of the normal to the curve at

A square piece of tin of side 30 cm is to be made into a box without top by cutting a square from each corner and folding up the flaps to form a box. If the vol

If a &#945; is the greatest term in the sequence a n = n 3 n 4 + 147 , n = 1 , 2 , 3 . . . . , then &#945; is equal to _ _ _ _ _ _

Let a curve y = f x , x &#8712; 0 , &#8734; pass through the points P 1 , 3 2 and Q a , 1 2 . If the tangent at any point R ( b , f ( b ) ) to the given curve c

The number of points, where the curve y = x 5 - 20 x 3 + 50 x + 2 crosses the x -axis, is _____.

Let the tangent to the curve x 2 + 2 x - 4 y + 9 = 0 at the point P 1 , 3 on it meet the y - axis at A . Let the line passing through P and parallel to the line

The sum of the abosolute maximum and minimum values of the function f x = x 2 - 5 x + 6 - 3 x + 2 in the interval - 1 , 3 is equal to :

Let f x = 2 x + tan - 1 x and g x = log e 1 + x 2 + x , x &#8712; 0 , 3 . Then

Let f x = 1 + sin 2 x cos 2 x sin 2 x sin 2 x 1 + cos 2 x sin 2 x sin 2 x cos 2 x 1 + sin 2 x , x &#8712; &#960; 6 , &#960; 3 . If &#945; and &#946; respectivel

If f x = x 2 + g &#39; 1 x + g &#34; 2 and g x = f 1 x 2 + x f ' x + f &#34; x , then the value of f 4 - g 4 is equal to _____ .

The absolute minimum value, of the function f x = x 2 - x + 1 + x 2 - x + 1 , where t denotes the greatest integer function, in the interval - 1 , 2 , is

A wire of length 20 m is to be cut into two pieces. A piece of length &#8467; 1 is bent to make a square of area A 1 and the other piece of length &#8467; 2 is

If the functions f x = x 3 3 + 2 b x + a x 2 2 and g x = x 3 3 + a x + b x 2 , a &#8800; 2 b have a common extreme point, then a + 2 b + 7 is equal to

The number of points on the curve y = 54 x 5 - 135 x 4 - 70 x 3 + 180 x 2 + 210 x at which the normal lines are parallel to x + 90 y + 2 = 0 is:

If the equation of the normal to the curve y = x - a x + b x - 2 at the point 1 , - 3 is x - 4 y = 13 then the value of a + b is equal to ______

Let the function f ( x ) = 2 x 3 + ( 2 p - 7 ) x 2 + 3 ( 2 p - 9 ) x - 6 have a maxima for some value of x &#60; 0 and a minima for some value of x &#62; 0 . Th

Let x = 2 be a local minima of the function f x = 2 x 4 - 18 x 2 + 8 x + 12 , x &#8712; - 4 , 4 . If M is local maximum value of the function f in - 4 , 4 , the

Other years

Let S be the set of all twice differentiable functions f from ℝ to ℝ such that d 2 f d x 2 x > 0 for all x ∈ - 1 , 1 . For f ∈ S , l

max 0 ≤ x ≤ π x - 2 sin x cos x + 1 3 sin 3 x =

The set of all a ∈ ℝ for which the equation x | x - 1 | + | x + 2 | + a = 0 has exactly one real root, is

If the total maximum value of the function f x = 3 e 2 sin x sin 2 x , x ∈ 0 , π 2 , is k e , then k e 8 + k 8 e 5 + k 8 is equal to

Let f : 2 , 4 → ℝ be a differentiable function such that x log e x f ' x + log e x f x + f x ≥ 1 , x ∈ 2 , 4 with f 2 = 1 2 and f 4

Let g x = f x + f 1 - x and f " x > 0 , x ∈ 0 , 1 . If g is decreasing in the interval 0 , α and increasing in the interval α , 1 , then

In the figure, θ 1 + θ 2 = π 2 and 3 BE = 4 AB . If the area of ∆ CAB is 2 3 - 3 unit 2 , when θ 2 θ 1 is the largest, then the p

If a α is the greatest term in the sequence a n = n 3 n 4 + 147 , n = 1 , 2 , 3 . . . . , then α is equal to _ _ _ _ _ _

Let a curve y = f x , x ∈ 0 , ∞ pass through the points P 1 , 3 2 and Q a , 1 2 . If the tangent at any point R ( b , f ( b ) ) to the given curve c

Let f x = 2 x + tan - 1 x and g x = log e 1 + x 2 + x , x ∈ 0 , 3 . Then

Let f x = 1 + sin 2 x cos 2 x sin 2 x sin 2 x 1 + cos 2 x sin 2 x sin 2 x cos 2 x 1 + sin 2 x , x ∈ π 6 , π 3 . If α and β respectivel

If f x = x 2 + g ' 1 x + g " 2 and g x = f 1 x 2 + x f ' x + f " x , then the value of f 4 - g 4 is equal to _____ .

A wire of length 20 m is to be cut into two pieces. A piece of length ℓ 1 is bent to make a square of area A 1 and the other piece of length ℓ 2 is

If the functions f x = x 3 3 + 2 b x + a x 2 2 and g x = x 3 3 + a x + b x 2 , a ≠ 2 b have a common extreme point, then a + 2 b + 7 is equal to

Let the function f ( x ) = 2 x 3 + ( 2 p - 7 ) x 2 + 3 ( 2 p - 9 ) x - 6 have a maxima for some value of x < 0 and a minima for some value of x > 0 . Th

Let x = 2 be a local minima of the function f x = 2 x 4 - 18 x 2 + 8 x + 12 , x ∈ - 4 , 4 . If M is local maximum value of the function f in - 4 , 4 , the