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JEE Mathematics 2021 previous year questions with solutions

663 JEE Mathematics questions from 2021 in the Quantrex bank. Featured questions below open unique solution pages. Browse by chapter on JEE Mathematics.

663 questions2021
1

Let f₁:(0, ) R and f₂:(0, ) R be defined by f₁(x)= ₀^ x _ j=1 ²¹(t-j)^ j d t, x>0 and f₂(x)=98(x-1)⁵⁰-600(x-1)⁴⁹+2450, x>0 where, for any positive integer n and

JEE Advanced 2021 Application of Derivatives Solution View → 2

Let f₁:(0, ) R and f₂:(0, ) R be defined by f₁(x)= ₀^ x _ j=1 ²¹(t-j)^ j d t, x > 0 and f₂(x)=98(x-1)⁵⁰-600(x-1)⁴⁹+2450, x > 0 where, for any positive integer n

JEE Advanced 2021 Application of Derivatives Solution View → 3

Paragraph: Let ₁:[0, ) R , ₂:[0, ) R , f:[0, ) R and g:[0, ) R be functions such that f(0)=g(0)=0 , ₁(x)=e^ -x +x, x 0 , ₂(x)=x²-2 x-2 e^ -x +2, x 0 , f(x)= _ -

JEE Advanced 2021 Application of Derivatives Solution View → 4

Paragraph: Let ₁:[0, ) R , ₂:[0, ) R , f:[0, ) R and g:[0, ) R be functions such that f(0)=g(0)=0 , ₁(x)=e^ -x +x, x 0 , ₂(x)=x²-2 x-2 e^ -x +2, x 0 , f(x)= _ -

JEE Advanced 2021 Application of Derivatives Solution View → 5

Let f : R → R be defined by f x = x 2 - 3 x - 6 x 2 + 2 x + 4 Then which of the following statements is(are) TRUE?

JEE Advanced 2021 Application of Derivatives Solution View → 6

The function f x = x 3 - 6 x 2 + a x + b is such that f 2 = f 4 = 0 . Consider two statements: S 1 there exists x 1 , x 2 ∈ 2 , 4 , x 1 < x 2 , such t

JEE Main 2021 Application of Derivatives Solution View → 7

An angle of intersection of the curves, x 2 a 2 + y 2 b 2 = 1 and x 2 + y 2 = a b , a > b , is :

JEE Main 2021 Application of Derivatives Solution View → 8

Let f be any continuous function on 0 , 2 and twice differentiable on 0 , 2 . If f 0 = 0 , f 1 = 1 and f 2 = 2 , then :

JEE Main 2021 Application of Derivatives Solution View → 9

Let f x be a cubic polynomial with f 1 = - 10 , f - 1 = 6 , and has a local minima at x = 1 , and f ' x has a local minima at x = - 1 . Then f 3 is equal to .

JEE Main 2021 Application of Derivatives Solution View → 10

The number of real roots of the equation e 4 x + 2 e 3 x - e x - 6 = 0 is :

JEE Main 2021 Application of Derivatives Solution View → 11

If R is the least value of a such that the function f x = x 2 + a x + 1 is increasing on [ 1 , 2 ] and S is the greatest value of a such that the function f ( x

JEE Main 2021 Application of Derivatives Solution View → 12

A box open from top is made from a rectangular sheet of dimension a × b by cutting squares each of side x from each of the four corners and folding up the

JEE Main 2021 Application of Derivatives Solution View → 13

Let M and m respectively be the maximum and minimum values of the function f ( x ) = tan - 1 ( sin x + cos x ) in 0 , π 2 . Then the value of tan ( M - m )

JEE Main 2021 Application of Derivatives Solution View → 14

A wire of length 20 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a regular hexagon. Then the length of the s

JEE Main 2021 Application of Derivatives Solution View → 15

The number of distinct real roots of the equation 3 x 4 + 4 x 3 - 12 x 2 + 4 = 0 is _________.

JEE Main 2021 Application of Derivatives Solution View → 16

The local maximum value of the function, f x = 2 x x 2 , x > 0 , is

JEE Main 2021 Application of Derivatives Solution View → 17

A wire of length 36 m is cut into two pieces, one of the pieces is bent to form a square and the other is bent to form a circle. If the sum of the areas of the

JEE Main 2021 Application of Derivatives Solution View → 18

Let f : a , b → R be twice differentiable function such that f x = ∫ a x g t d t for a differentiable function g x . If f x = 0 has exactly five dis

JEE Main 2021 Application of Derivatives Solution View → 19

If a rectangle is inscribed in an equilateral triangle of side length 2 2 as shown in the figure, then the square of the largest area of such a rectangle is ___

JEE Main 2021 Application of Derivatives Solution View → 20

Let a curve y = f x pass through the point 2 , log e 2 2 and have slope 2 y x log e x for all positive real values of x . Then the value of f e is equal to ____

JEE Main 2021 Application of Derivatives Solution View → 21

Let f x = 3 sin 4 x + 10 sin 3 x + 6 sin 2 x - 3 , x ∈ - π 6 , π 2 . Then, f is :

JEE Main 2021 Application of Derivatives Solution View → 22

The number of real roots of the equation e 6 x - e 4 x - 2 e 3 x - 12 e 2 x + e x + 1 = 0 is:

JEE Main 2021 Application of Derivatives Solution View → 23

Let f : R → R be defined as f x = - 4 3 x 3 + 2 x 2 + 3 x , x > 0 3 x e x , x ≤ 0 . Then f is increasing function in the interval

JEE Main 2021 Application of Derivatives Solution View → 24

The sum of all the local minimum values of the twice differentiable function f : R → R defined by f x = x 3 - 3 x 2 - 3 f " ( 2 ) 2 x + f " 1 is:

JEE Main 2021 Application of Derivatives Solution View →

Other years

2014 · 1182015 · 872016 · 882017 · 882018 · 1302019 · 3492020 · 1,1412022 · 6502023 · 7522024 · 6342025 · 5072026 · 509
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