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Application of Derivatives — JEE Main & Advanced Mathematics PYQs

795 previous year questions from Application of Derivatives with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

795 questionsMathematicsSolutions on every page
1

Consider the function f: (0, ) (- , ) given by f(x) = x , _e(x) - x + 1 . Then which one of the following statements is TRUE?

JEE Advanced 2026 Solution View → 2

Let P be the point on the parabola y = x^2 such that the slope of the tangent to the parabola at the point P is 4 . Let Q be the point in the first quadrant lying on the circle x^2

JEE Advanced 2026 Solution View → 3

Let f: R R be a differentiable function such that f ( x+y 3 ) = f(x) + f(y) 3 for all x, y R , and f'(0) = 3 . Then the minimum value of the function g(x) = 3 + e^x f(x) , is:

JEE Main 2026 Solution View → 4

_ 0 x (16 ( x 2 ) ^3 ( x 2 ) ) is equal to:

JEE Main 2026 Solution View → 5

Let f(x) be a polynomial of degree 5 , and have extrema at x = 1 and x = -1 . If _ x 0 ( f(x) x^3 ) = -5 , then f(2) - f(-2) is equal to:

JEE Main 2026 Solution View → 6

The number of critical points of the function f(x) = cases | x x |, & x 0 1, & x = 0 cases in the interval (-2 , 2 ) is equal to :

JEE Main 2026 Solution View → 7

Let f be a differentiable function satisfying f(x)=1-2 x+ ₀^ x e ^ (x-t) f(t) dt , x R and let g (x)= ₀^ x (f( t )+2)¹⁵( t -4)⁶( t +12)¹⁷ dt , x R . If p and q are respectively the

JEE Main 2026 Solution View → 8

Consider the following three statements for the function f:(0, ) R defined by f(x)= | _ e x |-|x-1| : (I) f is differentiable at all x>0 . (II) f is increasing in (0,1) . (III) f i

JEE Main 2026 Solution View → 9

Let (2 , ) be the largest interval in which the function f(t)= |t+1| t² , t 2 , is _ _ _ _

JEE Main 2026 Solution View → 10

Let f(x)=x²⁰²⁵-x²⁰⁰⁰, x [0,1] and the minimum value of the function f(x) in the interval [0,1] be (80)⁸⁰(n)⁻⁸¹ . Then n is equal to

JEE Main 2026 Solution View → 11

Let f: R R be a twice differentiable function such that f''(x) > 0 for all x R and f'(a-1) = 0 , where a is a real number. Let g(x) = f ( ²x - 2 x + a ), ; 0 Consider the following

JEE Main 2026 Solution View → 12

Let f: R R be a twice differentiable function such that the quadratic equation f(x) m ²-2 f^ (x) m +f^ (x)=0 in m, has two equal roots for every x R . If f(0)=1, f^ (0)=2 , and ( ,

JEE Main 2026 Solution View → 13

Let R denote the set of all real numbers. Define the function f: R R by f( x )= array cc 2-2 x^2-x^2 1 x & if x 0 2 & if x=0 array . Then which one of the following statements is T

JEE Advanced 2025 Solution View → 14

Let R denote the set of all real numbers. For a real number x , let [x] denote the greatest integer less than or equal to x . Let n denote a natural number. Match each entry in Lis

JEE Advanced 2025 Solution View → 15

Let R denote the set of all real numbers. Let f: R R be defined by f(x)= cases 6 x+ x 2 x+ x & if x 0 7 3 & if x=0 cases Then which of the following statements is (are) TRUE?

JEE Advanced 2025 Solution View → 16

Let the function f(x)= x 3 + 3 x +3, x 0 be strictly increasing in (- , ₁ ) U ( ₂, ) and strictly decreasing in ( ₃, ₄ ) U ( ₄, ₅ ) . Then _ i =1 ^5 _ i ^2 is equal to :-

JEE Main 2025 Solution View → 17

Let f: R R be a polynomial function of degree four having extreme values at x=4 and x=5 . If _ x 0 f(x) x^2 =5 , then f(2) is equal to :

JEE Main 2025 Solution View → 18

Let x=-1 and x=2 be the critical points of the function f ( x )= x ^3+ ax ^2+ b _ c | x |+1, x 0 . Let m and M respectively be the absolute minimum and the absolute maximum values

JEE Main 2025 Solution View → 19

Let a 0 . If the function f ( x )=6 x ^3-45 a x ^2+108 a ^2 x +1 attains its local maximum and minimum values at the points x₁ and x₂ respectively such that x₁ x₂=54 , then a + x ₁

JEE Main 2025 Solution View → 20

Let f be a differentiable function on R such that f (2) = 1 , f^ (2)=4 . Let _ x 0 (f(2+x))^ 3 / x =e^ . Then the number of times the curve y=4 x^3-4 x^2-4( -7) x- meets x -axis is

JEE Main 2025 Solution View → 21

The shortest distance between the curves y^2=8 x and x^2+y^2+12 y+35=0 is :

JEE Main 2025 Solution View → 22

Let f : R R be a function defined by f(x)= |x+2|-2| x | . If m is the number of points of local minima and n is the number of points of local maxima of f , then m+n is

JEE Main 2025 Solution View → 23

If the function f(x)=2 x^3-9 ax ^2+12 a ^2 x +1 , where a 0 , attains its local maximum and local minimum values at p and q , respectively, such that p ^2= q , then f(3) is equal t

JEE Main 2025 Solution View → 24

The sum of all local minimum values of the function f(x)= array lr 1-2 x, & x -1 1 3 (7+2|x|), & -1 x 2 11 18 (x-4)(x-5), & x 2 array . is

JEE Main 2025 Solution View → 25

Let (2,3) be the largest open interval in which the function f(x)=2 _ e (x-2)-x^2+a x+1 is strictly increasing and (b, c) be the largest open interval, in which the function g (x)=

JEE Main 2025 Solution View → 26

A spherical chocolate ball has a layer of ice-cream of uniform thickness around it. When the thickness of the ice-cream layer is 1 cm , the ice-cream melts at the rate of 81 ~cm ^3

JEE Main 2025 Solution View → 27

If the set of all values of a, for which the equation 5 x^3-15 x-a=0 has three distinct real roots, is the interval ( , ) , then -2 is equal to ______

JEE Main 2025 Solution View → 28

Let the function f: R R be defined by f(x)= x e^ x (x²⁰²³+2024 x+2025 ) (x^2-x+3 ) + 2 e^ x (x²⁰²³+2024 x+2025 ) (x^2-x+3 ) . Then the number of solutions of f(x)=0 in R is

JEE Advanced 2024 Solution View → 29

Let the set of all values of p , for which f(x)= (p^2-6 p+8 ) ( ^2 2 x- ^2 2 x )+2(2-p) x+7 does not have any critical point, be the interval (a, b) . Then 16 a b is equal to _____

JEE Main 2024 Solution View → 30

A variable line L passes through the point (3,5) and intersects the positive coordinate axes at the points A and B . The minimum area of the triangle OAB , where O is the origin, i

JEE Main 2024 Solution View → 31

Let the set of all positive values of , for which the point of local minimum of the function (1+x ( ^2-x^2 ) ) satisfies x^2+x+2 x^2+5 x+6 < 0 , be ( , ) . Then ^2+ ^2 is equal to

JEE Main 2024 Solution View → 32

If the function f(x)=2 x^3-9 x^2+12 a ^2 x+1, a >0 has a local maximum at x= and a local minimum at x= ^2 , then and ^2 are the roots of the equation :

JEE Main 2024 Solution View → 33

Let A be the region enclosed by the parabola y^2=2 x and the line x=24 . Then the maximum area of the rectangle inscribed in the region A is________

JEE Main 2024 Solution View → 34

For the function f(x)=( x)-x+1, x R , between the following two statements (S1) f(x)=0 for only one value of x in [0, ] . (S2) f(x) is decreasing in [0, 2 ] and increasing in [ 2 ,

JEE Main 2024 Solution View → 35

Let f(x)=4 ^3 x+3 3 ^2 x-10 . The number of points of local maxima of f in interval (0,2 ) is

JEE Main 2024 Solution View → 36

The number of critical points of the function f(x)=(x-2)^ 2 / 3 (2 x+1) is

JEE Main 2024 Solution View → 37

If the function f(x)= ( 1 x )^ 2 x ; x>0 attains the maximum value at x= 1 e then :

JEE Main 2024 Solution View → 38

The interval in which the function f(x)=x^x, x>0 , is strictly increasing is

JEE Main 2024 Solution View → 39

Let the maximum and minimum values of ( 8 x-x^2-12 -4 )^2+(x-7)^2, x R be M and m , respectively. Then M ^2- m ^2 is equal to _________

JEE Main 2024 Solution View → 40

Let a rectangle A B C D of sides 2 and 4 be inscribed in another rectangle P Q R S such that the vertices of the rectangle A B C D lie on the sides of the rectangle P Q R S . Let a

JEE Main 2024 Solution View → 41

For the function f(x)= x+3 x- 2 (x^2+x ), where x [0, 2 ], consider the following two statements : (I) f is increasing in (0, 2 ) . (II) f^ is decreasing in (0, 2 ) . Between the a

JEE Main 2024 Solution View → 42

Let f(x)=3 x-2 + 4-x be a real valued function. If and are respectively the minimum and the maximum values of f , then ^2+2 ^2 is equal to

JEE Main 2024 Solution View → 43

Let f: R R be a thrice differentiable function such that f(0)=0, f(1)=1, f(2)=-1, f(3)=2 and f(4)=-2 . Then, the minimum number of zeros of (3 f^ f^ +f f^ )(x) is _______

JEE Main 2024 Solution View → 44

If 5 f x + 4 f 1 x = x 2 − 2 , ∀ x ≠ 0 and y = 9 x 2 f x , then y is strictly increasing in:

JEE Main 2024 Solution View → 45

Let f x = x + 3 2 x - 2 3 , x ∈ [ - 4 , 4 ] . If M and m are the maximum and minimum values of f , respectively in [ - 4 , 4 ] , then the value of M - m is :

JEE Main 2024 Solution View → 46

Let g : R → R be a non constant twice differentiable such that g ' 1 2 = g ' 3 2 . If a real valued function f is defined as f ( x ) = 1 2 [ g ( x ) + g ( 2 - x ) ] , then

JEE Main 2024 Solution View → 47

The function f x = 2 x + 3 x 2 3 , x ∈ R , has

JEE Main 2024 Solution View → 48

The function f x = x x 2 - 6 x - 16 , x ∈ ℝ - - 2 , 8

JEE Main 2024 Solution View → 49

Let g ( x ) = 3 f x 3 + f ( 3 - x ) and f " ( x ) > 0 for all x ∈ ( 0 , 3 ) . If g is decreasing in ( 0 , α ) and increasing in ( α , 3 ) , then 8 α is

JEE Main 2024 Solution View → 50

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 , let X f be the number

JEE Advanced 2023 Solution View → 51

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

JEE Main 2023 Solution View → 52

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

JEE Main 2023 Solution View → 53

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

JEE Main 2023 Solution View → 54

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 = 1 2 . Consider the

JEE Main 2023 Solution View → 55

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 tan - 1 2 &#945; +

JEE Main 2023 Solution View → 56

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 perimeter (in unit) o

JEE Main 2023 Solution View → 57

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 the point &#945; , &

JEE Main 2023 Solution View → 58

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 volume of the box is ma

JEE Main 2023 Solution View → 59

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 _ _ _ _ _ _

JEE Main 2023 Solution View → 60

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 cuts the y -axis at t

JEE Main 2023 Solution View → 61

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

JEE Main 2023 Solution View → 62

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 x - 3 y = 6 meet th

JEE Main 2023 Solution View → 63

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 Solution View → 64

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

JEE Main 2023 Solution View → 65

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; respectively are the maximum an

JEE Main 2023 Solution View → 66

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 _____ .

JEE Main 2023 Solution View → 67

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 Solution View → 68

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 made into a circle o

JEE Main 2023 Solution View → 69

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

JEE Main 2023 Solution View → 70

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 Solution View → 71

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 Solution View → 72

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 . Then, the set of all v

JEE Main 2023 Solution View → 73

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 , then M =

JEE Main 2023 Solution View → 74

If the tangent to the curve y = x 3 - x 2 + x at the point a , b is also tangent to the curve y = 5 x 2 + 2 x - 25 at the point 2 , - 1 , then 2 a + 9 b is equal to ______.

JEE Main 2022 Solution View → 75

Let f x = 3 x 2 - 2 3 + 4 , x &#8712; R . Then which of the following statements are true? P : x = 0 is a point of local minima of f Q : x = 2 is a point of inflection of f R : f &

JEE Main 2022 Solution View → 76

The function f x = x e x 1 - x , x &#8712; R , is

JEE Main 2022 Solution View → 77

The sum of the absolute maximum and absolute minimum values of the function f x = tan - 1 sin x - cos x in the interval 0 , &#960; is

JEE Main 2022 Solution View → 78

Let f : 0 , 1 &#8594; R be a twice differentiable function in 0 , 1 such that f 0 = 3 and f 1 = 5 . If the line y = 2 x + 3 intersects the graph of f at only two distinct points in

JEE Main 2022 Solution View → 79

A water tank has the shape of a right circular cone with axis vertical and vertex downwards. Its semivertical angle is tan - 1 3 4 . Water is poured in it at a constant rate of 6 c

JEE Main 2022 Solution View → 80

Let M and N be the number of points on the curve y 5 - 9 x y + 2 x = 0 , where the tangents to the curve are parallel to x -axis and y -axis, respectively. Then the value of M + N

JEE Main 2022 Solution View → 81

Let P and Q be any points on the curves x - 1 2 + y + 1 2 = 1 and y = x 2 , respectively. The distance between P and Q is minimum for some value of the abscissa of P in the interva

JEE Main 2022 Solution View → 82

If the maximum value of a , for which the function f a x = tan - 1 2 x - 3 a x + 7 is non-decreasing in - &#960; 6 , &#960; 6 , is a &#175; , then f a &#175; &#960; 8 is equal to

JEE Main 2022 Solution View → 83

Let f x = x 3 - x 2 + 10 x - 7 , x &#8804; 1 - 2 x + log 2 b 2 - 4 , x &#62; 1 Then the set of all values of b , for which f x has maximum value at x = 1 , is:

JEE Main 2022 Solution View → 84

The number of distinct real roots of the equation x 5 x 3 - x 2 - x + 1 + x 3 x 3 - 4 x 2 - 2 x + 4 - 1 = 0 is

JEE Main 2022 Solution View → 85

Let the function f x = 2 x 2 - log e x , x &#62; 0 , be decreasing in 0 , a and increasing in a , 4 . A tangent to the parabola y 2 = 4 a x at a point P on it passes through the po

JEE Main 2022 Solution View → 86

Let the area enclosed by the x -axis, and the tangent and normal drawn to the curve 4 x 3 - 3 x y 2 + 6 x 2 - 5 x y - 8 y 2 + 9 x + 14 = 0 at the point - 2 , 3 be A . Then 8 A is e

JEE Main 2022 Solution View → 87

If the absolute maximum value of the function f x = x 2 - 2 x + 7 e 4 x 3 - 12 x 2 - 180 x + 31 in the interval - 3 , 0 is f &#945; , then

JEE Main 2022 Solution View → 88

The curve y x = a x 3 + b x 2 + c x + 5 touches the x -axis at the point P - 2 , 0 and cuts the y -axis at the point Q , where y &#39; is equal to 3 . Then the local maximum value

JEE Main 2022 Solution View → 89

Let f : R &#8594; R be a function defined by f x = x - 3 n 1 x - 5 n 2 , n 1 , n 2 &#8712; N . The, which of the following is NOT true?

JEE Main 2022 Solution View → 90

Let f and g be twice differentiable even functions on - 2 , 2 such that f 1 4 = 0 , f 1 2 = 0 , f 1 = 1 and g 3 4 = 0 , g 1 = 2 Then, the minimum number of solutions of f x g &#34;

JEE Main 2022 Solution View → 91

A wire of length 22 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into an equilateral triangle. Then, the length of the side of the eq

JEE Main 2022 Solution View → 92

The number of real solutions of x 7 + 5 x 3 + 3 x + 1 = 0 is equal to _____.

JEE Main 2022 Solution View → 93

Let l be a line which is normal to the curve y = 2 x 2 + x + 2 at a point P on the curve. If the point Q 6 , 4 lies on the line l and O is origin, then the area of the triangle O P

JEE Main 2022 Solution View → 94

If m and n respectively are the number of local maximum and local minimum points of the function f x = &#8747; 0 x 2 t 2 - 5 t + 4 2 + e t d t , then the ordered pair m , n is equa

JEE Main 2022 Solution View → 95

The number of distinct real roots of x 4 - 4 x + 1 = 0 is

JEE Main 2022 Solution View → 96

The lengths of the sides of a triangle are 10 + x 2 , 10 + x 2 and 20 - 2 x 2 . If for x = k , the area of the triangle is maximum, then 3 k 2 is equal to

JEE Main 2022 Solution View → 97

If the sum of all the roots of the equation e 2 x - 11 e x - 45 e - x + 81 2 = 0 is log e P , then P is equal to _____.

JEE Main 2022 Solution View → 98

Consider a cuboid of sides 2 x , 4 x and 5 x and a closed hemisphere of radius r . If the sum of their surface areas is constant k , then the ratio x : r , for which the sum of the

JEE Main 2022 Solution View → 99

The sum of the absolute minimum and the absolute maximum values of the function f x = 3 x - x 2 + 2 - x in the interval - 1 , 2 is

JEE Main 2022 Solution View → 100

Let S be the set of all the natural numbers, for which the line x a + y b = 2 is a tangent to the curve x a n + y b n = 2 at the point a , b , a b &#8800; 0 . Then

JEE Main 2022 Solution View → 101

Let f x = 2 cos - 1 x + 4 cot - 1 x - 3 x 2 - 2 x + 10 , x &#8712; - 1 , 1 . If a , b is the range of the function, then 4 a - b is equal to

JEE Main 2022 Solution View → 102

Water is being filled at the rate of 1 cm 3 sec - 1 in a right circular conical vessel (vertex downwards) of height 35 cm and diameter 14 cm . When the height of the water level is

JEE Main 2022 Solution View → 103

If the line y = 4 + k x , k &#62; 0 , is the tangent to the parabola y = x - x 2 at the point P and V is the vertex of the parabola, then the slope of the line through P and V is

JEE Main 2022 Solution View → 104

Let f x = x - 1 x 2 - 2 x - 3 + x - 3 , x &#8712; &#8477; . If m and M are respectively the number of points of local minimum and local maximum of f in the interval 0 , 4 , then m

JEE Main 2022 Solution View → 105

If the angle made by the tangent at the point x 0 , y 0 on the curve x = 12 t + sin t cos t , y = 12 1 + sin t 2 , 0 &#60; t &#60; &#960; 2 , with the positive x -axis is &#960; 3

JEE Main 2022 Solution View → 106

Let f : R &#8594; R and g : R &#8594; R be two functions defined by f x = log e x 2 + 1 - e - x + 1 and g x = 1 - 2 e 2 x e x &#183; Then, for which of the following range of &#945

JEE Main 2022 Solution View → 107

The number of distinct real roots of the equation x 7 - 7 x - 2 = 0 is

JEE Main 2022 Solution View → 108

Let &#955; * be the largest value of &#955; for which the function f &#955; x = 4 &#955; x 3 - 36 &#955; x 2 + 36 x + 48 is increasing for all x &#8712; &#8477; . Then f &#955; * 1

JEE Main 2022 Solution View → 109

For the function f x = 4 log e x - 1 - 2 x 2 + 4 x + 5 , x &#62; 1 , which one of the following is NOT correct?

JEE Main 2022 Solution View → 110

If the tangent at the point x 1 , y 1 on the curve y = x 3 + 3 x 2 + 5 passes through the origin, then x 1 , y 1 does NOT lie on the curve

JEE Main 2022 Solution View → 111

The sum of absolute maximum and absolute minimum values of the function f x = 2 x 2 + 3 x - 2 + sin x cos x in the interval 0 , 1 is

JEE Main 2022 Solution View → 112

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 real numbers a₁, a₂

JEE Advanced 2021 Solution View → 113

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 real numbers a₁

JEE Advanced 2021 Solution View → 114

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)= _ -x ^ x (|t|-t² ) e^ -

JEE Advanced 2021 Solution View → 115

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)= _ -x ^ x (|t|-t² ) e^ -

JEE Advanced 2021 Solution View → 116

Let f : R &#8594; 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 Solution View → 117

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 &#8712; 2 , 4 , x 1 &#60; x 2 , such that f ' x 1 = - 1 an

JEE Main 2021 Solution View → 118

An angle of intersection of the curves, x 2 a 2 + y 2 b 2 = 1 and x 2 + y 2 = a b , a &#62; b , is :

JEE Main 2021 Solution View → 119

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 Solution View → 120

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 Solution View →
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