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JEE Mathematics 2022 previous year questions with solutions

650 JEE Mathematics questions from 2022 in the Quantrex bank. Featured questions below open unique solution pages. Browse by chapter on JEE Mathematics.

650 questions2022
1

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 equa

JEE Main 2022 Application of Derivatives Solution View → 2

Let f x = 3 x 2 - 2 3 + 4 , x ∈ 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 inf

JEE Main 2022 Application of Derivatives Solution View → 3

The function f x = x e x 1 - x , x ∈ R , is

JEE Main 2022 Application of Derivatives Solution View → 4

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 , π is

JEE Main 2022 Application of Derivatives Solution View → 5

Let f : 0 , 1 → 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 tw

JEE Main 2022 Application of Derivatives Solution View → 6

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

JEE Main 2022 Application of Derivatives Solution View → 7

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

JEE Main 2022 Application of Derivatives Solution View → 8

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

JEE Main 2022 Application of Derivatives Solution View → 9

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 - π 6 , π 6 , is a ¯ , then f a ¯ &#

JEE Main 2022 Application of Derivatives Solution View → 10

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

JEE Main 2022 Application of Derivatives Solution View → 11

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 Application of Derivatives Solution View → 12

Let the function f x = 2 x 2 - log e x , x > 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 p

JEE Main 2022 Application of Derivatives Solution View → 13

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

JEE Main 2022 Application of Derivatives Solution View → 14

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 α , then

JEE Main 2022 Application of Derivatives Solution View → 15

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 ' is equal to 3 . Then the

JEE Main 2022 Application of Derivatives Solution View → 16

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

JEE Main 2022 Application of Derivatives Solution View → 17

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 solu

JEE Main 2022 Application of Derivatives Solution View → 18

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 o

JEE Main 2022 Application of Derivatives Solution View → 19

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

JEE Main 2022 Application of Derivatives Solution View → 20

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

JEE Main 2022 Application of Derivatives Solution View → 21

If m and n respectively are the number of local maximum and local minimum points of the function f x = ∫ 0 x 2 t 2 - 5 t + 4 2 + e t d t , then the ordere

JEE Main 2022 Application of Derivatives Solution View → 22

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

JEE Main 2022 Application of Derivatives Solution View → 23

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 Application of Derivatives Solution View → 24

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 Application of Derivatives Solution View →

Other years

2014 · 1182015 · 872016 · 882017 · 882018 · 1302019 · 3492020 · 1,1412021 · 6632023 · 7522024 · 6342025 · 5072026 · 509
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