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JEE Mathematics 2018 previous year questions with solutions

130 JEE Mathematics questions from 2018 in the Quantrex bank. Featured questions below open unique solution pages. Browse by chapter on JEE Mathematics.

130 questions2018

For every twice differentiable function f : R → - 2 , 2 w i t h f 0 2 + f ′ 0 2 = 85 , which of the following statement(s) is (are) TRUE?

JEE Advanced 2018 Application of Derivatives Solution View → 2

The number of real solutions of the equation sin - 1 ⁡ ∑ i = 1 ∞ x i + 1 - x ∑ i = 1 ∞ x 2 i = π 2 - cos - 1 ⁡ ∑

JEE Advanced 2018 Application of Derivatives Solution View → 3

A farmer F 1 has a land in the shape of a triangle with vertices at P ( 0, 0 ) , Q ( 1, 1 ) and R ( 2, 0 ) . From this land, a neighbouring farmer F 2 takes awa

JEE Advanced 2018 Area Under Curves Solution View → 4

If the area of the region bounded by the curves, y = x 2 , y = 1 x and the lines y = 0 and x = t t > 1 is 1 sq . unit , then t is equal to

JEE Main 2018 Area Under Curves Solution View → 5

The area (in sq. units) of the region x R: x 0, y 0, y x-2 and y x , is

JEE Main 2018 Area Under Curves Solution View → 6

The area (in sq. units) of the region x ∈ R : x ≥ 0 , y ≥ 0 , y ≥ x - 2 and y ≤ x is

JEE Main 2018 Area Under Curves Solution View → 7

Let g x = cos x 2 , f x = x , and α , β α < β be the roots of the quadratic equation 18 x 2 - 9 π x + π 2 = 0 . Then the area

JEE Main 2018 Area Under Curves Solution View → 8

The value of log 2 ⁡ 9 2 1 log 2 ⁡ log 2 ⁡ 9 × 7 1 log 4 ⁡ 7 is_____.

JEE Advanced 2018 Basics of Mathematics Solution View → 9

Let S = x ∈ R : x ≥ 0 & 2 x - 3 + x x - 6 + 6 = 0 . Then S :

JEE Main 2018 Basics of Mathematics Solution View → 10

Let X = 10 C 1 2 + 2 10 C 2 2 + 3 10 C 3 2 + … + 10 10 C 10 2 , where 10 C r , r ∈ 1,2 , … . , 10 denote binomial coefficients. Then, the valu

JEE Advanced 2018 Binomial Theorem Solution View → 11

Let T be the line passing through the points P - 2 , 7 and Q 2 , - 5 . Let F 1 be the set of all pairs of circles S 1 , S 2 such that T is tangents to S 1 at P

JEE Advanced 2018 Circle Solution View → 12

Paragraph: Let S be the circle in the x y – plane defined by the equation x 2 + y 2 = 4 . Question : Let E 1 E 2 and F 1 F 2 be the chords of S passing th

JEE Advanced 2018 Circle Solution View → 13

Paragraph: Let S be the circle in the x y – plane defined by the equation x 2 + y 2 = 4 . Question : Let P be a point on the circle S with both coordinate

JEE Advanced 2018 Circle Solution View → 14

If a circle C , whose radius is 3 , touches externally the circle x 2 + y 2 + 2 x - 4 y - 4 = 0 at the point 2 , 2 , then the length of the intercept cut by thi

JEE Main 2018 Circle Solution View → 15

The tangent to the circle C₁: x^2+y^2-2 x-1=0 at the point (2,1) cuts off a chord of length 4 from a circle C₂ whose centre is (3,-2) . The radius of C₂ is

JEE Main 2018 Circle Solution View → 16

A circle passes through the points (2,3) and (4 , 5). If its centre lies on the line, y-4 x+3=0 , then its radius is equal to

JEE Main 2018 Circle Solution View → 17

A circle passes through the points 2 , 3 and 4 , 5 . If its centre lies on the line y - 4 x + 3 = 0 , then its radius is equal to :

JEE Main 2018 Circle Solution View → 18

Let s , t , r be non-zero complex numbers and L be the set of solutions z = x + i y x , y ∈ ℝ , i = - 1 of the equation s z + t z - + r = 0 , where

JEE Advanced 2018 Complex Number Solution View → 19

For a non-zero complex number z , let arg ( z ) denote the principal argument with - π < a r g z ≤ π then, which of the following statement(

JEE Advanced 2018 Complex Number Solution View → 20

The least positive integer n for which 1 + i 3 1 - i 3 n = 1 is

JEE Main 2018 Complex Number Solution View → 21

If |z-3+2 i| 4 then the difference between the greatest value and the least value of |z| is

JEE Main 2018 Complex Number Solution View → 22

The set of all R , for which w= 1+(1-8 ) z 1-z is a purely imaginary number, for all z C satisfying |z|=1 and Re z 1 , is

JEE Main 2018 Complex Number Solution View → 23

The set of all α ∈ R , for which w = 1 + 1 - 8 α z 1 - z is a purely imaginary number, for all z ∈ C satisfying z = 1 and R e z ≠ 1

JEE Main 2018 Complex Number Solution View → 24

If α , β ∈ C are the distinct roots of the equation x 2 - x + 1 = 0 , then α 101 + β 107 is equal to

JEE Main 2018 Complex Number Solution View →

Other years

2014 · 118 2015 · 87 2016 · 88 2017 · 88 2019 · 349 2020 · 1,141 2021 · 663 2022 · 650 2023 · 752 2024 · 634 2025 · 507 2026 · 509

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JEE Mathematics 2018 previous year questions with solutions

For every twice differentiable function f : R &#8594; - 2 , 2 w i t h f 0 2 + f &#8242; 0 2 = 85 , which of the following statement(s) is (are) TRUE?

The number of real solutions of the equation sin - 1 &#8289; &#8721; i = 1 &#8734; x i + 1 - x &#8721; i = 1 &#8734; x 2 i = &#960; 2 - cos - 1 &#8289; &#8721;

A farmer F 1 has a land in the shape of a triangle with vertices at P ( 0, 0 ) , Q ( 1, 1 ) and R ( 2, 0 ) . From this land, a neighbouring farmer F 2 takes awa

If the area of the region bounded by the curves, y = x 2 , y = 1 x and the lines y = 0 and x = t t &#62; 1 is 1 sq . unit , then t is equal to

The area (in sq. units) of the region x R: x 0, y 0, y x-2 and y x , is

The area (in sq. units) of the region x &#8712; R : x &#8805; 0 , y &#8805; 0 , y &#8805; x - 2 and y &#8804; x is

Let g x = cos x 2 , f x = x , and &#945; , &#946; &#945; &#60; &#946; be the roots of the quadratic equation 18 x 2 - 9 &#960; x + &#960; 2 = 0 . Then the area

The value of log 2 &#8289; 9 2 1 log 2 &#8289; log 2 &#8289; 9 &#215; 7 1 log 4 &#8289; 7 is_____.

Let S = x &#8712; R : x &#8805; 0 &#38; 2 x - 3 + x x - 6 + 6 = 0 . Then S :

Let X = 10 C 1 2 + 2 10 C 2 2 + 3 10 C 3 2 + &#8230; + 10 10 C 10 2 , where 10 C r , r &#8712; 1,2 , &#8230; . , 10 denote binomial coefficients. Then, the valu

Let T be the line passing through the points P - 2 , 7 and Q 2 , - 5 . Let F 1 be the set of all pairs of circles S 1 , S 2 such that T is tangents to S 1 at P

Paragraph: Let S be the circle in the x y &ndash; plane defined by the equation x 2 + y 2 = 4 . Question : Let E 1 E 2 and F 1 F 2 be the chords of S passing th

Paragraph: Let S be the circle in the x y &ndash; plane defined by the equation x 2 + y 2 = 4 . Question : Let P be a point on the circle S with both coordinate

If a circle C , whose radius is 3 , touches externally the circle x 2 + y 2 + 2 x - 4 y - 4 = 0 at the point 2 , 2 , then the length of the intercept cut by thi

The tangent to the circle C₁: x^2+y^2-2 x-1=0 at the point (2,1) cuts off a chord of length 4 from a circle C₂ whose centre is (3,-2) . The radius of C₂ is

A circle passes through the points (2,3) and (4 , 5). If its centre lies on the line, y-4 x+3=0 , then its radius is equal to

A circle passes through the points 2 , 3 and 4 , 5 . If its centre lies on the line y - 4 x + 3 = 0 , then its radius is equal to :

Let s , t , r be non-zero complex numbers and L be the set of solutions z = x + i y x , y &#8712; &#8477; , i = - 1 of the equation s z + t z - + r = 0 , where

For a non-zero complex number z , let arg ( z ) denote the principal argument with - &#960; &#60; a r g z &#8804; &#960; then, which of the following statement(

The least positive integer n for which 1 + i 3 1 - i 3 n = 1 is

If |z-3+2 i| 4 then the difference between the greatest value and the least value of |z| is

The set of all R , for which w= 1+(1-8 ) z 1-z is a purely imaginary number, for all z C satisfying |z|=1 and Re z 1 , is

The set of all &#945; &#8712; R , for which w = 1 + 1 - 8 &#945; z 1 - z is a purely imaginary number, for all z &#8712; C satisfying z = 1 and R e z &#8800; 1

If α , β ∈ C are the distinct roots of the equation x 2 - x + 1 = 0 , then α 101 + β 107 is equal to

Other years

For every twice differentiable function f : R → - 2 , 2 w i t h f 0 2 + f ′ 0 2 = 85 , which of the following statement(s) is (are) TRUE?

The number of real solutions of the equation sin - 1 ⁡ ∑ i = 1 ∞ x i + 1 - x ∑ i = 1 ∞ x 2 i = π 2 - cos - 1 ⁡ ∑

If the area of the region bounded by the curves, y = x 2 , y = 1 x and the lines y = 0 and x = t t > 1 is 1 sq . unit , then t is equal to

The area (in sq. units) of the region x ∈ R : x ≥ 0 , y ≥ 0 , y ≥ x - 2 and y ≤ x is

Let g x = cos x 2 , f x = x , and α , β α < β be the roots of the quadratic equation 18 x 2 - 9 π x + π 2 = 0 . Then the area

The value of log 2 ⁡ 9 2 1 log 2 ⁡ log 2 ⁡ 9 × 7 1 log 4 ⁡ 7 is_____.

Let S = x ∈ R : x ≥ 0 & 2 x - 3 + x x - 6 + 6 = 0 . Then S :

Let X = 10 C 1 2 + 2 10 C 2 2 + 3 10 C 3 2 + … + 10 10 C 10 2 , where 10 C r , r ∈ 1,2 , … . , 10 denote binomial coefficients. Then, the valu

Paragraph: Let S be the circle in the x y – plane defined by the equation x 2 + y 2 = 4 . Question : Let E 1 E 2 and F 1 F 2 be the chords of S passing th

Paragraph: Let S be the circle in the x y – plane defined by the equation x 2 + y 2 = 4 . Question : Let P be a point on the circle S with both coordinate

Let s , t , r be non-zero complex numbers and L be the set of solutions z = x + i y x , y ∈ ℝ , i = - 1 of the equation s z + t z - + r = 0 , where

For a non-zero complex number z , let arg ( z ) denote the principal argument with - π < a r g z ≤ π then, which of the following statement(

The set of all α ∈ R , for which w = 1 + 1 - 8 α z 1 - z is a purely imaginary number, for all z ∈ C satisfying z = 1 and R e z ≠ 1