Atomos Test Generator Free PYQs ExamsMy practice Log in / Sign up free

Relations and Functions

JEE Main 2026 (Online) 2nd April Morning ShiftNumericalHard📈 Topic in 31% papers+4
Ques. 1JEE Main 2026, 2 April (Morning Shift)

If the domain of the function f(x)= (0.6) ( | 2x-5x2-4 | ) is (- , a] \b\ [c, d) (e, ), then the value of a+b+c+d+e is .

Answer

4

Solution

f is defined when (0.6) | 2x - 5x2 - 4 | 0.

∵ The base 0.6 < 1, this needs 0 < | 2x - 5x2 - 4 | 1, with x 2 and x 52, so

|2x - 5| |x2 - 4|

(x2 - 4)2 - (2x - 5)2 0

(x2 - 2x + 1)(x2 + 2x - 9) 0

(x - 1)2(x2 + 2x - 9) 0

x = 1 or x -1 - 10 or x -1 + 10

Here x = 2 are not in this set, but -1 + 10 2.16 < 52, so x = 52 must be removed. Hence

Domain = (- , -1 - 10 ] \1\ [-1 + 10, 52 ) ( 52, )

so a = -1 - 10, b = 1, c = -1 + 10 and d = e = 52.

∴ a + b + c + d + e = -1 + 1 - 1 + 5 = 4

Answer: 4

Keep practising — Relations and Functions

Ques. 2JEE Main 2026, 2 April (Evening Shift)

Let A=\2, 3, 4, 5, 6\. Let R be a relation on the set A A given by (x, y)R(z, w) if and only if x divides z and y w. Then the number of elements in R is .

Ques. 3JEE Main 2026, 24 January (Morning Shift)

If the domain of the function f(x) = (10x2 - 17x + 7) (18x2 - 11x + 1 ) is (- , a) (b, c) (d, ) - \e\, then 90(a + b + c + d + e) equals:

  1. 170
  2. 316
  3. 177
  4. 307
Ques. 4JEE Main 2026, 23 January (Evening Shift)

The sum of all the real solutions of the equation (x+3) (6x2 + 28x + 30 ) = 5 - 2 (6x+10) (x2 + 6x + 9 ) is equal to :

  1. 1
  2. 4
  3. 0
  4. 2
Ques. 5JEE Main 2026, 22 January (Morning Shift)

If the domain of the function f(x) = -1 ( 5 - x3 + 2x ) + 1 e(10 - x) is (- , ] [ , ) - \ \, then 6( + + + ) is equal to

  1. 66
  2. 68
  3. 70
  4. 67
Ques. 6JEE Main 2026, 22 January (Evening Shift)

Let f(x) = [x]2 - [x + 3] - 3, x R, where [.] is the greatest integer function. Then

  1. f(x) = 0 for finitely many values of x
  2. f(x) < 0 only for x [-1, 3)
  3. 02 f(x) dx = -6
  4. f(x) > 0 only for x [4, )
Ques. 7JEE Main 2026, 22 January (Evening Shift)

Let the domain of the function f(x) = 3 5 (7 - 2 (x2 - 10x + 85 ) ) + -1 ( | 3x - 717 - x | ) be ( , ]. Then + is equal to :

  1. 12
  2. 8
  3. 10
  4. 9
Ques. 8JEE Main 2026, 22 January (Evening Shift)

The number of elements in the relation R = \(x, y) : 4x2 + y2 < 52, x, y Z \ is

  1. 86
  2. 67
  3. 89
  4. 77
Ques. 9JEE Main 2025, 8 April (Evening Shift)

Let the domain of the function f(x) = -1 ( 4x + 53x - 7 ) be [ , ] and the domain of g(x) = 2 (2 - 6 27(2x + 5) ) be ( , ). Then |7( + ) + 4( + )| is equal to .

Ques. 10JEE Main 2025, 7 April (Evening Shift)

If the range of the function f(x) = 5-xx2-3x+2, x 1, 2, is (- , ] [ , ), then 2 + 2 is equal to :

  1. 188
  2. 192
  3. 190
  4. 194
Ques. 11JEE Main 2025, 4 April (Evening Shift)

Let the domains of the functions f(x) = 4 3 7 (8 - 2 (x2 + 4x + 5 ) ) and g(x) = -1 ( 7x + 10x - 2 ) be ( , ) and [ , ], respectively. Then 2 + 2 + 2 + 2 is equal to :

  1. 15
  2. 13
  3. 16
  4. 14

All Relations and Functions PYQs →

PDFDownload Relations and Functions PYQs as PDF Free, with answer key and a QR code to every solution — print it or study offline⬇
All JEE Main Mathematics chapters
Class 11SetsRelations and FunctionsTrigonometric FunctionsComplex Numbers and Quadratic EquationsPermutations and CombinationsBinomial TheoremSequences and SeriesStraight LinesConic SectionsIntroduction to Three Dimensional GeometryLimits and DerivativesStatisticsProbability
Class 12Relations and Functions (Class 12)Inverse Trigonometric FunctionsMatricesDeterminantsContinuity and DifferentiabilityApplication of DerivativesIntegralsApplication of IntegralsDifferential EquationsVector AlgebraThree Dimensional GeometryProbability (Class 12)