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Relations and Functions

JEE Main 2025 (Online) 24th January Evening ShiftMCQHard📈 Topic in 5% papers+4−1
Ques. 1JEE Main 2025, 24 January (Evening Shift)

The number of real solution(s) of the equation x2+3x+2= \|x-3|,|x+2|\ is :

  1. 2
  2. 3
  3. 1
  4. 0

Answer

(1) 2

Solution

\|x-3|,|x+2|\=|x+2| for x< 12 and |x-3| for x 12.

[figure]

x< 12: (x+1)(x+2)=|x+2| x=-2 or x+1= 1 x=-2, 0

x 12: the parabola ( 3.75) stays above |x-3| ( 2.5) no root

real solutions: x=-2, 0 — 2 solutions

Answer: (1)

Keep practising — Relations and Functions

Ques. 2JEE Main 2025, 23 January (Morning Shift)

Let f(x)= e x and g(x)= x4-2x3+3x2-2x+22x2-2x+1. Then the domain of f g is

  1. (0, )
  2. [1, )
  3. R
  4. [0, )
Ques. 3JEE Main 2025, 22 January (Morning Shift)

The product of all solutions of the equation e5( ex)2+3=x8, x>0, is :

  1. e2
  2. e
  3. e6/5
  4. e8/5

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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)