Please enter the following details
Free Daily Targets & Mocks
Study Material & Formulas PDFs
1 on 1 Mentorship
Question 60
The largest real value of a for which the equation $$\mid x + a \mid + \mid x - 1 \mid = 2$$ has an infinite number of solutions for x is
Solution
In the question, it is given that the equation $$\mid x + a \mid + \mid x - 1 \mid = 2$$ has an infinite number of solutions for any value of x. This is possible when x in |x+a| and x in |x-1| cancels out.
Case 1:
x + a < 0, x - 1 $$\ge\ $$ 0
- a - x + x - 1 = 2
a = -3
Case 2:
x + a $$\ge\ $$ 0 and x - 1 < 0
x + a - x + 1 = 2
a = 1
Largest value of a is 1.
The answer is option C.
Video Solution
Create a FREE account and get:
- All Quant CAT complete Formulas and shortcuts PDF
- 35+ CAT previous year papers with video solutions PDF
- 5000+ Topic-wise Previous year CAT Solved Questions for Free
CAT Quant Questions | CAT Quantitative Ability
CAT Inequalities QuestionsCAT Linear Equations QuestionsCAT Time, Distance and Work QuestionsCAT Time And Work QuestionsCAT Venn Diagrams Questions
CAT DILR Questions | LRDI Questions For CAT
CAT 2D & 3D LR QuestionsCAT Miscellaneous LR QuestionsCAT Maxima-Minima QuestionsCAT DI with connected data sets QuestionsCAT Table with Missing values Questions
