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Modulus - Past Year Questions

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Q1:

The number of real solutions of the equation x2−10∣x∣−56=0x^2 - 10|x| - 56 = 0 is
Answer options
Option: 4
Correct Answer
Explanation →

Q2:

If ∣x+1∣+(y+2)2=0|x+1| + (y+2)^2 = 0 and ax−3ay=1ax - 3ay = 1, then the value of aa is
Answer options
Option: 1
Correct Answer
Explanation →

Q3:

The number of pairs (x,y)(x, y) of integers satisfying the inequality ∣x−5∣+∣y−5∣≤6|x - 5| + |y - 5| \leq 6 is:
85
Correct Answer
Explanation →

Q4:

The length of the line segment joining the two intersection points of the curves y=4970−∣x∣y = 4970 - |x| and y=x2y = x ^ 2 is
140
Correct Answer
Explanation →

Q5:

The sum of the squares of all the roots of the equation x2+∣x+4∣+∣x−4∣−35=0x^{2}+|x+4|+|x-4|-35=0 is
Answer options
Option: 3
Correct Answer
Explanation →

Q6:

Given that f(x)=∣x∣+2∣x−1∣+∣x−2∣+∣x−4∣+∣x−6∣+2∣x−10∣,x∈(−∞,∞) f(x)=|x|+2|x-1|+|x-2|+|x-4|+|x-6|+2|x-10|, x \in(-\infty, \infty) the minimum value of f(x)f(x) is _________.
26
Correct Answer
Explanation →

Q7:

The area enclosed by 2∣x∣+3∣y∣≤62|x|+3|y| \leq 6 is ____________ sq. units.
12
Correct Answer
Explanation →

Q8:

The minimum value of f(x)=∣3−x∣+∣2+x∣+∣5−x∣f(x)=|3-x|+|2+x|+|5-x| is equal to __________.
7
Correct Answer
Explanation →

Q9:

For a>b>c>0a > b > c > 0, the minimum value of the function f(x)=∣x−a∣+∣x−b∣+∣x−c∣f(x) = |x - a| + |x - b| + |x - c| is
Answer options
Option: 4
Correct Answer
Explanation →

Q10:

The area enclosed by the curve 2∣x∣+3∣y∣=62|x| + 3|y| = 6 is
Answer options
Option: 1
Correct Answer
Explanation →

Modulus - Past Year Questions (Free PDF Download)

Practice with our comprehensive collection of Modulus Past Year Questions (PYQs of IPMAT Indore, IPMAT Rohtak & JIPMAT) with detailed solutions. These questions are carefully curated from previous year papers to help you understand the exam pattern and improve your preparation.

Our free resources include handwritten solutions for all questions, making it easier to understand the concepts and approach. Use these PYQs to assess your preparation level and identify areas that need more focus. No login required. Compilation of IPMAT Indore, IPMAT Rohtak & JIPMAT Questions!