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Modulus - Past Year Questions

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Q1:

If a, b, c are three distinct natural numbers, all less than 100, such that ∣a−b∣+∣b−c∣=∣c−a∣|a - b| + |b - c| = |c - a|, then the maximum possible value of b is ______
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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
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Q3:

The number of real solutions of the equation x2−10∣x∣−56=0x^2 - 10|x| - 56 = 0 is
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Q4:

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:
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Q5:

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
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Q6:

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
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Q7:

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 _________.
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Q8:

The area enclosed by 2∣x∣+3∣y∣≤62|x|+3|y| \leq 6 is ____________ sq. units.
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Q9:

The minimum value of f(x)=∣3−x∣+∣2+x∣+∣5−x∣f(x)=|3-x|+|2+x|+|5-x| is equal to __________.
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Q10:

The area enclosed by the curve 2∣x∣+3∣y∣=62|x| + 3|y| = 6 is
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Q11:

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
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Modulus - Past Year Questions (Free PDF Download)

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