Properties of Modulus Function

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JEE Advanced 1995

The function $f (x) = ∣ p x - q ∣ + r ∣ x ∣, x \in (- \infty, \infty)$ where $p > 0, q > 0, r > 0$ assumes its minimum value only on one point if

p \neq = q

(B)

r \neq = q

(C)

r \neq = p

(D)

p = q = r

JEE Advanced 1982

LEVELBoard

If $p, q, r$ are any real numbers, then

(A)

max (p, q) < max (p, q, r)

(B)

min (p, q) = \frac{1}{2} (p + q - ∣ p - q ∣)

(C)

max (p, q) < min (p, q, r)

Solve $∣ x^{2} + 4 x + 3∣ + ∣2 x + 5∣ = 0$

JEE Main 2021 (March)

LEVELJEE Main

The number of elements in the set $x \in R : (∣ x ∣ - 3) ∣ x + 4∣ = 6$ is equal to

JEE Main 2022 (25 June Shift 2)

LEVELJEE Main

Let $A = {x \in R : ∣ x + 1∣ < 2}$ and $B = {x \in R : ∣ x - 1∣ \geq 2}$ . Then which one of the following statements is NOT true?

(A)

A - B = (- 1, 1)

(B)

B - A = R - (- 3, 1)

(C)

A \cap B = (- 3, - 1]

(D)

A \cup B = R - [1, 3)

JEE Main 2022 (28 July Shift 2)

LEVELJEE Main

Let $S = {x \in [- 6, 3] - {- 2, 2} : \frac{∣ x + 3∣ - 1}{∣ x ∣ - 2} \geq 0}$ and $T = {x \in Z : x^{2} - 7∣ x ∣ + 9 \leq 0}$ . Then the number of elements in $S \cap T$ is

JEE Main 2023 (10 Apr Shift 1)

LEVELJEE Main

The number of elements in the set ${n \in Z : ∣ n^{2} - 10 n + 19∣ < 6}$ is

JEE Main 2024 (30 Jan Shift 2)

LEVELBoard

The number of real solutions of the equation $x (x^{2} + 3∣ x ∣ + 5∣ x - 1∣ + 6∣ x - 2∣) = 0$ is

JEE Main 2025 April

LEVELJEE Main

The number of real roots of the equation $x ∣ x - 2∣ + 3∣ x - 3∣ + 1 = 0$ is :

JEE Main 2026 (24 January Shift 1)

LEVELJEE Main

The number of the real solutions of the equation: $x ∣ x + 3∣ + ∣ x - 1∣ - 2 = 0$ is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The function f(x)=∣px−q∣+r∣x∣,x∈(−∞,∞) where p>0,q>0,r>0 assumes its minimum value only on one point if

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If p,q,r are any real numbers, then

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Solve ∣x2+4x+3∣+∣2x+5∣=0

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The number of elements in the set x∈R:(∣x∣−3)∣x+4∣=6 is equal to

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let A={x∈R:∣x+1∣<2} and B={x∈R:∣x−1∣≥2}. Then which one of the following statements is NOT true?

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Let S={x∈[−6,3]−{−2,2}:∣x∣−2∣x+3∣−1​≥0} and T={x∈Z:x2−7∣x∣+9≤0}. Then the number of elements in S∩T is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The number of elements in the set {n∈Z:∣n2−10n+19∣<6} is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The number of real solutions of the equation x(x2+3∣x∣+5∣x−1∣+6∣x−2∣)=0 is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The number of real roots of the equation x∣x−2∣+3∣x−3∣+1=0 is :

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The number of the real solutions of the equation: x∣x+3∣+∣x−1∣−2=0 is

The function $f (x) = ∣ p x - q ∣ + r ∣ x ∣, x \in (- \infty, \infty)$ where $p > 0, q > 0, r > 0$ assumes its minimum value only on one point if

If $p, q, r$ are any real numbers, then

Solve $∣ x^{2} + 4 x + 3∣ + ∣2 x + 5∣ = 0$

The number of elements in the set $x \in R : (∣ x ∣ - 3) ∣ x + 4∣ = 6$ is equal to

Let $A = {x \in R : ∣ x + 1∣ < 2}$ and $B = {x \in R : ∣ x - 1∣ \geq 2}$ . Then which one of the following statements is NOT true?

Let $S = {x \in [- 6, 3] - {- 2, 2} : \frac{∣ x + 3∣ - 1}{∣ x ∣ - 2} \geq 0}$ and $T = {x \in Z : x^{2} - 7∣ x ∣ + 9 \leq 0}$ . Then the number of elements in $S \cap T$ is

The number of elements in the set ${n \in Z : ∣ n^{2} - 10 n + 19∣ < 6}$ is

The number of real solutions of the equation $x (x^{2} + 3∣ x ∣ + 5∣ x - 1∣ + 6∣ x - 2∣) = 0$ is

The number of real roots of the equation $x ∣ x - 2∣ + 3∣ x - 3∣ + 1 = 0$ is :

The number of the real solutions of the equation: $x ∣ x + 3∣ + ∣ x - 1∣ - 2 = 0$ is