Which one of the following pairs of linear equations is/are inconsistent? (A). 7x + y = 5, 14x + 2y = 10 (B). 2x - 3y = 7, 4x - 6y = 12 (C). x - y = 10, 3x - 3y = 16 (D). 2x - 2y - 2 = 0, 4x - 4y - 5 = 0 Choose the correct option from the given below: Option 1: (A), (B), (C) and (D) all are inconsistent Option 2: (B), (C) and (D) are inconsistent Option 3: (A), (C) and (D) are inconsistent Option 4: (A), (B) and (C) are inconsistent

Answer: (B), (C) and (D) are inconsistent. Solution: A pair is inconsistent when a_1/a_2 = b_1/b_2 ≠ c_1/c_2. (A): all three ratios equal 1/2, so the lines coincide and the pair is consistent. (B): 1/2 = 1/2 ≠ 7/12, inconsistent. (C): 1/3 = 1/3 ≠ 10/16, inconsistent. (D): 1/2 = 1/2 ≠ 2/5, inconsistent.

Quantitative Reasoning

Linear Equation

Medium

Which one of the following pairs of linear equations is/are inconsistent?

(A). $7x + y = 5, 14x + 2y = 10$

(B). $2x - 3y = 7, 4x - 6y = 12$

(C). $x - y = 10, 3x - 3y = 16$

(D). $2x - 2y - 2 = 0, 4x - 4y - 5 = 0$

Choose the correct option from the given below:

(A), (B), (C) and (D) all are inconsistent

(B), (C) and (D) are inconsistent

(A), (C) and (D) are inconsistent

(A), (B) and (C) are inconsistent

✅ Correct Option: 2

A pair is inconsistent when $\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} \neq \dfrac{c_1}{c_2}$ .

(A): all three ratios equal $\dfrac{1}{2}$ , so the lines coincide and the pair is consistent.

(B): $\dfrac{1}{2} = \dfrac{1}{2} \neq \dfrac{7}{12}$ , inconsistent.

(C): $\dfrac{1}{3} = \dfrac{1}{3} \neq \dfrac{10}{16}$ , inconsistent.

(D): $\dfrac{1}{2} = \dfrac{1}{2} \neq \dfrac{2}{5}$ , inconsistent.

2026: 20 May Shift 2

Which of the following pairs of linear equations is/are consistent?

A. x + y – 5 = 0, 3x + 2y – 10 = 0

B. 3x – 2y – 6 = 0, 6x – 4y – 12 = 0

C. x – y – 9 = 0, 3x – 3y – 27 = 0

D. x + y – 4 = 0 , 3x + 3y – 12 = 0

Choose the correct option from the given below:

2025: 28 May Shift 2

Find the value of p for which the lines, $px + 3y + 5 = 0$ and $8x + 2y - 3 = 0$ are parallel.

2026: 22 May Shift 2

Which of the following pair of linear equations has no solution?

(A) $2x + 3y - 1 = 0$ and $4x + 6y - 4 = 0$

(B) $x - 2y = 0$ and $3x + 4y - 20 = 0$

(D) $x + 2y - 4 = 0$ and $2x + 4y - 12 = 0$

Choose the correct answer from the options given below:

2026: 29 May Shift 1

Laxmi's father is 51 years old. He is three years older than three times Laxmi's age. The age of Laxmi is :

2026: 19 May Shift 1

Solve for $x$ , if $4(x + 1) - 3(2x - 1) = x + 7$

2026: 12 May Shift 2

Which one of the following pair of linear equations is/are inconsistent?

(A) 2x – 2y = 10, 3x – 3y = 15

(B) 3x – y = 7, 6x – 2y = 18

(D) 7x – 3y = 3, 14x – 6y = 8

Choose the correct answer from the options given below:

Solution

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