Quantitative Reasoning

Linear Equation

Medium

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 $3x + 4y - 20 = 0$

(C) $x + 2y - 3 = 0$ and $5x + 10y + 7 = 0$

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

Choose the correct answer from the options given below:

(A), (B) and (D) only

(A), (C) and (D) only

(A), (B), (C) and (D)

(B), (C) and (D) only

✅ Correct Option: 2

No solution requires $\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}$ . In (A) $\frac12=\frac12\neq\frac14$ , in (C) $\frac15=\frac15\neq-\frac37$ , in (D) $\frac12=\frac12\neq\frac13$ , so all three are parallel. In (B) $\frac13\neq-\frac12$ , giving a unique solution. Answer: (A), (C) and (D).

2025: 24 May Shift 2

The equations: x + 4y - 3 = 0 and 2x + 8y - 6 = 0 have

2025: 26 May Shift 1

Seven chairs and three tables together cost ₹ 7400, three chairs and five tables together cost ₹ 5400. The total cost (in ₹) of 1 chair and 2 tables is:

2023: 24 May Shift 3

Match List - I with List - II.

List - I	List - II
(1) $14 - \frac{1}{10}(x+3) = \frac{5}{6}x$	(I) 4
(2) $(x-5)^2 - (x+3)^2 = 48$	(II) $-\frac{23}{2}$
(3) $6(x-4) = 4(x-3) - (3x-8)$	(III) 61
(4) $(2x-1)(2x+3) = (2x-7)(2x+7)$	(IV) $-2$

Choose the correct answer from the options given below:

2025: 29 May Shift 1

Which of the following pair of linear equations is inconsistent?

(A) x - y = 5; 3x - 3y = 10

(B) 2x + 3y = 4; 4x + 6y = 8

(D) 2x + 5y = 2; 6x - 15y = 4

Choose the correct answer from the options given below:

2026: 19 May Shift 2

Five years ago, Sanjana was thrice as old as Sanjay. Ten years later, Sanjana will be twice as old as Sanjay. The age of Sanjay and Sanjana are respectively

A. 20

B. 30

C. 40

D. 50

Choose the correct answer from the options given below:

2025: 19 May Shift 1

The sum of digits of a two-digit number is 14 and the difference between the two digits of the number is 2. The product of the two digits of the number is:

Solution

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