Equations reducible to linear MCQs

Q1. If 1/x = 2 from the reduced system, then x equals:

• A.1/2
• B.4
• C.2
• D.-2

Answer: A. 1/2

Spot-the-setup - a typical math numerical. The data on the table: 1, 2. We are after the quantity the stem asks for. Tool of choice - 1/x = 2. Rearrange it for the unknown before substituting. Numbers in: 1/x = 2 → x = 1/2. Lock in option A) 1/2. Trap-watch: option B) '4' misses the point - x = 1/2, not 4; option C) '2' is wrong because x = 1/(1/x) = 1/2, not 2.

Q2. If u = 1/x = 2 and v = 1/y = 3, then (x, y) is (NCERT):

• A.(1/2, 1/3)
• B.(3, 2)
• C.(1/3, 1/2)
• D.(2, 3)

Answer: A. (1/2, 1/3)

Q3. A train covers a distance at uniform speed. If it were 10 km/h faster it would take 2 h less; 10 km/h slower, 3 h more. Such problems reduce to (NCERT):

• A.a pair of equations in speed and time
• B.a quadratic only
• C.no equations
• D.a single linear equation

Answer: A. a pair of equations in speed and time

Given 10 km, asked for the unknown. By apply the distance formula d = sqrt((x2-x1)^2 + (y2-y1)^2) to the two given points. apply the distance formula d = sqrt((x2-x1)^2 + (y2-y1)^2) to the two given points. substitute the coordinates and square the differences. Therefore option A) a pair of equations in speed and time. Others fail: option B) 'a quadratic only' doesn't hold - It sets up a solvable pair; option C) 'no equations' is incorrect: Each condition gives an equation.