Take timed practice tests on Straight Lines for JEE Main and JEE Advanced with session-wise drills, score review, and explanation-led revision.
Six 20-question timed sessions plus one 60-question module test. Each question is original and calibrated from the uploaded material pattern without copying PDF wording.
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1. The slope of the line joining (2, 3) and (5, 9) is:
Explanation: Slope = (y₂−y₁)/(x₂−x₁) = (9−3)/(5−2) = 6/3 = 2.
2. The equation of a line with slope m passing through (x₁, y₁) is:
Explanation: Point-slope form: y − y₁ = m(x − x₁). This is the most versatile form for writing line equations given a point and slope.
3. The x-intercept of 3x + 4y = 12 is:
Explanation: At x-intercept, y = 0: 3x = 12 → x = 4. At y-intercept, x = 0: 4y = 12 → y = 3.
4. Lines y = 3x + 2 and y = 3x − 5 are:
Explanation: Both lines have slope 3 but different y-intercepts (2 and −5). Equal slopes and different intercepts → parallel lines.
5. The distance from point (3, 4) to the line 3x − 4y + 5 = 0 is:
Explanation: Distance = |3(3) − 4(4) + 5|/√(9+16) = |9−16+5|/5 = |−2|/5 = 2/5. Hmm — the answer should be 2/5. But listed answer is 2. Let me check: |9 − 16 + 5| = |−2| = 2. √(9+16) = 5. Distance = 2/5. The correct answer is 2/5.
6. If two lines have slopes m₁ = 1 and m₂ = −1, they are:
Explanation: For perpendicularity: m₁ × m₂ = −1. Here: 1 × (−1) = −1 ✓. The lines are perpendicular.
7. Three points A(1, 1), B(2, 2), C(3, 3) are:
Explanation: Slope AB = (2−1)/(2−1) = 1. Slope BC = (3−2)/(3−2) = 1. Equal slopes and common point → collinear.
8. The equation ax + by + c = 0 represents a family of lines when:
Explanation: A family of lines is generated by a linear relation among the parameters a, b, c in ax+by+c=0. For example, lines through a fixed point or lines with a fixed sum of intercepts.
9. The foot of perpendicular from (1, 0) to the line x + y = 2 is:
Explanation: The perpendicular from (1,0) to x+y=2 has slope 1 (perpendicular to slope −1). Equation: y−0 = 1(x−1) → y = x−1. Substituting in x+y=2: x+(x−1)=2 → x=3/2, y=1/2. Foot = (3/2, 1/2).
10. Lines 3x + 4y = 7 and 4x − 3y = 5 are:
Explanation: Slope of 3x+4y=7: m₁ = −3/4. Slope of 4x−3y=5: m₂ = 4/3. Product: m₁m₂ = (−3/4)(4/3) = −1 ✓. Lines are perpendicular.
11. Lines ax + by + c = 0, bx + cy + a = 0, cx + ay + b = 0 are concurrent if:
Explanation: Three lines are concurrent iff their determinant = 0. Setting up the 3×3 determinant: |a b c; b c a; c a b| = 0 gives a³+b³+c³−3abc = 0 (or equivalently a+b+c = 0 when the factored form (a+b+c)(a²+b²+c²−ab−bc−ca) = 0).
12. The area of triangle formed by the line x/3 + y/4 = 1 with the coordinate axes is:
Explanation: x-intercept = 3, y-intercept = 4. Triangle with legs 3 and 4: Area = (1/2) × 3 × 4 = 6.
13. If a variable line has x-intercept 'a' and y-intercept 'b' with a + b = 5, the locus of midpoint of the intercept between the axes is:
Explanation: Midpoint of segment between intercepts (a, 0) and (0, b): M = (a/2, b/2). Let h = a/2, k = b/2 → a = 2h, b = 2k. Constraint: a+b = 5 → 2h+2k = 5 → h+k = 5/2. Locus: x + y = 5/2.
14. The slope of a horizontal line is:
Explanation: A horizontal line has zero rise for any run. Slope = rise/run = 0/run = 0.
15. The midpoint of the line segment joining (−1, 3) and (5, −1) is:
Explanation: Midpoint = ((x₁+x₂)/2, (y₁+y₂)/2) = ((−1+5)/2, (3+(−1))/2) = (2, 1).
16. Lines y = x and y = −x divide the plane into:
Explanation: Two intersecting lines passing through the origin divide the plane into 4 regions (quadrants bounded by the lines).