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Straight Lines Maths - Straight Lines

CBSE - STD 11 Science - Maths (CBSE - English Medium). 59 questions in this chapter.

Question types

Straight Lines question types

59 questions across 6 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

59
Questions
6
Question groups
5
Question types
Sample Questions

Straight Lines questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark
$A$ point equidistant from the lines $4x + 3y + 10 = 0, 5x – 12y + 26 = 0$ and $7x + 24y – 50 = 0$ is:
  • A
    $(1, -1)$
  • B
    $(1, 1)$
  • ✓
    $(0, 0)$
  • D
    $(0, 1)$

Answer: C.

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Q 2M.C.Q (1 Marks)1 Mark
Equation of the line passing through $(1, 2)$ and parallel to the line $y = 3x - 1$ is:
  • A
    $y + 2 = x + 1$
  • B
    $y + 2 = 3 (x + 1)$
  • ✓
    $y - 2 = 3 (x - 1)$
  • D
    $y - 2 = x - 1$

Answer: C.

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Q 3M.C.Q (1 Marks)1 Mark
The tangent of angle between the lines whose intercepts on the axes are $a, -b$ and $b, -a,$ respectively, is
  • A
    $\frac{\text{a}^2-\text{b}^2}{\text{ab}}$
  • B
    $\frac{\text{b}^2-\text{a}^2}{2}$
  • ✓
    $\frac{\text{b}^2-\text{a}^2}{2\text{ab}}$
  • D
    None of these.

Answer: C.

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Q 4M.C.Q (1 Marks)1 Mark
The equation of the line passing through the point $(1, 2)$ and perpendicular to the line $x + y + 1 = 0$ is:
  • A
    $y - x + 1 = 0$
  • ✓
    $y - x - 1 = 0$
  • C
    $y - x + 2 = 0$
  • D
    $y - x - 2 = 0$

Answer: B.

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Q 5M.C.Q (1 Marks)1 Mark
The equations of the lines passing through the point $(1, 0)$ and at a distance $\frac{\sqrt{3}}{2}$ from the origin, are
  • ✓
    $\sqrt{3}\text{x}+\text{y}-\sqrt{3}=0,\sqrt{3}\text{x}-\text{y}-\sqrt{3}=0$
  • B
    $\sqrt{3}\text{x}+\text{y}+\sqrt{3}=0,\sqrt{3}\text{x}-\text{y}+\sqrt{3}=0$
  • C
    $\text{x}+\sqrt{3}\text{y}-\sqrt{3}=0,\text{x}-\sqrt{3}\text{y}-\sqrt{3}=0$
  • D
    None of these.

Answer: A.

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Q 7True False[1 Marks ]1 Mark
The line $\frac{\text{x}}{\text{a}}+\frac{\text{y}}{\text{b}}=1$ moves in such a way that $\frac{1}{\text{a}^2}+\frac{1}{\text{b}^2}=\frac{1}{\text{c}^2},$ where c is a constant. The locus of the foot of the perpendicular from the origin on the given line is $x^2 + y^2 = c^2.$
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Q 9True False[1 Marks ]1 Mark
The vertex of an equilateral triangle is (2, 3) and the equation of the opposite side is x + y = 2. Then the other two sides are $\text{y}-3=(2\pm\sqrt{3})(\text{x}-2).$
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Q 132 Marks Questions2 Marks
A straight line moves so that the sum of the reciprocals of its intercepts made on axes is constant. Show that the line passes through a fixed point.
[Hint: $\frac{\text{x}}{\text{a}}+\frac{\text{y}}{\text{b}}=1$ where $\frac{1}{\text{a}}+\frac{1}{\text{b}}=\text{constant}=\frac{1}{\text{k}}(\text{say}).$ This implies that $\frac{\text{k}}{\text{a}}+\frac{\text{k}}{\text{b}}=1$ line passes through the fixed point (k, k).]
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Q 153 Marks Question3 Marks
Match the questions given under $\text{Column} \ C_1$ with their appropriate answers given under the $\text{Column} \ C_2:$
  $\text{Column} \ C_1$   $\text{Column}\  C_2$
$(a)$ The coordinates of the points $P$ and $Q$ on the line $x + 5y = 13$ which are at a distance of $2$ units from the line $12x - 5y + 26 = 0$ are (i) $(3, 1), (-7, 11) $
$(b)$ The coordinates of the point on the line $x + y = 4,$ which are at a unit distance from the line $4x + 3y - 10 = 0$ are (ii) $-\frac{1}{3},\frac{11}{3},\frac{4}{3},\frac{7}{3}$
$(c)$ The coordinates of the point on the line joining $A (-2, 5)$ and $B (3, 1)$ such that$ AP = PQ = QB$ are (iii) $1,\frac{12}{5},-3,\frac{16}{5}$
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Q 163 Marks Question3 Marks
Find the equation of the lines which passes through the point (3, 4) and cuts off intercepts from the coordinate axes such that their sum is 14.
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Q 173 Marks Question3 Marks
For what values of a and b the intercepts cut off on the coordinate axes by the line ax + by + 8 = 0 are equal in length but opposite in signs to those cut off by the line 2x - 3y + 6 = 0 on the axes.
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Q 193 Marks Question3 Marks
Find the equation of the line passing through the point of intersection of 2x + y = 5 and x + 3y + 8 = 0 and parallel to the line 3x + 4y = 7.
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Q 255 Marks Questions5 Marks
The equation of the line through the intersection of the the lines $2x - 3y = 0$ and $4x - 5y = 2$ and
  column $I$   column $II$
$(a)$ Throught the point $(2, 1)$ is $(a)$ $2x - y = 4$
$(b)$ perpendicular to the line $x + 2y + 1 = 0$ is $(b)$ $x + y - 5 = 0$
$(c)$ parpallel to the line $3x + 4y + 5 = 0$ $(c)$ $x - y - 1$
$(d)$ Equally inlined to the axis is $(d)$ $3x - 4y - 1 = 0$
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Q 265 Marks Questions5 Marks
Match the questions given under $\text{Column}\  C_1$ with their appropriate answers given under the $\text{Column}\  C_2$: The value of the $\lambda ,$ if the lines $(2x + 3y + 4) + \lambda (6x - y + 12) = 0$ are:
  $\text{Column}\  C_1$   $\text{Column}\  C_2$
$(a)$ Parallel to $y-$axis is $(i)$ $\lambda=-\frac{3}{4}$
$(b)$ Perpendicular to $7x + y - 4 = 0$ is $(ii)$ $\lambda=-\frac{1}{3}$
$(c)$ Passes through $(1, 2)$ is $(iii)$ $\lambda=-\frac{17}{41}$
$(d)$ Parallel to $x$ axis is $(iv)$ $\lambda=3$
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Q 275 Marks Questions5 Marks
Find the equation of the line which passes through the point (-4, 3) and the portion of the line intercepted between the axes is divided internally in the ratio 5 : 3 by this point.
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Q 295 Marks Questions5 Marks
If the equation of the base of an equilateral triangle is x + y = 2 and the vertex is (2, - 1), then find the length of the side of the triangle.
[Hint: Find length of perpendicular (p) from (2, - 1) to the line and use $\text{p}=\text{l}\sin60^\circ$ where l is the length of side of the triangle].
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