Question types

Pair of Straight Lines question types

282 questions across 7 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

282
Questions
7
Question groups
5
Question types
Sample Questions

Pair of 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 1MCQ1 Mark
If distance between lines $(x-2 y)^2+k(x-2 y)=0$ is 3 units, then $k=$
  • A
    ± 3
  • B
    $\pm 5 \sqrt{5}$
  • C
    ± 5
  • $\pm 3 \sqrt{5}$

Answer: D.

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Q 2MCQ1 Mark
If slope of one of the lines $a x^2+2 h x y+b y^2=0$ is 5 times the slope of the other, then $5 h^2=$________
  • A
    ab
  • B
    2 ab
  • C
    7 ab
  • 9 ab

Answer: D.

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Q 3MCQ1 Mark
If $h^2=a b$, then slope of lines $a x^2+2 h x y+b y^2=0$ are in the ratio _________
  • A
    1 : 2
  • B
    2 : 1
  • C
    2 : 3
  • 1 : 1

Answer: D.

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Q 4MCQ1 Mark
The combined equation of the co-ordinate axes is _________.
  • A
    x + y = 0
  • B
    x y = k
  • xy = 0
  • D
    x – y = k

Answer: C.

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Q 5MCQ1 Mark
The area of triangle formed by the lines $x^2+4 x y+y^2=0$ and $x-y-4=0$ is __________
  • A
    $\frac{4}{\sqrt{3}}$ Sq. units
  • $\frac{8}{\sqrt{3}}$ Sq. units
  • C
    $\frac{16}{\sqrt{3}} \mathrm{Sq}$. units
  • D
    $\frac{15}{\sqrt{3}}$ Sq. units

Answer: B.

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If lines representedby $a x^2+2 h x y+b y^2=0$ make angles of equal measures with the co-ordinate
axes then show that a = ± b.

OR

Show that, one of the lines represented by $a x^2+2 h x y+b y^2=0$ will make an anqle of the same measure with the X-axis as the other makes with the Y-axis, if a = ± b.

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Find the acute angle between lines represented by:
i) $x^2+x y=0$
ii) $x^2-4 x y+y^2=0$
iii) $3 x^2+2 x y-y^2=0$
iv) $2 x^2-6 x y+y^2=0$
v) $x y+y^2=0$
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