Straight lines Questions and answers

  1. Elementary Mathematics
    1. Quadratic Equations
    2. Simplification
    3. Area and perimeter
    4. Volume and surface area
    5. Geometry
    6. Trigonometry
    7. Polynomials
    8. Height and Distance
    9. Simple and Decimal fraction
    10. Indices and Surd
    11. Logarithms
    12. Trigonometric ratio
    13. Straight lines
    14. Triangle
    15. Circles
    16. Quadrilateral and parallelogram
    17. Loci and concurrency
    18. Statistics
    19. Rectangular and Cartesian products
    20. Rational expression
    21. Set theory
    22. Factorisation
    23. LCM and HCF
    24. Clocks
    25. Real Analysis
11). The line passing. through \( \Large \left(1-\frac{ \pi }{2}\right) \) and perpendicular to \( \Large \sqrt{3} \sin \theta + 2\cos \theta =\frac{4}{r} \), is:
A). \( \Large 2=\sqrt{3}r\cos \theta-2r\sin \theta \)
B). \( \Large 5=2\sqrt{3}r\sin \theta +4r\cos \theta \)
C). \( \Large 2=\sqrt{3}r\cos \theta + 2r\sin \theta \)
D). \( \Large 5=2\sqrt{3}r\sin \theta + 4r\cos \theta \)
12). If the straight line \( \Large ax+by+c=0 \) always passes through \( \Large \left(1-2\right) \) then abc are
A). in AP
B). in HP
C). in GP
D). none of these
13). Two points A and B have co-ordinates (1, 1) and (3, -2) respectively. The co-ordinates of a point distant \( \Large \sqrt{85} \) from B on the line through B perpendicular to AB are:
A). (5, 7)
B). (7, 4)
C). (4, 7)
D). (-5, -3)
14). The equation of pair of lines joining origin to the points of intersection of \( \Large x^{2}+y^{2}=9 \) and \( \Large x+y=3 \) is:
A). \( \Large x^{2}+ \left(3-x^{2}\right)=9 \)
B). \( \Large \left(3+y\right)^{2}+y^{2}=9 \)
C). \( \Large xy=0 \)
D). \( \Large \left(x-y\right)^{2}=9 \)
15). Separate equations of lines for a pair of lines whose equation is \( \Large x^{2}+xy-12y^{2}y^{2}=0 \), are
A). \( \Large x+4y=0\ and\ x+3y=0 \)
B). \( \Large x+4y=0\ and\ x-3y=0 \)
C). \( \Large x-6y=0\ and\ x-3y=0 \)
D). \( \Large 2x-3y=0\ and\ x-4y=0 \)


16). The equation \( \Large 12x^{2}+7xy+ay^{2}+13x-y+3=0 \) represents a pair of perpendicular lines. Then the value of 'a' is:
A). \( \Large \frac{7}{2} \)
B). -19
C). -12
D). 12
17). If the \( \Large \angle \theta \) is acute, then the acute angle between \( \Large x^{2} \left(\cos \theta -\sin \theta \right)+2xy \cos \theta +y^{2} \left(\cos \theta +\sin \theta \right)=0 \) is
A). \( \Large 2 \theta \)
B). \( \Large \frac{ \theta }{3} \)
C). \( \Large \theta \)
D). \( \Large \frac{ \theta }{2} \)
18). The equation \( \Large 2x^{2}-24y+11y^{2}=0 \) represents:
A). two parallel lines
B). two lines passing through the origin
C). two perpendicular lines
D). a circle.
19). Lines \( \Large 2x+y=1\ and\ 2x+y=7 \) are
A). on the same side of a point \( \Large \left(0,\ \frac{1}{2}\right) \)
B). on the Opposite side of a point \( \Large \left(0,\ \frac{1}{2}\right) \)
C). same lines
D). perpendicular lines.
20). Set of lines \( \Large \left(x-2y+1\right)+h \left(x+y\right)=0 \) (where h is a parameter) passing through a fixed point:
A). \( \Large \left(\frac{1}{3},\ -\frac{1}{3}\right) \)
B). \( \Large \left(-\frac{1}{3},\ \frac{1}{3}\right) \)
C). (1, 1)
D). none of these
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