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
21). The equation of the line equidistant from the lines \( \Large 2x+3y-5=0\ and\ 4x+6y=11 \) is
A). \( \Large 2x+3y-1=0 \)
B). \( \Large 4x+6y-1=0 \)
C). \( \Large 8x+12y-1=0 \)
D). none of these
22). The equation of line parallel to lines \( \Large L_{1}=x+2y-5=0\ and\ x+2y+9=0 \) and dividing the distance between \( \Large L_{1} \) and \( \Large L_{2} \) in the ratio 1 : 6 (internally) is:
A). \( \Large x+2y-3=0 \)
B). \( \Large x+2y+2=0 \)
C). \( \Large x+2y+7=0 \)
D). none of these
23). The family of lines making an angle \( \Large 30 ^{\circ} \) with the line \( \Large \sqrt{3}y=x+1 \) is:
A). \( \Large x=h \) (h is parameter)
B). \( \Large y=-\sqrt{3}x+h \) (h is parameter)
C). \( \Large y=\sqrt{3}+h \)
D). none of these
24). A square of area 25 sq unit is formed by talking two sides as \( \Large 3x+4y=k_{1}\ and\ 3x+4y=k_{2} \) then \( \Large |k_{1}-k_{2}| \) is:
A). 5
B). 1
C). 25
D). none of these
25). The lines \( \Large ax+by+c=0,\ bx+cy+a=0\ and\ cx+ay+b=0 \) \( \Large a \ne b \ne c \) are concurrent if:
A). \( \Large a^{3}+b^{3}+c^{3}+3abc=0 \)
B). \( \Large a^{2}+b^{2}+c^{2}-3abc=0 \)
C). \( \Large a+b+c=0 \)
D). none of these


26). A straight line through the point (2, 2) intersects the lines \( \Large \sqrt{3}x+y=0\ and\ \sqrt{3}x-y=0 \) at the points A and B. The equation to the line AB so that the triangle OAB is equilateral is:
A). \( \Large x-2=0 \)
B). \( \Large y-2=0 \)
C). \( \Large x+y-4=0 \)
D). none of these
27). Equation to the straight line cutting of an intercept from the negative direction of the axis of y and inclined at \( \Large 30 ^{\circ} \) to the positive direction of axis of x is:
A). \( \Large y+x-\sqrt{3}=0 \)
B). \( \Large y-x+2=0 \)
C). \( \Large y-\sqrt{3}x-2=0 \)
D). \( \Large \sqrt{3}y-x+2\sqrt{3}=0 \)
28). Two consecutive side of parallelogram are \( \Large 4x+5y=0\ and\ 7x+2y=0 \). One diagonal of the parallelogram is \( \Large 11x+7y=9 \) the other diagonal is\( \Large ax+by+c=0 \), then
A). \( \Large a=-1,\ b=-1,\ c=2 \)
B). \( \Large a=1,\ b=-1,\ c=0 \)
C). \( \Large a=-1,\ b=-1,\ c=0 \)
D). \( \Large a=1,\ b=1,\ c=1 \)
29). The line parallel to the x-axis and passing through the intersection of the lines \( \Large ax+2by+3b=0\ and\ bx-2ay-3a=0 \), where \( \Large (a, b) \ne (0, 0) \), is
A). above the x-axis at a distance of \( \Large \frac{2}{3} \) from it.
B). above the x-axis at a distance of \( \Large \frac{3}{2} \) from it.
C). below the x-axis at a distance of \( \Large \frac{2}{3} \) from it.
D). below the x-axis at a distance of \( \Large \frac{3}{2} \) from it.
30). The number of integral values of m, for which the x-coordinate of the point of intersection of the line \( \Large 3x+4y=9\ and\ y=mx+1 \) is also an integer is:
A). 2
B). 0
C). 4
D). 1
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