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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

Correct Answer:



C) \( \Large y=\sqrt{3}+h \)

Description for Correct answer:
Slope of given line is \( \Large \frac{1}{\sqrt{3}} \) it's angle from positive x-axis is \( \Large 30 ^{\circ} \). Now lines making an angle \( \Large 30 ^{\circ} \) from it either x-axis (i.e. y = 0) or makes and angle \( \Large 60 ^{\circ} \) with positive x-axis (i.e. \( \Large y=\sqrt{3}x+n \)

Part of solved Straight lines questions and answers : >> Elementary Mathematics >> Straight lines

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Similar Questions

1). 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

2). 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

3). 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

4). 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). \( \Large \sqrt{3}y-x+2\sqrt{3}=0 \)

5). 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). \( \Large a=1,\ b=1,\ c=1 \)

6). 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.

7). 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

8). The number of integeral points (integral point means both the co-ordinates should be integer) exactly in the interior of the triangle with vertices (0, 0)(0, 21) and (21, 0) is

A). 133

B). 190

C). 233

D). 105

9). The arc (in sq unit) of the quadrilateral formed by two pairs of lines \( \Large l^{2}x^{2}-m^{2}y^{2}-n \left(lx+my\right)=0\ and\ l^{2}m^{2}-m^{2}y^{2}+n \left(lx-my\right)=0 \) is

A). \( \Large \frac{n^{2}}{2|lm|} \)

B). \( \Large \frac{n^{2}}{|lm|} \)

C). \( \Large \frac{n}{2|lm|} \)

D). \( \Large \frac{n^{2}}{4|lm|} \)

10). The point of lines represented by\( \Large 3ax^{2} + 5xy + \left(a^{2}-2\right)y^{2}=0 \) and perpendicular to each other for

A). two value of a

B). for all value of a

C). for one values of a

D). for no value of a