#### Important Question paper 1mark

11th Standard

Reg.No. :
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Maths

Time : 00:30:00 Hrs
Total Marks : 50
50 x 1 = 50
1. The equation of the locus of the point whose distance from y-axis is half the distance from origin is

(a)

x2+3y=0

(b)

x2-3y2=0

(c)

3x2+y2=0

(d)

3x2-y2=0

2. Which of the following equation is the locus of (at2; 2at)

(a)

$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

(b)

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

(c)

x2+y2=a2

(d)

y2=4ax

3. The line (p + 2q)x + (p - 3q)y = p - q for different values of p and q passes through the point

(a)

$\left(\frac{3}{5},\frac{5}{2}\right)$

(b)

$\left(\frac{2}{5},\frac{2}{5}\right)$

(c)

$\left(\frac{3}{5},\frac{3}{5}\right)$

(d)

$\left(\frac{2}{5},\frac{3}{5}\right)$

4. The point on the line 2x- 3y = 5 is equidistance from (1,2) and (3,4) is

(a)

(7,3)

(b)

(4,1)

(c)

(1,-1)

(d)

(-2,3)

5. If one of the lines given by 6x2 - xy + 4cy2 = 0 is 3x + 4y = 0, then c equals to

(a)

-3

(b)

-1

(c)

3

(d)

1

6. If the straight line y=mx+c passes through the point (1,2) and (-2,4) then the value of m and c are

(a)

$\frac{8}{3},\frac{-2}{3}$

(b)

$\frac{-2}{3},\frac{8}{3}$

(c)

$\frac{2}{3},\frac{-8}{3}$

(d)

$\frac{-2}{3},\frac{-8}{3}$

7. The inclination to the x-axis and intercept on y-axis of the line $\sqrt {2y}=x+2\sqrt 2$

(a)

$30^0,\sqrt 2$

(b)

300,2

(c)

$45^0,2\sqrt 2$

(d)

450,2

8. The equation of the bisectors of the angle between the co-ordinate axes are

(a)

x+y=0

(b)

x-y=0

(c)

x$\pm$y=0

(d)

x=0

9. The equation of a line which makes an angle of 135° with positive direction of x-axis and passes through the point (1,1) is

(a)

x+y=2

(b)

x-y=0

(c)

$2\sqrt {2x}-\sqrt {2y}=0$

(d)

x-3y=0

10. The equation of the straight line bisecting the line segment joining the points (2,4) and (4,2) and making an angle of 450 with positive direction of x-axis is

(a)

x+y=6

(b)

x-y=0

(c)

x-y=6

(d)

x+y=0

11. The equation of median from verten B of the triangle $\triangle ABC$  the co-ordinates of whose vertices are A(-1,6)B(-3,-9)C(5,-8)

(a)

29x+4y+5=0

(b)

8x-5y-21=0

(c)

13x+14y+47=0

(d)

x+y-7=0

12. The equation of the straight line which passes through the point (2,4) and have intercept on the axes equal in magnitude but opposite in sign is

(a)

x-y=2

(b)

x-y+2=0

(c)

x-y+1=0

(d)

x-y-1=0

13. The equation of the straight line upon which the length of perpendicular from the origin is p and this normal makes an angle $\theta$  with the positive direction of x-axis is

(a)

x sin$\theta$+ycot$\theta$=p

(b)

xsin$\theta$+ycos$\theta$=p

(c)

xsin$\theta$+ytan$\theta$cos$\theta$=p

(d)

xcos$\theta$+ysin$\theta$=p

14. The length of perpendicular from the origin to a line is 12 and the line makes an angle of 120° with the positive direction of y-axis. then the equation of line is

(a)

$x+y\sqrt 3=24$

(b)

$x+y=12\sqrt 2$

(c)

x+y=24

(d)

$x+y=12\sqrt 3$

15. The lines x cos $\alpha$+ysin$\alpha$=p and xcos$\beta$+ysin$\beta$=q will be perpendicular if

(a)

$\alpha =\beta$

(b)

$\alpha-\beta=\frac{\pi}{2}$

(c)

$|\alpha-\beta|=\frac{\pi}{2}$

(d)

$\alpha-\beta=0$

16. The distance of the point (2,3) from the line 2x-3y+9=0 measured along the line 2x-2y+5=0 is

(a)

$\sqrt 2$

(b)

$2\sqrt 2$

(c)

$4\sqrt 2$

(d)

4

17. Which one of the following statements in false?

(a)

A point $(\alpha,\beta)$ will lie on origin side of the line ax+by+c=0 if a$\alpha$+b$\beta$+c and c have the same sign

(b)

A point $(\alpha,\beta)$  will lie on non-origin side of the line ax+by+c=0 if a$\alpha$+b$\beta$ +c and c have opposite sign

(c)

If $\alpha=\frac{\pi}{2},p=0$ , then the equation xcos$\alpha$+ysin$\alpha$=p represents x-axis

(d)

If $\alpha =0,p=0$, then the equation xcos$\alpha$+ysin$\alpha$=presents x-axis

18. The lines ax+y+1=0,x+by+1=0 and x+y+c=0(a≠b≠c≠1) are concurrent, then the value of $\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}=$

(a)

-1

(b)

1

(c)

0

(d)

abc

19. The co-ordinates of the foot of the perpendicular drawn from the point (2,3) to the line 3x-y+4=0 is

(a)

$(\frac{1}{10},\frac{37}{10})$

(b)

$(\frac{-1}{10},-\frac{37}{10})$

(c)

$(\frac{-1}{10},\frac{37}{10})$

(d)

$(\frac{37}{10},\frac{-1}{10})$

20. Which one of the following statements is false?

(a)

The image of a point $(\alpha\beta)$ about x-axis $(\alpha,-\beta)$

(b)

The image of the line ax+by+c=0 about x-axis is ax-by+c=0

(c)

The image of a point $(\alpha,\beta)$ about y-axis $(-\alpha,\beta)$

(d)

The image of the line ax+by+c=0 about y-axis is ax-by+c=0

21. The image of the point (1,2) with respect to the line y=x is

(a)

(-1,-2)

(b)

(2,1)

(c)

(2,-1)

(d)

(2,1)

22. The condition that the slope of one of the lines represented by ax2+2hxy+by2=0 is n times the slope of the other is

(a)

4nh2=ab(1+n)2

(b)

8h2=9ab

(c)

4n=ab(1+n)2

(d)

4nh2=ab

23. The equation 3x2+2hxy+3y2=0 represents a pair of straight lines passing through the origin. The two lines are

(a)

real and distinct if h2>3

(b)

real and distinct if h2>0

(c)

real and distinct h2>6

(d)

real and distinct if h2-9=0

24. Pair of lines perpendicular to the lines represented by ax2+2hxy+by2=0 and through origin is

(a)

ax2+2hxy+by2=0

(b)

bx2+2hxy+ay2=0

(c)

bx2-2hxy+ay2=0

(d)

bx2-2hxy+ay2=0

25. The angle between the lines $(x^2+y^2)sin^2\alpha=(xcos\alpha-y\beta)^2$

(a)

$\alpha$

(b)

$2\alpha$

(c)

$\alpha+\beta$

(d)

None

26. If h2=ab, then the lines represented by ax2+2hx+by2=0 are

(a)

parallel

(b)

perpendicular

(c)

coincident

(d)

None

27. The equation of the bisectors of the angle between the lines represented by 3x2-5xy+4y2=0 is

(a)

3x2-5xy-3y2=0

(b)

3x2+5xy+4y2=0

(c)

5x2-2xy-5y2=0

(d)

5x2-2xy+5y2=0

28. If co-ordinate axes are the angle bisectors of the pair of lines ax2+2hxy+by2=0 then

(a)

a=b

(b)

h=0

(c)

a+b=0

(d)

a2+b2=0

29. The value $\lambda$ for which the equation 12x2-10xy+2y2+11x-5y+$\lambda$ =0 represent a pair of straight lines is

(a)

$\lambda$=1

(b)

$\lambda$=2

(c)

$\lambda$=3

(d)

$\lambda$=0

30. The points (k+1,1),(2k+1,3) and (2k+2,2k) are collinear if

(a)

k=-1

(b)

$k=\frac{1}{2}$

(c)

k=3

(d)

k=2

31. The image of the point (3,8) in the line x+3y=7 is

(a)

(1,4)

(b)

(-1,-4)

(c)

(-4,-1)

(d)

(1,-4)

32. If the points (2k,k)(k,2k) and (k,k)enclose a triangle of area 18 sq units, then the centroid of the triangle is

(a)

(8,8)

(b)

(4,4)

(c)

(3,3)

(d)

(2,2)

33. The points (a,0),(0,b) and (1,1) will be collinear if

(a)

a+b=1

(b)

a+b=2

(c)

$\frac{1}{a}+\frac{1}{b}=1$

(d)

a+b=0

34. The angle between the lines 2x-y+5=0 and 3x+y+4=0 is

(a)

450

(b)

300

(c)

600

(d)

900

35. The gradient of one of the lines of ax2+2hxy+by2=0 is twice that of the other, then

(a)

h2=ab

(b)

h=a+b

(c)

8h2=9ab

(d)

9h2=8ab

36. The equation x2+kxy+y2-5x-7y+6=0 represents a pair of straight lines then k=

(a)

$\frac{5}{3}$

(b)

$\frac{10}{3}$

(c)

$\frac{3}{2}$

(d)

$\frac{3}{10}$

37. The equation of the straight line joining the origin to the point of intersection of y-x+7=0 and y+2x-2=0 is

(a)

3x+4y=0

(b)

3x-4y=0

(c)

4x-3y=0

(d)

4x+3y=0

38. Separate equation of lines for a pair of lines whose equation is x2+xy-12y2=0 are

(a)

x+4y=0 and x+3y=0

(b)

2x-3y=0 and x-4y=0

(c)

x-6y=0 and x-3y=0

(d)

x+4y=0 and x-3y=0

39. The angle between the lines x2+4xy+y2=0 is

(a)

600

(b)

150

(c)

300

(d)

450

40. The distance between the parallel lines 3x-4y+9=0 and 6x-8y-15=0 is

(a)

$\frac{-33}{10}$

(b)

$\frac{10}{33}$

(c)

$\frac{33}{10}$

(d)

$\frac{33}{20}$

41. If one of the lines of my2+(1-m2)xy-mx2=0 is a bisector of the angle between the lines xy=0 then m is

(a)

$\frac{-1}{2}$

(b)

-2

(c)

1

(d)

2

42. If one of the lines by 6x2-xy+4cy2=0 is 3x+4y=0, then c=

(a)

1

(b)

-1

(c)

3

(d)

-3

43. The point (2,1) and (-3,5) are on

(a)

Same side of the line 3x-2y+1=0

(b)

Opposite sides of the line 3x-2y+1=0

(c)

On the line 3x-2y+1=0

(d)

On the line x+y=3

44. The co-ordinates of a point on x+y+3=0 whose distance from x+2y+2=0 is $\sqrt 5$, is

(a)

(9,6)

(b)

(-9,6)

(c)

(6,-9)

(d)

(-9,-6)

45. If p is the length of perpendicular from origin to the line $\frac{x}{a}+\frac{y}{b}=1$then

(a)

$\frac{1}{p^2}=\frac{1}{a^2}+\frac{1}{b^2}$

(b)

$\frac{1}{p^2}=\frac{1}{a^2}-\frac{1}{b^2}$

(c)

$\frac{1}{p^2}=-\frac{1}{a^2}+\frac{1}{b^2}$

(d)

$\frac{1}{p^2}=-\frac{1}{a^2}-\frac{1}{b^2}$

46. If O is the origin and Q is a variable point on y2=x, then the locus of the mid-point of OQ is

(a)

y2=2x

(b)

2y2=x

(c)

4y2=x

(d)

y=2x2

47. The locus of a point which is equidistant from (-1,1) and (4,2) is

(a)

5x+3y+9=0

(b)

5x+3y-9=0

(c)

3x-5y=0

(d)

3x+5y-9=0

48. The locus of a point which is equidistant from (1,0) and (-1,0) is

(a)

x-axis

(b)

y-axis

(c)

y=x

(d)

y=-x

49. If the co-ordinates of a variable point p be $(t+\frac{1}{t},t-\frac{1}{t})$where t is the parameter then the locus of p

(a)

xy=1

(b)

x2+y2=4

(c)

x2-y2=4

(d)

x2-y2=8

50. The locus of a point which is collinear with the points (a,0) and (0,b) is

(a)

x+y=1

(b)

$\frac{x}{a}+\frac{y}{b}=1$

(c)

x+y=ab

(d)

$\frac{x}{a}-\frac{y}{b}=1$