Differential Calculus - Important Question Paper

11th Standard

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Business Maths

Time : 01:00:00 Hrs
Total Marks : 50

    Part A

    15 x 1 = 15
  1. If m1 and m2 are the slopes of the pair of lines given by ax2+ 2hxy + by2 = 0, then the value of m1 + m2 is

    (a)

    2h/b

    (b)

    -2h/b

    (c)

    2h/a

    (d)

    -2h/a

  2. The angle between the pair of straight lines x2 - 7xy + 4y2 = 0

    (a)

    \(tan^{-1}\left(1\over 3\right)\)

    (b)

    \(tan^{-1}\left(1\over 2\right)\)

    (c)

    \(tan^{-1}\left(\sqrt{33}\over 5\right)\)

    (d)

    \(tan^{-1}\left(5\over\sqrt{33}\right)\)

  3. If the lines 2x - 3y - 5 = 0 and 3x - 4y - 7 = 0 are the diameters of a circle, then its centre is

    (a)

    (-1, 1)

    (b)

    (1,1)

    (c)

    (1, -1 )

    (d)

    (-1, -1)

  4. The locus of the point P which moves such that P is at equidistance from their coordinate axes is

    (a)

    \(y={1\over x}\)

    (b)

    y=-x

    (c)

    y=x

    (d)

    \(y=-{1\over x}\)

  5. The locus of the point P which moves such that P is always at equidistance from the line x + 2y+ 7 = 0 is

    (a)

    x+2y+2=0

    (b)

    x - 2y + 1 = 0

    (c)

    2x - y + 2 = 0

    (d)

    3x + y + 1=0

  6. If kx2 + 3xy - 2y2 = 0 represent a pair of lines which are perpendicular then k is equal to

    (a)

    1/2

    (b)

    -1/2

    (c)

    2

    (d)

    -2

  7. (1, - 2) is the centre of the circle x2 + y2 + ax + by - 4 = 0 , then its radius

    (a)

    3

    (b)

    2

    (c)

    4

    (d)

    1

  8. Length of the latus rectum of the parabola y2 = - 25x is

    (a)

    25

    (b)

    -5

    (c)

    5

    (d)

    -25

  9. The centre of the circle x2 + y - 2x + 2y - 9 = 0 is

    (a)

    (1,1)

    (b)

    (-1,-1)

    (c)

    (-1,1)

    (d)

    (1, -1)

  10. Combined equation of co-ordinate axes is

    (a)

    x2-y2=0

    (b)

    x2+y2=0

    (c)

    xy=c

    (d)

    xy=0

  11. If the perimeter of the circle is 8π units and centre is (2,2) then the equation of the circle is

    (a)

    (x - 2)2 + (y - 2)2 = 4

    (b)

    (x - 2)2 + (y - 2)2 = 16

    (c)

    (x - 4)2 + (y - 4)2 = 2

    (d)

    x2 + y2 =4

  12. The equation of the circle with centre (3,-4) and touches the x - axis

    (a)

    (x - 3)2 +(y - 4)2 = 4

    (b)

    (x - 3)2 +(y + 4)2 =16

    (c)

    (x-3)2+(y- 4)2=16

    (d)

    x2+y2=16

  13. The double ordinate passing through the focus is

    (a)

    focal chord

    (b)

    latus rectum

    (c)

    directrix

    (d)

    axis

  14. The distance between directrix and focus of a parabola y2 = 4ax is

    (a)

    a

    (b)

    2a

    (c)

    4a

    (d)

    3a

  15. The equation of directrix of the parabola y2 = - x is

    (a)

    4x+ 1 =0

    (b)

    4x - 1 = 0

    (c)

    x - 4=0

    (d)

    x + 4 = 0

  16. Part B

    6 x 2 = 12
  17. Find the centre and radius of the circle x2 + y2 = 16

  18. Find the center and radius of the circle  x2 + y2 - 22x - 4y + 25 = 0

  19. Find the center and radius of the circle 5x2 + 5y2 +4x - 8y - 16 = 0

  20. Find the equation of the circle whose centre is (2,3) and which passes through (1 , 4)

  21. Find the equation of the circle passing through the points (0, 1) , (4 ,3) and (1, -1)

  22. Find the equation of the circle on the line joining the points (1,0), (0,1) and having its centre on the line x + y= 1

  23. Part C

    6 x 3 = 18
  24. A point moves so that its distance from the point (-1, 0) is always three times its distance from the point (0, 2). Find its locus.

  25. For what value of \(\lambda \) are the three lines 2x-5y+3 = 0, 5x-9y+\(\lambda \)=0 and x-2y+1=0 are concurrent?

  26. For what value of k does 12x2+7xy+ky2+13x-y+3=0 represents a pair of straight lines?

  27. Find the equation of a circle of radius 5 whose centre lies on X-axis and passes through the point (2, 3).

  28. Find the equation of a circle whose diameters are 2x-3y+12=0 and x+4y-5=0 and area is 154 square units.

  29. Find the equation of the parabola whose focus is (-3, 2) and the directrix is x+y=4.

  30. Part D

    1 x 5 = 5
  31. Find the equation of the parabola whose vertex is (0, 0) passing through the point (2, 3) and axis is along X-axis.

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