#### Differential Calculus - Important Question Paper

11th Standard

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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.