68. Two vectors a and b are non-zero
    and non-collinear. What is the value of
    x for which the vectors p= (x – 2) a + b
    and q= (x + 1) a – b are collinear?

(a) 1 (b)^ (c)^ (d) 2

69. If | | and | |= 4, then for what
    value of λ is (a + λb) perpendicular to (a

• λb)?

(a)^ (b)^ (c) (d)^

71. Let u= i – j, v= 2i + 5j, w= 4i + 3j and
    p= u + v + w. Which one of the following
    is correct?
    (a) – 3 u + 2v= p

(b) 3u – 2 v= p

(c) 3u + 2v= p

(d) - 3 u – 2 v= p

71. If a and b are unit vectors inclined

at an angle of 30 to each other, which

one of the following is correct?

(a) | |

(b) 1<| |

(c) | | = 2

(d) | | > 2

APPLICATION ON DERIVATIVE

1. 
   

   If the radius of a circle be increasing
   at a uniform rate of 2cm/s. The rate of
   increasing of area of circle, at the
   instant when the radius is 20cm, is:
   (a) 70 π /s (b) 70 /s (c)
   80π /s
   (d) 80 /s

   
   


2. 
   

   The abscissa of the points, where the
   tangent to the curve y=
   is parallel to x-axis are:
   (a) x= 0 and 0 (b) x= 1 and -1 (c) x= 1
   and - 3
   (d) x= -1 and 3

   
   


3. 
   

   The equation of tangent at (-4, -4) on
   the curve = - 4y is:
   (a) 2x+y+4=0 (b) 2x-y-12=0 (c) 2x+y-
   4=0
   (d) 2x-y+4=0
   4. The point at which the tangent to the
   curve y= is parallel to y=
   3x+9 will be:
   (a) (2, 1) (b) (1, 2) (c) (3, 9) (d) (-2, 1)
   5. The slope of the tangent to the curve
   x= 3 +1, y= , at x=1 is:
   (a) 0 (b)^ (c) (d) - 2
   6. The equation of the tangent to the
   curve ( ) y= 2-x, where it crosses
   the x-axis is:
   (a) x+5y= 2 (b) x-5y= 2 (c) 5x-y= 2 (d)
   5x+y-2= 0