differentiation - 10042012
TRANSCRIPT
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1. If f(x) = sin x + sin4x.cosx , then
2'(2 ) x = is
2 2
f x at
+
a) 0
b) -1
c) -2 2
d) None of these
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2. If 2 2 2y x y++ = then the value of dydx at
x = 1 is
a) 0
b) -1c) 1
d) 2
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3. If 2 4 2(1 )(1 )(1 ).......(1 )ny x x x x= + + + + , then dydx
at x = 0 is
a) 1
b) -1c) 0
d) None of these
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9. Let( )
( )421 1
22
2
ln lncot cot
lnln
e exxy
eex
x
= +
, then
2
2
d y
dxat x = 0 is
a) 2 b) 1 c) 0 d) -1
10. Let f be the inverse of g and10
2'( )
1xg x
x=
+. If f(2) = k ,then f(2) =
a)10
2
1 k
k
+b)
10
5
2c)
2
10
1 k
k
+d)
10
21
k
k+
11. Tangents are drawn from (0,0) to the curve y = sin3x , then point of contact of tangents lie on the
curvea)
2 2
9 19
y x = b)
2 2
9 11
y x = c)
2 2
9 11
y x+ = d)
2 2
9 19
y x+ =
12. If the tangent to the curve x2y2+ax2+by2=0 at (1,1) is inclined at an angle of 1cot (3) with positive
direction of x-axis then a2 + b2=
a) 53
b) 52
c) 72
d) 92
13. If the slope of tangent of the curve 1 2 3 4y x x x x= + + + at the point where x = 4 is a ,
then the value of a2 is
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a) 3 b) 1 c) 9 d) 4
14. The number of points in 0,2
, where the curvecos3 cos5 cos 7
cos3 5 7
x x xy x= + + + has tangents
parallel to x axis isa) 1 b) 2 c) 3 d) 4
15. The co-ordinates of the point on the curve ay2 = x2(a-x) , where tangent is vertical area) (0,0) b) (a,0) c) (a,1) d) (a,2)
16. The curve y = ax2 + bx + 4 touches the line y = x at (1,1) , thena) a=0,b=3 b) a=-1,b=4 c) a=4,b=-7 d) a=3,b=-6
17. If x2 + y2 = 1 , ,x y R , then maximum value of 3x + 4y + 5 is
a) 10 b) 5 c) 0 d) 10