Q1. If the curves y=f(x) and y=g(x) intersect each other orthogonally at some point P, then at P
(a) f and g may be increasing
(b) f and g may be decreasing
(c) f and g may have opposite monotonity
(d) NOT
Q2. A/R
Statement 1 : 1+2a+3a^2+4a^3+...+(n-1)a^{n-2} = (a-a^2)(a-a^3)(a-a^4)...(a-a^{n-1})
Statement 2 : lal = 1
11) c ?
since orthogonal
d(f(x))dxat P*d(g(x))dxat P=-1
now
two cases may be der
d(f(x))dxat P can be negative and d(g(x))dxat P must be +ve
or
vice versa
so they hav opposite monotonocity
2) statement 2 false
1061. what if one of the derivatives was 0 at the pt of intersection?
I think may comes into picture there.
1firstly one of deravative cant be 0
Two curves intersect orthogonally when their tangent lines at each point of intersection are perpendicular.
so m1* m2 need to be -1
so any of m1 m2 cant be 0
actully c option has may have opposite monotonity
if it had ...must hav then C wud hav been correct
so NON of these
for second
substitute n=3
u can see statement 2 is false
1r u sure?
infact
curve 1 is decreasing
and
curve 2 is increasing at point of intersection
106at the point of intersection .... you cant say it is decreasing (strictly) isnt it?
Or else let curve (1) = x2
106this IS fiitjee isnt it.. (last yrs full test question)
so mistakes can b der na?
1well i dun hav any soln for 2nd
but u can alwys substitute :P
substitute n=3
so u can see statement second is false
may be i m rong 
