The orthogonal trajectory of the family of curves x^2-y^2 = a (where a is a constant) and passing through the point (1,1) is
a) y=-1/x b) y=1/x c) y=-x d) y=x
115. The value of the line integral ∫ y^2 dx + 2xydy over the curve x=accost, y=asint is
a) 0 b) 1 c) 2 d) 4
116. The n-th partial sum of the infinite series 1/1*2 + 1/2*3 + 1/3*4+……1/n*(n+1)……..
a) 1/n+1 b) n+2/n+1 c) n/n+1 d) n-1/n+1
117. The complex-valued function f(z)=e^z is analytic for
a) no z b) all z c) real z only d) imaginary z only
118. The inverse of the matrix [ cos A sin A
-sin A cos A] is
a) [ -cos A Sin A b) [cos A sin A} c) [cos A -sin A d) [cos A -sin A
sin A cos A] sin A -cos A] -sin A cos A] sin A cos A]
119. Consider the function f(x) defined as
F(x) = 3x-1, x<0
0, x=0
2x+5, x>0
In the following table, List I shows 4 expressions for limits of f(x) and List II indicates the values of the limits
List I List II
P.Lim x->2 f(x) 1. -1
Q.Lim x->0+ f(x) 2. 9
R.Lim x->0- f(x) 3. -10
S.Lim x->-3 f(x) 4. 5
The correct matches are
a) P-2,Q-4,R-1,S-3 B) P-2,Q-4,R-3,S-1 C) P-4,Q-2,R-1,S-3 D) P-4,Q-2,R-3,S-1
120. Two events A and B with probability 0.5 and 0.7, respectively, have joint probability of 0.4. The probability that neither A nor B happens is
a) 0.2 b) 0.4 c) 0.6 d) 0.8
