Processing math: 13%




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6.

Let ω=eiπ/3 and a,b,c,x,y,z be non  zero complex numbers such that a+b+c=x, a+bω+cω2=y,a+bω2+cω=z

then the value of |x|2+|y|2+|z|2|a|2+|b|2+|c|2 is 


A) 3

B) 5

C) 4

D) 6



7.

Let a=ˆiˆk,b=ˆi+ˆj and c=ˆi+2ˆj+3ˆk  be the three vectors. If r is a  vector such that  r x b=c x b and r.a=0 , then the value of r.b is 


A) 2

B) 3

C) 4

D) 9



8.

Let  y'(x)+y(x)g'(x)=g(x)g'(x)y(0)=0, x \epsilon R, where f'(x)  denoted \frac{d f(x)}{dx} and g(x) is a given non-constant differentiable function on R with g(0)=g(2)=0,  Then the value of y(2) is .....


A) 0

B) 4

C) 5

D) 6



9.

Let f: (0,1) \rightarrow R be defined by f(x)=\frac{b-x}{1-bx} where b is a constant such that 0<b<1, then 


A) f if not invertible on (0,1)

B) f \neq f^{-1} on (0,1) and f'(b)= \frac{1}{f'(0)}

C) f=f^{-1} on (0,1) and f'(b)=\frac{1}{f'(0)}

D) f^{-1} is differentiable on (0,1)



10.

Let E and F be two independent events. The probability that exactly one of them occurs is 11/25 and the probability of none of them occurring is 2/25.lf P(T) denotes the probability of occurrence of the event T, then


A) P(E)=\frac{4}{5},P(F)=\frac{3}{5}

B) P(E)=\frac{1}{5},P(F)=\frac{2}{5}

C) P(E)=\frac{2}{5},P(F)=\frac{1}{5}

D) P(E)=\frac{3}{5},P(F)=\frac{4}{5}



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