MATHs....

Not doubts.

1)Let f(x) = ax⁴ + bx³ + cx² + dx + e where a,b,c,d,e are integer. f(1) and f(2) are odd integer.If 'n₁' be the number of integral root(s) of f(x) = 0 and 'n₂' be the largest two digit prime factor of C (200,100) the find n₁ + n₂.

2)Let A = Summation (r = 0 to r= n) C (n,r) cos r∂. Find the value of A

3) (1- cot28⁰)(1-cot17⁰) = ?

4)If the complex number z1,z2,z3 represent the vertices of an equilateral triangle such that |z1| = |z2| = |z3|, then z1 + z2 + z3 = ?

5)If a²+ b² = 1 and x²+ y²=1 then find the maximum value of ax+ by

6)If \sum_{i=1}^{4}{}b_i = 0 , \sum_{i=1}^{4}{}b_iz_i= 0

b_i belongs to nonzero reals and z_i are complex numbers representing concyclic points, then find \sum_{i=1}^{4}{}b_i|z_i|²

7)If A and B represents complex numbers z1 and z2 such that |z1+z2| = |z1 - z2| then find the circumcentre of triangle OAB, where O is the origin.

8)Let P(ct1,c/t1) and Q (ct2,c/t2) be the points of a rectangular hyperbola xy = c² which subtends right angle at another point R of the given hyperbola. If S is the midpoint of PQ and O is the centre of the hyperbola then find area of the triangle ROS

9)find the maximum value of a b' + a'b|ab|, a,b are complex numbers and z' represents the conjugate of z

10)Find t (t is real number)
such that there is at least one z satisfying |z+3| ≤t²- 2t + 3 and |z- i3√3| < t²
where i = √-1

11) If the ellipse x²/4 + y² = 1 meets the ellipse x² + y²/a²=1 in four distinct points and a = b²-3b-9,then total number of integers which are not solution of b is ____________

source : AITS