IIT-JEE-Mathematics-Screening-2002

SCREENING
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1. Let ω=-1/2+i √3/2 . Then the value of the determinant

determinants

(A) 3ω
(B) 3ω(ω-1)
(C) 3ω²
(D) 3ω(1-ω)

2. For all complex numbers z₁,z₂ satisfying |z₁ |=12 and |z₂-3-4i|=5, the minimum value of |z₁-z₂ | is:
(A) 0
(B) 2
(C) 7
(D) 17

3. If a₁ a₂,…..,a_n are positive real numbers whose product is a fixed number c, then the minimum value of a₁+a₂+…+a_n-1+2a_n is

(A)       n(2c)^1/n
(B)       (n+1)c^1/n
(C)       2nc^1/n
(D)       (n+1)(2c)^1/n


4.         Suppose a, b, c are I A.P. and a², b², c² are in G.P. If a<b<c and  a+b+c=3/2, then the value of a is

(A)       1/2√2
(B)       1/ 2√3
(C)       ½ - 1/√3
(D)       ½ - 1/√3


5.         The number of arrangements of the letters of the word BANANA in which the two N' s do not appear adjacently is
(A)       40
(B)       60
(C)       80
(D)       100



6.         The sum

   iit-question

if p > q is maximum when m is
(A)       5
(B)       10
(C)       15
(D)       20


7.         The number of values of k for which the system of equations
(k+1)x + 8y=4k
kx +(k+3)y = 3k -1
has infinitely many solution is
(A)       0
(B)       1
(C)       2
(D)       Infinite

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IIT-JEE-Mathematics-Screening-2002

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