Important questions for AIEEE

1..An integer m is said to be related to another integer n if m is a multiple of n.then relation is
(a) reflexive and symmetric
(b) reflexive and transitive
(c) symmetric and transitive
(d) equivalence relation
Hint:2 is multiple of 6,but 6 is not multiple of 2.
2..The function f:R-R defined by
f(x)=(x-1)(x-2)(x-3) is
(a)one-one but not onto
(b) onto but not one-one
(c) both one-one and onto
(d) neither one-one and onto
Hint: here f(1)= f(2)=f(3)=0
3.If the complex numbers z1,z2,z3 are in A.P,then they lie on a
(a) circle (b) parabola (c) line (d) ellipse
Hint: Let z1,z2,z3 be affixes of points A,B,C respectively. Since they are A.P,means
2 z2=z1 + z3
So B is the midpoint of the line AC.
4..The product of n positive numbers is unity.Then their sum is
(a) a positive number (b) divisible by n
© equal to n + 1/n (d) never less than n
Hint: AM greater than or equal to GM.
5..The number of roots of the equation x – 2/(x-1) =1 – 2/(x-1) is
(a) 1 (b) 2 (c) 0 (d) infinitely many
Hint: division by zero is not possible.
6.The equation e*x=m(x+1), m is negative ,nature of its roots
(a) no real roots (b) exactly one real root
© two real roots (d) infinitely roots
Hint: Let f(x) = e*x , g(x) = m(x+1) ,now draw the graph
7..The number of non-negative integral soloutions of abc= 30 is
(a) 30 (b) 27 (c) 8 (d) none of these
Hint: 30= 2*3*5
8 If A is a skew-symmetric matrix,then trace of A is
(a) 1 (b) -1 (c) 0 (d) none of these
Hint: Diagonal elements of a skew-symmertic matrix are all zero.
9..From the matrix equation AB = AC,we can conclude B = C,provided
(a) A is singular (b) A is non-singular
© A is symmetric (d) A is square
Hint:divison by zero not possible.
10.The reflection of the point (3,8) with respect to the line x + 3 y = 7 ,is
(a) (5,-6) (b) (-1,-4) (c) (0,-1) (d) ( -9,-4)
Hint: reflection line is perpendcular bisector of the original line.