AIEEE(CBSE(ENG(03

1.A function f from the set of natural numbers to integers defined by

f (n) = [pic] is

(A) one(one but not onto(B) onto but not one(one

(C) one(one and onto both(D) neither one(one nor onto

2.Let z1 and z2 be two roots of the equation z2 + az + b = 0, z being complex. Further, assume that the origin, z1 and z2 form an equilateral triangle, then (A) a2 = b (B) a2 = 2b

(C) a2 = 3b (D) a2 = 4b

3.If z and ( are two non(zero complex numbers such that |z(| = 1, and Arg (z) ( Arg (() = [pic], then [pic] is equal to (A) 1(B) ( 1

(C) i (D) ( i

4.If [pic] = 1, then

(A) x = 4n, where n is any positive integer

(B) x = 2n, where n is any positive integer

(C) x = 4n + 1, where n is any positive integer

(D) x = 2n + 1, where n is any positive integer

5.If [pic] = 0 and vectors (1, a, a2) (1, b, b2) and (1, c, c2) are non(coplanar, then the product abc equals (A) 2(B) ( 1

(C) 1(D) 0

6.If the system of linear equations

x + 2ay + az = 0

x + 3by + bz = 0

x + 4cy + cz = 0

has a non(zero solution, then a, b, c

(A) are in A. P.(B) are in G.P.

(C) are in H.P.(D) satisfy a + 2b + 3c = 0

7.If the sum of the roots of the quadratic equation ax2 + bx + c = 0 is equal to the sum of the squares of their reciprocals, then [pic] and [pic] are in (A) arithmetic progression(B) geometric progression

(C) harmonic progression(D) arithmetic(geometric(progression

8.The number of real solutions of the equation x2 ( 3 |x| + 2 = 0 is (A) 2(B) 4

(C) 1(D) 3

9.The value of ‘a’ for which one root of the quadratic equation (a2 ( 5a + 3) x2 + (3a ( 1) x + 2 = 0 is twice as large as the other, is (A) [pic](B) ( [pic]

(C) [pic](D) ( [pic]

I10.If A = [pic] and A2 = [pic], then

(A) ( = a2 + b2, ( = ab (B) ( = a2 + b2, ( = 2ab

(C) ( = a2 + b2, ( =...

1.A function f from the set of natural numbers to integers defined by

f (n) = [pic] is

(A) one(one but not onto(B) onto but not one(one

(C) one(one and onto both(D) neither one(one nor onto

2.Let z1 and z2 be two roots of the equation z2 + az + b = 0, z being complex. Further, assume that the origin, z1 and z2 form an equilateral triangle, then (A) a2 = b (B) a2 = 2b

(C) a2 = 3b (D) a2 = 4b

3.If z and ( are two non(zero complex numbers such that |z(| = 1, and Arg (z) ( Arg (() = [pic], then [pic] is equal to (A) 1(B) ( 1

(C) i (D) ( i

4.If [pic] = 1, then

(A) x = 4n, where n is any positive integer

(B) x = 2n, where n is any positive integer

(C) x = 4n + 1, where n is any positive integer

(D) x = 2n + 1, where n is any positive integer

5.If [pic] = 0 and vectors (1, a, a2) (1, b, b2) and (1, c, c2) are non(coplanar, then the product abc equals (A) 2(B) ( 1

(C) 1(D) 0

6.If the system of linear equations

x + 2ay + az = 0

x + 3by + bz = 0

x + 4cy + cz = 0

has a non(zero solution, then a, b, c

(A) are in A. P.(B) are in G.P.

(C) are in H.P.(D) satisfy a + 2b + 3c = 0

7.If the sum of the roots of the quadratic equation ax2 + bx + c = 0 is equal to the sum of the squares of their reciprocals, then [pic] and [pic] are in (A) arithmetic progression(B) geometric progression

(C) harmonic progression(D) arithmetic(geometric(progression

8.The number of real solutions of the equation x2 ( 3 |x| + 2 = 0 is (A) 2(B) 4

(C) 1(D) 3

9.The value of ‘a’ for which one root of the quadratic equation (a2 ( 5a + 3) x2 + (3a ( 1) x + 2 = 0 is twice as large as the other, is (A) [pic](B) ( [pic]

(C) [pic](D) ( [pic]

I10.If A = [pic] and A2 = [pic], then

(A) ( = a2 + b2, ( = ab (B) ( = a2 + b2, ( = 2ab

(C) ( = a2 + b2, ( =...

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