1
AIEEE 2011
MCQ (Single Correct Answer)
+4
-1
If $$A = {\sin ^2}x + {\cos ^4}x,$$ then for all real $$x$$:
A
$${{13} \over {16}} \le A \le 1$$
B
$$1 \le A \le 2$$
C
$${3 \over 4} \le A \le {{13} \over {16}}$$
D
$${{3} \over {4}} \le A \le 1$$
2
AIEEE 2011
MCQ (Single Correct Answer)
+4
-1
Let $$\alpha \,,\beta $$ be real and z be a complex number. If $${z^2} + \alpha z + \beta = 0$$ has two distinct roots on the line Re z = 1, then it is necessary that :
A
$$\beta \, \in ( - 1,0)$$
B
$$\left| {\beta \,} \right| = 1$$
C
$$\beta \, \in (1,\infty )$$
D
$$\beta \, \in (0,1)$$
3
AIEEE 2011
MCQ (Single Correct Answer)
+4
-1
If $$\omega ( \ne 1)$$ is a cube root of unity, and $${(1 + \omega )^7} = A + B\omega \,$$. Then $$(A,B)$$ equals :
A
(1 ,1)
B
(1, 0)
C
(- 1 ,1)
D
(0 ,1)
4
AIEEE 2011
MCQ (Single Correct Answer)
+4
-1
These are 10 points in a plane, out of these 6 are collinear, if N is the number of triangles formed by joining these points. then:
A
$$N \le 100$$
B
$$100 < N \le 140$$
C
$$140 < N \le 190\,$$
D
$$N > 190$$
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