1
IIT-JEE 2005 Screening
MCQ (Single Correct Answer)
+2
-0.5
$$a,\,b,\,c$$ are integers, not all simultaneously equal and $$\omega $$ is cube root of unity $$\left( {\omega \ne 1} \right),$$ then minimum value of $$\left| {a + b\omega + c{\omega ^2}} \right|$$ is
A
0
B
1
C
$${{\sqrt 3 } \over 2}$$
D
$${1 \over 2}$$
2
IIT-JEE 2005 Screening
MCQ (Single Correct Answer)
+3
-0.75
If $$\int\limits_{\sin x}^1 {{t^2}f\left( t \right)dt = 1 - \sin x,} $$ then f$$\left( {{1 \over {\sqrt 3 }}} \right)$$ is
A
$${1 \over 3}$$
B
$${{1 \over {\sqrt 3 }}}$$
C
$$3$$
D
$${\sqrt 3 }$$
3
IIT-JEE 2005 Screening
MCQ (Single Correct Answer)
+2
-0.5
If $$P(x)$$ is a polynomial of degree less than or equal to $$2$$ and $$S$$ is the set of all such polynomials so that $$P(0)=0$$, $$P(1)=1$$ and $$P'\left( x \right) > 0\,\,\forall x \in \left[ {0,1} \right],$$ then
A
$$S = \phi $$
B
$$S = ax + \left( {1 - a} \right){x^2}\,\,\forall \,a \in \left( {0,2} \right)$$
C
$$S = ax + \left( {1 - a} \right){x^2}\,\,\forall \,a \in \left( {0,\infty } \right)$$
D
$$S = ax + \left( {1 - a} \right){x^2}\,\,\forall \,a \in \left( {0,1} \right)$$
4
IIT-JEE 2005 Screening
MCQ (Single Correct Answer)
+2
-0.5
In a triangle $$ABC$$, $$a,b,c$$ are the lengths of its sides and $$A,B,C$$ are the angles of triangle $$ABC$$. The correct relation is given by
A
$$\left( {b - c} \right)\sin \left( {{{B - C} \over 2}} \right) = a\cos {A \over 2}$$
B
$$\left( {b - c} \right)cos\left( {{A \over 2}} \right) = a\,sin{{B - C} \over 2}$$
C
$$\left( {b + c} \right)\sin \left( {{{B + C} \over 2}} \right) = a\cos {A \over 2}$$
D
$$\left( {b - c} \right)cos\left( {{A \over 2}} \right) = 2a\,sin{{B + C} \over 2}$$
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