1
AIEEE 2011
MCQ (Single Correct Answer)
+4
-1
The vectors $$\overrightarrow a $$ and $$\overrightarrow b $$ are not perpendicular and $$\overrightarrow c $$ and $$\overrightarrow d $$ are two vectors satisfying $$\overrightarrow b \times \overrightarrow c = \overrightarrow b \times \overrightarrow d $$ and $$\overrightarrow a .\overrightarrow d = 0\,\,.$$ Then the vector $$\overrightarrow d $$ is equal to :
A
$$\overrightarrow c + \left( {{{\overrightarrow a .\overrightarrow c } \over {\overrightarrow a .\overrightarrow b }}} \right)\overrightarrow b $$
B
$$\overrightarrow b + \left( {{{\overrightarrow b .\overrightarrow c } \over {\overrightarrow a .\overrightarrow b }}} \right)\overrightarrow c $$
C
$$\overrightarrow c - \left( {{{\overrightarrow a .\overrightarrow c } \over {\overrightarrow a .\overrightarrow b }}} \right)\overrightarrow b $$
D
$$\overrightarrow b - \left( {{{\overrightarrow b .\overrightarrow c } \over {\overrightarrow a .\overrightarrow b }}} \right)\overrightarrow c $$
2
AIEEE 2011
MCQ (Single Correct Answer)
+4
-1
If $$C$$ and $$D$$ are two events such that $$C \subset D$$ and $$P\left( D \right) \ne 0,$$ then the correct statement among the following is :
A
$$P\left( {{C \over D}} \right)$$$$ \ge P\left( C \right)$$
B
$$P\left( {{C \over D}} \right)$$$$ < P\left( C \right)$$
C
$$P\left( {{C \over D}} \right)$$$$ = {{P\left( D \right)} \over {P\left( C \right)}}$$
D
$$P\left( {{C \over D}} \right)$$$$ = P\left( C \right)$$
3
AIEEE 2011
MCQ (Single Correct Answer)
+4
-1
If $${{dy} \over {dx}} = y + 3 > 0\,\,$$ and $$y(0)=2,$$ then $$y\left( {\ln 2} \right)$$ is equal to :
A
$$5$$
B
$$13$$
C
$$-2$$
D
$$7$$
4
AIEEE 2011
MCQ (Single Correct Answer)
+4
-1
Let $$I$$ be the purchase value of an equipment and $$V(t)$$ be the value after it has been used for $$t$$ years. The value $$V(t)$$ depreciates at a rate given by differential equation $${{dv\left( t \right)} \over {dt}} = - k\left( {T - t} \right),$$ where $$k>0$$ is a constant and $$T$$ is the total life in years of the equipment. Then the scrap value $$V(T)$$ of the equipment is
A
$$I - {{k{T^2}} \over 2}$$
B
$$I - {{k{{\left( {T - t} \right)}^2}} \over 2}$$
C
$${e^{ - kT}}$$
D
$${T^2} - {1 \over k}$$
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