1
AIEEE 2012
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Let $$A = \left( {\matrix{ 1 & 0 & 0 \cr 2 & 1 & 0 \cr 3 & 2 & 1 \cr } } \right)$$. If $${u_1}$$ and $${u_2}$$ are column matrices such
that $$A{u_1} = \left( {\matrix{ 1 \cr 0 \cr 0 \cr } } \right)$$ and $$A{u_2} = \left( {\matrix{ 0 \cr 1 \cr 0 \cr } } \right),$$ then $${u_1} + {u_2}$$ is equal to :
A
$$\left( {\matrix{ -1 \cr 1 \cr 0 \cr } } \right)$$
B
$$\left( {\matrix{ -1 \cr 1 \cr -1 \cr } } \right)$$
C
$$\left( {\matrix{ -1 \cr -1 \cr 0 \cr } } \right)$$
D
$$\left( {\matrix{ 1 \cr -1 \cr -1 \cr } } \right)$$
2
AIEEE 2012
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Let $$P$$ and $$Q$$ be $$3 \times 3$$ matrices $$P \ne Q.$$ If $${P^3} = {Q^3}$$ and
$${P^2}Q = {Q^2}P$$ then determinant of $$\left( {{P^2} + {Q^2}} \right)$$ is equal to :
A
$$-2$$
B
$$1$$
C
$$0$$
D
$$-1$$
3
AIEEE 2012
MCQ (Single Correct Answer)
+4
-1
If the $$\int {{{5\tan x} \over {\tan x - 2}}dx = x + a\,\ln \,\left| {\sin x - 2\cos x} \right| + k,} $$ then $$a$$ is
equal to :
A
$$-1$$
B
$$-2$$
C
$$1$$
D
$$2$$
4
AIEEE 2012
MCQ (Single Correct Answer)
+4
-1
The area between the parabolas $${x^2} = {y \over 4}$$ and $${x^2} = 9y$$ and the straight line $$y=2$$ is :
A
$$20\sqrt 2 $$
B
$${{10\sqrt 2 } \over 3}$$
C
$${{20\sqrt 2 } \over 3}$$
D
$$10\sqrt 2 $$
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