1
AIEEE 2011
MCQ (Single Correct Answer)
+4
-1
Let $R$ be the set of real numbers.

Statement I : $A=\{(x, y) \in R \times R: y-x$ is an integer $\}$ is an equivalence relation on $R$.

Statement II : $ B=\{(x, y) \in R \times R: x=\alpha y$ for some rational number $\alpha\}$ is an equivalence relation on $R$.
A
Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I.
B
Statement I is true, Statement II is false.
C
Statement I is false, Statement II is true.
D
Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I.
2
AIEEE 2011
MCQ (Single Correct Answer)
+4
-1
Let $$\overrightarrow a $$, $$\overrightarrow b $$, $$\overrightarrow c $$ be three non-zero vectors which are pairwise non-collinear. If $\overrightarrow a+3 \overrightarrow b$ is collinear with $\overrightarrow c$ and $\overrightarrow b+2 \overrightarrow c$ is collinear with $\overrightarrow a$, then $\overrightarrow a+\overrightarrow b+6 \overrightarrow c$ is :
A
$\overrightarrow a+\overrightarrow c$
B
$\overrightarrow c$
C
$\overrightarrow a$
D
$\overrightarrow 0$
3
AIEEE 2011
MCQ (Single Correct Answer)
+4
-1
This question has Statement - $$1$$ and Statement - $$2$$. Of the four choices given after the statements, choose the one that best describes the two statements.

Statement - $$1$$ : A metallic surface is irradiated by a monochromatic light of frequency $$v > {v_0}$$ (the threshold frequency). The maximum kinetic energy and the stopping potential are $${K_{\max }}$$ and $${V_0}$$ respectively. If the frequency incident on the surface is doubled, both the $${K_{\max }}$$ anmd $${V_0}$$ are also doubled.
Statement - $$2$$ : The maximum kinetic energy and the stopping potential of photoelectrons emitted from a surface are linearly dependent on the frequency of incident light.

A
Statement - $$1$$ is true, Statement - $$2$$ is true, Statement - $$2$$ is the correct explanation of Statement - $$1$$.
B
Statement - $$1$$ is true, Statement - $$2$$ is true, Statement - $$2$$ is not the correct explanation of Statement - $$1$$.
C
Statement - $$1$$ is false, Statement - $$2$$ is true.
D
Statement - $$1$$ is true, Statement - $$2$$ is false.
4
AIEEE 2011
MCQ (Single Correct Answer)
+4
-1
Energy required for the electron excitation in $$L{i^{ + + }}$$ from the first to the third Bohr orbit is :
A
$$36.3$$ $$eV$$
B
$$108.8$$ $$eV$$
C
$$122.4$$ $$eV$$
D
$$12.1$$ $$eV$$
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