1
AIEEE 2008
MCQ (Single Correct Answer)
+4
-1
If the straight lines $$\,\,\,\,\,$$ $$\,\,\,\,\,$$ $${{x - 1} \over k} = {{y - 2} \over 2} = {{z - 3} \over 3}$$ $$\,\,\,\,\,$$ and$$\,\,\,\,\,$$ $${{x - 2} \over 3} = {{y - 3} \over k} = {{z - 1} \over 2}$$ intersects at a point, then the integer $$k$$ is equal to
A
$$-5$$
B
$$5$$
C
$$2$$
D
$$-2$$
2
AIEEE 2008
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Let p be the statement “x is an irrational number”, q be the statement “y is a transcendental number”, and r be the statement “x is a rational number iff y is a transcendental number”.

Statement –1: r is equivalent to either q or p.

Statement –2: r is equivalent to $$ \sim \left( {p \leftrightarrow \sim q} \right)$$
A
Statement − 1 is false, Statement − 2 is false
B
Statement −1 is false, Statement −2 is true
C
Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1
D
Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1
3
AIEEE 2008
MCQ (Single Correct Answer)
+4
-1
Let $$f:N \to Y$$ be a function defined as f(x) = 4x + 3 where
Y = { y $$ \in $$ N, y = 4x + 3 for some x $$ \in $$ N }.
Show that f is invertible and its inverse is
A
$$g\left( y \right) = {{3y + 4} \over 4}$$
B
$$g\left( y \right) = 4 + {{y + 3} \over 4}$$
C
$$g\left( y \right) = {{y + 3} \over 4}$$
D
$$g\left( y \right) = {{y - 3} \over 4}$$
4
AIEEE 2008
MCQ (Single Correct Answer)
+4
-1
Let $$f\left( x \right) = \left\{ {\matrix{ {\left( {x - 1} \right)\sin {1 \over {x - 1}}} & {if\,x \ne 1} \cr 0 & {if\,x = 1} \cr } } \right.$$

Then which one of the following is true?
A
$$f$$ is neither differentiable at x = 0 nor at x = 1
B
$$f$$ is differentiable at x = 0 and at x = 1
C
$$f$$ is differentiable at x = 0 but not at x = 1
D
$$f$$ is differentiable at x = 1 but not at x = 0
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