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3D Geometry question

2010 · Shift 2 · Q20

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PYQ Library
JEE Advanced
Mathematics
3D Geometry
2010 · Shift 2 · Q20

3D Geometry question

2010 · Shift 2 · Q20

JEE AdvancedMathematics3D GeometryMCQ+4 / −1

Match the statement in Column-

I

with the values in Column-

II\,\,\,\,\,\,\,\,\,\,\,\,

Column-

I

(A)

\,\,\,\,

A line from the origin meets the lines

\,{{x - 2} \over 1} = {{y - 1} \over { - 2}} = {{z + 1} \over 1}

and

{{x - {8 \over 3}} \over 2} = {{y + 3} \over { - 1}} = {{z - 1} \over 1}

at

P

and

Q

respectively. If length

PQ=d,

then

{d^2}

is (B)

\,\,\,\,

The values of

x

satisfying

{\tan ^{ - 1}}\left( {x + 3} \right) - {\tan ^{ - 1}}\left( {x - 3} \right) = {\sin ^{ - 1}}\left( {{3 \over 5}} \right)

are (C)

\,\,\,\,

Non-zero vectors

\overrightarrow a ,\overrightarrow b

and

\overrightarrow c \,\,

satisfy

\overrightarrow a \,.\,\overrightarrow b \, = 0.

\left( {\overrightarrow b - \overrightarrow a } \right).\left( {\overrightarrow b + \overrightarrow c } \right) = 0

and

2\left| {\overrightarrow b + \overrightarrow c } \right| = \left| {\overrightarrow b - \overrightarrow a } \right|.

If

\overrightarrow a = \mu \overrightarrow b + 4\overrightarrow c \,\,,

then the possible values of

\mu

are (D)

\,\,\,\,

Let

f

be the function on

\left[ { - \pi ,\pi } \right]

given by

f(0)=9

and

f\left( x \right) = \sin \left( {{{9x} \over 2}} \right)/\sin \left( {{x \over 2}} \right)

for

x e 0

The value of

{2 \over \pi }\int_{ - \pi }^\pi {f\left( x \right)dx}

is

\,\,\,\,\,\,\,\,\,\,\,\,

Column-

II

(p)

\,\,\,\,-4

(q)

\,\,\,\,0

(r)

\,\,\,\,4

(s)

\,\,\,\,5

(t)

\,\,\,\,6

A
$\left( A \right) \to t;\,\,\left( B \right) \to p,r;\,\,\left( C \right) \to q,s;\,\,\left( D \right) \to r$
B
$\left( A \right) \to r;\,\,\left( B \right) \to p;\,\,\left( C \right) \to q,s;\,\,\left( D \right) \to r$
C
$\left( A \right) \to t;\,\,\left( B \right) \to p,r;\,\,\left( C \right) \to q;\,\,\left( D \right) \to r$
D
$\left( A \right) \to t;\,\,\left( B \right) \to r;\,\,\left( C \right) \to q,s;\,\,\left( D \right) \to r$

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