Model Question Paper Mathematics Class Xii Worksheet Page 4
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1
2
3
4
5
6
7−
−
−
−
−
−
x
1
y
2
z
3
x
1
y
1
z
6
=
=
=
=
17.
If the given lines
and
are perpendicular, then k
−
−
3
2
k
2
3
k
1
5
is
10
(A) –10
(B)
7
−
−
10
7
(C)
(D)
7
10
r
r
−
+
− −
ˆ
ˆ
18.
The angle between the planes
ˆ
ˆ
= 0 and
ˆ ˆ
is
r
.(3
i
4
j
5 )
k
r
.(2
i
j
2 )
k
π
π
(A)
(B)
3
2
π
π
(C)
(D)
6
4
19.
The probability of obtaining an even prime numbr on each die, when a pair of
dice is rolled is
1
(A) 0
(B)
3
1
1
(C)
(D)
12
36
20.
If R is the set of real numbers and f : R→R be the function defined by f (x) =
1
3 3
, then (fof) (x) is equal to
(3 –
x
)
1
3
(A)
(B) x
3
x
3
(C) x
(D) (3 – x
)
Part B
21.
Let R be the set of real numbers, f : R→R be the function defined by f (x) = 4x +
3, x ∈ R. Show that f is invertible. Find the inverse of f.
⎛
⎞
+ −
−
π
−
1
x
1
x
1
1
= −
−
≤
≤
1
⎜
⎟
cos
x
,
x
1
–1
22.
Prove that tan
+ +
−
⎝
⎠
4 2
1
x
1
x
2
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