Model Question Paper Mathematics Class Xii Worksheet Page 5
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1
2
3
4
5
6
7+
2
3
x
x
1
x
Δ =
+
=
2
3
y
y
1
y
0
23.
If x, y, z are different numbers and
, then show that 1 + x y z
+
2
3
z
z
1
z
= 0
+
≤
⎧
x
5,if
x
1
⎨
24.
Is the function f defined by f (x) =
a continuous function? Justify
>
⎩
x
–5,if
x
1
your answer.
2
d y
25.
If x = a (cos t + t sin t), y = a (sin t – t cos t). Find
2
dx
∫
–1
2
26.
Find
(sin
) x dx
OR
+
2
x
1
∫
dx
Find
−
+
2
x
5
x
6
∫
2
2
27.
Evaluate
1-x dx
−
2
2
2
28.
Find the solution of the differential equation (x
+ y
) dx = 2xy dy
OR
Find the equation of the curve passing through the origin and satisfying the dif-
dy
2
2
ferential equation (1 + x
)
+ 2xy = 4x
dx
29.
If the magnitude of the vectors,
,
,
are 3, 4, 5 respectively and
and
+
a
c
a
b
b
,
and (
+
),
and (
+
) are mutually perpendicular, then find the
c
c
a
c
a
b
b
magnitude
of
(
+
+
)
a
c
b
30.
Find the equation of the straight line passing through (1, 2, 3) and perpendicular
to
the
plane
x + 2y – 5z + 9 = 0
OR
Find the equation of the plane passing through the point (–1, 3, 2) and perpen-
dicular to each of the planes x + 2y + 3z = 5 and 3x + 3y + z = 0
31.
A man and his wife appear for an interview for two posts. The probability of
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