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CBSE 12TH MATHEMATICS - Online Test
cbse 12th mathematics
TEST : 60
Determinants
Prepare / Learn
Q1.
If A is a non singular matrix of order 3 , then
∣
∣
a
d
j
(
A
3
)
∣
∣
=
A.
|
A
|
6
B.
|
A
|
9
C.
None of these
D.
|
A
|
8
View Solution
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Answer :
Option A
Explaination / Solution:
If A is anon singular matrix of order , then
∣
∣
a
d
j
(
A
3
)
∣
∣
=
(
∣
∣
A
3
∣
∣
)
2
=
(
|
A
A
A
|
)
2
=
(
|
A
|
|
A
|
|
A
|
)
2
=
(
|
A
|
3
)
2
=
|
A
|
6
Application of Integrals
Prepare / Learn
Q2.
A.
8/3
B.
4
C.
None of these
D.
3
View Solution
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Answer :
Option A
Explaination / Solution:
The tangents are
y
=
m
x
+
a
m
,
y
=
m
x
+
1
2
m
,
since
a
=
1
2
.
It passes through ( -2 , 0 ).
∴
4
m
2
=
1
⇒
m
=
±
1
2
The tangents are :
y
=
x
2
+
1
,
y
=
−
x
2
−
1
Required area :
−
2
y
+
2
)
d
y
=
2
[
4
3
−
4
+
4
]
=
8
3
s
q
.
u
n
i
t
s
Vector Algebra
Prepare / Learn
Q3.
If a unit vector
⃗
a
makes angles
π
3
w
i
t
h
i
^
π
4
w
i
t
h
j
^
a
n
d
a
n
a
c
u
t
e
a
n
g
l
e
θ
w
i
t
h
k
^
, then find
θ
A.
2(π/3)
B.
π/10
C.
π/3
D.
π/5
View Solution
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Answer :
Option C
Explaination / Solution:
Let
a
→
=
a
1
i
ˆ
+
a
2
j
ˆ
+
a
3
k
ˆ
,
It is given that
∣
∣
a
→
∣
∣
=
1
, then,
Putting these values in (1), we get:
1
4
+
1
2
+
cos
2
θ
=
1
=
1
−
cos
2
θ
⇒
sin
2
θ
=
3
4
⇒
sin
θ
=
3
√
2
⇒
θ
=
60
∘
Integrals
Prepare / Learn
Q4.
If f (x) = f (a –x), then ,
∫
0
a
x
f
(
x
)
d
x
is equal to
A.
−
a
2
2
∫
0
a
f
(
x
)
d
x
B.
∫
0
a
f
(
x
)
d
x
C.
a
2
∫
0
a
f
(
x
)
d
x
D.
a
2
2
∫
0
a
f
(
x
)
d
x
View Solution
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Answer :
Option C
Explaination / Solution:
Inverse Trigonometric Functions
Prepare / Learn
Q5.
cos
(
cos
−
1
(
7
25
)
)
=
A.
25/7
B.
24/25
C.
25/24
D.
none of these.
View Solution
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Answer :
Option D
Explaination / Solution:
Matrices
Prepare / Learn
Q6.
The equations, x + 4 y – 2 z = 3, 3 x + y + 5 z = 7, 2 x + 3y +z = 5 have
A.
a unique solution
B.
none of these
C.
infinitely many solutions
D.
no solution
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Answer :
Option D
Explaination / Solution:
The given system of equations does not have solution if :
=
0
⇒
1
(
−
14
)
−
4
(
−
7
)
−
2
(
7
)
=
0
Continuity and Differentiability
Prepare / Learn
Q7.
If x = a
c
o
s
3
t
,
y
=
a
s
i
n
3
then
d
y
d
x
is equal to
A.
cos t
B.
– tan t.
C.
cot t
D.
cosec t
View Solution
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Answer :
Option B
Explaination / Solution:
d
y
d
x
=
d
y
d
t
d
x
d
t
=
3
a
sin
2
t
cos
t
3
a
cos
2
t
(
−
sin
t
)
=
−
tan
t
Three Dimensional Geometry
Prepare / Learn
Q8.
Find the distance of the point (– 6, 0, 0) from the plane 2x – 3y + 6z – 2 = 0
A.
4
B.
2
C.
3
D.
5
View Solution
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Answer :
Option B
Explaination / Solution:
Differential Equations
Prepare / Learn
Q9.
Solution of
x
d
y
−
y
d
x
=
x
2
+
y
2
−
−
−
−
−
−
−
√
d
x
is
A.
y
+
x
3
+
y
2
−
−
−
−
−
−
√
=
C
x
2
B.
y
+
x
2
+
y
2
−
−
−
−
−
−
√
=
C
x
2
C.
y
+
x
2
+
y
3
−
−
−
−
−
−
√
=
C
x
2
D.
y
+
3
+
y
2
−
−
−
−
−
√
=
C
x
4
View Solution
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Answer :
Option C
Explaination / Solution:
Application of Derivatives
Prepare / Learn
Q10.
Rolle’s Theorem is not applicable to the function f(x) = | x | for −2⩽x⩽2 because
A.
none of these.
B.
f ( – 2) = f (2)
C.
f (x) is not derivable for x = 0
D.
f (x) is continuous for −2⩽x⩽2
View Solution
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Answer :
Option C
Explaination / Solution:
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cbse 12th mathematics
TEST : 60
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