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Shubhrajyoti Ghosh
Subject: Maths
, asked on 22/1/18
f
x
=
x
3
-
12
x
2
+
36
x
+
17
Answer
1
Shubhrajyoti Ghosh
Subject: Maths
, asked on 22/1/18
Q
.
F
i
n
d
t
h
e
i
n
t
e
r
v
a
l
s
i
n
w
h
i
c
h
t
h
e
f
o
l
l
o
w
i
n
g
f
u
n
c
t
i
o
n
s
a
r
e
a
i
n
c
r
e
a
sin
g
b
d
e
c
r
e
a
sin
g
f
x
=
2
x
3
-
15
x
2
+
36
x
+
1
Answer
3
Shubhrajyoti Ghosh
Subject: Maths
, asked on 22/1/18
No links please
Answer
0
Shubhrajyoti Ghosh
Subject: Maths
, asked on 22/1/18
No links please
Q.4. If x > 0, prove that,
(iii)
log
(
x
+
x
2
+
1
)
<
x
Answer
1
Shubhrajyoti Ghosh
Subject: Maths
, asked on 22/1/18
No links please
Chapter Name:
INCREASING AND DECREASING FUNCTIONS
Q.3. If
0
<
x
<
π
2
, show that
(iii)
cos
x
>
1
-
x
2
2
!
Answer
0
Shubhrajyoti Ghosh
Subject: Maths
, asked on 22/1/18
Prove that the function
f
(
x
) = 4
x
3
+ 6
x
2
– 24
x
+ 1 decreases in the interval (–2, 1)
Answer
1
Shubhrajyoti Ghosh
Subject: Maths
, asked on 15/1/18
Q The order and degree of the differential equation representing the family of curves .
y
2
= 2k ( x +
k
) (where k is a positive parameter) are respectively —
1,3
2,4
1,4
1,2
Answer
1
Shanaya
Subject: Maths
, asked on 14/1/18
How did we put the value of v in the equation and where did -2log|x| in RHS go?
Answer
1
Shubhrajyoti Ghosh
Subject: Maths
, asked on 9/1/18
Evaluate:
1
1
1
1
ω
2
ω
1
ω
ω
2
(where ω is an imaginary cube root of unity).
Answer
1
Shubhrajyoti Ghosh
Subject: Maths
, asked on 9/1/18
20. Find the common tangents to the hyperbola x
2
- 2y
2
= 4 and the circle .
Answer
1
Shubhrajyoti Ghosh
Subject: Maths
, asked on 9/1/18
Without expanding prove that:
log
x
x
y
z
log
x
y
log
x
z
log
y
x
y
z
1
log
y
z
log
z
x
y
z
log
z
y
1
=
0
Answer
1
Shubhrajyoti Ghosh
Subject: Maths
, asked on 9/1/18
Without expanding prove that [22-24]:
1
b
c
b
c
b
+
c
1
c
a
c
a
c
+
a
1
a
b
a
b
a
+
b
=
0
Answer
0
Shubhrajyoti Ghosh
Subject: Maths
, asked on 9/1/18
Without expanding prove that
7
12
-
3
9
14
-
1
8
13
-
2
=
0
Answer
1
Shubhrajyoti Ghosh
Subject: Maths
, asked on 9/1/18
Prove that,
0
cos
α
-
sin
α
sin
α
0
cos
α
cos
α
sin
α
0
2
=
1
x
-
x
x
1
x
-
x
x
1
where
x
= sin α cos α
Answer
0
Shubhrajyoti Ghosh
Subject: Maths
, asked on 9/1/18
20. Find the common tangents to the hyperbola x2- 2y2 = 4 and the circle...
C
h
a
p
t
e
r
n
a
m
e
:
T
A
N
G
E
N
T
A
N
D
N
O
R
M
A
L
P
r
o
v
e
:
17
.
y
+
z
z
+
x
x
+
y
z
+
x
x
+
y
y
+
z
x
+
y
y
+
z
z
+
x
=
2
x
y
z
y
z
x
z
x
y
=
-
2
x
3
+
y
3
+
z
3
-
3
x
y
z
C
B
S
E
'
01
,
'
04
,
'
06
C
,
'
07
Answer
1
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What are you looking for?
Q.4. If x > 0, prove that,
(iii)
Chapter Name:
INCREASING AND DECREASING FUNCTIONS
Q.3. If , show that
(iii)
= 2k ( x + ) (where k is a positive parameter) are respectively —