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Exam: Maharashtra HSC Class 12
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Q776
#776
Mathematics → Differentiation → Higher Order Derivatives
·
Hard
Add
If
x
=
sin
t
x = \sin t
x
=
sin
t
,
y
=
e
m
t
y = e^{mt}
y
=
e
m
t
then show that
(
1
−
x
2
)
d
2
y
d
x
2
−
x
d
y
d
x
−
m
2
y
=
0
(1 - x^2) \frac{d^2y}{dx^2} - x \frac{dy}{dx} - m^2 y = 0
(
1
−
x
2
)
d
x
2
d
2
y
−
x
d
x
d
y
−
m
2
y
=
0
.
Show model answer
[Q1.5.1 SolvedEx.5 · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Set · 6 questions
Find the
n
t
h
n^{th}
n
t
h
derivative of the following :
Q777
#777
Mathematics → Differentiation → Higher Order Derivatives
·
Hard
Add
x
m
x^m
x
m
Show model answer
[Q1.5.2 SolvedEx.1 (i) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q778
#778
Mathematics → Differentiation → Higher Order Derivatives
·
Moderate
Add
1
a
x
+
b
\frac{1}{ax + b}
a
x
+
b
1
Show model answer
[Q1.5.2 SolvedEx.1 (ii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q779
#779
Mathematics → Differentiation → Higher Order Derivatives
·
Moderate
Add
log
x
\log x
lo
g
x
Show model answer
[Q1.5.2 SolvedEx.1 (iii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q780
#780
Mathematics → Differentiation → Higher Order Derivatives
·
Moderate
Add
sin
x
\sin x
sin
x
Show model answer
[Q1.5.2 SolvedEx.1 (iv) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q781
#781
Mathematics → Differentiation → Higher Order Derivatives
·
Moderate
Add
cos
(
a
x
+
b
)
\cos(ax + b)
cos
(
a
x
+
b
)
Show model answer
[Q1.5.2 SolvedEx.1 (v) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q782
#782
Mathematics → Differentiation → Higher Order Derivatives
·
Hard
Add
e
a
x
sin
(
b
x
+
c
)
e^{ax}\sin(bx + c)
e
a
x
sin
(
b
x
+
c
)
Show model answer
[Q1.5.2 SolvedEx.1 (vi) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
Report
Set · 6 questions
Find the second order derivative of the following :
Q783
#783
Mathematics → Differentiation → Higher Order Derivatives
·
Easy
Add
2
x
5
−
4
x
3
−
2
x
2
−
9
2x^5 - 4x^3 - \frac{2}{x^2} - 9
2
x
5
−
4
x
3
−
x
2
2
−
9
Show model answer
[QEx 1.5 Q.1 (i) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q784
#784
Mathematics → Differentiation → Higher Order Derivatives
·
Moderate
Add
e
2
x
⋅
tan
x
e^{2x} \cdot \tan x
e
2
x
⋅
tan
x
Show model answer
[QEx 1.5 Q.1 (ii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q785
#785
Mathematics → Differentiation → Higher Order Derivatives
·
Moderate
Add
e
4
x
⋅
cos
5
x
e^{4x} \cdot \cos 5x
e
4
x
⋅
cos
5
x
Show model answer
[QEx 1.5 Q.1 (iii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q786
#786
Mathematics → Differentiation → Higher Order Derivatives
·
Easy
Add
x
3
log
x
x^3 \log x
x
3
lo
g
x
Show model answer
[QEx 1.5 Q.1 (iv) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q787
#787
Mathematics → Differentiation → Higher Order Derivatives
·
Moderate
Add
log
(
log
x
)
\log (\log x)
lo
g
(
lo
g
x
)
Show model answer
[QEx 1.5 Q.1 (v) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q788
#788
Mathematics → Differentiation → Higher Order Derivatives
·
Hard
Add
x
x
x^x
x
x
Show model answer
[QEx 1.5 Q.1 (vi) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Set · 4 questions
Find
d
2
y
d
x
2
\frac{d^2y}{dx^2}
d
x
2
d
2
y
of the following :
Q789
#789
Mathematics → Differentiation → Higher Order Derivatives
·
Hard
Add
x
=
a
(
θ
−
sin
θ
)
x = a\,(\theta - \sin \theta)
x
=
a
(
θ
−
sin
θ
)
,
y
=
a
(
1
−
cos
θ
)
y = a\,(1 - \cos \theta)
y
=
a
(
1
−
cos
θ
)
Show model answer
[QEx 1.5 Q.2 (i) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q790
#790
Mathematics → Differentiation → Higher Order Derivatives
·
Hard
Add
x
=
2
a
t
2
x = 2at^2
x
=
2
a
t
2
,
y
=
4
a
t
y = 4at
y
=
4
a
t
Show model answer
[QEx 1.5 Q.2 (ii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q791
#791
Mathematics → Differentiation → Higher Order Derivatives
·
Hard
Add
x
=
sin
θ
x = \sin \theta
x
=
sin
θ
,
y
=
sin
3
θ
y = \sin^3 \theta
y
=
sin
3
θ
when
θ
=
π
2
\theta = \frac{\pi}{2}
θ
=
2
π
Show model answer
[QEx 1.5 Q.2 (iii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q792
#792
Mathematics → Differentiation → Higher Order Derivatives
·
Hard
Add
x
=
a
cos
θ
x = a \cos \theta
x
=
a
cos
θ
,
y
=
b
sin
θ
y = b \sin \theta
y
=
b
sin
θ
at
θ
=
π
4
\theta = \frac{\pi}{4}
θ
=
4
π
Show model answer
[QEx 1.5 Q.2 (iv) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Set · 8 questions
Q793
#793
Mathematics → Differentiation → Higher Order Derivatives
·
Hard
Add
If
x
=
a
t
2
x = at^2
x
=
a
t
2
and
y
=
2
a
t
y = 2at
y
=
2
a
t
then show that
x
y
d
2
y
d
x
2
+
a
=
0
xy \frac{d^2y}{dx^2} + a = 0
x
y
d
x
2
d
2
y
+
a
=
0
Show model answer
[QEx 1.5 Q.3 (i) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q794
#794
Mathematics → Differentiation → Higher Order Derivatives
·
Hard
Add
If
y
=
e
m
tan
−
1
x
y = e^{m \tan^{-1} x}
y
=
e
m
t
a
n
−
1
x
, show that
(
1
+
x
2
)
d
2
y
d
x
2
+
(
2
x
−
m
)
d
y
d
x
=
0
(1 + x^2) \frac{d^2y}{dx^2} + (2x - m) \frac{dy}{dx} = 0
(
1
+
x
2
)
d
x
2
d
2
y
+
(
2
x
−
m
)
d
x
d
y
=
0
Show model answer
[QEx 1.5 Q.3 (ii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q795
#795
Mathematics → Differentiation → Higher Order Derivatives
·
Hard
Add
If
x
=
cos
t
x = \cos t
x
=
cos
t
,
y
=
e
m
t
y = e^{mt}
y
=
e
m
t
show that
(
1
−
x
2
)
d
2
y
d
x
2
−
x
d
y
d
x
−
m
2
y
=
0
(1 - x^2) \frac{d^2y}{dx^2} - x \frac{dy}{dx} - m^2 y = 0
(
1
−
x
2
)
d
x
2
d
2
y
−
x
d
x
d
y
−
m
2
y
=
0
Show model answer
[QEx 1.5 Q.3 (iii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q796
#796
Mathematics → Differentiation → Higher Order Derivatives
·
Hard
Add
If
y
=
x
+
tan
x
y = x + \tan x
y
=
x
+
tan
x
, show that
cos
2
x
⋅
d
2
y
d
x
2
−
2
y
+
2
x
=
0
\cos^2 x \cdot \frac{d^2y}{dx^2} - 2y + 2x = 0
cos
2
x
⋅
d
x
2
d
2
y
−
2
y
+
2
x
=
0
Show model answer
[QEx 1.5 Q.3 (iv) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q797
#797
Mathematics → Differentiation → Higher Order Derivatives
·
Hard
Add
If
y
=
e
a
x
⋅
sin
(
b
x
)
y = e^{ax} \cdot \sin (bx)
y
=
e
a
x
⋅
sin
(
b
x
)
, show that
y
2
−
2
a
y
1
+
(
a
2
+
b
2
)
y
=
0
y_2 - 2a y_1 + (a^2 + b^2)\, y = 0
y
2
−
2
a
y
1
+
(
a
2
+
b
2
)
y
=
0
Show model answer
[QEx 1.5 Q.3 (v) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q798
#798
Mathematics → Differentiation → Higher Order Derivatives
·
Hard
Add
If
sec
−
1
(
7
x
3
−
5
y
3
7
x
3
+
5
y
3
)
=
m
\sec^{-1}\left(\frac{7x^3 - 5y^3}{7x^3 + 5y^3}\right) = m
sec
−
1
(
7
x
3
+
5
y
3
7
x
3
−
5
y
3
)
=
m
, show that
d
2
y
d
x
2
=
0
\frac{d^2y}{dx^2} = 0
d
x
2
d
2
y
=
0
.
Show model answer
[QEx 1.5 Q.3 (vi) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q799
#799
Mathematics → Differentiation → Higher Order Derivatives
·
Hard
Add
If
2
y
=
x
+
1
+
x
−
1
2y = \sqrt{x + 1} + \sqrt{x - 1}
2
y
=
x
+
1
+
x
−
1
, show that
4
(
x
2
−
1
)
y
2
+
4
x
y
1
−
y
=
0
4(x^2 - 1)\, y_2 + 4x\, y_1 - y = 0
4
(
x
2
−
1
)
y
2
+
4
x
y
1
−
y
=
0
.
Show model answer
[QEx 1.5 Q.3 (vii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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Q800
#800
Mathematics → Differentiation → Higher Order Derivatives
·
Hard
Add
If
y
=
log
(
x
+
x
2
+
a
2
)
m
y = \log \left(x + \sqrt{x^2 + a^2}\right)^m
y
=
lo
g
(
x
+
x
2
+
a
2
)
m
, show that
(
x
2
+
a
2
)
d
2
y
d
x
2
+
x
d
y
d
x
=
0
(x^2 + a^2) \frac{d^2y}{dx^2} + x \frac{dy}{dx} = 0
(
x
2
+
a
2
)
d
x
2
d
2
y
+
x
d
x
d
y
=
0
Show model answer
[QEx 1.5 Q.3 (viii) · Maharashtra State Board (Class 12) — Differentiation (Balbharati textbook)]
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