PYQ Vault
Bank
Guides
Notes
Mocks
Board
NDA
Sign in
Filtered questions
2,251 questions match
Filters
2
Download
· 2251
Filtering by:
Exam: Maharashtra HSC Class 12
Clear all
Copy link
Q276
#276
Mathematics → Indefinite Integration → Integration by Parts
·
Hard
Add
∫
e
2
x
sin
3
x
d
x
\int e^{2x} \sin 3x\, dx
∫
e
2
x
sin
3
x
d
x
Show model answer
[Q3.3 SolvedEx.4 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
Report
Q277
#277
Mathematics → Indefinite Integration → Integration by Parts
·
Hard
Add
∫
[
log
(
log
x
)
+
1
(
log
x
)
2
]
d
x
\int \left[ \log (\log x) + \frac{1}{(\log x)^2} \right] dx
∫
[
lo
g
(
lo
g
x
)
+
(
l
o
g
x
)
2
1
]
d
x
Show model answer
[Q3.3 SolvedEx.5 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
Report
Q278
#278
Mathematics → Indefinite Integration → Integration by Parts
·
Hard
Add
∫
a
2
−
x
2
d
x
\int \sqrt{a^2 - x^2}\, dx
∫
a
2
−
x
2
d
x
Show model answer
[Q3.3 SolvedEx.6 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
Report
Q279
#279
Mathematics → Indefinite Integration → Integration by Parts
·
Moderate
Add
∫
a
2
+
x
2
d
x
\int \sqrt{a^2 + x^2}\, dx
∫
a
2
+
x
2
d
x
Show model answer
[Q3.3 SolvedEx.7 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
Report
Q280
#280
Mathematics → Indefinite Integration → Integration by Parts
·
Moderate
Add
∫
x
2
−
a
2
d
x
\int \sqrt{x^2 - a^2}\, dx
∫
x
2
−
a
2
d
x
Show model answer
[Q3.3 SolvedEx.8 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
Report
Q281
#281
Mathematics → Indefinite Integration → Integration by Parts
·
Hard
Add
∫
x
sin
−
1
x
d
x
\int x \sin^{-1} x\, dx
∫
x
sin
−
1
x
d
x
Show model answer
[Q3.3 SolvedEx.9 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
Report
Q282
#282
Mathematics → Indefinite Integration → Integration by Parts
·
Moderate
Add
∫
cos
−
1
x
d
x
\int \cos^{-1} \sqrt{x}\, dx
∫
cos
−
1
x
d
x
Show model answer
[Q3.3 SolvedEx.10 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
Report
Q283
#283
Mathematics → Indefinite Integration → Integration by Parts
·
Hard
Add
∫
4
+
3
x
−
2
x
2
d
x
\int \sqrt{4 + 3x - 2x^2}\, dx
∫
4
+
3
x
−
2
x
2
d
x
Show model answer
[Q3.3 SolvedEx.11 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
Report
Q284
#284
Mathematics → Indefinite Integration → Integration by Parts
·
Moderate
Add
∫
e
x
(
2
+
sin
2
x
1
+
cos
2
x
)
d
x
\int e^x \left( \frac{2 + \sin 2x}{1 + \cos 2x} \right) dx
∫
e
x
(
1
+
c
o
s
2
x
2
+
s
i
n
2
x
)
d
x
Show model answer
[Q3.3.3 SolvedEx.1 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
Report
Q285
#285
Mathematics → Indefinite Integration → Integration by Parts
·
Moderate
Add
∫
e
x
[
x
+
2
(
x
+
3
)
2
]
d
x
\int e^x \left[ \frac{x + 2}{(x + 3)^2} \right] dx
∫
e
x
[
(
x
+
3
)
2
x
+
2
]
d
x
Show model answer
[Q3.3.3 SolvedEx.2 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
Report
Q286
#286
Mathematics → Indefinite Integration → Integration by Parts
·
Hard
Add
∫
e
tan
−
1
x
(
1
+
x
+
x
2
1
+
x
2
)
d
x
\int e^{\tan^{-1} x} \left( \frac{1 + x + x^2}{1 + x^2} \right) dx
∫
e
t
a
n
−
1
x
(
1
+
x
2
1
+
x
+
x
2
)
d
x
Show model answer
[Q3.3.3 SolvedEx.3 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
Report
Q287
#287
Mathematics → Indefinite Integration → Integration by Parts
·
Hard
Add
∫
(
x
2
+
1
)
⋅
e
x
(
x
+
1
)
2
d
x
\int \frac{(x^2 + 1) \cdot e^x}{(x + 1)^2}\, dx
∫
(
x
+
1
)
2
(
x
2
+
1
)
⋅
e
x
d
x
Show model answer
[Q3.3.3 SolvedEx.4 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
Report
Q288
#288
Mathematics → Indefinite Integration → Integration by Partial Fractions
·
Moderate
Add
∫
3
x
2
+
4
x
−
5
(
x
2
−
1
)
(
x
+
2
)
d
x
\int \frac{3x^2 + 4x - 5}{(x^2 - 1)(x + 2)}\, dx
∫
(
x
2
−
1
)
(
x
+
2
)
3
x
2
+
4
x
−
5
d
x
Show model answer
[Q3.4 SolvedEx.1 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
Report
Q289
#289
Mathematics → Indefinite Integration → Integration by Partial Fractions
·
Hard
Add
∫
2
x
2
−
3
(
x
2
−
5
)
(
x
2
+
4
)
d
x
\int \frac{2x^2 - 3}{(x^2 - 5)(x^2 + 4)}\, dx
∫
(
x
2
−
5
)
(
x
2
+
4
)
2
x
2
−
3
d
x
Show model answer
[Q3.4 SolvedEx.2 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
Report
Q290
#290
Mathematics → Indefinite Integration → Integration by Partial Fractions
·
Hard
Add
∫
1
(
sin
θ
)
(
3
+
2
cos
θ
)
d
θ
\int \frac{1}{(\sin \theta)(3 + 2 \cos \theta)}\, d\theta
∫
(
s
i
n
θ
)
(
3
+
2
c
o
s
θ
)
1
d
θ
Show model answer
[Q3.4 SolvedEx.3 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
Report
Q291
#291
Mathematics → Indefinite Integration → Integration by Partial Fractions
·
Hard
Add
∫
1
2
cos
x
+
sin
2
x
d
x
\int \frac{1}{2 \cos x + \sin 2x}\, dx
∫
2
c
o
s
x
+
s
i
n
2
x
1
d
x
Show model answer
[Q3.4 SolvedEx.4 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
Report
Q292
#292
Mathematics → Indefinite Integration → Integration by Partial Fractions
·
Hard
Add
∫
tan
θ
+
tan
3
θ
1
+
tan
3
θ
d
θ
\int \frac{\tan \theta + \tan^3 \theta}{1 + \tan^3 \theta}\, d\theta
∫
1
+
t
a
n
3
θ
t
a
n
θ
+
t
a
n
3
θ
d
θ
Show model answer
[Q3.4 SolvedEx.5 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
Report
Set · 7 questions
Find the equations of tangents and normals to the curve at the point on it.
Q293
#293
Mathematics → Application of Derivatives → Tangents and Normals
·
Easy
Add
y
=
x
2
+
2
e
x
+
2
y = x^2 + 2e^x + 2
y
=
x
2
+
2
e
x
+
2
at
(
0
,
4
)
(0, 4)
(
0
,
4
)
Show model answer
[QEx 2.1 Q.1 (i) · Maharashtra State Board (Class 12) — Application of Derivatives (Balbharati textbook)]
Report
Q294
#294
Mathematics → Application of Derivatives → Tangents and Normals
·
Moderate
Add
x
3
+
y
3
−
9
x
y
=
0
x^3 + y^3 - 9xy = 0
x
3
+
y
3
−
9
x
y
=
0
at
(
2
,
4
)
(2, 4)
(
2
,
4
)
Show model answer
[QEx 2.1 Q.1 (ii) · Maharashtra State Board (Class 12) — Application of Derivatives (Balbharati textbook)]
Report
Q295
#295
Mathematics → Application of Derivatives → Tangents and Normals
·
Moderate
Add
x
2
−
3
x
y
+
2
y
2
=
5
x^2 - \sqrt{3}xy + 2y^2 = 5
x
2
−
3
x
y
+
2
y
2
=
5
at
(
3
,
2
)
(\sqrt{3}, 2)
(
3
,
2
)
Show model answer
[QEx 2.1 Q.1 (iii) · Maharashtra State Board (Class 12) — Application of Derivatives (Balbharati textbook)]
Report
Q296
#296
Mathematics → Application of Derivatives → Tangents and Normals
·
Moderate
Add
2
x
y
+
π
sin
y
=
2
π
2xy + \pi \sin y = 2\pi
2
x
y
+
π
sin
y
=
2
π
at
(
1
,
π
2
)
\left(1, \dfrac{\pi}{2}\right)
(
1
,
2
π
)
Show model answer
[QEx 2.1 Q.1 (iv) · Maharashtra State Board (Class 12) — Application of Derivatives (Balbharati textbook)]
Report
Q297
#297
Mathematics → Application of Derivatives → Tangents and Normals
·
Hard
Add
x
sin
2
y
=
y
cos
2
x
x \sin 2y = y \cos 2x
x
sin
2
y
=
y
cos
2
x
at
(
π
4
,
π
2
)
\left(\dfrac{\pi}{4}, \dfrac{\pi}{2}\right)
(
4
π
,
2
π
)
Show model answer
[QEx 2.1 Q.1 (v) · Maharashtra State Board (Class 12) — Application of Derivatives (Balbharati textbook)]
Report
Q298
#298
Mathematics → Application of Derivatives → Tangents and Normals
·
Moderate
Add
x
=
sin
θ
x = \sin \theta
x
=
sin
θ
and
y
=
cos
2
θ
y = \cos 2\theta
y
=
cos
2
θ
at
θ
=
π
6
\theta = \dfrac{\pi}{6}
θ
=
6
π
Show model answer
[QEx 2.1 Q.1 (vi) · Maharashtra State Board (Class 12) — Application of Derivatives (Balbharati textbook)]
Report
Q299
#299
Mathematics → Application of Derivatives → Tangents and Normals
·
Moderate
Add
x
=
t
x = \sqrt{t}
x
=
t
,
y
=
t
−
1
t
y = t - \dfrac{1}{\sqrt{t}}
y
=
t
−
t
1
at
t
=
4
t = 4
t
=
4
.
Show model answer
[QEx 2.1 Q.1 (vii) · Maharashtra State Board (Class 12) — Application of Derivatives (Balbharati textbook)]
Report
Q300
#300
Mathematics → Application of Derivatives → Tangents and Normals
·
Moderate
Add
Find the point on the curve
y
=
x
−
3
y = \sqrt{x - 3}
y
=
x
−
3
where the tangent is perpendicular to the line
6
x
+
3
y
−
5
=
0
6x + 3y - 5 = 0
6
x
+
3
y
−
5
=
0
.
Show model answer
[QEx 2.1 Q.2 · Maharashtra State Board (Class 12) — Application of Derivatives (Balbharati textbook)]
Report
Prev
Page 12 of 91
Next
1
…
11
12
13
…
91
PYQ Vault
Bank
Guides
Notes
Mocks
Board
NDA
Sign in