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Exam: Maharashtra HSC Class 12
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Q251
#251
Mathematics → Indefinite Integration → Special Integrals of Quadratic Forms
·
Moderate
Add
∫
1
1
+
x
−
x
2
d
x
\int \frac{1}{\sqrt{1 + x - x^2}}\, dx
∫
1
+
x
−
x
2
1
d
x
Show model answer
[Q3.2B SolvedEx.7 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q252
#252
Mathematics → Indefinite Integration → Special Integrals of Quadratic Forms
·
Hard
Add
∫
sin
2
x
3
sin
4
x
−
4
sin
2
x
+
1
d
x
\int \frac{\sin 2x}{3\sin^4 x - 4\sin^2 x + 1}\, dx
∫
3
s
i
n
4
x
−
4
s
i
n
2
x
+
1
s
i
n
2
x
d
x
Show model answer
[Q3.2B SolvedEx.8 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q253
#253
Mathematics → Indefinite Integration → Special Integrals of Quadratic Forms
·
Hard
Add
∫
e
x
2
e
−
x
−
e
x
d
x
\int \frac{e^{\frac{x}{2}}}{\sqrt{e^{-x} - e^{x}}}\, dx
∫
e
−
x
−
e
x
e
2
x
d
x
Show model answer
[Q3.2B SolvedEx.9 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q254
#254
Mathematics → Indefinite Integration → Special Integrals of Quadratic Forms
·
Hard
Add
∫
(
tan
x
+
cot
x
)
d
x
\int \left(\sqrt{\tan x} + \sqrt{\cot x}\right) dx
∫
(
tan
x
+
cot
x
)
d
x
Show model answer
[Q3.2B SolvedEx.10 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q255
#255
Mathematics → Indefinite Integration → Special Integrals of Quadratic Forms
·
Hard
Add
∫
1
5
−
4
cos
x
d
x
\int \frac{1}{5 - 4\cos x}\, dx
∫
5
−
4
c
o
s
x
1
d
x
Show model answer
[Q3.2B SolvedEx.11 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q256
#256
Mathematics → Indefinite Integration → Special Integrals of Quadratic Forms
·
Hard
Add
∫
1
2
−
3
sin
2
x
d
x
\int \frac{1}{2 - 3\sin 2x}\, dx
∫
2
−
3
s
i
n
2
x
1
d
x
Show model answer
[Q3.2B SolvedEx.12 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q257
#257
Mathematics → Indefinite Integration → Special Integrals of Quadratic Forms
·
Hard
Add
∫
1
3
−
2
sin
x
+
5
cos
x
d
x
\int \frac{1}{3 - 2\sin x + 5\cos x}\, dx
∫
3
−
2
s
i
n
x
+
5
c
o
s
x
1
d
x
Show model answer
[Q3.2B SolvedEx.13 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q258
#258
Mathematics → Indefinite Integration → Special Integrals of Quadratic Forms
·
Hard
Add
∫
1
sin
x
−
3
cos
x
d
x
\int \frac{1}{\sin x - \sqrt{3}\cos x}\, dx
∫
s
i
n
x
−
3
c
o
s
x
1
d
x
Show model answer
[Q3.2B SolvedEx.14 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q259
#259
Mathematics → Indefinite Integration → Special Integrals of Quadratic Forms
·
Hard
Add
∫
1
3
+
2
sin
2
x
+
5
cos
2
x
d
x
\int \frac{1}{3 + 2\sin^2 x + 5\cos^2 x}\, dx
∫
3
+
2
s
i
n
2
x
+
5
c
o
s
2
x
1
d
x
Show model answer
[Q3.2B SolvedEx.15 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q260
#260
Mathematics → Indefinite Integration → Special Integrals of Quadratic Forms
·
Hard
Add
∫
cos
θ
cos
3
θ
d
θ
\int \frac{\cos\theta}{\cos 3\theta}\, d\theta
∫
c
o
s
3
θ
c
o
s
θ
d
θ
Show model answer
[Q3.2B SolvedEx.16 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q261
#261
Mathematics → Indefinite Integration → Integrals of the Type (px+q) over a Quadratic
·
Moderate
Add
∫
2
x
−
3
3
x
2
+
4
x
+
5
d
x
\int \frac{2x-3}{3x^2+4x+5}\, dx
∫
3
x
2
+
4
x
+
5
2
x
−
3
d
x
Show model answer
[Q3.2C SolvedEx.1 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q262
#262
Mathematics → Indefinite Integration → Integrals of the Type (px+q) over a Quadratic
·
Moderate
Add
∫
x
−
5
x
−
7
d
x
\int \sqrt{\frac{x-5}{x-7}}\, dx
∫
x
−
7
x
−
5
d
x
Show model answer
[Q3.2C SolvedEx.2 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q263
#263
Mathematics → Indefinite Integration → Integrals of the Type (px+q) over a Quadratic
·
Moderate
Add
∫
8
−
x
x
d
x
\int \sqrt{\frac{8-x}{x}}\, dx
∫
x
8
−
x
d
x
Show model answer
[Q3.2C SolvedEx.3 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Set · 9 questions
Evaluate :
Q264
#264
Mathematics → Indefinite Integration → Integrals of the Type (px+q) over a Quadratic
·
Moderate
Add
∫
3
x
+
4
x
2
+
6
x
+
5
d
x
\int \frac{3x+4}{x^2+6x+5}\, dx
∫
x
2
+
6
x
+
5
3
x
+
4
d
x
Show model answer
[QEx 3.2(C) I (i) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q265
#265
Mathematics → Indefinite Integration → Integrals of the Type (px+q) over a Quadratic
·
Moderate
Add
∫
2
x
+
1
x
2
+
4
x
−
5
d
x
\int \frac{2x+1}{x^2+4x-5}\, dx
∫
x
2
+
4
x
−
5
2
x
+
1
d
x
Show model answer
[QEx 3.2(C) I (ii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q266
#266
Mathematics → Indefinite Integration → Integrals of the Type (px+q) over a Quadratic
·
Moderate
Add
∫
2
x
+
3
2
x
2
+
3
x
−
1
d
x
\int \frac{2x+3}{2x^2+3x-1}\, dx
∫
2
x
2
+
3
x
−
1
2
x
+
3
d
x
Show model answer
[QEx 3.2(C) I (iii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q267
#267
Mathematics → Indefinite Integration → Integrals of the Type (px+q) over a Quadratic
·
Moderate
Add
∫
3
x
+
4
2
x
2
+
2
x
+
1
d
x
\int \frac{3x+4}{\sqrt{2x^2+2x+1}}\, dx
∫
2
x
2
+
2
x
+
1
3
x
+
4
d
x
Show model answer
[QEx 3.2(C) I (iv) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q268
#268
Mathematics → Indefinite Integration → Integrals of the Type (px+q) over a Quadratic
·
Moderate
Add
∫
7
x
+
3
3
+
2
x
−
x
2
d
x
\int \frac{7x+3}{\sqrt{3+2x-x^2}}\, dx
∫
3
+
2
x
−
x
2
7
x
+
3
d
x
Show model answer
[QEx 3.2(C) I (v) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q269
#269
Mathematics → Indefinite Integration → Integrals of the Type (px+q) over a Quadratic
·
Hard
Add
∫
x
−
7
x
−
9
d
x
\int \sqrt{\frac{x-7}{x-9}}\, dx
∫
x
−
9
x
−
7
d
x
Show model answer
[QEx 3.2(C) I (vi) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q270
#270
Mathematics → Indefinite Integration → Integrals of the Type (px+q) over a Quadratic
·
Hard
Add
∫
9
−
x
x
d
x
\int \sqrt{\frac{9-x}{x}}\, dx
∫
x
9
−
x
d
x
Show model answer
[QEx 3.2(C) I (vii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q271
#271
Mathematics → Indefinite Integration → Integrals of the Type (px+q) over a Quadratic
·
Hard
Add
∫
3
cos
x
4
sin
2
x
+
4
sin
x
−
1
d
x
\int \frac{3\cos x}{4\sin^2 x + 4\sin x - 1}\, dx
∫
4
s
i
n
2
x
+
4
s
i
n
x
−
1
3
c
o
s
x
d
x
Show model answer
[QEx 3.2(C) I (viii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q272
#272
Mathematics → Indefinite Integration → Integrals of the Type (px+q) over a Quadratic
·
Hard
Add
∫
e
3
x
−
e
2
x
e
x
+
1
d
x
\int \sqrt{\frac{e^{3x} - e^{2x}}{e^x + 1}}\, dx
∫
e
x
+
1
e
3
x
−
e
2
x
d
x
Show model answer
[QEx 3.2(C) I (ix) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q273
#273
Mathematics → Indefinite Integration → Integration by Parts
·
Hard
Add
∫
x
2
5
x
d
x
\int x^2\, 5^x\, dx
∫
x
2
5
x
d
x
Show model answer
[Q3.3 SolvedEx.1 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q274
#274
Mathematics → Indefinite Integration → Integration by Parts
·
Moderate
Add
∫
x
tan
−
1
x
d
x
\int x \tan^{-1} x\, dx
∫
x
tan
−
1
x
d
x
Show model answer
[Q3.3 SolvedEx.2 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q275
#275
Mathematics → Indefinite Integration → Integration by Parts
·
Hard
Add
∫
x
1
−
sin
x
d
x
\int \frac{x}{1 - \sin x}\, dx
∫
1
−
s
i
n
x
x
d
x
Show model answer
[Q3.3 SolvedEx.3 · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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