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Exam: Maharashtra HSC Class 12
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Set · 13 questions
Evaluate the following :
Q76
#76
Mathematics → Indefinite Integration → Special Integrals of Quadratic Forms
·
Moderate
Add
∫
2
+
x
2
−
x
d
x
\int \sqrt{\frac{2 + x}{2 - x}} \, dx
∫
2
−
x
2
+
x
d
x
Show model answer
[QEx 3.2(B) I (viii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q77
#77
Mathematics → Indefinite Integration → Special Integrals of Quadratic Forms
·
Moderate
Add
∫
10
+
x
10
−
x
d
x
\int \sqrt{\frac{10 + x}{10 - x}} \, dx
∫
10
−
x
10
+
x
d
x
Show model answer
[QEx 3.2(B) I (ix) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q78
#78
Mathematics → Indefinite Integration → Special Integrals of Quadratic Forms
·
Moderate
Add
∫
1
x
2
+
8
x
+
12
d
x
\int \frac{1}{x^2 + 8x + 12} \, dx
∫
x
2
+
8
x
+
12
1
d
x
Show model answer
[QEx 3.2(B) I (x) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q79
#79
Mathematics → Indefinite Integration → Special Integrals of Quadratic Forms
·
Moderate
Add
∫
1
1
+
x
−
x
2
d
x
\int \frac{1}{1 + x - x^2} \, dx
∫
1
+
x
−
x
2
1
d
x
Show model answer
[QEx 3.2(B) I (xi) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q80
#80
Mathematics → Indefinite Integration → Special Integrals of Quadratic Forms
·
Moderate
Add
∫
1
4
x
2
−
20
x
+
17
d
x
\int \frac{1}{4x^2 - 20x + 17} \, dx
∫
4
x
2
−
20
x
+
17
1
d
x
Show model answer
[QEx 3.2(B) I (xii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q81
#81
Mathematics → Indefinite Integration → Special Integrals of Quadratic Forms
·
Moderate
Add
∫
1
5
−
4
x
−
3
x
2
d
x
\int \frac{1}{5 - 4x - 3x^2} \, dx
∫
5
−
4
x
−
3
x
2
1
d
x
Show model answer
[QEx 3.2(B) I (xiii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q82
#82
Mathematics → Indefinite Integration → Special Integrals of Quadratic Forms
·
Moderate
Add
∫
1
3
x
2
+
5
x
+
7
d
x
\int \frac{1}{\sqrt{3x^2 + 5x + 7}} \, dx
∫
3
x
2
+
5
x
+
7
1
d
x
Show model answer
[QEx 3.2(B) I (xiv) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q83
#83
Mathematics → Indefinite Integration → Special Integrals of Quadratic Forms
·
Moderate
Add
∫
1
x
2
+
8
x
−
20
d
x
\int \frac{1}{\sqrt{x^2 + 8x - 20}} \, dx
∫
x
2
+
8
x
−
20
1
d
x
Show model answer
[QEx 3.2(B) I (xv) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q84
#84
Mathematics → Indefinite Integration → Special Integrals of Quadratic Forms
·
Moderate
Add
∫
1
8
−
3
x
+
2
x
2
d
x
\int \frac{1}{\sqrt{8 - 3x + 2x^2}} \, dx
∫
8
−
3
x
+
2
x
2
1
d
x
Show model answer
[QEx 3.2(B) I (xvi) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q85
#85
Mathematics → Indefinite Integration → Special Integrals of Quadratic Forms
·
Moderate
Add
∫
1
(
x
−
3
)
(
x
+
2
)
d
x
\int \frac{1}{\sqrt{(x - 3)(x + 2)}} \, dx
∫
(
x
−
3
)
(
x
+
2
)
1
d
x
Show model answer
[QEx 3.2(B) I (xvii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q86
#86
Mathematics → Indefinite Integration → Integrals of Trigonometric Functions
·
Hard
Add
∫
1
4
+
3
cos
2
x
d
x
\int \frac{1}{4 + 3\cos^2 x} \, dx
∫
4
+
3
c
o
s
2
x
1
d
x
Show model answer
[QEx 3.2(B) I (xviii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q87
#87
Mathematics → Indefinite Integration → Integrals of Trigonometric Functions
·
Hard
Add
∫
1
cos
2
x
+
3
sin
2
x
d
x
\int \frac{1}{\cos 2x + 3\sin^2 x} \, dx
∫
c
o
s
2
x
+
3
s
i
n
2
x
1
d
x
Show model answer
[QEx 3.2(B) I (xix) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q88
#88
Mathematics → Indefinite Integration → Integrals of Trigonometric Functions
·
Hard
Add
∫
sin
x
sin
3
x
d
x
\int \frac{\sin x}{\sin 3x} \, dx
∫
s
i
n
3
x
s
i
n
x
d
x
Show model answer
[QEx 3.2(B) I (xx) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Set · 9 questions
Integrate the following functions w. r. t. x :
Q89
#89
Mathematics → Indefinite Integration → Integrals of Trigonometric Functions
·
Moderate
Add
∫
1
3
+
2
sin
x
d
x
\int \frac{1}{3 + 2\sin x} \, dx
∫
3
+
2
s
i
n
x
1
d
x
Show model answer
[QEx 3.2(B) II (i) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q90
#90
Mathematics → Indefinite Integration → Integrals of Trigonometric Functions
·
Moderate
Add
∫
1
4
−
5
cos
x
d
x
\int \frac{1}{4 - 5\cos x} \, dx
∫
4
−
5
c
o
s
x
1
d
x
Show model answer
[QEx 3.2(B) II (ii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
Report
Q91
#91
Mathematics → Indefinite Integration → Integrals of Trigonometric Functions
·
Moderate
Add
∫
1
2
+
cos
x
−
sin
x
d
x
\int \frac{1}{2 + \cos x - \sin x} \, dx
∫
2
+
c
o
s
x
−
s
i
n
x
1
d
x
Show model answer
[QEx 3.2(B) II (iii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
Report
Q92
#92
Mathematics → Indefinite Integration → Integrals of Trigonometric Functions
·
Moderate
Add
∫
1
3
+
2
sin
x
−
cos
x
d
x
\int \frac{1}{3 + 2\sin x - \cos x} \, dx
∫
3
+
2
s
i
n
x
−
c
o
s
x
1
d
x
Show model answer
[QEx 3.2(B) II (iv) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q93
#93
Mathematics → Indefinite Integration → Integrals of Trigonometric Functions
·
Moderate
Add
∫
1
3
−
2
cos
2
x
d
x
\int \frac{1}{3 - 2\cos 2x} \, dx
∫
3
−
2
c
o
s
2
x
1
d
x
Show model answer
[QEx 3.2(B) II (v) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q94
#94
Mathematics → Indefinite Integration → Integrals of Trigonometric Functions
·
Moderate
Add
∫
1
2
sin
2
x
−
3
d
x
\int \frac{1}{2\sin 2x - 3} \, dx
∫
2
s
i
n
2
x
−
3
1
d
x
Show model answer
[QEx 3.2(B) II (vi) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
Report
Q95
#95
Mathematics → Indefinite Integration → Integrals of Trigonometric Functions
·
Moderate
Add
∫
1
3
+
2
sin
2
x
+
4
cos
2
x
d
x
\int \frac{1}{3 + 2\sin 2x + 4\cos 2x} \, dx
∫
3
+
2
s
i
n
2
x
+
4
c
o
s
2
x
1
d
x
Show model answer
[QEx 3.2(B) II (vii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
Report
Q96
#96
Mathematics → Indefinite Integration → Integrals of Trigonometric Functions
·
Moderate
Add
∫
1
cos
x
−
sin
x
d
x
\int \frac{1}{\cos x - \sin x} \, dx
∫
c
o
s
x
−
s
i
n
x
1
d
x
Show model answer
[QEx 3.2(B) II (viii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
Report
Q97
#97
Mathematics → Indefinite Integration → Integrals of Trigonometric Functions
·
Moderate
Add
∫
1
cos
x
−
3
sin
x
d
x
\int \frac{1}{\cos x - \sqrt{3}\,\sin x} \, dx
∫
c
o
s
x
−
3
s
i
n
x
1
d
x
Show model answer
[QEx 3.2(B) II (ix) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Set · 3 questions
Evaluate the following :
Q98
#98
Mathematics → Indefinite Integration → Integration by Parts
·
Moderate
Add
∫
x
2
⋅
log
x
d
x
\int x^2 \cdot \log x\, dx
∫
x
2
⋅
lo
g
x
d
x
Show model answer
[QEx 3.3 I (i) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q99
#99
Mathematics → Indefinite Integration → Integration by Parts
·
Moderate
Add
∫
x
2
⋅
sin
3
x
d
x
\int x^2 \cdot \sin 3x\, dx
∫
x
2
⋅
sin
3
x
d
x
Show model answer
[QEx 3.3 I (ii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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Q100
#100
Mathematics → Indefinite Integration → Integration by Parts
·
Moderate
Add
∫
x
⋅
tan
−
1
x
d
x
\int x \cdot \tan^{-1} x\, dx
∫
x
⋅
tan
−
1
x
d
x
Show model answer
[QEx 3.3 I (iii) · Maharashtra State Board (Class 12) — Indefinite Integration (Balbharati textbook)]
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