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Exam: Maharashtra HSC Class 12
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Q301
#301
Mathematics → Application of Derivatives → Tangents and Normals
·
Easy
Add
Find the points on the curve
y
=
x
3
−
2
x
2
−
x
y = x^3 - 2x^2 - x
y
=
x
3
−
2
x
2
−
x
where the tangents are parallel to
3
x
−
y
+
1
=
0
3x - y + 1 = 0
3
x
−
y
+
1
=
0
.
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[QEx 2.1 Q.3 · Maharashtra State Board (Class 12) — Application of Derivatives (Balbharati textbook)]
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Q302
#302
Mathematics → Application of Derivatives → Tangents and Normals
·
Moderate
Add
Find the equations of the tangents to the curve
x
2
+
y
2
−
2
x
−
4
y
+
1
=
0
x^2 + y^2 - 2x - 4y + 1 = 0
x
2
+
y
2
−
2
x
−
4
y
+
1
=
0
which are parallel to the X-axis.
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[QEx 2.1 Q.4 · Maharashtra State Board (Class 12) — Application of Derivatives (Balbharati textbook)]
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Q303
#303
Mathematics → Application of Derivatives → Tangents and Normals
·
Moderate
Add
Find the equations of the normals to the curve
3
x
2
−
y
2
=
8
3x^2 - y^2 = 8
3
x
2
−
y
2
=
8
, which are parallel to the line
x
+
3
y
=
4
x + 3y = 4
x
+
3
y
=
4
.
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[QEx 2.1 Q.5 · Maharashtra State Board (Class 12) — Application of Derivatives (Balbharati textbook)]
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Q304
#304
Mathematics → Application of Derivatives → Tangents and Normals
·
Moderate
Add
If the line
y
=
4
x
−
5
y = 4x - 5
y
=
4
x
−
5
touches the curve
y
2
=
a
x
3
+
b
y^2 = ax^3 + b
y
2
=
a
x
3
+
b
at the point
(
2
,
3
)
(2, 3)
(
2
,
3
)
find
a
a
a
and
b
b
b
.
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[QEx 2.1 Q.6 · Maharashtra State Board (Class 12) — Application of Derivatives (Balbharati textbook)]
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Q305
#305
Mathematics → Application of Derivatives → Derivative as a Rate Measure
·
Easy
Add
A particle moves along the curve
6
y
=
x
3
+
2
6y = x^3 + 2
6
y
=
x
3
+
2
Find the points on the curve at which y-coordinate is changing 8 times as fast as the X-coordinate.
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[QEx 2.1 Q.7 · Maharashtra State Board (Class 12) — Application of Derivatives (Balbharati textbook)]
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Q306
#306
Mathematics → Application of Derivatives → Derivative as a Rate Measure
·
Easy
Add
A spherical soap bubble is expanding so that its radius is increasing at the rate of
0.02
0.02
0.02
cm/sec. At what rate is the surface area is increasing, when its radius is 5 cm?
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[QEx 2.1 Q.8 · Maharashtra State Board (Class 12) — Application of Derivatives (Balbharati textbook)]
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Q307
#307
Mathematics → Application of Derivatives → Derivative as a Rate Measure
·
Moderate
Add
The surface area of a spherical balloon is increasing at the rate of 2 cm
2
^2
2
/ sec. At what rate the volume of the balloon is increasing when radius of the balloon is 6 cm?
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[QEx 2.1 Q.9 · Maharashtra State Board (Class 12) — Application of Derivatives (Balbharati textbook)]
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Q308
#308
Mathematics → Application of Derivatives → Derivative as a Rate Measure
·
Moderate
Add
If each side of an equilateral triangle increases at the rate of
2
\sqrt{2}
2
cm/ sec, find the rate of increase of its area when its side of length 3 cm .
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[QEx 2.1 Q.10 · Maharashtra State Board (Class 12) — Application of Derivatives (Balbharati textbook)]
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Q309
#309
Mathematics → Application of Derivatives → Derivative as a Rate Measure
·
Moderate
Add
The volume of a sphere increase at the rate of 20 cm
3
^3
3
/ sec. Find the rate of change of its surface area when its radius is 5 cm.
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[QEx 2.1 Q.11 · Maharashtra State Board (Class 12) — Application of Derivatives (Balbharati textbook)]
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Q310
#310
Mathematics → Application of Derivatives → Derivative as a Rate Measure
·
Easy
Add
The edge of a cube is decreasing at the rate of
0.6
0.6
0.6
cm/sec. Find the rate at which its volume is decreasing when the edge of the cube is 2 cm.
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[QEx 2.1 Q.12 · Maharashtra State Board (Class 12) — Application of Derivatives (Balbharati textbook)]
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Q311
#311
Mathematics → Application of Derivatives → Derivative as a Rate Measure
·
Moderate
Add
A man of height 2 meters walks at a uniform speed of 6 km/hr away from a lamp post of 6 meters high. Find the rate at which the length of the shadow is increasing.
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[QEx 2.1 Q.13 · Maharashtra State Board (Class 12) — Application of Derivatives (Balbharati textbook)]
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Q312
#312
Mathematics → Application of Derivatives → Derivative as a Rate Measure
·
Hard
Add
A man of height
1.5
1.5
1.5
meters walks toward a lamp post of height
4.5
4.5
4.5
meters, at the rate of
(
3
4
)
\left(\dfrac{3}{4}\right)
(
4
3
)
meter/sec. Find the rate at which (i) his shadow is shortening. (ii) the tip of the shadow is moving.
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[QEx 2.1 Q.14 · Maharashtra State Board (Class 12) — Application of Derivatives (Balbharati textbook)]
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Q313
#313
Mathematics → Application of Derivatives → Derivative as a Rate Measure
·
Moderate
Add
A ladder 10 meter long is leaning against a vertical wall. If the bottom of the ladder is pulled horizontally away from the wall at the rate of
1.2
1.2
1.2
meters per second, find how fast the top of the ladder is sliding down the wall when the bottom is 6 meters away from the wall.
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[QEx 2.1 Q.15 · Maharashtra State Board (Class 12) — Application of Derivatives (Balbharati textbook)]
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Q314
#314
Mathematics → Application of Derivatives → Derivative as a Rate Measure
·
Hard
Add
If water is poured into an inverted hollow cone whose semi-vertical angel is
30
∘
30^\circ
3
0
∘
, so that its depth (measured along the axis) increases at the rate of 1 cm/ sec. Find the rate at which the volume of water increasing when the depth is 2 cm.
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[QEx 2.1 Q.16 · Maharashtra State Board (Class 12) — Application of Derivatives (Balbharati textbook)]
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Set · 5 questions
Find the approximate value of given functions, at required points.
Q315
#315
Mathematics → Application of Derivatives → Approximations
·
Easy
Add
8.95
\sqrt{8.95}
8.95
Show model answer
[QEx 2.2 Q.1 (i) · Maharashtra State Board (Class 12) — Application of Derivatives (Balbharati textbook)]
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Q316
#316
Mathematics → Application of Derivatives → Approximations
·
Easy
Add
28
3
\sqrt[3]{28}
3
28
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[QEx 2.2 Q.1 (ii) · Maharashtra State Board (Class 12) — Application of Derivatives (Balbharati textbook)]
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Q317
#317
Mathematics → Application of Derivatives → Approximations
·
Easy
Add
31.98
5
\sqrt[5]{31.98}
5
31.98
Show model answer
[QEx 2.2 Q.1 (iii) · Maharashtra State Board (Class 12) — Application of Derivatives (Balbharati textbook)]
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Q318
#318
Mathematics → Application of Derivatives → Approximations
·
Easy
Add
(
3.97
)
4
(3.97)^4
(
3.97
)
4
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[QEx 2.2 Q.1 (iv) · Maharashtra State Board (Class 12) — Application of Derivatives (Balbharati textbook)]
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Q319
#319
Mathematics → Application of Derivatives → Approximations
·
Easy
Add
(
4.01
)
3
(4.01)^3
(
4.01
)
3
Show model answer
[QEx 2.2 Q.1 (v) · Maharashtra State Board (Class 12) — Application of Derivatives (Balbharati textbook)]
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Set · 4 questions
Find the approximate value of
Q320
#320
Mathematics → Application of Derivatives → Approximations
·
Moderate
Add
sin
(
61
∘
)
\sin(61^\circ)
sin
(
6
1
∘
)
given that
1
∘
=
0.0175
c
1^\circ = 0.0175^c
1
∘
=
0.017
5
c
,
3
=
1.732
\sqrt{3} = 1.732
3
=
1.732
Show model answer
[QEx 2.2 Q.2 (i) · Maharashtra State Board (Class 12) — Application of Derivatives (Balbharati textbook)]
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Q321
#321
Mathematics → Application of Derivatives → Approximations
·
Moderate
Add
sin
(
29
∘
30
′
)
\sin(29^\circ\,30')
sin
(
2
9
∘
3
0
′
)
given that
1
∘
=
0.0175
c
1^\circ = 0.0175^c
1
∘
=
0.017
5
c
,
3
=
1.732
\sqrt{3} = 1.732
3
=
1.732
Show model answer
[QEx 2.2 Q.2 (ii) · Maharashtra State Board (Class 12) — Application of Derivatives (Balbharati textbook)]
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Q322
#322
Mathematics → Application of Derivatives → Approximations
·
Moderate
Add
cos
(
60
∘
30
′
)
\cos(60^\circ\,30')
cos
(
6
0
∘
3
0
′
)
given that
1
∘
=
0.0175
c
1^\circ = 0.0175^c
1
∘
=
0.017
5
c
,
3
=
1.732
\sqrt{3} = 1.732
3
=
1.732
Show model answer
[QEx 2.2 Q.2 (iii) · Maharashtra State Board (Class 12) — Application of Derivatives (Balbharati textbook)]
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Q323
#323
Mathematics → Application of Derivatives → Approximations
·
Moderate
Add
tan
(
45
∘
40
′
)
\tan(45^\circ\,40')
tan
(
4
5
∘
4
0
′
)
given that
1
∘
=
0.0175
c
1^\circ = 0.0175^c
1
∘
=
0.017
5
c
.
Show model answer
[QEx 2.2 Q.2 (iv) · Maharashtra State Board (Class 12) — Application of Derivatives (Balbharati textbook)]
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Set · 2 questions
Find the approximate value of
Q324
#324
Mathematics → Application of Derivatives → Approximations
·
Moderate
Add
tan
−
1
(
0.999
)
\tan^{-1}(0.999)
tan
−
1
(
0.999
)
Show model answer
[QEx 2.2 Q.3 (i) · Maharashtra State Board (Class 12) — Application of Derivatives (Balbharati textbook)]
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Q325
#325
Mathematics → Application of Derivatives → Approximations
·
Moderate
Add
cot
−
1
(
0.999
)
\cot^{-1}(0.999)
cot
−
1
(
0.999
)
Show model answer
[QEx 2.2 Q.3 (ii) · Maharashtra State Board (Class 12) — Application of Derivatives (Balbharati textbook)]
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