SECOND TERM CLASS 12 - 2020 - 21 PART 2

CHINMAYA VIDYALAYA, KANNUR

SECOND TERM ONLINE EXAMINATION

Class - 1220-2 MATHEMATICS Max. Marks – 25
Time – 1 Hr

PART - 2

MATHEMATICS - 1

1. Integrate:∫ x3+4x2−3x−2 dx [2]
x+2
[2]
OR [3]

Integrate: ∫ 1 dx
√x+3−√x+2

2. Integrate:∫ x sin2x dx

3. Integrate:∫ 1 dx
1+3sin2 x

OR

Integrate: ∫ x2−1 dx
x4+x2+1

4. π 3 [3]
[3]
Evaluate:∫02 sin2x dx [3]
[5]
33

sin2x+ cos2x

5. Find: ∫ cosx dx
(1−sinx) (2−sinx)

6. Integrate:∫ 1 dx
4+5 cosx

7. Integrate: ∫ 3x−2 dx
(x+1)2(x+3)

OR
Evaluate:∫14 f(x) dx, where f(x) = |x − 1| + |x − 2| + |x − 3|

8. CASE STUDY [ Answer any four out of five]
A house owner decided to construct a garden with a pond
surrounded by an elliptical lawn as shown in the figure.

1. Equation of AC is [1]

a) b) c) d)
y=− 3(x-5) y=3(x-5)
y=5(x-5) y=− 5(x-5)
5 5
3 3
c) 15(unit)2 [1]
2. The area of the pond is
d) (unit)2
a) (unit)2 b) 30(unit)2



3. Equation of the ellipse is [1]

a) b) c) d)
2 2 x2 y2 2 2 2 2
9 + 25 = 1 9 − 25 = 1 25 + 9 = 1 25 − 9 = 1

4. Area of the garden, including the pond is [1]

a)15 (unit)2 b)15 (unit)2 c)15 (unit)2 d) 30 (unit)2

4 2

5. How much he should invest in order to plant the lawn [1]
area at the rate of Rs 210 per square units.

a) Rs 360 b) Rs3591 c) Rs 3600 d) Rs 359

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