second term class 12 - part 1

CHINMAYA VIDYALAYA, KANNUR

SECOND TERM ONLINE EXAMINATION

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

PART - 1

MATHEMATICS - 2 [1]
1. Evaluate |a⃑ × ⃑b|, if ⃑a ∙ ⃑b = 12, |⃑a| = 10, |⃑b| = 2

a) 5 b) 10 c) 14 d) 16

OR

Write a vector of magnitude 10 units opposite to the vector

2î + 3ĵ − 6k̂

a) 20 ̂+30 −̂ 60 ̂ b) −20î−30ĵ+60k ̂

7 7

c) 20i ̂ + 30j ̂ − 60k̂ d) −20î − 30ĵ + 60 ̂

2. Find α so that ⃑a = 3î+2ĵ + 9k̂&b⃑ = î + αĵ + 3k̂are [1]
perpendicular to each other.

a) 10 b) 15 c) −15 d) 1

3. Find |⃑x|, if for a unit vector a⃑ , (⃑x − a⃑ ) ∙ (⃑x + ⃑a) = 15 [1]

a) 16 b) 9 c) 4 d) 1

4. What is the projection of a vector 7î + ĵ − 4k̂ on [1]
the vector 2î + 6ĵ + 3k̂

a) 5 b) 8 c) 1 d) 1

7 7 2

5. ∫ sin2x1cos2xdx equals [1]
b) log(sin2x cos2x) + c
a) −cotx cosecx + c

c) tanx – cotx + c d) tanx+ cotx + c

6. If ∫ 1 dx = 1 sin−1( ) + c, then the value of ‘a’ is [1]
√4−9x2 3

a) 3 b) 2 c) 1 d) 1

2 3 2 3
[1]
7. ∫ 3+3cosx dx equals
x+sinx

a) log|x + sinx| + c b) 3log|x + sinx| + c

c) log|1 + cosx| + c d) 1log|1 + cosx| + c

3

8. ∫ axex dx = [1]

a) b) c) d)
axex + c axex + c (ae)x + c axex
loga x+1
1 + loga +
9. ∫−ππ x3cos3x dx =
[1]

a) b) c) d) 0

4 2

10. π [1]

∫02 cos2x dx = d) 1

a) π b) c) d) − 12

2 4 5
OR
∫0π sin2x cos3xdx =
c) 5
a) 4 b) − 4
12
5 5

11. ∫ 1 dx = [1]
√(x−3)2 b) log|x − √x2 − 6x + 8| +c
−1

a) log|(x − 3) − √x2 − 6x + 8| +c

c) log|( − 3) + √ 2 − 6 + 8| +c d) log| + √ 2 − 6 + 8| +c

∫ ex(1 + logx) dx = OR
c)exlogx + c
x
x
a)exlogx + c b)ex + c d) ex + c

x logx

12. × ⃑ = 3 ̂ + 2 ̂ + 6 ̂ , | | = 2, | ⃑ | = 7 , find the angle [2]
between ⃑⃑ ⃑⃑ & ⃑ .

13. Given three points A(1,-2,-8), B(5,0,-2) &C(11,3,7) [2]
are collinear, find the ratio in which B divides AC.
OR

If a⃑ = î + ĵ + k̂ , ⃑b = 2î − ĵ + 3k̂ and c = î − 2ĵ + k̂ ,

find a unit vector parallel to the vector 2 − ⃑ + 3

14. The two adjacent sides of a parallelogram are [2]
2î − 4ĵ + 5k̂ &î − 2ĵ − 3k̂. Find the unit vector
parallel to its diagonal.

15. Find the area of a triangle with vertices [3]
A(1,1,2), B(2,3,5)& (1,5,5).
OR
If î + ĵ + k̂, 2î + 5j,̂ 3 î + 2ĵ − 3k̂&î − 6ĵ − k̂are the
position vectors of points A, B, C & D respectively,

find the angle between A⃑⃑⃑⃑B⃑ &⃑⃑C⃑⃑⃑D⃑ . From the angle

found, deduce that A⃑⃑⃑⃑B⃑ &C⃑⃑⃑⃑D⃑ are collinear.

16. If a⃑ = î + 4ĵ + 2k̂ , b⃑ = 3î − 2ĵ + 7k̂ and [5]

c = 2î − ĵ + 4k̂, find a vector d⃑ which is

perpendicular to both ⃑a⃑ &⃑b and c ∙ d⃑ = 15

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