a b 1st Year Maths IA (En… · Manabadi.com is no where claiming this to be the Main Examination...
Transcript of a b 1st Year Maths IA (En… · Manabadi.com is no where claiming this to be the Main Examination...
Disclaimer: This Question paper is purely for preparation purpose only. Manabadi.com is no where claiming this to be the Main Examination Paper.
MARCH – 2020MATHEMATICS PAPER- IA
Time :3 Hrs Total Marks : 75 M
SECTION-A
I. Answer all the questions. Each question carries ‘2’ marks. 10 x 2 = 20M
1) If :f Q Q is defined by 5 4f x x for all x Q , find 1f x .
2) Find the domain of the real valued function 2 2x xf x
x
.
3) Give examples of two square matrices A and B of the same order for which
0AB but 0BA .
4) If
1 0 0
2 3 4
5 6
A
x
and det 45A , then Find x .
5) Show that the points whose position vectors are 2 3 5a b c , 2 3a b c ,
7a c are collinear, when , ,a b c are non - coplanar vectors.
6) Let 2 4 5a i j k , b i j k and 2c j k . Find unit vector in the
opposite direction of a b c .
7) If 2 3 5a i j k , 4 2b i j k then find a b a b and unit vector
perpendicular to both a b and a b .
8) Prove that 0 0
00 0
cos90 sin 90cot 36
cos90 sin 90
.
9) Sketch the region enclosed by siny x , cosy x and X-axis in the interval
0, .
10)If 3
sinh4
x , find cosh 2x and sinh 2x .
Disclaimer: This Question paper is purely for preparation purpose only. Manabadi.com is no where claiming this to be the Main Examination Paper.
SECTION-B
II. Answer ANY FIVE questions. Each question carries ‘4’ marks. 5 x 4 = 20M
11)If 1 0
0 1I
and 0 1
0 0E
then, show that 3 3 23aI bE a I a bE .
12) , ,a b c are non – coplanar vectors. Prove that the four points 6 2a b c ,
2 3a b c , 2 4a b c , 12 3a b c are coplanar.
13)Find the vector having magnitude 6 units and perpendicular to both 2i k
and 3 j i k .
14)Prove that 4 4 4 43 5 7 3sin sin sin sin
8 8 8 8 2
.
15)Find the general solution of the equation 21 sin 3sin cos .
16)Prove that 2
1 12
1cos Tan sin cot
2
xx
x
.
17)In triangle ABC, show that 2 2 2cot cot cotabc
a A b B c CR
.
SECTION-C
III. Answer ANY FIVE questions. Each question carries ‘7’ marks. 5 x 7 = 35M
18)If : ,f A B :g B C are two bijective functions then prove that
1 1 1gof f og and if 1 1 1 2, , 4, , 1, , 3,gof f og a b c d
and then
show that 1 1 1gof f og .
19)By using mathematical induction, show that n N ,
3 3 3 3 3 31 1 2 1 2 3.......
1 1 3 1 3 5
up to ‘n’ terms 22 9 13
24
nn n .
20)Show that 2 2 2 2
22 2 2 3 3 3
2 2 2
2
2 3
2
a b c bc a c b
b c a c ac b a a b c abc
c a b b a ab c
.
Disclaimer: This Question paper is purely for preparation purpose only. Manabadi.com is no where claiming this to be the Main Examination Paper.
21)Solve the equations by using Gauss – Jordan Method 1x y z ,
2 2 3 6x y z , 4 9 3x y z .
22)Find the shortest distance between the skew lines
6 2 2 2 2r i j k t i j k and 4 3 2 2r i k s i j k .
23)In triangle ABC, prove that
sin sin sin 1 4cos cos sin2 2 2 4 4 4
A B C A B C
24)In triangle ABC, show that 31 2 1 1
2
rr r
bc ca ab r R .