156maths jr.inter -1(a)_opt

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1

Intermediate Public Examination

Time: 3 hrs

Max. Marks:75

Section-A

I) Very short Answer type Questions. 10x2=20 M

i) Answer all questions.

ii) Each question carries two marks

1) If ! " ! " ! "# $1,3,3,2,2,1 %%& f then find (i) 28 (ii) f

2) Find the domain and range of x

x x f

%

'&

2

2)(

3) Defind skew-symmetric matrin and give one example

4) If ()

*+,

-

%&

K A

1

42 and 02 & A find the value of K.

5) OABC is a parallelogram. If then,and C OC aOA && find the vector equation of the side BC.6) Find the vector equation of the line joining the points K J and K J %'%'' 3i43i2

7) Let K jiand K ji %'&'%& 43 b2a . If ''. is the angle between , ba and then find . Sin .

8) Find the period of / 0

123

4 '&

5

94 )(

xCos x f

9) Find the value of 000 46434 CosCosSin %'

10) If ,. SechnCos & then prove that2

2

2

2Tkn . Tanh n &

Section-B

II. Short answer type Questions. 5x4=20 M

i) Answer any five questions

ii) Each question carries four marks

11) If ()

*+,

-

%

%&

11

43 A then for any integer 15n show that (

)

*+,

-

%

%'&

nn

nnn A21

421

12) Let ABCDEF be a regular henagon with centre ‘O’ show that AO AD AF AD AC AB 63AE &&''''

13) Find a unit vector perpendicular to the plane determined by the points 1).2,(0,R and1)0,(2,Q2),1,(1, %%

14) If ''. is not an integral multiple of26 then prove that .884422 . . . . . Cot Cot TanTanTan &'''

15) Solve 23 &% . . CosSin

16) Find the value of321

541-CosTan %' Tan

17) If ,)( . Seccba %& prove that2

2 A

Sincb

bcTan

%&.

Section-C

III. Long Answer Type Questions 5x7=35 M

i) Answer any five questions

ii) Each question carries seven marks.

18) Let C B B A f 99 :9,: be bijecting. Then show that ! " 11109908 %%% & f

19) Show that .....10.7

1

7.4

1

4.1

1, ''':; N n upto n terms

13 '&

n

n

Jr. Inter

Sub: Maths-I (A)

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20) Show that ! "3

22

22

22

cba

baccc

bacbb

aacba

''&

%%

%%

%%

21) Solve the following equations by Ganss-Jordan method 2,6,932 &'%&''&'% z y x z y x z y x

22) Find the shortest distance between the skew lines

! " ! "k jit k jir 22226 '%'''& and

! " ! "k jiS k ir 2234 %%'%%& where s, t are scalars.

23) If A, B, C are angles of a triangle, then prove that222

2

2

2

2

2 21 C BC B A SinCosSinSinSin %&%'

24) If ,12:5:2,:: &r Rr then prove that the triangle is right angled at A.









156maths jr.inter -1(a)_opt

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