156maths jr.inter -1(a)_opt

8/17/2019 156Maths Jr.inter -1(a)_opt

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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)

Intermediate Results available in the month of April in www.manabadi.com

nabadi.com is not responsible for any inadvertent error that may have crept in the guess paper bess paper published on net is for the information to the examines. this does not constitute to beuld NOT follow the same. While all efforts have been made to make the guess paper available on tsible. manabadi or any staff persons will not be responsible for any loss to persons caused by aaccuracy in the Guess papers provided by Manabadi.com website.

Intermediate Results available in the month of April in www.manabadi.com

nabadi.com is not responsible for any inadvertent error that may have crept in the guess paper bess paper published on net is for the information to the examines. this does not constitute to beuld NOT follow the same. While all efforts have been made to make the guess paper available on tsible. manabadi or any staff persons will not be responsible for any loss to persons caused by aaccuracy in the Guess papers provided by Manabadi.com website.

8/17/2019 156Maths Jr.inter -1(a)_opt

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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.

Intermediate Results available in the month of April in www.manabadi.com

nabadi.com is not responsible for any inadvertent error that may have crept in the guess paper bess paper published on net is for the information to the examines. this does not constitute to beuld NOT follow the same. While all efforts have been made to make the guess paper available on tsible. manabadi or any staff persons will not be responsible for any loss to persons caused by aaccuracy in the Guess papers provided by Manabadi.com website.

Intermediate Results available in the month of April in www.manabadi.com

nabadi.com is not responsible for any inadvertent error that may have crept in the guess paper bess paper published on net is for the information to the examines. this does not constitute to beuld NOT follow the same. While all efforts have been made to make the guess paper available on tsible. manabadi or any staff persons will not be responsible for any loss to persons caused by aaccuracy in the Guess papers provided by Manabadi.com website.