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&RGH 1R exam paper/Class 12/Math... FRQWDLQV UHG DQG EODFN EDOOV DQG EDJ & FRQWDLQV UHG DQG EODFN EDOOV $ EDJ RXW RI WKH WKUHH LV VHOHFWHG DW UDQGRP DQG D EDOO LV GUDZQ IURP LW UDQGRPO\

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Text of &RGH 1R exam paper/Class 12/Math... FRQWDLQV UHG DQG EODFN EDOOV DQG EDJ & FRQWDLQV UHG DQG...

  • 65(B) 1 C/1

    amob Z§. Roll No.

     (    )

    MATHEMATICS (FOR BLIND CANDIDATES ONLY)

      : 3    : 100 Time allowed : 3 hours Maximum Marks : 100

    Series : SGN/C

     H¥$n¶m Om±M H$a b| {H$ Bg àíZ-nÌ ‘| ‘w{ÐV n¥ð 15 h¢ &  àíZ-nÌ ‘| Xm{hZo hmW H$s Amoa {XE JE H$moS> Zå~a H$mo N>mÌ CÎma-nwpñVH$m Ho$

    ‘wI-n¥ð> na {bI| &  H¥$n¶m Om±M H$a b| {H$ Bg àíZ-nÌ ‘| 29 àíZ h¢ &  H¥$n¶m àíZ H$m CÎma {bIZm ewê$ H$aZo go nhbo, àíZ H$m H«$‘m§H$ Adí¶ {bI| &  Bg àíZ-nÌ H$mo n‹T>Zo Ho$ {bE 15 {‘ZQ> H$m g‘¶ {X¶m J¶m h¡ & àíZ-nÌ H$m

    {dVaU nydm©• ‘| 10.15 ~Oo {H$¶m OmEJm & 10.15 ~Oo go 10.30 ~Oo VH$ N>mÌ Ho$db àíZ-nÌ H$mo n‹T>|Jo Am¡a Bg Ad{Y Ho$ Xm¡amZ do CÎma-nwpñVH$m na H$moB© CÎma Zht {bI|Jo &

     Please check that this question paper contains 15 printed pages.  Code number given on the right hand side of the question paper

    should be written on the title page of the answer-book by the candidate.

     Please check that this question paper contains 29 questions.  Please write down the Serial Number of the question before

    attempting it.  15 minute time has been allotted to read this question paper. The

    question paper will be distributed at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the students will read the question paper only and will not write any answer on the answer-book during this period.

    SET – 4

    narjmWu H$moS> H$mo CÎma-nwpñVH$m Ho$ ‘wI- n¥ð> na Adí¶ {bI| & Candidates must write the Code on the title page of the answer- book.

    H$moS> Z§. Code No.

    65(B)

  • 65(B) 2 C/1

      :

    (i)     

    (ii)  -  29   

    (iii) -   . 1-4  -    ,   1    

    (iv) -   . 5-12  -         2    

    (v) -   . 13-23  - I          4    

    (vi) -   . 24-29  - II          6    

    General Instructions :

    (i) All questions are compulsory.

    (ii) This question paper contains 29 questions.

    (iii) Questions No. 1-4 in Section A are very short-answer type questions carrying 1 mark each.

    (iv) Questions No. 5-12 in Section B are short-answer type questions carrying 2 marks each.

    (v) Questions No. 13-23 in Section C are long-answer – I type questions carrying 4 marks each.

    (vi) Questions No. 24-29 in Section D are long-answer – II type questions carrying 6 marks each.

  • 65(B) 3 C/1

     – 

    SECTION – A

      1  4    1    

    Question numbers 1 to 4 carry 1 mark each.

    1.  A = 3 B   A  B  3    ,  | B | = 2 , 

    | A |   

    If A = 3B, where A and B are square matrices of order 3 and | B |

    = 2, then find | A |.

    2.   :  .

    .

    sin–1 x 1 – x2

    dx.

    Find :  .

    .

    sin–1 x 1 – x2

    dx.

    3. tan x  sec x     

    Write the derivative of tan x with respect to sec x.

    4.  â  ^b      | â – ^b | = 1 ,  â  ^b   

       

    If â and ^b are two unit vectors and | â – ^b | = 1, then find the acute

    angle between â and ^b.

  • 65(B) 4 C/1

     – 

    SECTION – B

      5  12     2   

    Question numbers 5 to 12 carry 2 marks each.

    5.   : cot –1 (–x) = – cot –1 x, x  .

    Prove that : cot –1 (–x) = – cot –1 x, x  .

    6.  sin   

      

    sin–1 2 7 + cos

    –1 2x = 1 ,  x     

    If sin   

      

    sin–1 2 7 + cos

    –1 2x = 1, then find the value of x.

    7.  X    Y =   

       3 2

    1 4  2X + 3Y =  

       7 4

    –1 10  

    Find the matrix X if Y =   

       3 2

    1 4 and 2X + 3Y =   

       7 4

    –1 10

    8.  f(x) = x3 – 5x2 – 3x    [1, 3]    

     

    Verify Mean value theorem, for the function f(x) = x3 – 5x2 – 3x in

    the interval [1, 3].

  • 65(B) 5 C/1

    9.  ,  6y = x3 + 2             

      x-    y –  2       

    A particle moves along the curve 6y = x3 + 2. Find the points on the

    curve at which the y – co-ordinate is changing 2 times as fast as the

    x – co-ordinate.

    10.   :  .

    . xx

    x d

    )a(sin

    a) ( sin

     

    .

    Find :  .

    . xx

    x d

    )a(sin

    a) ( sin

     

    11.        a = î – ĵ + 3k̂  b = 2 î – 7 ĵ

    + k̂              

           

    The adjacent sides of a parallelogram are determined by the

    vectors a = î – ĵ + 3k̂ and  b = 2 î – 7 ĵ + k̂. Find the vectors

    determining its diagonals and hence find the area of the

    parallelogram.

    12.                  

       

    A die is tossed thrice. Find the probability of getting an odd

    number at least once.

  • 65(B) 6 C/1

     – 

    SECTION – C

      13  23     4   

    Question numbers 13 to 23 carry 4 marks each.

    13.         :

      

       xy xz x2 + 1

    y2 + 1 yz xy yz z2 + 1 xz

    = 1 + x2 + y2 + z2

    

     A =   

       3 2 0

    1 4 0 0 0 5

    ,    A2 – 7A + 10 I3 = O  A–1 

     

    Using properties of determinants, prove that :

      

       xy xz x2 + 1

    y2 + 1 yz xy yz z2 + 1 xz

    = 1 + x2 + y2 + z2

    OR

    If A =   

       3 2 0

    1 4 0 0 0 5

    , show that A2 – 7A + 10 I3 = O, hence find A –1.

  • 65(B) 7 C/1

    14.   f (x) =   

    (3sin x –1)2

    x log (1 + 5x) , x  0

    k , x = 0

    x = 0   ,  k     

    

     y = 1 – x1 + x ,     (1 – x 2)

    dy dx + y = 0.

    If the function f (x) =   

    (3s