Cbse 12 class question paper 2020 scanned copy of notes, Schemes and Mind Maps of Sociology

Download Cbse 12 class question paper 2020 scanned copy of notes and more Schemes and Mind Maps Sociology in PDF only on Docsity! .65/4/1. 1 P.T.O. 333A  . Roll No.  NOTE (I)       -    15   (I) Please check that this question paper contains 15 printed pages. (II) -            -  -    (II) 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. (III)       -  36    (III) Please check that this question paper contains 36 questions. (IV)         ,       (IV) Please write down the Serial Number of the question in the answer-book before attempting it. (V)  -     15        -     10.15     10.15   10.30     -         -       (V) 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.  MATHEMATICS {ZYm©[aV g‘¶ : 3 KÊQ>o A{YH$V‘ A§H$ : 80 Time allowed : 3 hours Maximum Marks : 80 65/4/1  . Code No.    -  -     Candidates must write the Code on the title page of the answer-book. SET – 1 Series : HMJ/4 CBSE Class 12 Maths Question Paper 2020 Set 65/4/1 .65/4/1. 2   :             (i) -        – , ,      -   36         (ii) -    1  20  20           (iii) -    21  26  6           (iv) -    27  32  6           (v) -    33  36  4           (vi) -          -     , -     , -       -                       (vii)  , ,             (viii)          –    1  10             1     1. sin–1     cos 3 5     (a)  10 (b) 3 5 (c) – 10 (d) –3 5 .65/4/1. 5 P.T.O. 2. If A = [2 – 3 4], B =         3 2 2 , X = [1 2 3] and Y =         2 3 4 , then AB + XY equals (a) [28] (b) [24] (c) 28 (d) 24 3. If         2 3 2 x x x 4 9 1 + 3 = 0, then the value of x is (a) 3 (b) 0 (c) –1 (d) 1 4.   0 /8 . . tan2 (2x) is equal to (a) 4 –  8 (b) 4 +  8 (c) 4 –  4 (d) 4 –  2 5. If  a .  b = 1 2 |  a| |  b|, then the angle between  a and  b is (a) 0° (b) 30° (c) 60° (d) 90° 6. The two lines x = ay + b, z = cy + d; and x = ay + b, z = cy + d are perpendicular to each other, if (a) a a + c c = 1 (b) a a + c c = –1 (c) aa + cc = 1 (d) aa + cc = –1 7. The two planes x – 2y + 4z = 10 and 18x + 17y + kz = 50 are perpendicular, if k is equal to (a) –4 (b) 4 (c) 2 (d) –2 8. In an LPP, if the objective function z = ax + by has the same maximum value on two corner points of the feasible region, then the number of points at which zmax occurs is (a) 0 (b) 2 (c) finite (d) infinite .65/4/1. 6 9.  { 1,2,3,4,5 }    a  b (a ≠ b)      ab       : (a) 1 3 (b) 1 4 (c) 1 2 (d) 3 5 10.    3 , 4   2      2        ,           : (a) 1 18 (b) 1 36 (c) 1 12 (d) 1 24  11  15         /  : 11.  f : R → R, f(x) = (3 – x3)1/3   ,  fof (x) = _________ 12.     x + y 7 9 x – y =    2 7 9 4 ,  x . y = _________ 13. f(x) = |x| – |x + 1|    f      _________   14.  y = x3 – x   (2, 6)       _______.        ,   r  ,  r = 3  ,  _________. 15.   a    ,  (a . î ) î + (  a . ĵ ) ĵ + (  a .k̂) k̂   _________.   î + ĵ   î – ĵ    _________. .65/4/1. 7 P.T.O. 9. From the set { 1,2,3,4,5 }, two numbers a and b (a ≠ b) are chosen at random. The probability that a b is an integer is : (a) 1 3 (b) 1 4 (c) 1 2 (d) 3 5 10. A bag contains 3 white, 4 black and 2 red balls. If 2 balls are drawn at random (without replacement), then the probability that both the balls are white is (a) 1 18 (b) 1 36 (c) 1 12 (d) 1 24 In Q. Nos. 11 to 15, fill in the blanks with correct word / sentence : 11. If f : R → R be given by f(x) = (3 – x3)1/3, then fof (x) = ________ 12. If    x + y 7 9 x – y =    2 7 9 4 , then x . y = ________ 13. The number of points of discontinuity of f defined by f(x) = |x| – |x + 1| is ____________. 14. The slope of the tangent to the curve y = x3 – x at the point (2, 6) is _______. OR The rate of change of the area of a circle with respect to its radius r, when r = 3 cm, is _________. 15. If  a is a non-zero vector, then (  a . î ) î + (  a . ĵ ) ĵ + (  a .k̂) k̂ equals _________. OR The projection of the vector î – ĵ on the vector î + ĵ is _________. .65/4/1. 10 22.  =  3  dy dx    ,  x = cos  – cos 2, y = sin  – sin 2. 23.    f  f(x) = (x – 1) ex + 1,      x > 0       24.  |  a| = 2|  b|  (a +  b)  (  a –  b) = 12 ,  | a|  |  b|       a = 4 î + 3 ĵ + k̂   b = 2 î – ĵ + 2k̂           25.        y-  3     xz –      26.  P(A) = 3 10 , P(B) = 2 5  P(AB) = 3 5 ,  [P(B/A) + P(A/B)]     –    27  32    4     27.     Z  R = {(x, y) : (x – y)   5  }    R,      28.  y = sin–1      1 + x + 1 – x 2 ,    dy dx = –1 2 1 – x2       –  2 ,  2    f(x) = ex cos x         .65/4/1. 11 P.T.O. 22. Find the value of dy dx at  =  3, if x = cos  – cos 2, y = sin  – sin 2. 23. Show that the function f defined by f(x) = (x – 1) ex + 1 is an increasing function for all x > 0. 24. Find |  a| and |  b|, if |  a| = 2|  b| and (  a +  b) . (  a –  b) = 12. OR Find the unit vector perpendicular to each of the vectors  a = 4 î + 3 ĵ + k̂ and  b = 2 î – ĵ + 2k̂. 25. Find the equation of the plane with intercept 3 on the y-axis and parallel to xz – plane. 26. Find [P(B/A) + P(A/B)], if P(A) = 3 10, P(B) = 2 5 and P(AB) = 3 5. Section – C Q. Nos. 27 to 32 carry 4 marks each. 27. Prove that the relation R on Z, defined by R {(x, y) : (x – y) is divisible by 5} is an equivalence relation. 28. If y = sin–1      1 + x + 1 – x 2 , then show that dy dx = –1 2 1 – x2 OR Verify the Rolle’s Theorem for the function f(x) = ex cos x in     –  2 ,  2 .65/4/1. 12 29.    :   0  . . x sin x 1 + cos2 x dx. 30.                 (x + 1) dy dx = 2e–y + 1; y = 0  x = 0 31.        I, II  III     I  II  12            III      5           M  N    ,             M  N               ( )            ( ) I II III M 1 2 1 N 2 1 1.25   M  ` 600     N  ` 400                  ,     ,            ,      ?     ? 32.                                                   100   5  1000   25                 ,            .65/4/1. 15 P.T.O. Section – D Q. Nos. 33 to 36 carry 6 marks each. 33. Using properties of determinates prove that :         a – b b + c a b – c c + a b c – a a + b c = a3 + b3 + c3 – 3 abc. OR If A =         1 3 2 2 0 –1 1 2 3 , then show that A3 – 4A2 – 3A + 11 I = O. Hence find A–1. 34. Find the intervals on which the function f(x) = (x – 1)3 (x – 2)2 is (a) strictly increasing (b) strictly decreasing. OR Find the dimensions of the rectangle of perimeter 36 cm which will sweep out a volume as large as possible, when revolved about one of its side. Also, find the maximum volume. 35. Find the area of the region lying in the first quadrant and enclosed by the x – axis, the line y = x and the circle x2 + y2 = 32. 36. Show that the lines  r =  a +   b and  r =  b +   a are coplanar and the plane containing them is given by  r . (  a ×  b)= 0. ____________ meus Be (ser i