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  Sample Paper 2010
  Subject – Mathematics
  Class – XII
  Time:3hrs
  Maximum Marks: 80
  General Instructions:
  (i) All questions are compulsory.
  (ii) The question paper consists of 30 questions divided into four sections – A, B,C and
  Section
  A
  contains 10 questions of 1 marks each. Section B contains 5 questions of 2 marks each. Section C contains
  10 questions of 3 marks each and Section D contains 5 questions of 6 marks each.
  (iii) Use of calculators is not permitted.
  SECTION – A
  Q.1
  The decimal expansion of the rational number
  43
  will terminate after how many
  2 4  53
  places of decimals?
  Q.2
  If sin(A) - cos(A) = 0 , find the value of cot25(A) + tan25(A)
  Q.3
  Let the sequence be defined by a1 = 1, an = 3an-1 + 1 for all n > 1. Find next four terms of
  sequence
  Q.4
  If 1 is the zero the polynomial p(x) = ax2 – 3(a – 1)x - 1, then find the value of a.
  Q.5
  The probability guessing the correct answer to certain test questions is x/12. If the
  probability of not guessing the correct answer to this question is 3/4, find x.
  Q.6
  ΔABC is an isosceles triangle right angled at B. Similar triangles ACD and ABE are
  constructed on sides AC and AB. Find the ratio between the areas of ΔABE and ΔACD.
  Q.7
  If the intersection point of the more than and less than ogive is
  (34.8, 30), then find
  the median of the data.
  Q.8
  Find the distance between two parallel tangents to a circle, whose radius is 4.8 cm.
  Q.9
  Find the value of k for which x2 + kx + 64 = 0 has equal roots.
  Q.10
  The perimeter and area of a circle are numerically equal. Find the radius of the circle.
  SECTION – B
  Q.11
  4
  3
  If the polynomial 6x + 8x + 17x2 + 21x + 7 is divided by another polynomial 3x2 + 4x +
  1, the remainder comes to be (ax + b), find a and b
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  Q.12
  Find area of the quadrilateral whose vertices in order are (2,1), (4,2), (5,4) and (3,3)
  Q.13
  Find the probability of getting 53 Sunday and Monday in a leap year.
  OR
  Out of pack of 52 playing cards, black aces and black queens are removed. From the
  remaining cards, a card is drawn at random. Find the probability that the card drawn is a
  (i) black card
  (ii) queen (iii) red card (iv) king or queen
  2 sin 68 2 cot 15 3 tan 45 tan 20 tan 40 tan 50 tan 70
  
  
  cos 22 5 tan 75
  5cos 2 29  cos 2 61
  Q.14
  Evaluate
  Q.15
  In ΔABC having sides BC = 8 cm, AC = 10 cm and AB = 12 cm a circle is inscribed
  touching the sides AB at D, BC at E and AC at F. Find AD, BE and CF.
  SECTION – C
  Q.16
  Show that n2 + n + 1 is not divisible by 5 for any n, where n is a natural number.
  Prove that √5 + √3 is irrational number.
  OR
  2
  Q.17
  If (x-3) is factor of 2x + ax + b and a + b = 2, find the values of a & b.
  Q.18
  Solve a  b x  a  b y  a 2  2ab  b2 , a  b x  y   a 2  b2
  Q.19
  In a flower bed there are 23 rose plants in first row, 21 in second row, 19 in third row,
  and so on. There are 5 rose plants in last row. How many rose plants are there in the
  flower
  bed?
  OR
  
  
  Prove that the sum of n natural numbers = 1 
  1
   times the sum of n odd natural
  n
  numbers.
  Q.20
  Prove
   1  sin   cos  
  
  
   1  cos   sin  
  
  1  sin 
  cos 
  OR
  If a cos   b sin   c prove that
  Q.21
  b cos   a sin    a 2  b 2  c 2
  The vertices of ΔABC are A(4,6), B(1,5) and C(7,2). A line is drawn to intersect sides
  AB and AC at D and E respectively, such that
  AD/AB = AE/AC = 1/4. Calculate the
  area of the ΔADE and compare it with the area of ΔABC.
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  Q.22
  The coordinate of centroid of a ΔPQR is (5,2). If the vertices of the ΔPQR are P(3,2) and
  Q(10,3). Find the coordinates of R, also the length of median PS
  Q.23
  In trapezium ABCD, AB ││DC and DC = 2AB. EF drawn parallel to AB cuts AD in F
  and BC in E, such that BE/EC = ¾. Diagonal BD intersects EF at G. Prove that 7FE =
  10AB.
  Q.24
  Construct a ΔABC with BC = 7 cm, angle B = 45o, angle A = 105o Then construct a
  triangle similar to given triangle such that each side of the new triangle is 4/3 of given
  triangle.
  Q.25
  Three horses are tethered at 3 corner of a triangular plot having 20m, 30m and 40m with
  ropes of 7m length each. Find the area where the horses can graze.
  SECTION – D
  Q.26
  A rectangular park is to be designed whose breath is 3 m less than its length. Its area is to
  be 4 sq. mts more than the area of that park that has already been made in shape of an
  isosceles triangle with its base as the breadth of the rectangular park and of altitude 12 m.
  Q.27
  From a point on a bridge across a river, the angles of depression of the banks on opposite
  sides of the river are 30o & 45o respectively. If the bridge is at height of 3 m from the
  banks, find the width of the river.
  OR
  The angle of elevation of an unfurnished tower at a point of distance 120 m from its base
  is 45o. How much the height must be raised so that the angle of elevation be 60o?
  Q.28
  Prove that the lengths of two tangents drawn from external point are equal .
  Making use of above prove the following:
  Two tangents TP and TQ are drawn to a
  circle with centre O from an external point T. Prove that PTQ  2OPQ
  Q.29
  A wooden toy rocket is in shape of a cone mounted on a cylinder as shown in figure. The
  height of entire rocket is 24 cm while the height of conical part is 6 cm. The base of
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  conical portion has a diameter of 5 cm, while the base diameter of cylindrical portion is 3
  cm. If the conical portion is to be painted orange and cylindrical portion yellow, find the
  area of the rocket painted with each of these colours. ( Take π = 3.14 )
  OR
  A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank
  in her field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at
  the rate of 3 km/hr, in how much time will the tank be filled?
  Q.30
  Draw both less than and more than ogive on same graph and hence find median from the
  graph
  Wages
  No.
  10 - 20
  of
  4
  20 -
  30 -
  40 -
  50 -
  60 -
  70 -
  30
  40
  50
  60
  70
  80
  8
  10
  12
  10
  4
  2
  workers
  Paper Submitted By:Deepak Dutta {MRA DAV Sr. Sec. P School Solan}
  Email :- dd_duttamath@yahoo.co.in
  Phone No. 09816055445
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