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guess paper 3

Guess Paper – 3

Class – X

Subject - Mathematics

 

MAX.MARKS:  80                                                                                                       TIME   : 3 HRS

 

Instructions:-

 

  1. All questions are compulsory
  2. This question paper is divided into four sections- Section A, B, C & D.
  3. Each question in section A carries 1 mark, each question in Section B carries 2 marks, each question in Section C carries 3 marks and each question in Section D carries 6 marks.                                                                                                                

SECTION A

 

 

  1. If H.C.F.(26,91)=13, find the L.C.M.(26,91).

 

 

  1. If -2 is one of the zero of the quadratic polynomial x2-kx-8, find the other zero of the polynomial.

 

 

  1. For what value of ‘k’, the numbers 3k+2, 4k+3 and 6k-1 are the consecutive terms of an AP?

 

 

  1. For what value of  ‘a’, the following pair of equations will have a unique solution?

4x + 3y = 3 and 8x + ay =5

 

  1. If each side of an equilateral triangle is ‘2a’ units, what is the length of its altitude?

 

 

  1. If Sin (A + 2B) = √3 ∕ 2 and Cos (A + 4B) = 0, find A and B.

 

 

  1. Two concentric circles are of radii ‘a’ cm and ‘b’ cm.  Find the length of the chord of the larger circle which touches the smaller circle.

 

 

  1. A solid cylinder of radius ‘r’ cm and height ‘h’ cm is melted and changed into a right circular cone of radius ‘4r; cm. Find the height of the cone. 

 

 

 

  1. What is the probability of a prime number in the factors of the number 20?

 

 

  1. The median can graphically be found from

 

(a) Ogive                                          (b) histogram

 

© Frequency curve                            (d) none of these

 

SECTION B

 

  1. Find the value of ‘k’ for which the quadratic equation (k+1) x2 + (k+4) x + 1 = 0 has equal 

      roots.

 

 

  1. If 3 tan A = 4, find the value of     5 sin A – 3 cos A

                                                             5 sin A + 2 cos A

 

 

  1. Find the value of p for which the points (-1, 3), (2, p) and (5, -1) are collinear.

 

 

                                                          OR

 

      If the point P(x, y) is equidistant from the points A (5,1) and  B(-1, 5), prove that 3x = 2y.

 

 

 

14 . Prove that the intercept of a tangent between two parallel tangents to a circle subtends a right

       angle at the centre.

 

 

 

15. One card is drawn from well-shuffled deck of 52 cards.  Find the probability of getting

(i)  a king or a spade

(ii) a  king and a red card

 

SECTION C

 

  1. Show that for any odd positive integer to be a perfect square, it should be of the form 8k  +1

      for some integer k.

 

 

  1. Obtain all the zeroes of the polynomial  3x4 + 6x3 - 2x3 – 10x + 5, if two of its zeroes are       

            √5 / √3  and  -√5 / √3

 

 

 

 

  1. Solve the following system of equations graphically:  3x – 5y = 19, 3y -7x + 1 = 0.  Does the 

             point (4, 9) lie on any of these lines?  Write its equation.

 

 

 

  1. Find the sum of all multiples of 13 lying between 100 and 999.

                                                                      OR

   If the sum of first n terms of an A.P. is given by Sn = 4n2 – 3n, find the nth term of the A.P.

 

 

 

 

  1. Without using trigonometric table evaluate the following

 

 

              Sec 39◦     + 2    tan 17◦ tan 38◦ tan 60◦ tan 52◦ tan 73◦ - 3(sin2 31 + sin2  59)

             Cosec 51◦      √3

                                                       

                                                                      OR

 

      Prove that            cot A + cosec A – 1      =  1 + Cos A

                                  cot A - cosec A + 1              Sin A

 

 

  1. Prove that the centroid of triangle ABC whose vertices A(x1,y1), B(x2,y2)  and  C(x3, y3)

   are given by   ( x1+ x2+ x3,  y1+ y2+ y3  )

                                 3               3

                                                                OR

       In what ratio is the line segment joining the points (-2,-3) and (3,7) divided by the y-

    axis?  Also, find the coordinates of the point.

 

22.    Show that the points A(5,6), B(1,5), C(2,1) and D(6,2) are the vertices of a square.

       

 

 

23.    In an equilateral triangle PQR, the side QR is trisected at S.  Prove that 9 PS2 = 7 PQ2

 

 

 

  1.   Construct a triangle with sides 5 cm,6 cm and 7 cm and then construct another 

        triangle whose sides are 7/5 of the corresponding sides of the first triangle.

 

 

 

 

 

  1.   PQRS is a diameter of a circle of radius 6 cm.  The lengths PQ, OR and RS as

       diameters.  Find the perimeter of the shaded region.

                        

 

                                                        SECTION D

 

  1. Abdul traveled 300 Km by train and 200 Km by taxi, it took him 5 hous 30 minutes.  But if he travels 260 Km by train and 240 Km by taxi, he takes 6 minutes longer.  Find the speed of the train and that of the taxi.

OR

              Two pipes running together can fill a cistern in 2 8/11 minutes.  If one pipe takes

            1 minute more than the other to fill the cistern, find the time in which each pipe

            would fill the cistern.

 

 

  1. If the radii of the ends of a bucket,45 cm high, are 28 cm and 7 cm, find the capacity and surface area.

 

 

 

  1. If the median of the distribution is 28.5, find the values of x and y.

 

 

Class interval

Frequency

 

0-10

 

10-20

 

20-30

 

30-40

 

40-50

 

50-60

 

5

 

x

 

20

 

15

 

y

 

5

Total

50

 

  1. If the angle of elevation of the cloud from a point h m above a lake is α and the angle    of depression of its reflection in the lake is β, prove that the height of the cloud is    h(tan β + tan α)

                                tan β - tan α 

                                                                                    OR

              The angle of elevation of a jet plane from a point A on the ground is 60◦.  After a

   flight of 15 seconds, the angle of elevation changes to 30◦.  If the jet plane is flying at a

   constant height at a constant height of 1500√3 m, find the speed of the jet plane.

 

  1. The ratio of areas of similar triangles is equal to the ratio of the squares on the corresponding sides.  Prove.

Using the above theorem, prove that the area of the equilateral triangle described on the side of a square is half the area of the equilateral triangle described on the diagonal.

 

                                                       

 



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