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guess Paper 10


GUESS PAPER 10– 2009
CLASS – X


SUBJECT - MATHEMATICS


Time: 3 hours                                                                                                                              M.M:80


General Instructions:



  1. All questions are compulsory.
  2. The question paper consists of thirty questions divided into four sections A, B, C and D. Section A carries ten questions of 1 mark each, section B carries five questions of 2 marks each, section C carries ten questions of 3 marks each and section D carries five questions of 6 marks each.
  3. All questions in Section A are to be answered in one word, one sentence or as per the exact requirement of the question.
  4. There is no overall choice. However, internal choice has been provided in one question of 2 marks each, three questions of 3 marks each and two questions of 6 marks each. You have to attempt only one of the alternatives in all such questions.
  5. In question on construction, drawing should be neat and exactly as per given measurements.
  6. Use of calculator is not permitted. However you may ask for mathematical tables.

 


SECTION – A



  1. Write a quadratic equation whose roots are 3+Ö3 and 3-Ö3.
  2. Write the prime factors of 49.
  3. If tanB = ¾, and A+B = 90°, then find the value of cotA.
  4. Find the zeroes of the quadratic polynomial x2 – 2x + 1.
  5. A cylinder, a cone and a hemi-sphere have equal base and same height. What is the ratio of their volumes?
  6. Give an example of polynomial p(x), g(x), q(x) and r(x), satisfying

      P(x) = g(x).q(x) + r(x), deg r(x) = 0



  1. A die is thrown once. What is the probability of getting an even prime number?
  2. Find the 20th term of the sequence -2, 0, 2, 4 ------------.
  3. Find the perimeter of the sector whose base radius is 14 cm and central angle is 120°.
  4. For what value of ‘k’ the following pair of linear equations has infinitely many solutions?

      10x + 5y – (k-5) = 0 and 20x + 10y – k = 0.


 


SECTION – B



  1. Express sin 52° + cos 67° in terms of trigometric ratios of angles between 0° and 45°.                                                                                    ‘OR’

Sin (A+B) =1/2 and cos (A+B) =1/2, 0°<A+B≤90°, A>B, find A and B.



  1. How many three digit numbers are divisible by 7?
  2. Find the values of y for which the distance between the points A (-3, 2) and B (4, y) is 7.
  3. ABC is a triangle right angled at A and AD^BC. Show that AC2 = BC.CD.
  4. Two dice are thrown once. What is the probability that the sum of the two numbers appearing on the top of the dice is less than or equal to 12?

SECTION – C



  1. Prove that Ö3 is irrational.

                                                          ‘OR’


      Solve 8x2 – 77x + 45 = 0 by factorization.



  1. Find a quadratic polynomial, whose zeroes are 2+Ö5 and 2-Ö5

                                                                                                2                2


      18. Solve for x and y: 47x + 31y = 63


                                              31x + 47y = 15.


     19. The third term of an AP is 16 and difference between 7th term and 5th is 12. Find AP.     


                                                         ‘OR’


     Which term of the AP: 114, 109, 104, --------- is the first negative term?



  1. Draw the graph of the following pair of linear equations: x + 3y = 6 and 2x – 3y = 12 and find the area of the region bounded by x = 0, y = 0 and 2x – 3y = 12.
  2. Prove that sinA + cosA      +      sinA – cosA        =                      2

      SinA – cosA                 sinA + cosA            sin2A – cos2A


                                                                        OR


      If 2 tan A = 1, find the value of 3 Cos A + 2 Sin A


                                                                      2 Cos A – Sin A



  1. For what value of ‘k’ the points A (1, 5), B (k, 1) and C (4, 11) are collinear?
  2. Construct a circle with radius 3 cm and draw two tangents from a point not lying on it.
  3. If a student had walked 1 km/hr faster, he would have taken 15 minutes less to walk 3 km. find the rate of his walking.
  4. Find the ratio in which the line segment joining the points A (3, -6) and B (5, 3) is divided by x-axis.

                                                                           


SECTION – D



  1. Prove that in a right triangle the square of the hypotenuse is equal to the sum of square of the other two sides. Using the result of this theorem prove that the sum of squares on the sides of a rhombus is equal to the sum of squares on its diagonals.

OR


           State and prove Thales theorem. Using this theorem prove that the line segment drawn through


            the mid point of one side parallel to other side bisects the third side.



  1. The shadow of a tower standing on a level ground is found to be 40m longer when the sun’s altitude is 30° then when it is 60°. Find the height of the tower.

                                                     ‘OR’


      A vertical tower stands on a horizontal plane is surmounted by a vertical flag staff of height 5 m.


       At a point on the ground the angles of elevation of the bottom and the top of the flag staff are


      respectively 300 and 600. Find the height of the tower.



  1. A cylindrical bucket 32cm high and with radius of base 18cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24cm, find the radius and slant height of the heap.
  2. The radii of the ends of a bucket 45cm high are 28cm and 7cm. find its volume and the total surface area.
  3. Find the median from the following table:






























                         Marks      


                 No. of  Students


                     Below 10


                     15


                     Below 20


                     35


                     Below 30


                     60


                     Below 40


                     84


                     Below 50


                     94


                     Below 60


                     127


                     Below 70


                     198


                     Below 80


                     249


 


 


 


 


 



CBSE Sample Guess Paper 1
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