CBSE Board Class 10 Math Sample Papers 2007

                                                           Mathematics

General Instructions

All questions are compulsory.
The question paper consists of 25 questions divided into three sections- A, B and C. Section A contains 7 questions of 2 marks each, Section B is of 12 questions of 3 marks each and Section C is of 6 questions of 5 marks each.
There is no overall choice. However, an internal choice has been provided in two questions of two marks each, two questions of three marks each and two questions of five marks each.
 In question on construction, the drawing should be neat and exactly as per the given measurements.
 Use of calculators is not permitted. However, you may ask for Mathematical tables
 

Question 1 : If Find the GCD of the following polynomials :
                   12x4 +324x; 36x3 +90x2 – 54x      Marks: 2

Question 2 : Solve for x and y:
                    2x/a + y/b = 2; x/a - y/b = 4

OR

Solve: 31x + 29y = 33; 29x +31y = 27     Marks: 2

Question 3 : Find the sum of all three digit numbers which are multiples of 7.   Marks: 2

Question 4 : In figure, PQ ∥ AB and PR ∥ AC. Prove that QR ∥ BC.              Marks: 2

Question 5 :  A wrist watch is available for Rs. 1,000 cash or Rs. 500 as cash down payment followed by three equal monthly installments of Rs. 180. Calculate the rate of interest charged under the installment plan.    Marks: 2

Question 6 : An unbiased die is tossed once. Find the probability of getting A multiple of 2 or 3 A prime number greater than 2       Marks: 2

Question 7 : Solve the following system of equations graphically:
                    2x + y = 8; x + 1 = 2y         Marks: 3
   
Question 8 : Simplify the following rational expression in the lowest terms:
                    [(ax^2-x^2)/(a^2+x^2 ) × (a^2-ax+x^2)/(a^2 x^2+x^4 ) ]÷ (a^2-2ax+x^2)/(a^4-x^4 )       Marks: 2

Question 9 : If the sum of first n terms of an A.P. is given by Sn = n (n+1)
                      find the 20th term of the A.P.      Marks: 2

Question 10 : In a cyclic quadrilateral ABCD, diagonal AC bisects ∠C. Prove that the tangent to the circle at A is parallel to the diagonal BD. Marks 3

Question 11 : Construct a ∆ABC in which base BC = 6 cm, ∠B = 45°  and ∠C =60°. Draw the circumcircle of ∆ABC.  Marks: 3

Question 12 : The diameter of a solid copper sphere is 18 cm. It is melted and drawn into a wire of uniform cross-section. If the length of the wire is 108 m, find its diameter.     Marks: 3

Question 13 : From a pack of 52 cards, red face cards are removed. After that a card is drawn at random at the pack. Find the probability that the card drawn is:
a)    a queen
b)   a red card
c)    a spade card          Marks: 3

Question 14 : Prove that: [1 +  1/(〖tan〗^2 θ) ] [1 +  1/(〖cot〗^2 θ) ] = 1/(〖sin〗^2 θ+ 〖sin〗^4 θ)

Question 15 : If A, B and C are the interior angles of a triangle ABC, show that cos [(B+C)/2] = sin A/2    Marks: 3

Question 16 : The coordinates of the mid-points of the sides of a triangle are (4, 3), (6, 0) and (7, −2). Find the coordinates of the centroid of the triangle.       Marks: 3

Question 17 :  If the distance of P(x, y) from two points with coordinates (5, 1) and (−1, 5) is equal, prove that 3x = 2y   Marks: 3

Question 18 : A loan of Rs. 24,600 is to be paid back in two equal semi-annual installments. If the interest is charged at 10% per annum, compounded semi annually, find the installment.       Marks: 3

Question 19 : Prove that the angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle. Using above, prove the following: In figure, O is the centre of the circle. If ∠BAO = 30° and ∠BCO = 40°, find the value of ∠AOC.             Marks: 5

Question 20 : State and prove Pythagoras theorem. Use the above to prove the following:
ABC is an isosceles right triangle, right angled at C.
Prove that AB2 = 2AC2          Marks: 5

Question 21 : The side of a square exceeds the side of another square by 4 cm and the sum of areas of two squares is 400 sq.cm. Find the dimensions of the squares.

OR

A fast train takes 3 hours less than a slow train for a journey of 600 km. If the speed of the slow train is 10 km/hour less than that of the fast train, find the speeds of the two trains.        Marks: 5

Question 22 : A hollow copper sphere of external and internal diameter 8 cm and 4 cm respectively is melted into a solid cone of base diameter 8 cm. Find the height of the cone.

OR

If the radii of the circular ends of a bucket 45 cm high, are 28 cm and 7 cm, find the capacity and surface area of the bucket. (Use π= 22/7 )      Marks: 5

Question 23 : An observer in a lighthouse observes two ships on the same side of the lighthouse, and in the same straight line in with the base of the lighthouse. The angles of depression of the ships approaching it are 30 and 60. If the height of the lighthouse is 150 cm; find the distance between the ships.      Marks: 6 

Question 24 : Satish (aged 67 years) has monthly income of Rs. 30,000 (excluding HRA). He donates Rs. 80,000 to a charitable orphanage (50% exemption). He contributes Rs. 30,000 towards Public Provident Fund and purchases NSCs worth Rs. 20,000. He pays Rs. 1,500 as income tax per month for 11 months. Calculate the income tax to be paid by him in the12th month of the year
Use the following to calculate income tax:
(a) Savings 100% exemption for permissible savings
upto Rs. 1,00,000

(b) Rates of Income tax for Senior Citizens (over 65 years)
Slab Income tax
       (i) Upto Rs. 1, 85,000 No tax
       (ii) From Rs. 1, 85,001 to Rs. 2, 50,000 20% of the taxable income                 
            Exceeding Rs. 1, 85,000
       (iii) From Rs. 2, 50, 001 and above Rs. 13,000 + 30% of the taxable
             Exceeding Rs. 2, 50.000
                                                                                                                                  
(c) Education Cess 2% of Income tax payable      Marks: 5