# CBSE Board Math Sample Papers for Class 10

CBSE Mathematics Sample Paper-2013

General Instructions

1.All questions are compulsory.

2.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.

3.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.

4.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

The question paper consists of 25 questions divided into three sections- A, B and C. Section A contains 7 questions of 2m marks each, Section B is of 12 questions of 3 marks each and Section C is of 6 questions of 5 marks each.

Question 1 : Find the LCM of  x3 +x2 + x + 1 and x4 – 1       Marks: 2

Question 2 : Solve for x and y:
8x – 9y = 6xy     10x + 6y = 19xy                  Marks: 2

Question 3 : In an A.P., the sum of its first n terms is n2+2n.  Find its 18th term.                                            Marks: 2

Question 4 : In below figure , two circles touch each other externally at C.  Prove that the common tangent at C bisects the other two common tangents.                                                                    Marks: 2

Question 5 : A ceiling fan is marked at Rs. 970 cash or for Rs. 210 as cash down payment followed by three equal monthly instalments of Rs. 260. Find the rate of interest charged under the instalment plan.             marks: 2

Question 6 : A box contains 5 red balls, 4 green balls and 7 white balls.  A ball is drawn at random from the box.  Find the probability that the ball drawn is
(a)      White.
(b)     Neither red nor white.           Marks: 2

Question 7 : Solve the following system of linear equations graphically:
2x + 3y = 12 and 2y – 1 = 2x               marks 3

Question 8 : Simplify: [1 - 4ax/((a+x)^2 )] × ((x+a)^2)/(x^2-a^2 )           Marks: 3

Question 9 : The first term, common difference and last term of an A.P are 12, 6 and 252 respectively. Find the sum of all terms of this A.P                       Marks: 3

Question 10 : Prove that any four vertices of a regular pentagon are cyclic.  Marks: 3

Question 11 : Draw a circle of radius 4.5 cm. At a point A on it, draw a tangent to the circle without using the centre.  Marks: 3

Question 12 : A toy in the form of a cone mounted on a hemisphere with same radius. The diameter of the base of the conical portion is 7 cm and the total height of the toy is 14.5 cm. Find the volume of the toy. (use π =22/7  )
Marks: 3

Question 13 : The expenditure on different heads of a household ( in hundreds of rupees) is as follows: Marks: 3

Question 14 : All the three face cards of spades are removed from a well shuffled pack of 52 cards. A card is then drawn at random from the remaining pack. Find the probability of getting (a) a black face card, (b) a queen, (c) a black card. Marks: 3

Question 15 : Prove that  (tanA+secA-1)/(tanA-secA+1) = (1+sinA)/cosA               Marks: 3

Question 16 : Three consecutive vertices of a parallelogram are (2, 1); (1, 0) and (4, 3). Find the coordinates of the fourth vertex.            Marks: 3

Question 17 : If the point C (1, 2) divides internally the line segment AB in the ratio 3 : 4, where the coordinates of A are (2, 5), find the coordinates of B.            Marks: 3

Question 18 :  A loan of Rs. 2550 is to be paid back in two equal half-yearly instalments. How much is each instalment if interest is compounded half-yearly at 8% per annum?          Marks: 3

Question 19 : Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.
Use the above for the following :
If the areas of two similar triangles are equal, prove that they are congruent.           marks: 5

Question 20 : If a line touches a circle and from the point of contact a chord is drawn, the angles which this chord makes with the given line are equal respectively to the angles formed in the corresponding alternate segments.
Use the above for the following: In Figure 3, ABCD is a cyclic quadrilateral and PQ is the tangent to the circle at C.
If BD is the diameter and DCQ = 40° and ABD = 60°, find
(ii) ∠ BCP.
Marks: 5

Question 21 : The numerator of a fraction is one less than its denominator. If three is added to each of the numerator and denominator, the fraction is increased by 3/28 . Find the fraction.

OR

The difference of squares of two natural numbers is 45. The square of the smaller number is four times the larger number. Find the numbers.           Marks: 5

Question 22 : A hemispherical bowl of internal diameter 36 cm is full of some liquid. This liquid is to be filled in cylindrical bottles of radius 3 cm and height 6 cm. Find the number of bottles needed to empty the bowl.

OR

Water flows out through a circular pipe whose internal radius is 1 cm, at the rate of 80 cm/second into an empty cylindrical tank, the radius of whose base is 40 cm. By how much will the level of water rise in the tank in half an hour?    Marks: 5

Question 23 : A pole 5 m high is fixed on the top of a tower. The angle of elevation of the top of the pole observed from a point A on the ground is 60° and the angle of depression of point A from the top of the tower is 45°. Find the height of the tower. (Take √3 = 1.732)                                                                                 Marks: 5

Question 24 : The salary of Hukam Singh is Rs. 42,000 per month (exclusive of HRA). He donates Rs. 30,000 to Prime Minister’s Relief Fund (100% exemption). He contributes Rs. 6,500 per month towards Provident Fund and Rs. 5,000 quarterly towards LIC premium. He also purchases NSC worth Rs. 10,000. He pays income tax of Rs. 5,100 per month for 11 months. Calculate the income tax he has to pay in the 12th month of the year.Use the following to calculate income tax :
Savings 100% exemption for permissible savings
upto Rs. 1,00,000
Rates of Income tax
lab Income tax
Upto Rs. 1,00,000 No tax
From Rs. 1,00,001 to Rs. 1,50,000 10% of the taxable income exceeding Rs. 1,00,000
From Rs. 1,50,001 to Rs. 2,50,000 Rs. 5,000 + 20% of the amount
exceeding Rs. 1,50,000
Rs. 2,50,001 and above Rs. 25,000 + 30% of the amount
exceeding Rs. 2,50,000
Education Cess 2% of Income tax :                   Marks: 5

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