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Sample Paper – 2013

Class – X

Subject – MATHEMATICS

F.M:- 100TIME: 2 ½ Hrs

SECTION – A (Attempt all questions from this section)

No 1.[4 + 3 + 3]

a) Solve the following inequation and represent the solution set on the number line

b) Tarun buys a scooty for Rs.12,960 including sales tax. If the rate of sales tax is 8%, what is the marked price of the scooty ?

c) Mr. Gupta opened a recurring deposit account in a bank. He deposited Rs. 2,500 per month for two years. At the time of maturity he got Rs. 67,500. Find the rate of interest per annum.

No 2.[3 + 4 + 3]

a) Solve the quadratic equation and give the answer correct to two significant figures:

b) Calculate the ratio in which the line joining A (6 , 5) and B (4 , -3) is divided by the line y = 2.

c) If , find the value of .

No 3.[4 + 3 + 3]

a) Show that (x – 2) is a factor of x3 -6x2 + 11x – 6. Hence find the remaining factors.

b) Find two numbers such that mean proportional between them is 18 and the third proportional is 144.

c) Prove that A(2 , 1), B(0 , 3) and C(-2 , 1) are the vertices of an isosceles right angled triangle.

No 4.[4 + 3 + 3]

a) If A = find AB – 2A – 3B.

b) Garima invests RS 7500 for two years at a certain rate of interest compounded annually. At the end of first year it amount to Rs 8175. Calculate :

i) The rate of interest.

ii) The amount at the end of second year.

c) Two coins are tossed once. Find the probability of getting :

  1. Exactly one head
  2. At least one head

SECTION – B (Answer any FOUR)

No 5.[5 + 5]

a) Marks obtained by 36 students of a class in a unit test are given below :

Marks obtained / 3 / 4 / 6 / 8 / 9 / 10
No. of students / 6 / P / 10 / 7 / q / 3

If the mean of the distribution is 6.5, find the values of p and q.

b) In the adjoining figure, OABC is a square inscribed B C

in a quadrant OPBQ of a circle. If OA = 14 cm, find

the area of the shaded region. Take π = .

O A

No 6.[4 + 3 + 3]

a) A shopkeeper buys an article whose marked price is Rs 4000 from a manufacturing company at a discount of 20%. The rate of sales tax (under VAT) on the article is 8%. If he sells the article to a customer at at discount of 5%, find :

  1. The VAT paid by the manufacturing company,
  2. The VAT paid by the shopkeeper.
  3. The amount paid by the consumer. A

b) Prove that : = 2

c) In the adjoin figure, D is a point on BC such that BAD = ACD.

Given AB = 7 cm and BD = 4 cm. B D C

  1. Prove that ∆ ABD ∆ CBA
  2. Find the area of ∆ABC : area of ∆ ADC.

No 7.[6 + 4]

a) Renu has a saving account in Bank of Maharastra. Her passbook has the following enteries :

Date year
2009 / Particulars / Withdraws / Deposits / Balance
April 1 / B/F / 9400
May 15 / To cheque / 2250 / 7150
June 6 / By cash / 3400 / 10550
August 4 / To self / 5000 / 5550
August 8 / To cheque / 2536 / 3014
October 29 / By transfer / 12020 / 15034
November 3 / To self / 7000 / 8034
December 17 / By clearing / 9362 / 17396

If the bank pays interest at the rate of 4.5% p.a, find the interest due to Renu at the end of the year 2009. Give your answer correct to the nearest rupee.

b) If x = , using properties of proportion, prove that x2 – 4ax + 1 = 0.

No 8.[5 + 5]

a) Mr. Dass has 60 shares of nominal value Rs 100 and he sells them when these are at a premium of 60%. He invests the proceeds in shares of nominal value Rs 50, quoted at 4% discount, paying 18% dividend annually. Calculate :

  1. The number of shares he buys.
  2. His annual dividend from these shares.

b) A car covers a distance of 400 km at a certain speed . had the speed been 12 Km/hr more, the time taken for the journey would have been 1 hour 40 minutes less. Find the original speed of the car.

No 9.[3 + 3 + 4]

a) A card is drawn from a well – shuffled pack of 52 playing cards. Find the probability that the card drawn is :

  1. A red face card.
  2. Neither an ace nor a king of red colour.
  3. Neither a card of diamonds nor a red queen.

b) In the adjoining figure, the radii of two concentric p S

circles are 17 cm and 10 cm. A line PQRS cuts the

larger circle at P and S and the smaller circle at Q and R.

If QR = 12 cm, find the length of PQ.

c) A man standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank is 600. When he moves 30 m away from the bank, he find the angle of elevation to be 300.

  1. The width of the river.
  2. The height of the tree. Give your answer correct to the nearest centimeter.

No 10.[5 + 5]

a) The adjoining figure represents a hemisphere of radius 7 cm

surmounted by a right circular cone of same base radius.

If the slant height of the cone is 25 cm, find :

  1. The height of the cone
  2. The volume of the solid
  3. The surface area of the solid. Take π = .

b) Draw a histogram and estimate the mode for the following frequency distribution :

Classes / 0 – 10 / 10 – 20 / 20 – 30 / 30 – 40 / 40 – 50 / 50 - 60
Frequency / 3 / 8 / 10 / 5 / 4 / 2

No 11.[4 + 6]

a) Using factor theorem, factorise the following polynomial completely : 3x3 – 11x2 + 5x +3

b) Use graph paper for this question.:

Marks obtained by 60 students in an examination are given below :

Marks / 0 -10 / 10 - 20 / 20 – 30 / 30 – 40 / 40 – 50 / 50 – 60 / 60 – 70 / 70 - 80
No. of students / 3 / 8 / 12 / 14 / 10 / 6 / 5 / 2

Draw an ogive for the given distribution. From your ogive, determine :

  1. The median marks.
  2. The number of students who obtained 75 % marks or more marks.

Submitted by : Mr Kiran Kumar Dash

Email id:


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