# SECTION a (Attempt All Questions from This Section)

**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 :

- Exactly one head
- 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 / 10No. 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 :

- The VAT paid by the manufacturing company,
- The VAT paid by the shopkeeper.
- 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

- Prove that ∆ ABD ∆ CBA
- 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 year2009 / 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 :

- The number of shares he buys.
- 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 :

- A red face card.
- Neither an ace nor a king of red colour.
- 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.

- The width of the river.
- 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 :

- The height of the cone
- The volume of the solid
- 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 - 60Frequency / 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 - 80No. of students / 3 / 8 / 12 / 14 / 10 / 6 / 5 / 2

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

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

Submitted by : Mr Kiran Kumar Dash

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