13361 Model Test Paper-7

8/6/2019 13361 Model Test Paper-7

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Guess Paper – 2010Class – X

Subject – Mathematics

SECTION – A

Q1. a. The value of a machine is Rs27000 at the end of 2002 and Rs21870 at the beginning of2005. Themachine depreciates at a constant rate per year of its value at the beginning of the year. Calculate therate of depreciation

[3]

b. Anuj wants to buy a bike whole sale price is Rs 39600 with an extra sales tax of 10%.He requestedthe seller to reduce the price of the bike to such an extent that he has not to pay more than Rs39600 including

sales tax. Find the percentage reduction needed in the sale price of the bike.[4]

Q2. Find the area and perimeter of the shaded region[4]

Q3. a. If 2x + 1 is a factor of (3k + 2)x3 + (k – 1), find the value of k.[3]b. The mean of 7,11,3,11,13,15 is m. The median of 6,7,12,m,1,25,13,17,15,3 is p, find p – m[4]

Q4. The triangle A (1, 2), B (4, 4) and C (3, 7) is first reflected in the line y = 0 onto the triangle A 'B 'C' and thentriangle

A 'B 'C' is reflected in the origin onto triangle A "B "C". Write down the co-ordinates of (i) A 'B'C' (ii) A "B"C". Write down a single transformation that maps ABC onto A" B" C'.[4]

Q5. A box contains cards marked from 4 to 104; a card is drawn at random. If each card is equally likely be drawn,find the probability of getting

(i) an odd number (ii) a multiple of 1 2 or 16 (iii) number divisible by 10 and 15[3]

Q6. The scale of the map is 1: 300000. A plot of land of area 30 km2 is to be represented on the map. Find:(i) The number of kilometers on the ground which is represented by 1 cm on the map.(ii) The area in km2 that can be represented by 1 cm2.(iii) The area on the map that represents the plot of land.[4]

Q7. a Evaluate without using trigonometric tables: °°−°

°+

°

°20eccos70cos2

70sec

20eccos

20cos

70sin

[3] b Solve for x and give your answer correct to 2 decimal places x2 + 5x + 5 = 0 .[4]

c. Find the mean of the following distributionClass interval 18-24 24-30 30-36 36-42 42-48 48-54

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Frequency 6 8 12 8 4 2[4]

SECTION – B

Q8. (a) If a : b = c : d, show that

(a + b):(c + d) = 2 2 2 2a b : c d+ +

[3]

(b) Find the value(s) of k for which the following quadratic equation has equal roots:(3k + 1) x2 + 2 (k + 1) x + k = 0

[3]

(c) Solve the following inequation, and graph the solution set on the number line:2x – 3 < x + 2 ≤ 3x + 5, x ∈ R

[4]

Q9. a P (–2, 1), Q (2, 2), R (6, –2) are vertices of a triangle. Find(i) the gradient of the side QR;(ii) the equation of the line through P perpendicular to QR. [4]

b In the given figure, PQ is a tangent to the circle at A.

BD is a diameter and 0 is the centre. If ∠ADB = 30°

and∠DBC = 60°, find: (i) ∠QAB (ii)∠PAD (iii)∠CDB

[3]

c. Find x and y if x 3x 2 5y 4y 1 12

=

[3]

10. a. Prove the following identity2 4 2 4 4 42sec sec 2 cos ec cos ec cot tanθ − θ − θ + θ = θ − θ

[4]

b. Mr. Kapur's Savings Bank Account with Bank of India shows the following entries in his Pass Book.Calculate the interest he earned during the year 1996 at 6.5% p.a. payable in December.

[6]

Date Particulars Withdrawl Deposit Balance

2/1/1996 By cash 250 250

9/1/1996 By cheque 825 1075

13/3/96 By self 325 75024/7/96 Cash 1237 1987

6/10/1996 By cheque 250 1737

22/12/96 By cheque 958 2695








11. a Mr. C.K.Roy invested Rs 8000 in 8% Rs100 shares selling at Rs80.After a year he sold these shares aRs 75 each and invested the proceeds in Rs 90 shares selling at Rs 100 with a dividend of 12%. Calculate

(i) his income from the first investment; (ii) his income from the second investment.[3]

b In ∆ABC, LM is parallel to BC;AB = 6 cm, AL = 2 cm, and AC = 9 cm. Calculate

(i) the length of CM; (ii) the value of the ratio ar ∆ ALM and Area of trapezium

LBCM [4]

c. A boat takes 1 hour longer to go 36 km up a river than to return. If the river flows at 3km/hr, find the rateat which the boat travels in still water.

[3]

12. a The shadow of a vertical tower on level T ground increases by 10m, when the altitude of the sunchanges from 45° to 30°. find the height of the tower, correct to one place of decimals.

[5]

b A buoy is made in the form of a hemisphere surmounted by a right cone whose circular base coincideswith the plane surface of the hemisphere. The radius of the base of the cone is 3.5 metres and its volume isthree fifth of the hemisphere. Calculate the height of the cone and the surface of the buoy,

[5]

13. a. In the year 1947, M/s Ramakant kakabali and sons, bought Silk worth Rs 978000 at 12% VAT, Jute oRs 275000 at the rate of 10%. They processed the material and received sales turn over of Rs157800 on silk and Rs450000 on Jute. If the silk processings worth Rs 250000, were returned, find the tax liabilityfor the year. [5]

b. Use a graph paper for this question. Use 2 cm = 1 unit on both axes. Plot the points A(– 2, 4),B (2, 1) and

C(– 6,1)(i) Draw the line of symmetry of triangle ABC.(ii) Mark the point D if the line in (I) and the line BC are both lines of

symmetry of the quadrilateral ABCD ; write down the co-ordinates of pointD.

(iii) What kind of quadrilateral is figure ABCD ?(iv) Write down the equations of BC and the line of symmetry named in (i)

[5]

14. a Draw a triangle ABC in which BC = 4 cm, CA = 4.5 cm, and AB = 5.3 cm Without using set squares andprotractor, construct the inscribed circle of triangle ABC, and measure its radius;

[5]

b. 100 pupils in a school have heights as tabulated belowHeight(in cm): 121-130 131-140 141- 150 151 – 160 161 - 170 171 - 180

No. of pupils: 12 16 30 20 14 8Draw the Ogive for the above data and from it determine the median. (Use graph paper) [5]

Paper Submitted By: Mr. Navtej Mahajan








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13361 Model Test Paper-7

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