ramaiah-modelpaper2009

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Sri Sri Academy

SRI SRI ACADEMY IIT RAMAIAH MODEL QUESTION PAPER - 2009

MATHEMATICS

Time : TWO HOURS MAX Marks : 60

(8.30am 10.30am)

NOTE:-1. Attempt all questions2. Rough work must be enclosed with answer book3. While answering, refer to a question by its serial number as well as section heading

(eg. Q2/Sec.A)4. There is no negative marking5. Answer each of Section A,B,C at one place6. Elegant solutions will be rewarded7. Use of calculators, slide rule, graph paper and logarithmic, trigonometric and statistical

tables is not permitted.

Note: All answers to questions in section A , section B and section C must be supportedby mathematical arguments. In each of these sections order of the questions must bemaintained.

SECTION A 6 x 2 = 12 M

1. The equation of line midway between the lines 2x + y + 2009 = 0 and y = -2 x 5 andparallel to them is.a) 4 b) 3 c) 2 d) 1 e) 0

2. The coefficient of 2009 x in2( ) ( )1 .......

1 2a bx a bx is equal to

a)40340734034072

b)40340724034073

c)40430724043073

d)40430734043072

e) None

3. A circle touches the y - axis at A (0,9) and cuts the x- axis at B (3,0). Find the other pointon the x- axis through which the circle passes.a) (0, 27) b) (9, 0) c) (0, 9) d) (27, 0) e) (9, 27)

4. Let , be the roots of x 2 x+ p = 0 and , be the roots of x 2 4x + q = 0. If , , , are in G.P then integral values of P and q respectively area) 2, -32 b) 2, 3 c) 6, 3 d) 6 , -32 e) 2,3

5. 50 50 50 ........ (Where there are hundred 50s) is how many times 100 100 100 (Where there are fifty 100s)?a) 25 25 25 .(where there are fifty 25s) b) 4 4 4(where there are fifty 4s)c) 2 2 2 (Where there are fifty 2s) d) 1 time e) none of these

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Sri Sri Academy6. D,G are points on the side AB of ABC , E and F are points on the sides AC and BC

respectively such that DE || BC , EF || AB and FG || CA . Then D,E,F,G are theconsecutive vertices of a quadrilateral .

a) Always b) only ifAD AB

> c) only if AD AB

=

d) Only if AD

AB< e) none of these

SECTION B 6 x 2 = 12 M

This section has Six Questions. In each question a blank is left. Fill in the blank.

1. Highest power of 3 contained in 2009! Is --------------

2. In the binomial expansion of (a-b) n, n 5 the sum of the 5 th and 6 th terms is zero. Then

a/b is equal to -------------

3. The number of points P strictly lying inside an equilateral triangle ABC such that thesum of the perpendicular distances from P to the three sides of the triangle is minimumis________

4. In ABC, AB =15, BC =18, CA =25, A semicircle is inscribed in triangle ABC such thatdiameter of semi circle lies on AC. If O is the centre of circle the length ofAO_________

5. The quadratic equation ax 2+bx+a=0 has a positive coincident root . Then =_________

6. 2009th term in the series 2009, 2008, 2007, 2006 is -------------

SECTION C 6 x 2 = 12M

1. The sum of 2 2 2 2 2 21 1 1 1 1 1

1 1 ...... 11 2 2 3 (2008) (2009)

2. Determine the radius of the circle inscribed in a rhombus whose diagonals measure 10

units and 24 units.3. The sum of three numbers in G.P is 14 . If the first two terms are each increased by 1

and third term decreased by 1 the resulting numbers are in A.P. Find the numbers?

4. The measure of the vertex angle of isosceles triangle ABC is and sides of triangle aresin , ,Sin Sin . Compute the area of ABC.

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Sri Sri Academy5. The people living on street S of Y-City all decide to buy new house numbers so they

line up at the only Hardware store in order of their address: 1, 2, 3 . If the store has100 of each digit, what is the first address that wont be able to buy the digits for itshouse number?

6. If 3yz+2y+z+1=0 and 3zx +2z+x+1=0, then prove that 3xy +2x+y+1=0.

SECTION D 6 x 4 = 24 M

1. If (1 + 1/n) n < 3 then find the greatest number of 2009 2009 and 2010 2008

2. If a triangle and a convex quadrilateral are drawn on the same base and no part of the

quadrilateral is outside the triangle, show that the perimeter of the triangle is greaterthan the perimeter of the quadrilateral

3. Lines l and m intersect in O. Explain how you will construct a triangle OPQ such that Pl, Q m, OP and OQ are equal in length and PQ is of given length a.

4. State and prove the test of divisibility of a positive integer a by 11.

5. Find the value of1 1 1

1 ............1 2 1 2 3 1 2 3 ................2009

6. f and g are two real variable real valued functions defined by

3 7, 2

2, 0, 1, 2 2.

2 3, 01, 2

x if x x if x

f x g x x if x Find gof x if x

x if x

Tomorrow IITians Todayschoice Sri Sri Academy

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Sri Sri Academy


PHYSICS

Time : ONO HOUR MAX Marks : 60

Instructions:(1) Answer must be written either in English or the medium of instruction of the candidate

in high school.(2) Answer all the questions in the booklets provided for the purpose.(3) There will be no negative marking.(4) The relevant working or the argument in arriving at an answer has to be included in

your answer.(5) Use of calculators or graph papers is not permitted.(6) Questions in Part A carry 6 marks each and questions in part B carry 3 marks each.

PART A 6 x 6 = 36 M

1. A particle p is located at A. Another particle Q is located at B 200 m south of A. P starts

moving at 2m/s towards east at some moment and simultaneously Q starts moving at4m/s. (i) If Q moved first towards A and on reaching A quickly changed direction andmoved towards east, find the time, it takes to catch up with p. (ii) If instead Q aimed ata point C east of A at which it arrives at the same time as P, find the elapsed time (iii)what should be the minimum speed of Q to catch up with P before it moves 50m fromits initial position ? (Assume Q catches up by aiming at the position P would reach atthe same time as it does).

2. The devices 1 D and 2 D shown below are called diodes and have an interestingproperty. When current flows in the direction of the arrow the resistance is low and is

called forward bias resistance. If the current were to flow in the opposite direction theresistance is high and it is called reverse bias resistance. for 1 D forward bias resistanceis 20 Ohm and reverse bias resistance is 600 Ohm. For 2 D forward bias resistance is 30ohm and reverse bias resistance is 200 Ohm. Find the equivalent resistance between Aand B if (i) A is at a higher potential (ii) B is at a higher potential

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3. Consider the light ray as shown in the fig. Find the angle for which the light ray justgrazes at the vertical surface as shown in fig. after refraction.

4. Two liquids of masses 600g and 500g and densities 0.6 gcm 3 and 1.5 gcm 3 arecombined to form a homogenous mixture. A solid block of mass 420g just floats in thismixture. Find the density of the block material. If the equal volumes of the two liquids

were mixed instead, would this block float in that mixture? If it floats find the fractionof the block that is visible above the mixture.

5. In the given circuit, if a current of 12 m A exists in 5 k resistor. Find the currents inthe other three resistors. What is the potential difference between the points A & B.

6. If the measured potential difference between A and B is 5.4V, find the rate of heatproduction in the ring. Also find the rate of heat production in sections ACB and ADB.

PART B 8 x 3 = 24 M

7. A metal rod R tightly fits in to a ring as shown.Will there be any distortion in the ring on heating or

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Sri Sri Academycooling it ?Discuss possible cases.

8. A train of length 300m passes through two tunnels with a gap of 400m between them.The tunnels are of length 800m and 600m respectively. From the moment it just emergesfrom the first tunnel to the moment it just disappears in to the second tunnel time

elapsed is 60s. Find the time elapsed between the moments the train just enters the firsttunnel to the moment it just leaves the second tunnel.

9. A hollow spherical body of inner and outer radii 6cm and 8 cm respectively floats halfsubmerged in water. Find the density of the material of the sphere.

10. Two wires made of same material have their thickness in the ratio 1:2 and have equallengths. When connected in parallel, their equivalent resistance is R. Find theequivalent resistance when they are connected in series.

11. The refractive index of water is 4/3, for glass it is 3/2 .A ray of light travelling in wateris incident at an angle of 30 0 on a water glass interface. Calculate the angle of refractionin glass.

12. Find the ratio /i f E E where i f E and E are the energies of a neutron before and afterinteraction with the nuclei of the moderator in a nuclear reactor.

13. A bucket full of water is revolved on a circular path in vertical circle by attaching at theend of the rope 0.8 m long. What should be minimum speed at top so that the waterdoes not fall down?

14. What is the time period of a seconds pendulum on a planet whose mass is half of themass of the earth and radius is double that of the radius of the earth.

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Sri Sri Academy


CHEMISTRY

Time : ONE HOUR MAX Marks : 60

Instructions:(1) Answer must be written either in English or the medium of instruction of the candidate

in high school.(2) There will be no negative marking.(3) Use of calculators or graph papers is not permitted(4) There are TWENTY questions. Answer all the questions.

I. Explain the following 5 x 3 = 15 M

1. Lithium is the strongest reducing agent.

2. Potassium hydroxide is stronger base than barium hydroxide .

3. Nitrogen in Ammonia is SP 3 hybridization but structure is pyramidal.

4. Aqueous solution of ammonium acetate is almost neutral.

5. Both coke and flux are used in smelting process of metallurgy

II. Differentiate the following. 5 x 3 = 15 M

1. 1- propanol and 2- propanol.

2. Acid strength and concentration.

3. Hard water and Heavy water.

4. Primary standard substance and Secondary standard substance.

5. Lattice energy and Hydration energy.

III. Answer the following 10 x 3 = 30 M

1. For the reaction(i) A B ; c K = 2(ii) B C ; c K = 4(iii) C D ; c K = 6For the reaction A D what is the c K ?

2. It is dangerous to add water to a concentrated acid such as sulphuric acid in a dilutionprocess. Why ?

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3. Calculate the molarity of the solution 30 grams of salt of molecular weight 30 isdissolved in 250 grams of water .

4. Carbon & Silicon belongs to IV- A Group of the periodic table and have the samevalance electron configuration ns 2 np 2. Why does silicon dioxide (SiO 2) have much

higher melting point than CO 2 .5. Every substance exists in three different physical states i,e gas , liquid and solid. What

are the factors that decide the physical state of the substance under given condition?

6. Write the Lewis dot structure of Co 2-3

7. A fuel gas contains carbon and hydrogen only. Burning a small sample of it in oxygengives 3.38gm carbon dioxide, 0.69gm of water and no other products. A volume of 10 lt(measured at STP) of this gas is found to weigh 11.6gm.

a) Calculate (i) empirical formula (ii) molecular mass of the gas(iii) molecular formula

b) Write one single step preparation of the gasc) Does it react with bromine? If so what colour change do you expect?d) What do you expect the calorific value of the gas with reference to marsh gas?

8. Identify (A) &(B) based on following reactions :

(i) NaOH HCl A White B gas fumes (ii) 2 2 A N O H O .

9. C2H 6O (A) an organic compound on dehydration with concentrated H 2SO4 gives olefin(B), addition of Hydro chloric acid to B, followed by heating gives a polymer.Compound A is heated with vinegar gives a fruity smell , compound of (c).a) Identify the functional group in compound Ab) Why the compound B undergoes addition reaction?c) Draw the structures of polymer ?d) Write the equation of A with vinegar?e) What is the functional Isomer of A.

10. Calculate the volume of 0.25 M NaOH required for the neutralization of 150 ml of 0.25

M H 2SO4 .

Sri Sri AcademyNo. 1

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Sri Sri Academy

For IIT FoundationFor 8 th , 9 th & 10 th classes in

A.P

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ramaiah-modelpaper2009

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