# Sample Paper for AIEEE Exam

**AIEEE**(All India Engineering Entrance Exam) , a National level exam conducted by Central Board of Secondary Education(CBSE) in India.It is introduced for admission to various under-graduate as well as architecture courses in various institutes who accept AIEEE score, along with 5 IIITs and 30 NITs as well as many other prestigious institutes.Candidates get two ranks-1)State rank 2)All India Rank.

To get more information on AIEEE exam regarding the pattern of exam,eligibility criteria etc visit the link.Want to give a mock test then take a online test on AIEEE at itest which will help you to improve yourself.

Sample Paper For AIEEE Exam :-

We have got you the questions (sample paper for AIEEE exam) to help you prepare for the Exam

**AIEEE CHEMISTRY PAPER:-**

1. The standard enthalpy of formation of NH3 is –46.0 kJ mol–1. If the enthalpy of formation of H2 from its atoms is –436 kJ mol–1 and that of N2 is –712 kJ mol–1, the average bond enthalpy of N–H bond in NH3 is

(1) –964 kJ mol–1 (2) +352 kJ mol–1 (3) + 1056 kJ mol–1 (4) –1102 kJ mol–1

ANS:- (2)

2. The time for half life period of a certain reaction A ® products is 1 hour. When the initial concentration of the reactant ‘A’, is 2.0 mol L–1, how much time does it take for its concentration to come from 0.50 to 0.25 mol L–1 if it is a zero order reaction ?

(1) 4 h (2) 0.5 h ( 3) 0.25 h (4) 1 h

ANS:-. (3)

3. A solution containing 2.675 g of CoCl3. 6 NH3 (molar mass = 267.5 g mol–1) is passed through a cation exchanger. The chloride ions obtained in solution were treated with excess of AgNO3 to give 4.78 g of AgCl (molar mass = 143.5 g mol–1). The formula of the complex is (At. Mass of Ag = 108 u)

(1) [Co(NH3)6]Cl3 (2) [CoCl2(NH3)4]Cl (3) [CoCl3(NH3)3] (4) [CoCl(NH3)5]Cl2

ANS:- (1)

4. Consider the reaction :

Cl2(aq) + H2S(aq) ® S(s) + 2H+(aq) + 2Cl– (aq)

The rate equation for this reaction is rate = k [Cl2] [H2S] Which of these mechanisms is/are consistent with this rate equation ?

(A) Cl2 + H2 ® H+ + Cl– + Cl+ + HS– (slow) Cl+ + HS– ® H+ + Cl– + S (fast)

(B) H2S Û H+ + HS– (fast equilibrium) Cl2 + HS– ® 2Cl– + H+ + S (slow)

(1) B only (2) Both A and B (3) Neither A nor B (4) A only

ANS :- (4)

5. If 10–4 dm3 of water is introduced into a 1.0 dm3 flask to 300 K, how many moles of water are in the vapour phase when equilibrium is established ?

(Given : Vapour pressure of H2O at 300 K is 3170 Pa ; R = 8.314 J K–1 mol–1)

(1) 5.56 x 10–3 mol (2) 1.53 x 10–2 mol (3) 4.46 x 10–2 mol (4) 1.27 x 10–3 mol

ANS:-. (4)

6. One mole of a symmetrical alkene on ozonolysis gives two moles of an aldehyde having a molecular mass of 44 u. The alkene is

(1) propene (2) 1–butene (3) 2–butene (4) ethene

ANS:- (3)

7. If sodium sulphate is considered to be completely dissociated into cations and anions in aqueous solution, the change in freezing point of water (DTf), when 0.01 mol of sodium sulphate is dissolved in 1 kg of water, is (Kf = 1.86 K kg mol–1)

(1) 0.0372 K (2) 0.0558 K (3) 0.0744 K (4) 0.0186 K

ANS:- (2)

8. From amongst the following alcohols the one that would react fastest with conc. HCl and anhydrous ZnCl2, is

(1) 2–Butanol (2) 2–Methylpropan–2–ol (3) 2–Methylpropanol (4) 1–Butanol

ANS:-(2)

9. 29.5 mg of an organic compound containing nitrogen was digested according to Kjeldahl’s method and the evolved ammonia was absorbed in 20 mL of 0.1 M HCl solution. The excess of the acid required 15 mL of 0.1 M NaOH solution for complete neutralization. The percentage of nitrogen in the compound is

(1) 59.0 (2) 47.4 (3) 23.7 (4) 29.5

ANS:-. (3)

10. The energy required to break one mole of Cl–Cl bonds in Cl2 is 242 kJ mol–1. The longest wavelength of light capable of breaking a single Cl – Cl bond is (c = 3 x 108 ms–1 and NA = 6.02 x 1023 mol–1)

(1) 594 nm (2) 640 nm (3) 700 nm (4) 494 nm

ANS:- (4)

11. Ionisation energy of He+ is 19.6 x 10–18 J atom–1. The energy of the first stationary state (n =1) of Li2+ is

(1) 4.41 x 10–16 J atom–1 (2) –4.41 x 10–17 J atom–1

(3) –2.2 x 10–15 J atom–1 (4) 8.82 x 10–17 J atom–1

ANS:- (2)

12. On mixing, heptane and octane form an ideal solution. At 373 K, the vapour pressures of the two liquid components (heptane and octane) are 105 kPa and 45 kPa respectively. Vapour pressure of the solution obtained by mixing 25.0g of heptane and 35 g of octane will be (molar mass of heptane = 100 g mol–1 an dof octane = 114 g mol–1).

(1) 72.0 kPa (2) 36.1 kPa (3) 96.2 kPa (4) 144.5 kPa

ANS:- (1)

13. Three reactions involving 2 4 H PO- are given below :

(i) H3PO4 + H2O ® H3O+ + 2 4 H PO- (ii) 24H PO- + H2O ® 24 HPO – + H3O+

(iii) 22 H PO- +OH- ®H PO + O – In which of the above does 24H PO- act as an acid ?

(1) (ii) only (2) (i) and (ii) (3) (iii) only (4) (i) only

ANS:- (1)

14. In aqueous solution the ionization constants for carbonic acid are K1 = 4.2 x 10–7 and K2 = 4.8 x 10–11 Select the correct statement for a saturated 0.034 M solution of the carbonic acid.

(1) The concentration of 23 CO – is 0.034 M.

(2) The concentration of 23 CO – is greater than that of 3 HCO- .

(3) The concentration of H+ and 3 HCO- are approximately equal.

(4) The concentration of H+ is double that of 23 CO – .

ANS:- (3)

15. The edge length of a face centered cubic cell of an ionic substance is 508 pm. If the radius of the cation is 110 pm, the radius of the anion is

(1) 288 pm (2) 398 pm (3) 618 pm (4) 144 pm

Ans:- (4)

16. The correct order of increasing basicity of the given conjugate bases (R = CH3) is

(1) 2 RCOO < HC = C < R < NH (2) 2 R < HC º C < RCOO < NH

(3) 2 RCOO < NH < HC º C < R (4) 2 RCOO < HC º C < NH < R

ANS :- . (4)

17. The correct sequence which shows decreasing order of the ionic radii of the elements is

(1) Al3+ > Mg2+ > Na+ > F– > O2– (2) Na+ > Mg2+ > Al3+ > O2– > F–

(3) Na+ > F– > Mg2+ > O2– > Al3+ (4) O2– > F– > Na+ > Mg2+ > Al3+

ANS . (4)

18. Solubility product of silver bromide is 5.0 x 10–13. The quantity of potassium bromide (molar mass taken as 120 g of mol–1) to be added to 1 litre of 0.05 M solution of silver nitrate to start the precipitation of AgBr is

(1) 1.2 x 10–10 g (2) 1.2 x 10–9 g (3) 6.2 x 10–5 g (4) 5.0 x 10–8 g

ANS:- (2)

19. At 25°C, the solubility product of Mg(OH)2 is 1.0 x 10–11. At which pH, will Mg2+ ions start precipitating in the form of Mg(OH)2 from a solution of 0.001 M Mg2+ ions ?

(1) 9 (2) 10 (3) 11 (4) 8

ANS:-. (2)

20. Percentage of free space in cubic close packed structure and in body centred packed structure are respectively

(1) 30% and 26% (2) 26% and 32% (3) 32% and 48% (4) 48% and 26%

ANS:-. (2)

21. Out of the following, the alkene that exhibits optical isomerism is

(1) 3–methyl–2–pentene (2) 4–methyl–1–pentene

(3) 3–methyl–1–pentene (4) 2–methyl–2–pentene

ANS:-. (3)

22. Biuret test is not given by

(1) carbohydrates (2) polypeptides (3) urea (4) proteins

ANS:-. (1)

23. The correct order of 0 M2 /M E + values with negative sign for the four successive elements Cr, Mn, Fe and Co is

(1) Mn > Cr > Fe > Co (2) Cr > Fe > Mn > Co (3) Fe > Mn > Cr > Co (4) Cr > Mn > Fe > Co

ANS:- (1)

24. The polymer containing strong intermolecular forces e.g. hydrogen bonding, is

(1) teflon (2) nylon 6,6 (3) polystyrene (4) natural rubber

ANS:-. (2)

25. For a particular reversible reaction at temperature T, DH and DS were found to be both +ve. If Te is the temperature at equilibrium, the reaction would be spontaneous when

(1) Te > T (2) T > Te (3) Te is 5 times T (4) T = Te

ANS:-. (2)

26. Lithium forms body centred cubic structure. The length of the side of its unit cell is 351 pm. Atomic radius of the lithium will be :

(1) 75 pm (2) 300 pm (3) 240 pm (4) 152 pm

ANS:- 4

27.. The molecule having smallest bond angle is :

(1) NCl3 (2) AsCl3 (3) SbCl3 (4) PCl3

ANS:-. 3

28. Which of the following compounds can be detected by Molisch’s test ?

(1) Nitro compounds (2) Sugars (3) Amines (4) Primary alcohols

ANS:-. 2

29. Which one of the following statements is correct ?

(1) All amino acids except lysine are optically active

(2) All amino acids are optically active

(3) All amino acids except glycine are optically active

(4) All amino acids except glutamic acid are optically active

ANS:- 3

30. Aspirin is known as :

(1) Acetyl salicylic acid (2) Phenyl salicylate

(3) Acetyl salicylate (4) Methyl salicylic acid

ANS:-(1)

** Questions on physics in” sample paper for AIEEE exam”**

** PHYSICS QUESTIONS:**

1. Let C be the capacitance of a capacitor discharging through a resistor R. Suppose t1 is the time taken for the energy stored in the capacitor to reduce to half its initial value and t2 is the time taken for the charge to reduce to one-fourth its initial value. Then the ratio t1/t2 will be

(1) 1 (2)1/2 (3)1/4 (4) 2

ANS:-. 3

** ****Directions**: Questions number 33 – 34 contain Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.

2. **Statement-1 **: Two particles moving in the same direction do not lose all their energy in a completely inelastic collision.

**Statement-2 **: Principle of conservation of momentum holds true for all kinds of collisions.

(1) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1.

(2) Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1

(3) Statement-1 is false, Statement-2 is true.

(4) Statement-1 is true, Statement-2 is false.

ANS:-1

3. **Statement-1 **: When ultraviolet light is incident on a photocell, its stopping potential is V0 and the maximum kinetic energy of the photo electrons is Kmax. When the ultraviolet light is replaced by Xrays, both V0 and Kmax increase.

** ****Statement-2 **: Photoelectrons are emitted with speeds ranging from zero to a maximum value

because of the range of frequencies present in the incident light.

(1) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1.

(2) Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1.

(3) Statement-1 is false, Statement-2 is true.

(4) Statement-1 is true, Statement-2 is false.

ANS:-. 4

4. The binding energy per nucleon for the parent nucleus is E1 and that for the daughter nuclei is E2. Then

(1) E2 = 2E1 (2) E1 > E2 (3) E2 > E1 (4) E1 = 2E2

ANS:- 3

5. A diatomic ideal gas is used in a Car engine as the working substance. If during the adiabatic expansion part of the cycle, volume of the gas increases from V to 32V the efficiency of the engine is (1) 0.5 (2) 0.75 (3) 0.99 (4) 0.25

ANS:-. 2

6. If a source of power 4 kW produces 1020 photons/second, the radiation belong to a part of the spectrum called

(1) X–rays (2) ultraviolet rays (3) microwaves (4) g–rays

ANS:-. (1)

** **7. The respective number of significant figures for the numbers 23.023, 0.0003 and 2.1 x 10–3 are

(1) 5, 1, 2 (2) 5, 1, 5 (3) 5, 5, 2 (4) 4, 4, 2

ANS:- (1)

** **8. In a series LCR circuit R = 200 W and the voltage and the frequency of the main supply is 220 V and 50 Hz respectively. On taking out the capacitance from the circuit the current lags behind the voltage by 30°. On taking out the inductor from the circuit the current leads the voltage by 30o. The power dissipated in the LCR circuit is

(1) 305 W (2) 210 W (3) Zero W (4) 242 W

ANS:- 4

9. Two identical charged spheres are suspended by strings of equal lengths. The strings make anangle of 30° with each other. When suspended in a liquid of density 0.8 g cm–3, the angle remains the same. If density of the material of the sphere is 16 g cm–3, the dielectric constant of the liquid is

(1) 4 (2) 3 (3) 2 (4) 1

ANS:- 3

** **10. As the beam enters the medium, it will

(1) diverge

(2) converge

(3) diverge near the axis and converge near the periphery

(4) travel as a cylindrical beam

ANS. (2)

11. The initial shape of the wave front of the beam is

(1) convex

(2) concave

(3) convex near the axis and concave near the periphery

(4) planar

ANS:- (4)

12.The speed of light in the medium is

(1) minimum on the axis of the beam (2) the same everywhere in the beam

(3) directly proportional to the intensity (4) maximum on the axis of the beam

ANS:-1

13. Hydrogen atom is excited from ground state to another state with principal quantum number equal to 4. Then the number of spectral lines in the emission spectra will be

(1) 2 (2) 3 (3) 5 (4) 6

ANS:-4

14. A coil is suspended in a uniform magnetic field, with the plane of the coil parallel to the magnetic lines of force. When a current is passed through the coil it starts oscillating; it is very difficult to stop. But if an aluminium plate is placed near to the coil, it stops. This is due to :

1) development of air current when the plate is placed.

(2) induction of electrical charge on the plate

(3) shielding of magnetic lines of force as aluminium is a paramagnetic material.

(4) electromagnetic induction in the aluminium plate giving rise to electromagnetic damping.

ANS:- 4

15. Two electric bulbs marked 25W – 220V and 100W – 220V are connected in series to a 440Vsupply. Which of the bulbs will fuse?

(1) both (2) 100 W (3) 25 W (4) neither

ANS:- 3

16. Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are 3% each, then error in the value of resistance of the wire is

(1) 6% (2) zero (3) 1% (4) 3%

ANS:-. 1

17. A boy can throw a stone up to a maximum height of 10 m. The maximum horizontal distance that the boy can throw the same stone up to will be

(1) 202 m (2) 10 m (3) 102 m (4) 20 m

ANS:-4

18. A Carnot engine, whose efficiency is 40%, takes in heat from a source maintained at a temperature of 500 K It is desired to have an engine of efficiency 60%. Then, the intake temperature for the same exhaust (sink) temperature must be

(1) efficiency of Carnot engine cannot be made larger than 50%

(2) 1200 K (3) 750 K (4) 600 K

ANS:-. 3

19. This question has statement 1 and statement 2. Of the four choices given after the statements, choose the one that best describes the two statements. If two springs S1 and S2 of force constants k1 and k2, respectively, are stretched by the same force, it is found that more work is done on spring S1 than on spring S2.

**Statement 1 : **If stretched by the same amount, work done on S1, will be more than that on S2

**Statement 2 : **k1 < k2

(1) Statement 1 is false, Statement 2 is true

(2) Statement 1 is true, Statement 2 is false

(3) Statement 1 is true, Statement 2 is the correct explanation for statement 1

(4) Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for statement 1.

ANS:-1

20. Two cars of masses m1 and m2 are moving in circles of radii r1 and r2, respectively. Their speeds are such that they make complete circles in the same time t. The ratio of their centripetal acceleration is

(1) m1r1 : m2r2 (2) m1 : m2 (3) r1 : r2 (4) 1 : 1

ANS:- 3

21. An object 2.4 m in front of a lens forms a sharp image on a film 12 cm behind the lens. A glass plate 1cm thick, of refractive index 1.50 is interposed between lens and film with its plane faces parallel to film. At what distance (from lens) should object be shifted to be in sharp focus on film?

(1) 7.2 m (2) 2.4 m (3) 3.2 m (4) 5.6 m

ANS:-. 4

22. A spectrometer gives the following reading when used to measure the angle of a prism. Main scale reading: 58.5 degree Vernier scale reading : 09 divisions Given that 1 division on main scale corresponds to 0.5 degree. Total divisions on the vernier scale is 30 and match with 29 divisions of the main scale. The angle of the prism from the above data

(1) 58.59o (2) 58.77o (3) 58.65o (4) 59o

ANS:-. 3

**23. **A Carnot engine operating between temperatures *T*1 and *T*2 has efficiency1/6. When *T*2 is lowered by 62 K, its efficiency increases to1/3. Then *T*1 and *T*2 are,respectively:

** ****(1) **310 K and 248 K **(2) **372 K and 310 K

**(3) **372 K and 330 K **(4) **330 K and 268 K

**Ans: (2)**

** ****24. **A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diamater of the disc to reach its other end. During the journey of the insect, the angular speed of the the disc:

** ****1) **first increases and then decreases

**(2) **remains unchanged

**(3) **continuously decreases

**(4) **continuously increases

** ****Ans: (1)**

** ****25. **A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diamater of the disc to reach its other end. During the journey of the insect, the angular speed of the the disc:

**(1) **first increases and then decreases

**(2) **remains unchanged

**(3) **continuously decreases

**(4) **continuously increases

** ****Ans: (1)**

**28. **The half life oa radioactive substance is 20 minutes. The approximate time interval (*t*2 –*t*1) between the time *t*2 when 2/3 of it has decayed and time *t*1 when1/3 of it had decayed is

**(1) **28 min **(2) **7 min

**(3) **14 min **(4) **20 min

**Ans: (4)**

** ****29. ***Direction:*

The question has paragraph fllowed by two statements,

*Statement-1 **and **Statement-2**. Of the given four **alternatives after the statements, choose the one that **describes the statements. *A thin air film is formed by putting the convex surface of a plen-convex lens over a plane glass plate. With monochromatic light, this film gives an interferencepattern due to light reflected from the top (convex) surface and the bottom (glass plate) surface of the film.

**Statement – 1: **When light reflects from the air-lgass plate interface, the reflected wave surfers a phase change of .

**Statement – 2: **The centre of the interference pattern is dark.

**(1) **Statement – 1 is flase, Statement – 2 is true.

**(2) **Statement – 1 is true, Statement – 2 is flase.

**(3) **Statement – 1 is true, Statement – 2 is true and Statement – 2 is the correct explanation of Statement – 1

**(4) **Statement – 1 is true, Statement – 2 is true and Statement – 2 is **not **the correct explantion of Statement – 1.

** ****Ans: (3)**

** ****30. **This equation has Statement – 1 and Statement – 2. Of the four choices given afterthe statements, choose the one that best decrribes the two statements.

**Statement – 1: **Sky wave signals are used for long distance radio communication. These signlas are in gneeral, less table than ground wave signals.

**Statement – 2: **The state of ionosphere varies from hour to hour, day to day and season to season.

**(1) **Statement – 1 is flase, Statement – 2 is true.

**(2) **Statement – 1 is true, Statement – 2 is flase.

**(3) **Statement – 1 is true, Statement – 2 is true and Statement – 2 is the correct explanation of Statement – 1

**(4) **Statement – 1 is true, Statement – 2 is true and Statement – 2 is **not **the correct explantion ofStatement – 1.

** ****Ans: (3)**

Questions on Maths in “sample Paper for AIEEE Exam”

** ****MATHS SAMPLE**

** **1. The equation of the tangent to the curve y = x + 4/x^2 that is parallel to the x-axis, is

(1) y = 1 (2) y = 2 ( 3) y = 3 (4) y = 0

ANS:-. **3**

2. Solution of the differential equation cos x dy = y(sin x – y) dx, 0 < x <2/p is

(1) y sec x = tan x + c (2) y tan x = sec x + c (3) tan x = (sec x + c)y (4) sec x = (tan x + c)y

ANS:- **4**

3. If two tangents drawn from a point P to the parabola y2 = 4x are at right angles, then the locus of P is

(1) 2x + 1 = 0 (2) x = –1 (3) 2x – 1 = 0 (4) x = 1

ANS:-. **2**

4. The number of 3 ´ 3 non-singular matrices, with four entries as 1 and all other entries as 0, is

(1) 5 (2) 6 (3) at least 7 (4) less than 4

ANS:-. **3**

**Directions: **Questions Number **72 to 76 **are Assertion – Reason type questions. Each of these questions contains two statements.

**Statement-1: (Assertion) **and **Statement-2: (Reason)**

Each of these questions also has four alternative choices, only one of which is the correct answer.You have to select the correct choice.

5.Four numbers are chosen at random (without replacement) from the set {1, 2, 3, ….., 20}.

** ****Statement-1: **The probability that the chosen numbers when arranged in some order will form an AP is 1/85

.**Statement-2: **If the four chosen numbers from an AP, then the set of all possible values of common difference is {±1, ±2, ±3, ±4, ±5}.

(1) Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1

(2) Statement-1 is true, Statement-2 is false

(3) Statement-1 is false, Statement-2 is true

(4) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1

ANS:-. **2**

.6. **Statement-1: **The point A(3, 1, 6) is the mirror image of the point B(1, 3, 4) in the plane x – y + z = 5.

**Statement-2: **The plane x – y + z = 5 bisects the line segment joining A(3, 1, 6) and B(1, 3, 4).

(1) Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1

(2) Statement-1 is true, Statement-2 is false

(3) Statement-1 is false, Statement-2 is true

(4) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1

ANS:- **1**

7. Let A be a 2 ´ 2 matrix with non-zero entries and let A2 = I, where I is 2 ´ 2 identity matrix. Define Tr(A) = sum of diagonal elements of A and |A| = determinant of matrix A.

**Statement-1: **Tr(A) = 0

**Statement-2: **|A| = 1

(1) Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1

(2) Statement-1 is true, Statement-2 is false

(3) Statement-1 is false, Statement-2 is true

(4) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1

ANS:- **2**

8. The number of complex numbers z such that |z – 1| = |z + 1| = |z – i| equals

(1) 1 (2) 2 (3) ¥ (4) 0

ANS:- **1**

9. A line AB in three-dimensional space makes angles 45° and 120° with the positive x-axis and the positive y-axis respectively. If AB makes an acute angle q with the positive z-axis, then q equals

(1) 45° (2) 60° (3) 75° (4) 30°

ANS:-. **2**

10. A person is to count 4500 currency notes. Let an denote the number of notes he counts in the nth minute. If a1 = a2 = …… = a10 = 150 and a10, a11, …… are in A.P. with common difference –2, then the time taken by him to count all notes is

(1) 34 minutes (2) 125 minutes (3) 135 minutes (4) 24 minutes

ANS:- **1**

11.There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is

(1) 36 (2) 66 (3) 108 (4) 3

ANS:-. **3**

12. Consider the system of linear equations:

x1 + 2×2 + x3 = 3

2×1 + 3×2 + x3 = 3

3×1 + 5×2 + 2×3 = 1

The system has

(1) exactly 3 solutions (2) a unique solution

(3) no solution (4) infinite number of solutions

ANS:-. **3**

13. An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colour is

(1)2/7

(2)1/21

(3) 2/23

(4) 1/3

ANS:- **1**

14. For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is

(1)11/2

(2) 6

(3)13/2

(4)5/2

ANS:- **1**

15. The circle x2 + y2 = 4x + 8y + 5 intersects the line 3x – 4y = m at two distinct points if

(1) –35 < m < 15 (2) 15 < m < 65 (3) 35 < m < 85 (4) –85 < m < –35_

ANS:-**1**

16.The equation esin x – e–sin x – 4 = 0 has

(1) infinite number of real roots (2) no real roots

(3) exactly one real root (4) exactly four real roots

ANS:-. 2

17. A spherical balloon is filled with 4500p cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of 72p cubic meters per minute, then the rate (in meters per minute) at which the radius of the balloon decreases 49 minutes after the leakage began is

(1)9/7

(2)7/9

(3)2/9

(4)9/2

ANS:- 3

18. The negation of the statement “If I become a teacher, then I will open a school” is

(1) I will become a teacher and I will not open a school

(2) Either I will not become a teacher or I will not open a school

(3) Neither I will become a teacher nor I will open a school

(4) I will not become a teacher or I will open a school

ANS:- 1

19. If 100 times the 100th term of an AP with non zero common difference equals the 50 times its 50th term, then the 150th term of this AP is

(1) –150 (2) 150 times its 50th term

(3) 150 (4) zero

ANS:-. 4

20. If the line 2x + y = k passes through the point which divides the line segment joining the points (1, 1) and (2, 4) in the ratio 3 : 2, then k equals

(1)29/5

(2) 5

(3) 6

(4)11/5

ANS:-. 3

**21. **Let R be the set of real numbers

**Statement -1 ***A * {(*x*, *y*) *R * *R *: *y * *x *is an integer} is an equivalence relation on R.

**Statement -2 ***B * {(*x*, *y*) *R * *R *: *x **y *for some rational number } is an equivalence relation on *R.*

**(1) **Statement -1 is false, Statement -2 is true

**(2) **Statement -1 is true, Statement -2 is true; Statement -2 is a correct explanation for statement-1

**(3) **Statement-1 is true, Statement -2 is true, Statement- 2 is not correct explanation for Statement-1

**(4) **Statement -1 is true, Statement-2 is false

**Ans: [4]**

**22. **The number of values of k for which the linear equations

4*x * *ky * 2*z * 0

*kx * 4*y * *z * 0

2*x * 2*y * *z * 0

possess a non-zero solutoin is

**(1) **zero

**(2) **3

**(3) **2

**(4) **1

** ****Ans: [3]**

** ****24. **If the mean deviation about the median of the numbers a, 2a, . . ., 50 a is 50, then *a *equals

**(1) **5 **(2) **2 **(3) **3 **(4) **4

** ****Ans: [4]**

** ****25. **Let A and B be two symmetric matrices of order 3

**Statement -1 **A (BA) and (AB) A are symmetric matrices

**Statement -2 **AB is symmetric matrix if matrix multiplication of A with B commutative.

** ****(1) **Statement -1 is false, Statement -2 is true

**(2) **Statement -1 is true, Statement -2 is true; Statement -2 is a correct explanation for statement-1

**(3) **Statement-1 is true, Statement -2 is true, Statement- 2 is not correct explanation for Statement-1

**(4) **Statement -1 is true, Statement-2 is false

**Ans: [3]**

**26 .Statement -1**The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is emptyis 93 *C *.

**Statement -2 **The number of ways of choosing any 3 places from 9 different places is 93 *C*

**(1) **Statement -1 is false, Statement -2 is true

**(2) **Statement -1 is true, Statement -2 is true; Statement -2 is a correct explanation for statement-1

**(3) **Statement-1 is true, Statement -2 is true, Statement- 2 is not correct explanation for Statement-1

**(4) **Statement -1 is true, Statement-2 is false

**Ans: [3]**

** ****27. **The area of the region enclosed by trhe curves

*y *= *x*, *x *= *e*, *y * =(1/ *x)* and the positive *x*-axis is

**(1) **5/2 square units

**(2) **1/2 square units

**(3) **1 square units

**(4) **3/21 square units

**Ans: [4]**

**28. **If *dy*/*dx=y *+ 3> 0 and *Y*(0)= 2, the y(ln2) is equal to:

**(1) **–2

**(2) **7

**(3) **5

**(4) **13

** ****Ans: [2]**

** ****29. **The lines L1:y-x=0 and L2: 2x+y= 0 intersect the line L3=y+2=0 at P and Q respectivley. The bisector of the acute angle between *L*1 and *L*2 intersects *L*3 at R.

**Statement -1 **The ratio PR : RQ equals 2 2 : 5 .

**Statement -2 **In any triangle, bisector an angle divides the triangle into two similar triangles.

**(1) **Statement -1 is false, Statement -2 is true

**(2) **Statement -1 is true, Statement -2 is true; Statement

-2 is a correct explanation for statement-1

**(3) **Statement-1 is true, Statement -2 is true, Statement-

2 is not correct explanation for Statement-1

**(4) **Statement -1 is true, Statement-2 is false

**Ans: [4]**

30.The coefficient of *x^7 *in the expansion of (1- *x-* *x*^2-x^3 )^6 is

**(1) **132

**(2)**144

**(3) – **132

**(4) **– 144

**Ans: [4]**

Above are the Questions of “Sample paper for AIEEE Exam”

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