This practice test consists of AIEEE 2008 questions to help you practice for actual AIEEE 2011 exam. Check AIEEE Question Papers & AIEEE Solutions for AIEEE 2012 exam preparation.

End Test Now

AB is a vertical pole with B at the ground level and A at the top. A man finds that the angle of elevation of the point A from a certain point C on the ground is 60Â°. He moves away from the pole along the line BC to a point D such that CD = 7 m. From D the angle of elevation of the point A is 45Â°. Then the height of the pole is

It is given that the events A and B are such that and . Then P(B) is

A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then is

1

0

A focus of an ellipse is at the origin. The directrix is the line x = 4 and the eccentricity is 1/2. Then the length of the semiâˆ’major axis is

A parabola has the origin as its focus and the line x = 2 as the directrix. Then the vertex of the parabola is at

(2, 0)

(0, 2)

(1, 0)

(0, 1)

The point diametrically opposite to the point P (1, 0) on the circle is

(-3,-4)

(3,-4)

(-3,4)

(3,4)

Let f : N â†’ Y be a function defined as f (x) = 4x + 3, where Show that f is invertible and its inverse is

The conjugate of a complex number is Then the complex number is

Let R be the real line. Consider the following subsets of the plane R Ã— R. S = {(x, y) : y = x + 1 and 0 < x < 2}, T = {(x, y) : x âˆ’ y is an integer}. Which one of the following is true?

T is an equivalence relation on R but S is not

both S and T are equivalence relations on R

S is an equivalence relation on R but T is not

neither S nor T is an equivalence relation on R

The perpendicular bisector of the line segment joining P (1, 4) and Q (k, 3) has yâˆ’intercept âˆ’ 4. Then a possible value of k is

2

-4

-2

The solution of the differential equation satisfying the condition y(1) =1 is

y = x ln x + x

y = ln x + x

y = x ln x +

The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following gives possible values of a and b?

a = 3, b = 4

a = 0, b = 7

a = 5, b = 2

a = 1, b = 6

The vector lies in the plane of the vectors and and bisects the angle between and .Then which one of the following gives possible values of Î± and Î²?

Î± = 1, Î² = 1

Î± = 2, Î² = 2

Î± = 1, Î² = 2

Î± = 2, Î² = 1

The non-zero vectors are realted by and . Then the angle between is

The line passing through the points (5, 1, a) and (3, b, 1) crosses the yzâˆ’plane at the point .Then

a = 2, b = 8

a = 4, b = 6

a = 6, b = 4

a = 8, b = 2

If the straight lines and intersect at a point, then the integer K is equal to

-5

5

Directions: Below mentions Five questions are Assertionâˆ’Reason type questions. Each of these questions contains two statements : Statement âˆ’ 1 (Assertion) and Statementâˆ’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.

Statement âˆ’ 1: For every natural number

Statement âˆ’2: For every natural number

Statement âˆ’1 is true, Statement âˆ’2 is true, Statement âˆ’2 is a correct explanation for Statement âˆ’1

Statement âˆ’1 is false, Statement âˆ’2 is true

Statement âˆ’1 is true, Statement âˆ’2 is true; Statement âˆ’2 is not a correct explanation for Statement âˆ’1.

Statement âˆ’ 1 is true, Statement âˆ’ 2 is false.

Let A be a 2 Ã— 2 matrix with real entries. Let I be the 2 Ã— 2 identity matrix. Denote by tr (A), the sum of diagonal entries of A. Assume that

Statement âˆ’2: If A â‰ I and A â‰ âˆ’ I, then tr (A) â‰ 0.

Statement âˆ’1: Statement âˆ’2:

Let p be the statement â€œx is an irrational numberâ€, q be the statement â€œy is a transcendental numberâ€, and r be the statement â€œx is a rational number iff y is a transcendental numberâ€.

In a shop there are five types of ice-creams available. A child buys six ice-creams. Statement -1: The number of different ways the child can buy the six ice-creams is Statement -2: The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging 6 Aâ€™s and 4 Bâ€™s in a row.

Let Then which one of the following is ture?

f is neither differentiable at x = 0 nor at x = 1

f is differentiable at x = 0 and at x = 1

f is differentiable at x = 1 but not at x = 0

f is differentiable at x = 0 but not at x = 1

The first two terms of a geometric progression add up to 12. The sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately positive and negative, then the first term is

-12

12

4

Suppose the cube has three distinct real roots where p > 0 and q > 0. Then which one of the following holds?

The cubic has minima at both and

The cubic has maxima at both and

The cubic has minima at and maxima at

How many real solutions does the equation have ?

7

3

The statement is equivalent to

The value of is

The differential equation of the family of circles with fixed radius 5 units and centre on the line y = 2 is

Let l and Then which one of the following is true?

The area of the plane region bounded by the curves and is equal to

How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?

Let a, b, c be any real numbers. Suppose that there are real numbers x, y, z not all zero such that x = cy + bz, y = az + cx and z = bx + ay. Then is equal to

-1

Let A be a square matrix all of whose entries are integers. Then which one of the following is true?

if detA = , then need not exist

if detA = , then exists but all its entries are not necessarily integers

if detA = , then exists and all its entries are integers

If detA , then exists and all its entries are non-integers

The quadratic equations and have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then the common root is

Toluene is nitrated and the resulting product is reduced with tin and hydrochloric acid. The product so obtained is diazotised and then heated with cuprous bromide. The reaction mixture so formed contains

mixture of oâˆ’ and pâˆ’bromoanilines

mixture of oâˆ’ and pâˆ’bromotoluenes

mixture of oâˆ’ and mâˆ’bromotoluenes

mixture of oâˆ’ and pâˆ’dibromobenzenes

The coordination number and the oxidation state of the element â€˜Eâ€™ in the complex (where (en) is ethylene diamine) are, respectively,

4 and 2

6 and 3

4 and 3

6 and 2

Phenol, when it first reacts with concentrated sulphuric acid and then with concentrated nitric acid, gives

p-nitrophenol

2,4,6-trinitrobenzene

nitrobenzene

o-nitrophenol

In the following sequence of reactions, the alkene affords the compound â€˜Bâ€™

The Compound B is

In which of the following octahedral complexes of Co (at. no. 27), will the magnitude of be the highest?

The equilibrium constants and for the reactions and , respectively are in the ration of 1:9 If the degree of dissociation of X and Z be equal then the ratio of total pressure at these equilibria is

1 : 36

1 : 1

1 : 9

1 : 3

Oxidising power of chlorine in aqueous solution can be determined by the parameters indicated below:

The energy invloved in the conversion of to

Bakelite is obtained from phenol by reacting with

For the following three reactions a, b and c, equilibrium constants are given:

A

B

C Which of the following relations is correct ?

Î±-D-()glucose and Î²-D()-glucose are

enantiomers

epimers

conformers

anomers

The absolute configuration of

R, S

R, R

S, S

S, R

Standard entropy of and are 60, 40 and 50 , respectively. For the reaction, , to be at equilibrium, the temperature will be

1000 K

750 K

500 K

1250 K

Four species aare listed below

iv < ii < iii < I

ii < iii < i < iv

iii < i < iv < ii

i < iii < ii < iv

Which one of the following constitutes a group of the isoelectronic species?

Which one of the following pairs of species have the same bond order?

The ionization enthalpy of hydrogen atom is . The energy required to excite the electron in the atom from n = 1 to n = 2 is

Which one of the following is the correct statement?

Chlorides of both beryllium and aluminium have bridged chloride structures in solid phase

Boric acid is a protonic acid

Beryllium exhibits coordination number of six

Given . The potential for the cell is

âˆ’0.26 V

âˆ’0.339 V

0.26 V

0.399 V

Amount of oxalic acid present in a solution can be determined by its titration with solution in the presence of . The titration gives unsatisfactory result when carried out in the presence of HCl, because HCl

furnishes ions in addition to those from oxalic acid

oxidises oxalic acid to carbon dioxide and water

reduces permanganate to

gets oxidised by oxalic acid to chlorine

The vapour pressure of water at is 17.5 mm Hg. If 18 g of glucose is added to 178.2 g of water at , the vapour pressure of the resulting solution will be

15.750 mm Hg

16.500 mm Hg

17.325 mm Hg

17.675 mm Hg

Among the following substituted silanes the one which will give rise to cross linked silicone polymer on hydrolysis is

In context with the industrial preparation of hydrogen from water gas , which of the following

CO is oxidised to with steam in the presence of a catalyst followed by absorption of in alkali

CO and are fractionally separated using differences in their densities

CO is removed by absorption in aqueous solution

In a compound atoms of element Y from ccp lattice and those of element X occupy of tetrahedral voids. The formula of the compound will be

Gold numbers of protective colloids A, B, C and D are 0.50, 0.01, 0.10 and 0.005, respectively. The correct order of their protective powers is

D < A < C < B

A < C < B < D

B < D < A < C

C < B < D < A

The hydrocarbon which can react with sodium in liquid ammonia is

The treatment of with produces

The correct decreasing order of priority for the functional groups of organic compounds in the IUPAC system of nomenclature is

The of a weak acid, HA, is 4.80. The of a weak base, BOH, is 4.78. The pH of an aqueous solution of the corresponding salt, BA, will be

7.01

9.22

9.58

4.79

The organic chloro compound, which shows complete stereochemical inversion during a reaction,is

Identify the wrong statements in the following:

Acid rains is mostly because of oxides of nitrogen and sulphur

Chlorofluorocarbons are responsible for ozone layer depletion

Greenhouse effect is responsible for global warming

Ozone layer does not permit infrared radiation from the sun to reach the earth

Larger number of oxidation states are exhibited by the actinoids than those by the lanthanoids, the main reason being

lesser energy difference between 5f and 6d than between 4f and 5d orbitals

4f orbitals more diffused than the 5f orbitals

more energy difference between 5f and 6d than between 4f and 5d orbitals

more reactive nature of the actinoids than the lanthanoids

Which of the following factors is of no significance for roasting sulphide ores to the oxides and not subjecting the sulphide ores to carbon reduction directly?

Metal sulphides are less stable than the corresponding oxides

Metal sulphides are thermodynamically more stable than

At , the vapour pressure of pure liquid â€˜Aâ€™ is 520 mm Hg and that of pure liquid â€˜Bâ€™ is 1000 mm Hg. If a mixture solution of â€˜Aâ€™ and â€˜Bâ€™ boils at and 1 atm pressure, the amount of â€˜Aâ€™ in the mixture is (1 atm = 760 mm Hg)

34 mol percent

48 mol percent

52 mol percent

50 mol percent

For a reaction rate of disappearance of â€˜Aâ€™ is related to the rate of appearance of â€˜Bâ€™ by the expression

The electrophile, attacks the benzene ring to generate the intermediate -complex. Of the following, which - complex is of lowest energy?

A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is the escape velocity from the surface of the planet would be

A spherical solid ball of volume V is made of a material of density . It is falling through a liquid of density . Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed v, i.e., . The terminal speed of the ball is

Below three questions are based on the following paragraph Wave property of electrons implies that they will show diffraction effects. Davisson and Germer demonstrated this by diffracting electrons from crystals. The law governing the diffraction from a crystal is obtained by requiring that electron waves reflected from the planes of atoms in a crystal interfere constructively (see in figure). Electrons accelerated by potential V are diffracted from a crystal. If and , V should be about

2000 V

50 V

500 V

1000 V

If a strong diffraction peak is observed when electrons are incident at an angle â€˜iâ€™ from the normal to the crystal planes with distance â€˜dâ€™ between them (see figure), de Broglie wavelength of electrons can be calculated by the relationship (n is an integer)

In an experiment, electrons are made to pass through a narrow slit of width â€˜dâ€™ comparable to their de Broglie wavelength. They are detected on a screen at a distance â€˜Dâ€™ from the slit (see figure).

Which of the following graph can be expected to represent the number of electrons â€˜Nâ€™ detected as a function of the detector position â€˜yâ€™(y = 0 corresponds to the middle of the slit)?

Shown in the figure below is a meter-bridge set up with null deflection in the galvanometer. The value of the unknown resistor R is

While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance condition at a column length of 18 cm during winter. Repeating the same experiment during summer, she measures the column length to be x cm for the second resonance. Then

x > 54

18 > x

36 > x > 18

54 > x > 36

The dimension of magnetic field in M, L, T and C (Coulomb) is given as

Consider a uniform square plate of side â€˜aâ€™ and mass â€˜mâ€™. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is

A body of mass m = 3.513 kg is moving along the x-axis with a speed of . The magnitude of its momentum is recorded as

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

20,000 J – 50,000 J

200 J – 500 J

2,000 J – 5,000 J

A parallel plate capacitor with air between the plates has a capacitance of 9 pF. The separation between its plates is â€˜dâ€™. The space between the plates is now filled with two dielectrics. One of the dielectrics has dielectric constant and thickness while the other one has dielectric constant and thickness . Capacitance of the capacitor is now

40.5 pF

20.25 pF

1.8 pF

45 pF

A thin rod of length â€˜Lâ€™ is lying along the x-axis with its ends at X = 0 and X = L. Its linear density (mass/length) varies with X as , where where n can be zero or any positive number. If the position of the centre of mass of the rod is plotted against â€˜nâ€™, which of the following graphs best approximates the dependence of on n ?

The speed of sound in oxygen at a certain temperature is . The speed of sound in helium (He) at the same temperature will be (assumed both gases to be ideal)

None

This question contains Statement -1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements. Statement â€“ I: Energy is released when heavy nuclei undergo fission or light nuclei undergo fusion. and Statement â€“ II For heavy nuclei, binding energy per nucleon increases with increasing Z while for light nuclei it decrease with increasing Z.

Statement â€“ 1is true, Statement â€“ 2 is true; Statement -2 is not a correct explanation for Statement-1.

Statement â€“ 1 is true, Statement â€“ 2 is False.

Statement â€“ 1is false, Statement â€“ 2 is true.

Statement â€“ 1is true, Statement â€“ 2 is true; Statement -2 is correct explanation for Statement-1.

This question contains Statement -1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements. Statement â€“ I: For a mass M kept at the centre of a cube of side â€˜aâ€™, the flux of gravitational field passing through its sides is and Statement â€“ II. If the direction of a field due to a point source is radial and its dependence on the distance â€˜râ€™ for the source is given as , its flux through a closed surface depends only on the strength of the source enclosed by the surface and not on the size or shape of the surface

A working transistor with its three legs marked P, Q and R is tested using a multimeter. No conduction is found between P and Q. By connecting the common (negative) terminal of the multimeter to R and the other (positive) terminal to P or Q, some resistance is seen on the multimeter. Which of the following is true for the transistor?

It is an npn transistor with R as collector

It is an npn transistor with R as base

It is a pnp transistor with R as emitter

It is a pnp transistor with R as collector

Given below two Question are based on the following paragraph. Consider a block of conducting material of resistivity ‘’ shown in the figure. Current â€˜Iâ€™ enters at â€˜Aâ€™ and leaves from â€˜Dâ€™. We apply superposition principle to find voltage ‘‘developed between â€˜Bâ€™ and â€˜Câ€™. The calculation is done in the following steps:(i) Take current â€˜Iâ€™ entering from â€˜Aâ€™ and assume it to spread over a hemispherical surface in the block. (ii) Calculate field E® at distance â€˜râ€™ from A by using Ohmâ€™s law , where j is the current per unit area at â€˜râ€™. (iii) From the â€˜râ€™ dependence of , obtain the potential at r. (iv) Repeat (i), (ii) and (iii) for current â€˜Iâ€™ leaving â€˜Dâ€™ and superpose results for â€˜Aâ€™ and â€˜Dâ€™.

For current entering at A, the electric field at a distance â€˜râ€™ from A is

A student measures the focal length of convex lens by putting an object pin at a distance â€˜uâ€™ from the lens and measuring the distance â€˜vâ€™ of the image pin. The graph between â€˜uâ€™ and â€˜vâ€™ plotted by the student should look like

A block of mass 0.50 kg is moving with a speed of 2.00 m/s on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

1.00 J

0.67 J

0.34 J

0.16 J

Suppose an electron is attracted towards the origin by a force k/r where â€˜kâ€™ is a constant and â€˜râ€™ is the distance of the electron from the origin. By applying Bohr model to this system, the radius of the orbital of the electron is found to be â€˜’ and the kinetic energy of the electron to be . Then which of the following is true?

A wave travelling along the X-axis is described by the equation If the

wavelength and the time period of the wave are 0.08 m and 2.0 s, respectively, then and in appropriate units are

Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross sectional area A = and length = 20 cm. If one of the solenoids has 300 turns and the other 400 turns, their mutual inductance is

OR gate

NOR gate

AND gate

NAND gate

A body is at rest at x = 0. At t = 0, it starts moving in the positive x-direction with a constant acceleration. At the same instant another body passes through x = 0 moving in the positive xdirection with a constant speed. The position of the first body is given by after time â€˜tâ€™ and that of the second body by after the same time interval. Which of the following graphs correctly describes as a function of time â€˜tâ€™?

An experiment is performed to find the refractive index of glass using a travelling microscope. In this experiment distance are measured by

A vernier scale provided on the microscope

A screw gauage provided on the microscope

A standard laboratory scale

A meter scale provided on the microscope

A horizontal overhead power line is at a height of 4m from the ground and carries a current of 100 A from east to west. The magnetic field directly below it on the ground is

Relative permittivity and permeability of a material are and Which of the following values of these quantities are allowed for a diamagnetic material?

Two full turns of the circular scale of a screw gauge cover a distance of 1 mm on its main scale. The total number of divisions on the circular scale is 50. Further, it is found that the screw gauge has a zero error of âˆ’ 0.03 mm while measuring the diameter of a thin wire, a student notes the main scale reading of 3 mm and the number of circular scale divisions in line with the main scale as 35. The diameter of the wire is

3.32 mm

3.38 mm

3.73 mm

3.67 mm

An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume and contains ideal gas at pressure and temperature . The other chamber has volume and contains ideal gas at pressure and temperature . If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be

A capillary tube (A) is dropped in water. Another identical tube (B) is dipped in a soap water solution. Which of the following shows the relative nature of the liquid columns in the two tubes?

A thin spherical shell of radius R has charge Q spread uniformly over its surface. Which of the following graphs most closely represents the electric field E® produced by the shell in the range , where r is distance from the centre of the shell?

A 5V battery with internal resistance and a 2V battery with internal resistance are connected to a resistor as shown in the figure. The current in the resistor is

When you are sure that you have answered as many questions as possible, click the ‘Done’ button below and view your results.