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Rao IIT Academy / JEE MAIN OFFICIAL ONLINE EXAM / 10 January19 Slot II / QP

PhysicsSingle Correct Questions +4 | 1.00

1. Charges and located at and respectively, constitute an electric dipole. Distance is the midpoint of the dipole and is perpendicular to charge is placed at where and Thecharge experiences an electrostatic force If is now moved along the equatorial line to such that

the force on will be close to :

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

2. A particle which is experiencing force, given by undergoes a displacement of If the particle hada kinetic energy of at the beginning of the displacement, what is its kinetic energy at the end of the displacement ?

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

3. Consider the nuclear fission Given that the binding energy/nucleon of and are,respectively, and identify the correct statement :(1 ) energy will be released

(2 ) energy of will be released

(3 ) energy of has to be supplied

(4 ) energy of will be supplied

4. A current of was passed through an unknown resistor which dissipated a power of . Dissipated power whenan ideal power supply of is connected across it is :

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

5. For the circuit shown below, the current through the Zener diode is :

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

6. The eye can be regarded as a single refracting surface. The radius of curvature of this surface is equal to that ofcornea This surface separates two media of refractive indices 1 and 1.34. Calculate the distance from therefracting surface at which a parallel beam of light will come to focus.

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

7. Two of a monoatomic gas is at a pressure of . The density of the gas is What is the order ofenergy of the gas due to its thermal motion ?

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

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8. A rigid massless rod of length has two masses attached at each end as shown in the figure. The rod is pivoted atpoint on the horizontal axis (see figure). When released from initial horizontal position, its instantaneous angularacceleration will be :

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

9. Half mole of an ideal monoatomic gas is heated at constant pressure of from to . Work done by gas isclose to :(Gas constant )

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

10. At some location on earth the horizontal component of earth's magnetic field is . At this location, magneticneedle of length and pole strength is suspended from its midpoint using a thread, it makes anglewith horizontal in equilibrium. To keep this needle horizontal, the vertical force that should be applied at one of its endsis :

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

11. Consider a Young's double slit experiment as shown in figure. What should be the slit separation in terms ofwavelength such that the first minima occurs directly in front of the slit ?

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

12. An unknown metal of mass heated to a temperature of was immersed into a brass calorimeter of mass containing of water at a temperature of Calculate the specific heat of the unknown metal if water

temperature stabilizes at (Specific heat of brass is )

(1 ) (2 )

(3 ) (4 )

13. A cylindrical plastic bottle of negligible mass is filled with of water and left floating in a pond with still water. Ifpressed downward slightly and released, it starts performing simple harmonic motion at angular frequency . If theradius of the bottle is then is close to : (density of water = )

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

14. Two forces and of magnitude and respectively, are at an angle with each other. If the force is doubled,then their resultant also gets doubled. Then, the angle is :

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

15. A parallel plate capacitor having capacitance 12 pF is charged by a battery to a potential difference of 10 V between itsplates. The charging battery is now disconnected and a porcelain slab of dielectric constant 6.5 is slipped between theplates.The work done by the capacitor on the slab is :

(1 ) 560 pJ (2 ) 692 pJ (3 ) 600 pJ (4 ) 508 pJ



16. A metal plate of area is illuminated by a radiation of intensity .The work function of the metalis . The energy of the incident photons is and only of it produces photo electrons. The number ofemitted photo electrons per second and their maximum energy, respectively, will be :

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

17. The modulation frequency of an AM radio station is 250 kHz, which is 10 % of the carrier wave. If another AM stationapproaches you for license what broadcast frequency will you allot ?

(1 ) 2900 kHz (2 ) 2000 kHz (3 ) 2750 kHz (4 ) 2250 kHz

18. A hoop and a solid cylinder of same mass and radius are made of a permanent magnetic material with their magneticmoment parallel to their respective axes. But the magnetic moment of hoop is twice of solid cylinder. They are placedin a uniform magnetic field in such a manner that their magnetic moments make a small angle with the field .If theoscillation periods of hoop and cylinder are and respectively, then:

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

19. A particle executes simple harmonic motion with an amplitude of 5 cm. When the particle is at 4 cm from the meanposition, the magnitude of its velocity in SI units is equal to that of its acceleration. Then, its periodic time in secondsis:

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

20. The actual value of resistance R, shown in the figure is .This is measured in an experiment as shown using thestandard formula where V and I are the reading of the voltmeter and ammeter, respectively. Ifthe measured

value of R is less ,then the internal resistance of the voltmeter is :

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

21. The diameter and height of a cylinder are measured by a meter scale to be and respectively. What will be the value of its volume in appropriate singificant figures ?

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

22. The wheatstone bridge shown in figure here, gets balanced when the carbon resistor used as has the colour code(Orange ,Red Brown) The resisators and are and ,respectively. Assuming that the colour code for thecarbon resistors gives their accurate values, the colour code for the carbon resistor, used as would be :

(1 ) Brown, Blue , Black (2 ) Brown , Blue , Brown (3 ) Red , Green , Brown (4 ) Grey , Black, Brown



23. Two stars of masses each, and at distance rotate in a plane about their common centre ofmass O. A meteorite passes through O moving perpendicular to the star's rotation plane.In order to escape from thegravitational field of this double star ,the minimum speed that meteorite should have at O is : (Take gravitationalconstant)

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

24. Two vectors and have equal magnitudes. The magnitude of is' n times the magnitude of Theangle between and is :

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

25. Two identical spherical balls of mass M and radius R each are stuck on two ends of a rod of length 2R and massM(see figure). The moment of inertia of the system about the axis passing perpendicularly through the centre of therod is :

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

26. A closed organ pipe has a fundamental frequency of 1.5 kHz. The number of overtones that can be distinctly heard bya person with this organ pipe will be : (Assume that the highest frequency a person can hear is 20 ,000 Hz)

(1 ) 7 (2 ) 4 (3 ) 6 (4 ) 5

27. The electric field of a plane polarized electromagnetic wave in free space at time is given by an expression The magnetic field is given by : (C is the velocity of light)

(1 ) (2 )

(3 ) (4 )

28. A particle starts from the origin at time t = 0 and moves along the positive xaxis. The graph of velocity with respect totime is shown in figure.What is the position of the particle at time t = 5 s ?

(1 ) 6 m (2 ) 3 m (3 ) 9 m (4 ) 10 m

29. Four equal point charges Q each are placed in the plane at and . The work requiredto put a fifth charge Q at the origin of the coordinate system will be :

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

30. The self induced emf of a coil is 25 volts. When the current in it is changed at uniform rate from 10 A to 25 A in 1s, thechange in the energy of the inductance is :

(1 ) 740 J (2 ) 437.5 J (3 ) 540 J (4 ) 637.5 J



Chemistry

1. The pair that contains two bonds in each of the oxoacids is(1 ) and (2 ) and

(3 ) and (4 ) and

2. Haemoglobin and gold sol are examples of(1 ) Negatively charged sols

(2 ) Negatively and positively charged sols, respectively

(3 ) Positively charged sols

(4 ) Positively and negatively charged sold, respectively

3. A compound of formula has the hcp lattice. Which atom forms the hcp lattice and what fraction of tetrahedralvoids is occupied by the other atoms

(1 ) hcp lattice Tetrahedral voids




4. The number of 2centre2electron and 3centre2electron bonds in respectively, are

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

5. Among the following reactions of hydrogen with halogens, the one that requires a catalyst is(1 ) (2 )(3 ) (4 )

6. The difference in the number of unpaired electrons of a metal ion in its highspine and lowspin octahedral complexesis two. The metal ion is

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

7. Which of the following tests cannot be used for identifying amino acids ?(1 ) Ninhydrin test (2 ) Biuret test

(3 ) Xanthoproteic test (4 ) Barfoed test

8. What is the IUPAC name of the following compound ?

(1 ) 3Bromo1, 2dimethylbut1ene (2 ) 4Bromo3methylpent2ene

(3 ) 3Bromo3methyl1, 2dimethylprop1ene (4 ) 2Bromo3methylpent3ene



9. For an elementary chemical reaction,

, the expression for is

(1 ) (2 )

(3 ) (4 )

10. Sodium metal on dissolution in liquid ammonia gives a deep blue solution due to the formation of(1 ) sodium ionammoina complex (2 ) sodiumammonia complex

(3 ) ammoniated electrons (4 ) sodamide

11. An aromatic compound having molecular formula on treating with aqueous ammonia and heating formscompound . The compound on reaction with molecular bromine and potassium hydroxide provides compound

having molecular formula . The structure of is

(1 ) (2 )

(3 ) (4 )

12. The amount of sugar required to prepare of its aqueous solution is

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

13. The correct match between item and item is

Item I(compound) Item II

(reagent)

(A) Lysine (P) 1naphthol

(B) Furfural (Q) Ninhydrin

(C) Benzyl alcohol (R)

(D) Styrene (S) Ceric ammoniumnitrate

(1 ) (A)(Q); (B)(R); (C)(S); (D)(P)

(2 ) (A)(Q); (B)(P); (C)(S); (D)(R)

(3 ) (A)(Q); (B)(P); (C)(R); (D)(S)

( ) (A)(R); (B)(P); (C)(Q); (D)(S)

14. A reaction of cobalt(III) chloride and ethylenediamine in a mole ratio generates two isomeric products A (violetcoloured) and B (green coloured). A can show optical activity, but B is optically inactive. What type of isomers does Aand B represent ?(1 ) Linkage isomers (2 ) Ionisation isomers

(3 ) Geometrical isomers (4 ) Coordination isomers

15. The process with negative entropy change is(1 ) Sublimation of dry ice

(2 ) Dissociation of to and

(3 ) Dissolution of iodine in water

(4 ) Synthesis of ammonia from and


4


16. The electrolytes usually used in the electroplating of gold and silver, respectivley, are

(1 ) and (2 ) and

(3 ) and (4 ) and

17. The ground state energy of hydrogen atom is . The energy of second excited state of ion in is

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

18. is introduced in evacuated flask at of the solid decomposed to and as gases. The of the reaction at is atm , Molar mass of ,

molar mass of

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

19. Which is the most suitable reagent for the following transformation ?

(1 ) alkaline (2 )

(3 ) (4 ) Tollen's reagent

20. The electron of an element with an atomic number of enters into the orbital

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

21. The major product obtained in the following reaction is

(1 ) (2 )

(3 ) (4 )

22. What will be the major product in the following mononitration reaction ?

(1 ) (2 )

(3 ) (4 )



23. The major product of the following reaction is:

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

24. In the reaction of oxalate with permanganate in acidic medium, the number of electrons involved in producing onemolecule of is:

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


(1 ) (2 )

(3 ) (4 )

26. An ideal gas undergoes isothermal compression from to against a constant external pressure of Heat released in this process is used to increase the temperature of of If molar heat capacity of is

the temperature of increases by:

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

27. Elevation in the boiling point for molal solution of glucose . The depression in the freezing point for molalsolution of glucose in the same solvent is . The relation between and is:

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


(1 )

(2 )

(3 )

(4 )



29. In the cell, the cell potential is when a molal solution is used. The standard electrode potential of

electrode is:

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

30. The reaction that is NOT involved in the ozone layer deplection mechanism in the stratosphere is:

(1 )

(2)

(3 )

(4 )

Mathematics

1. If the probability of hitting a target by a shooter, in any shot is then the minimum number of independent shots at the

target required by him so that the probability of hitting the target at elast once is greater than is :

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

2. If the area of an equilateral triangle inscribed in the circle, is sq. units then isequal to :

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

3. The length of the chord of the parabola having equation is:

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

4. Let be a differntiable function such that and Then

(1 ) does not exist (2 ) exists and equals

(3 ) exists and equals (4 ) exists and equals

5. The value of such that sum of the squares of the roots of the quadratic equation, has theleast value is:

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

6. The curve amongst for family of curves represented by the differential equation, which passes through is:

(1 ) a hyperbola with transverse axis along the xaxis.

(2 ) a circle with centre on the yaxis

(3 ) an ellipse with major axis along the yaxis.

(4 ) a circle with centre on the xaxis.

7.Let where Then the minimum value of is:

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



8. Let and be two given vectors where vectors and are noncollinear. Thevalue of for which vectors and are collinear, is :

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

9. Let where then represents:

(1 )an ellipse whose eccentricity is

when

(2 )a hyperbola whose eccentricity is

when

(3 )a hyperbola whose eccentricity is

when

(4 )an ellipse whose eccentricity is

when

10.If then is:

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

11. On which of the following lines lies the point of intersection of the line, and the plane,

(1 )

(2 )

(3 )

(4 )

12. The number of values of for which the system of linear equations

has a nontrivial solution, is:

(1 ) three (2) one (3 ) four (4 ) two

13. With the usual notation, in if and then the ratio is:

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

14. If mean and standard deviation of observations are and respectively, then the variance of observations and is equal to :

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



15. A helicopter is flying along the curve given by A soldier positioned at the point wants to

shoot down the helicopter when it is nearest to him. Then this nearest distance is:

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

16. The value of is:

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

177. Two sides of a parallelogram are along the lines, and If its diagonals intersect at thenone of its vertex is:

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

18. The tangent to the curve, passing through the point also passes through the point:

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

19. Let be in G.P. with for and be the set of pairs (the set ofnatural numbers) for which

Then the number of elements in is:

(1 ) (2 ) (3 ) (4 ) infinitely many

20. The plane which bisects the line segment joining the points and at right angles, passes throughwhich one of the following points?(1 ) (2 )

(3 ) (4 )

21.Let If and respectively denote the real and imaginary parts of then:

(1 ) (2 )

(3 ) (4 )

22.If then is equal to :

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


RAO IIT ACADEMY Rao IIT Academy / JEE MAIN OFFICIAL ONLINE EXAM / 10 January19 Slot II / QP

23. Let be the set of natural numbers and two functions and be defined as such that

and Then is:

(1 ) oneone but not onto.

(2 ) both oneone and onto.

(3 ) neither oneone nor onto.

(4 ) onto but not oneone

24. Consider the following three statements: is a prime number. is a factor of

of and is Then the truth value of which one of the following statements is true?

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

25.The value of is:

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

26. Let be a function defined by If be the set of all points at which is not differentiable, then has exactly:

(1 ) one element (2 ) three elements

(3 ) two elements (4 ) five elements

27. If where is a constant of integration, then is equal to:

(1 ) (2 )

(3 ) (4 )

288.The value of where denotes the greatest integer less than or equal to is:

(1 ) (2 )

(3 ) (4 )

29.The positive value of for which the coefficient of in the expression is is:

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

30. Two vertices of a triangle are and If its orthocentre is at the origin, then its third vertex lies in whichquadrant?

(1 ) fourth (2 ) second (3 ) first (4 ) third


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