rao physics - rao iit · 10/1/2019 · rao iit academy / jee - main official online exam / 10...

Rao IIT Academy / JEE - MAIN OFFICIAL ONLINE EXAM / 10 January-19 Slot- I / QP

PhysicsSingle Correct Questions +4 | -1.00

1. In an electron microscope, the resolution that can be achieved is of the order of the wavelength of electrons used. Toresolve a width of the minimum electron energy required is close to:

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2. In a Young's double slit experiment with slit separation one observes a bright fringe at angle by using

light of wavelength When the light of wavelength is used a bright fringe is seen at the same angle in the sameset up. Given that and are in visible range their values are :

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3. To mop-clean a floor, a cleaning machine presses a circular mop of radius vertically down with a total force androtates it with a constant angular speed about its axis. If the force is distributed uniformly over the mop and ifcoefficient of friction between the mop and the floor is the torque, applied by the machine on the mop is :

4. A magnet of total magnetic moment is placed in a time varying magnetic field, where Tesla and The work done for reversing the direction of the magnetic moment at second, is:

5. A piece of wood of mass is dropped from the top of a height building. At the same time, a bullet of mass is fired vertically upward, with a velocity from the ground. The bullet gets embedded in the wood.

Then the maximum height to which the combined system reaches above the top of the building before falling below is:

6. A block of mass is kept on a platform which starts from rest with constant acceleration upward, as shown in fig.Work done by normal reaction on block in time is:

7. Two guns and can fire bullets at speeds and respectively. From a point on a horizontal ground,they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by the two guns, on theground is :

8. A string of length and mass is fixed at both ends. The tension in the string is The string is set intovibration using an external vibration using an external vibrator of frequency The separation betweensuccessive nodes on the string is close to :

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9. In the given circuit the cells have zero internal resistance. The currents (in Amperes) passing through resistance and respectively, are :

10. A homogeneous solid cylindrical roller of radius and mass is pulled on a cricket pitch by a horizontal force.Assuming rolling without slipping, angular acceleration of the cylinder is:

11. A train moves towards a stationary observer with speed The train sounds a whistle and itsfrequency registered by the observer is If the speed of the train is reduced to the frequency registered is

If speed of sound is then the ratio is:

12. A plano convex lens of refractive index and focal length is kept in contact with another plano concave lens ofrefractive index and focal length If the radius of curvature of their spherical faces is each and then and are related as :

13. An insulating thin rod of length has a linear charge density on it. The rod is rotated about an axis passing

through the origin and perpendicular to the rod. If the rod makes rotations per second, then thetime averaged magnetic moment of the rod is:

14. A charge is distributed over three concentric spherical shells of radii such that their surfacecharge densities are equal to one another. The total potential at a point at distance from their common centre, where would be:

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15. A satellite is moving with a constant speed in circular orbit around the earth. An object of mass is ejected fromthe satellite such that it just escapes from the gravitational pull of the earth. At the time of ejection, the kinetic energy ofthe object is :

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16. To get output at for the given logic gate circuit the input values must be:

17. A uniform metallic wire has a resistance of and is bent into an equilateral triangle. Then, the resistance betweenany two vertices of the triangle is:

18. If the magnetic field of a plane electromagnetic wave is given by The speed of light then the maximum electric field associated with it is :

19. A solid metal cube of edge length is moving in a positive y-direction at a constant speed of There isa uniform magnetic field of in the positive z-direction. The potential difference between the two faces of the cubeperpendicular to the x-axis, is :

20. Three Carnot engines operate in series between a heat source at a temperature and a heat sink at temperature (see figure). There are two other reservoirs at temperature and as shown, with The threeengines are equally efficient if :

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21. A 2W carbon resistor is color coded with green, black, red and brown respectively. The maximum current which can bepassed through this resistor is :

63 mA 63 mA 0.4 mA 100 mA

22. The density of a material in SI units is In certain units in which the unit of length is 25 cm and the unit ofmass is 50 g, the numerial value of density of the material is :

16 640 410 40

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23. In the cube of side 'a' shown in the figure, the vector from the central point of the face ABOD to the central point of theface BEFO will be :

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24. Using a nuclear counter the count rate of emitted particles from a radioactive source is measured. At t = 0 it was 1600counts per second and t = 8 seconds it was 100 counts per second. The count rate observed, as counts per second, att = 6 seconds is close to :

150 200 360 400

25. Two electric dipoles, A, B with respective dipole moments and are placed on the x-axiswith a separation R, as shown in the figure.

The distance from A at which both of them produce the same potential is :

26. Water flows into a large tank with flat bottom at the rate of Water is also leaking out of a hole of area at its bottom. If the height of the water in the tank remains steady, then this height is :

17 cm 2.9 cm 4 cm 5.1 cm

27. A heat source at is connected to another heat reservoir at by a copper slab which is 1m thick.Given that the thermal conductivity of copper is the energy flux through it in the steady state is :

28. A TV transmission tower has a height of 140 m and the height of the receiving antenna is 40 m. What is the maximumdistance upto which signals can be broadcasted from this tower in LOS (Line of Sight) mode? (Given : radius of earth

40 km 80 km 65 km 48 km

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29. A potentiometer wire AB having length L and resistance 12 r is joined to a cell D of emf and internal resistance Acell C having emf and internal resistance is connected. The length at which the galvanometer as shwonin figure shows no deflection is :

30. A parallel plate capacitor is of area and a separation The gap is filled with three dielectric materials ofequal thickness (see figure) with dielectric constants The dielectric constant of amaterial which when fully inserted in above capacitor, gives same capacitance would be :

12 4 14 36

Chemistry

1. The electronegativity of aluminium is similar to:

Lithium Boron Carbon Beryllium

2. Which of the graphs shown in below does not represent the relationship between incident light and the electron ejectedfrom metal surface?

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3. The major product of the following reaction is:

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4. Which dicarboxylic acid in presence of a dehydrating agent is least reactive to give an anhydride?

(1) (2)

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5. The effect of lanthanoid contraction in the lanthanoid series of elements by and large means:(1) decrease in both atomic and ionic radii.

(2) increase in both atomic and ionic radii.

(3 ) increase in atomic radii and decrease in ionic radii.

(4 ) decrease in atomic radii and increase in ionic radii.

6. A process has and Out of the values given below, choose the minimumtemperature above which the process will be spontaneous:

7. The correct structure of product in the following reaction is:

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8. The metal used for making X-ray tube window is:

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9. A mixture of of and of sodium sulphate was dissolved in water and the volume was made upto The mass of calcium sulphate formed and the concentration of in resulting solution, respectively, are: Molar mass of and are and respectively; of is

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10. Water filled in two glasses and have BOD values of and respectively. The correct statement regardingthem,is:

(1) is more polluted than

(2) is more polluted than

(3 ) Both and are suitable for drinking.

(4 ) is suitable for drinking, whereas is not.

11. Hall-Heroult's process is given by:

(1)

(2)

(3 )

(4 )

12. The total number of isotopes of hydrogen and number of radioactive isotopes among them, respectively are:

and and and and

13. Wilkinson catalyst is:

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14. Two pi and half sigma bonds are present in:

15. If dichloromethane (DCM) and water are used for differential extraction, which one of the following statement iscorrect?

(1) and would stay as upper and lower layer respectively in the separating funnel (S.F.)

(2) and will make turbid/ colloidal mixture.

(3 ) and would stay as lower and upper layer respectively in the S.F.

(4 ) and will be miscible clearly.

16. Liquids and from an ideal solution in the entire composition range. At the vapor pressures of pure andpure and pure are and respectively. The composition of the vapor in equilibrium with asolution containing 40 mole precent of at this temperature is:

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17. Which of the following is not an example of heterogeneous catalytic reaction?(1) Haber's process (2) Hydrogenation of vegetable oils

(3 ) Ostwald's process (4 ) Combusation of coal

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18. The increasing order of the values of the following is:

19. The decreasing order of ease of alkaline hydrolysis for the following esters is

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20. The values of for the following reactions at are, respectively: (At )

(1)

(2)

(3 )

(4 )

21. Which priemitive unit cell has unequal edge lengths and all axial angles different from

(1) Monoclinic (2) Tetragonal (3 ) Triclinic (4 ) Hexagonal

22. The type of hybridisation and number of lone pair(s) of electrons of in respectively, are:

and 1 and 1 and 2 and 2

23. Consider the following reduction processes:g

The reducing power of the metals increases in the order:(1) (2)(3 ) (4 )

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24. Which hydrogen in compound (E) is easily replaceable during bromination reaction in presence of light?y g

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

25. Consider the given plots for a reaction obeying Arrhenius equation ( and are rate constantand activation energy, respectively)

Choose the correct option:(1) Both I and II are wrong (2) Both I and II are correct

(3 ) I is right but II is wrong (4 ) I is wrong but II is right

26. The total number of isomers for a square planar complex is:

27. The chemical nature of hydrogen peroxide is:(1) Oxidising agent in acidic medium, but not in basic medium

(2) Oxidising and reducing agent in acidic medium, but not in basic medium

(3 ) Reducing agent in basic medium, but not in acidic medium

(4 ) Oxidising and reducing agent in both acidic and basic medium

28. The major product of the following reaction is:

29. The major product formed in the reaction given below will be:

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30. The major product formed in the following reaction is:

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Mathematics

1. An unbiased coin is tossed. If the outcome is a head then a pair of unbiased dice rolled and the sum of the numbersobtained on them is noted. If the toss of the coin results in tail then a card from a well-shuffled pack of nine cardsnumbered is randomly picked and the number on the card is noted. The probability that the noted numberis either or is:

2. If the line intersects the -axis at the point and the -axis at the point then the incentre of thetriangle where is the origin, is:

3.Let If I is minimum then the ordered pair

4. If a circle C passing through the point (4, 0) touches the circle externally at the point then the radius of C is :

5.Let and If the minimum value of is 8,

then a value of d is:

6. A point P moves on the line If are fixed points, then the locus of the centroidof is a line :

parallel to y-axis with slope parallel to x-axis with slope

7. If the area enclosed betwen the curves is 1 square unit. The k is :

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8. The equation of a tangent to the hyperbola parallel to the line is :

9. Let be a function such that Then equals:

10. Consider a trianular plot with sides and A vertical lamp-post at the mid point of subtends an angle at . The height (in ) of the lamp-post is :

11. The sum of all two digit positive numbers which when divided by 7 yield 2 or 5 as remainder is:

1465 1256 1356 1365

12. If the third term in the binomial expansion of equals then a possible value of is

13. The sum of all velues of satisfying

14. If the parabolas and have a common normal, then which one of the following is a validchoice for the ordered triad

15. Let be a point on the line and be a point in the space. Then valueof for which the vector is parallel to the plane is:

16.

Let be the set of points in the interval at which is not differentiable. Then

(1) equals (2) is an empty set

(3 ) equals (4 ) equals

17. The plane passing through the point and parallel to the lines and

also passes through the point:

18. In a class of 140 students numbered 1 to 140, all even numbered students opted Mathematics course, those whosenumber is divisible by 3 opted physics course and those whose number is divisible by 5 opted Chemistry course. Thenthe number of students who did not opt for any of the three courses is:

102 38 42 1

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19. Let and be three vectors such that and is perpendicular to Then a possible value of

20.If then equals :

100 50 400 200

21. For each let be the greatest integer less than or equal to Then,

equals does not exist equals equals

22. Consider the statement: is prime. Then which one of the following is true?

(1) Both and are false (2) is false but is true

(3 ) is false but is true (4 ) Both and are true

23. Let and be any two non-zero complex numbers such that

If then :

24.The shortest distance between the point and the curve is:

25. If are the lengths of the sides of triangle, then cannot be equal to :

26. The mean of five observations is and their variance is . If three of the given five observations are and thena ratio of other two observations is:

27. Let be a natural number and .

Then is equal to:

(Where is a constant of intergration)

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28.If and then equals :

29. Consider the quadratic equation Let be the set of all integral values of forwhich one root of the equation lies in the interval and its other root lies in the interval Then the number ofelements in is:

10 18 12 11

30. If the system of equations

has infinitely many solutions, then equals:

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rao physics - rao iit · 10/1/2019 · rao iit academy / jee - main official online exam / 10...

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