Physics, Chemistry, Mathematics

Part A - Physics

1. If M is mass of rocket , r is rate of ejection of gases w. r. t. rocket, then acceleration rocket is

(a) (b)

2. A point moves in straight line so that its displacement x metre in time t second is given by x2 = 1 + t2. Its acceleration in ms-2 at time ¢t¢ second is

(a) (b)

3. A liquid of density d is pumped by a pump P from situation (i) to situated (ii) as shown in figure. If the cross section of each vessel is a the work done in pumping ( neglecting friction effects) is

(a) 2dgh (b) d gha

4. The centre of wheel rolling on a plane surface moves with speed v0. A particle on the rim of the wheel at the same level as the centre will be moving at speed.

(a) zero (b) v0

5. Water rises to the height h in a capillary at the surface of earth. On the surface of moon the height of water column in the same capillary will be:

(a) 6h (b)

6. An equilateral triangular loop is kept near to current carrying long wire as shown in figure. Under the action of magnetic force alone, the loop

(a) must move along x-axis

(b) must move in x y plane

(d) loop moves in way we cannot predict.

7. Find the equivalent thermal resistance of combination of rods as shown in figure. Every rod has same length l and cross sectional area A. Thermal conductivities are shown in figure.

(a) gf (b)

8. If the charge of 10mc and -2mc are given to two plates of a capacitor which are connected across battery of 12 V. Find capacitance of capacitor.

(a) 0.33 mf (b) 0.5 mf

9. Which of the following curves may represent the speed of electron in a hydrogen atom as function of the principal quantum number n.

(a) A (b) b

10. A uniform rectangular marble slab is 3.4 m long and 2m wide. It has mass of 180 kg. If it is originally lying on the flat ground. How much work is needed to stand on one end.

(a) 2KJ (b) 3.0 J

11. A uniform rope of mass m per unit length , hangs vertically from a support so that the lower end just touches the table top. If it is released , then at the time a length y of the rope has fallen the force on the table is equivalent to the weight of the length ky of the rope find value of K.

(a) 1 (b) 2

12. A Student constructed a vernier calipers as shown. He used two identical inclines and tries to measure the length of line PQ for this instrument determine the least count.

(a) (b)

13. Two radioactive nuclei A and B have their disintegration constant lA and lB respectively initially , NA and NB number of nuclei are taken then the time taken after which their undisintegrated nuclei are same is

(a) (b)

14. Two point charges are kept at a certain distance from one another. The graph represent the variation of potential along the straight line connecting the charges. At what point electric field is zero.

(a) 1 (b) 2

15. Two non-ideal batteries of unequal emf’s are connected in parallel consider the following statement.

(a) The equivalent emf is smaller than either of two emf’s.

(b) The equivalent internal resistance is smaller than either of two internal resistance.

(a) Both A & B are correct

(b) A is correct but B wrong

(d) both A and B wrong.

16. The path difference between two wavefront emitted by coherent source of wavelength 5460 Å is 2.1 micron. The phase difference between wavefronts at that point is

(a) 7.692 rad. (b) 7.692 p rad.

17. A concave lens and convex lens have same focal length of 20 cm and both are put in contact. The combination is used to view on object 5 cm long kept at 20 cm from the lens combination. As compared to object the image is

(a) magnified & inverted (b) reduced and erect

18. A metal rod of resistance 20W is fixed along a diameter of conducting ring of radius 0.1m and lies on x-y plane. There is magnetic field of B -(50 T) . The ring rotates with w = 20 rad s-1 about its axis. An external resistance of 10W is connected across the centre of ring & rim. The current through external resistance is

(a) (b)

19. A piston filled in cylindrical pipe is pulled as shown in figure. A tuning fork is sounded at open end & loudest sound is heard at open length 13cm, 41 cm and 69 cm. The frequency of tuning fork if velocity of sound is 350 ms-1.

(a) 1250 Hz (b) 625 Hz

20. The acceleration displacement graph of particle executing SHM as shown in diagram. The time period of SHM is

(a) (b)

21. The small satellites moves in circular orbits of radius r & r + Dr from centre of earth . The time period of rotation T and T & DT (D r < r, DT < T) . Then DT is equal to

(a) (b)

22. A swimmer of mass m rests on top of Styrofoam slab. Which has thickness h and density rs. The area of slab if it floats in water with is upper surface just awash is (take density of water = rw)

(a) (b)

23. The reading of ammeter in given figure is

(a) 6.56 A (b) 3.28 A

24. In the C - E configuration used in figure, as n-p-n transistor with current gain b = 100 is used. The output voltage of amplifier is

(a) 10 mV (b) 1.0 V

25. An electron is trapped in 1-D infinite well of width 250 pm & is in ground state. What is the longest wavelength of light that can excite the electron of light that can excite the electron from ground state via single proton.

(a) (b) l =

26. A uniform solid cylinder of mass 2kg and radius 0.2 m is released from rest at top of semicircular track of radius 0.7 m cut in block of mass M= 3 kg as shown in figure. The block is resting on smooth surface & cylinder rolls down without slipping . The distance moved by the block when cylinder reaches the bottom of track

(a) 0.3 m (b) 0.5 m

Directions (Q. No. 27 to 28) : Each of these questions contains two statements : Statement I (Assertion) and Statement II (reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select one of the codes (a), (b), (c), (d) given below :

(a) Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I

(b) Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I

(d) Statement I is false; Statement II is true

27. Statement-I An Astronaut in the orbiting space station above earth experience weightlessness.

Statement-II An object is always in the state of tree-fall motion.

28. Statement-I A double convex lens (n = 1.5) has focal length 10 cm. When lens is immersed in water its focal length becomes 40cm.

Statement-II =

29. The binding energy of two nuceli Pn & Q2n are x joule & Y joule respectively. If 2x > y , then energy released in reaction will be

(a) 2x + 4 (b) 2x - 4

30. 2 moles of an ideal mono atomic gas is taken from state A to state B along path ACB. Temperature of B is TO.

for process A ¾ D C ¾ B The heat absorbed by gas is

(a) (b)

Part B - Chemistry

31. The crystal are bounded by plane faces(f) straight edges (e) and interfacial angle(c). The relationship between then is

(a) f + c = e + 2 (b) f + e = c + 2

32. The total ionic strength ( total molarity of all the ions) containing 0.1 M of CuSO4 and 0.1 M of Al2 (SO4)3 is :

(a) 0.2 M (b) 0.7 M

33. A 0.518g sample of line stone is dissolved in HCI and then the calcium is ppt as CaC2O4. After filtering and washing the ppt , it requires 40.0 mL of 0.25 N KMnO4 solution acidified with H2SO4 to titrate it as,

The % of CaO in the sample is

(a) 54% (b) 27.1%

34. Arrange the vander waal constant for the gases.

I C6H6(g) / A. 0.212
II C6H5 CH3(g) / B. 5.464
III Ne(g) / C. 18.000
IV H2O(g) / D. 24.060

(a) I - A, II- D, III - C, IV - B

(b) I - D, II - A, III - B, IV - C

(d) I - B, II - C, III - A, IV - D.

35. Longest mean free path under similar condition of P and T stands for

(a) N2 (b) O2

36. The angular momentum of eQ of H-atom is proportional to :

(a) r2 (b)

37. A hydrogen atom is in its ground state absorbs a photon. The mass energy of such a photon is :

(a) 1.5 eV (b) 3.4 eV

38. The radioactive decay rate of a radioactive element is found to be 103 dps at a certain time. If the half life of element is 1 sec, the decay rate after 1 sec is……..and after 3 sec is ……

(a) 500, 125 (b) 125, 500

39. Which aqueous solution has minimum freezing point.

(a) 0.01 M NaCI (b) 0.005 M C2H5 OH

40. The direct conversion of A to B is difficult hence it is carried out as

A ¾® C ¾® D ¾® B

Given DS (A ® C) = 50 eU DS (B ® D) = 20 eU

DS (C ® D) = 30 eU

Where eU is entropy unit. Thus change in entropy in (A ® B) is :

(a) 100 eU (b) 60 eU

41. Heat of neutralisation of HF is

(a) 57.32 KJ (b) > 57.32 KJ

42. The cell Zn / Zn+2 (1m) || Cu+2 (1m) | Cu was allowed to be completely discharged at 298 K. The relative conc. of Zn+2 to Cu+2 is :

(a) antilog (24.08) (b) 37.3

43. Which is correct relation in between and where c, n, p represent concentration, mole and pressure terms for gas reactant (A (g) ¾® product)

(a) (b)

44. For the reaction N2 + 3H2 2NH3 in a vessel, after the addition of equal no. of mole of N2 & H2, equilibrium state is formed. Which of following is correct.

(a) [H2] = [N2] (b) [H2] < [N2]

45. In an experiment to determine the enthalpy of neutralisation of NaOH with H2SO4, 50 cm3 of 0.4 M NaOH were titrated Thermo metrically with 0.25 M H2SO4. Which of the following plots gives the correct respectively.

(a) (b)

46. Which plot is adsorption isobar for chemisorption where x is the amount of gas adsorbed on mass m (at constant pressure at temperature T).

(a) (b)

47. Gold no. of protective colloid A, B, C and D are 0.50, 0.01 , 0.10, 0.005 respectively . The correct order of their protective power is

(a) D < A < C < B (b) C < B < D < A

48. The distribution law holds good for ¸

(a) Hetero geneous system (b) Homogeneous system

49. which of the following is least statement

(a) I (b) II

50.

Hydrogenation of above compound in the presence of poisoned palladium catalyst gives

(a) an optically active compound

(b) an optically inactive compound