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AIEEE 6

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AIEEE 6

Parteek S / Jaipur

4 years of teaching experience

Qualification: Pursuing Graduation

Teaches: Mental Maths, Chemistry, English, Logic, Mathematics, Economics, NSTSE, AIEEE, BITSAT, IIT JEE Mains, WBJEE

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  1. N/A
  2. (c) Yes (b) No (d) X, No 13. A piece of ice of mass 4 kg initially at —200C has to be transformed into steam at 2000C, tind the total amount of heat given to it L f = 3.36 x 10%/ kg, = 2.25 x 106J/kg = 2100 J/ kg- K and s 4200 J/ kg-K water = 3300 J/ kg-K (a) 121.92* 105 J (b) 120.24x 105 J (9 135.12 x 105 J (df 45.12 x 105 J C 18. 619. C 20. 121 A panicle starts from origin at 1' O with a velocity 5i m/s and moves in x-y plane under action of a force which produces a constant acceleration of (3i + 2 j) m/s2. What 'is the y co-ordinate of the particle at the instant its x co-ordinate is 84 m ? •€ 6 (9 36m Which of following curves may represent the speed of the electron in hydrogen atom as a function of the principal quantum number n ? (b) 84 m (d) 18 m QL 14. If i is increasing continuously, then find the direction of induced current in the loop. (3) Anticlockwise (bf Clockwise (c) In any direction (d) No curront will be induced 15. A proton moves in a straight line from point a to point b, inside a linear accelerator, a total distance d = 0.5m. The electric field is uniform along this line, with magnitude E = 1.5 x 10 7 V/ m in the direction from a to b. Determine the work done on it by the field and the potential difference Va — 16. (a) 7.5 Mev, SMV (b) 7.5 ev, 7.5 vs (c 7.5 Mev, 7.5 df- 7.5 MeV,- 7.5 MV b When lg of water changes from liquid to n vapour phase at constant pressure of 1 atm, the 21. volume increases from 1 cc to 1671 cc. The heat of vaporization at this pressure is 540 cal/g. Find the increase in internal energy of A small source of sound moves on a circle as shown in figure and an observer is sitting at O. Let , , be the frequencies heard when the source is at A, B and C respectively : 2 A steel rod of cross-sectional area 5mm is held between two fixed supports. If the rod is unstrained at IOOC, find the force exerted by rod on the supports, if temperature increases to 250c : = 1.2 x 10-6/0C, Y = 2x 1011N/m2) steel water. (a) 2268 J (Y 2099.33 J (d) 2019.65 J --17. Mark the correct option : (a) Bohr magneton is the fundamental unit of magnetic moment (b) Magnetic moment can be expressed in terms of angular momentum (c) The electron revolving around a nucleus has two types of angular momentum, spin (d) All of the above (a) 12 N (c) 18 N (d) 16 N 22. C 23. A solid sphere has moment of inertia I about any of its diameter. If the temperature of body is increased by AT, then its moment of inertia will increase by : (a) no increase (b) la AT (d) 4u IAT Two particles x and y having equal charge after being accelerated through the same potential diffevence enter a region of uniform magnetic
  3. AIEEE MOCK TEST-5 field and describe circular paths of radii R) and R 2 respectively. The ratio of the mass of x to that of y is , (b) 9 (ft)2 C 24. When two particles q and — q are placed at a distance r, then Coulomb's force Of attraction between them has magnitude F. If another charge particle having charge + 3q is placed near to —i q then the force exerted by — q on q will be : ( (a) 4F, repulsive (b). 2F, attractive (d) 2F, repulsive (c) F, attractive 25. Find the equivalent thermal resistance of combination of rods as shown in figure. Every rod has same length I and cross-sectional area A. Thermal conductivities are mentioned in figure. 1 3 4K 2 2K (b) (c) E (d) If the blood vessels in a human being acted as simple pipes (which they do not in actual), what would be the difference in blood pressure between the blood in a 1.80 m tall man's feet and in his head when he is standing? Assume the specific gravity of blood to 'be 1.06. 32 1 28. D 29. 30. 31. (a) 16.23 kPa (c) 17.3 loa (b) 18.7 kPa (d) 15.9 kPa 71 (c) 71 4104 12104 In JJ Thomson experiment, the potential difference of 320 V is accelerating the electron. The electron béam is entering a region having uniform magnetic field 6 x 10-5 T acting perpendicular to it. Find the value of electric field in this region so that the electron does not experience any deflection. (me = 9.1 x 10 31 kg) A particle is kept at rest at a distance R (earth's radius) above the earth's surface. The minimum speed with which it should be projected so that it does not return is : (a) 6.4 V/ m (c) 640 V/m (b) 64 V/ m (d) 6.4 x 104 V/m GM (a) GM GM (b) 2VIG (d) A wire of length 100 cm is connected to a cell of emf 2V and negligible internal resistance. The resistance of the wire is 3Q. The additional resistance required to produce a potential difference of 1 mV per cm is : (a) 470 (c) 600 (b) 57 Q (d) SSQ C 7. A charge Q is distributed uniformly on a conducting solid sphere of radius R then correct plot for E versus r (the distance from centre of sphere) and V versus r is : (a) A 20 g büTlet is fired horizontally with a speed of 600 m/s into a 7 kg block sitting on a table top; the bullet (b) lodges 'in the block' (B). If the coefficient of kinetic friction between the block and the table top is 0.4, what is b the distance the block will slide ? B = 0.4
  4. ,4/EEg MOCK TESL5 (a) 0.5 m (b) 1.2 m (c) 0.37 m (d) 0.85 m Q 32. In which of the following situations is there non-zero net force on the body ? (a) An aeroplane flying due north at a steady speed of 120 m/s and at constant altitude (b) A car driving straight up a hill with a 30 slope at constant speed 90 km/h (c) A hawk circling at a constant speed of 20 km/h at constant height of 15 m above an open field (d) A box with slick, frictionless surfaces in the back of the truck as the truck accelerates forward on a level road at 5 m/s2 33. Figure shows two rays A and B being reflected by a mirror and going as At and B f. The mirror : (a) is plane (b) is convex (c) is concave (d) may be any spherical mirror Q 34. A gasoline engine in a large truck takes in 10 kJ of heat and does 2000 J of mechanical work per cycle. Find the thermal efficiency of engine. 35. A uniform rectangular marble slab is 3.4 m long C (a) 12 w 123 (b) -12W (d) Zero 37. 38. 40. You have eaten a lot of "gulab jamun" (a sweet dish) which gives you a energy of 900 food cal, now you want to work off the energy you have taken. For this you are running up several flights of stairs. Find for how high you will climb? (Take your mass = 60 kg). (b) 800 m (a) 6410 m (d) 2100 m (c) 9000 m 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 the value of K. Consider the situation shown in figure. The switch is closed at t = O, when the (d) 3.5 E C 36. and 2.0 m wide. It has a mass of 180 kg. If it is originally lying on the flat ground, how much work is needed to stand it on an end ? (a) 2.0kJ (b) 3.0 J (c) 3.0 W (d) 3000 kJ For the circuit shown in the figure, the battery having emf 12 V is acting as power supply and other is rechargeable one. Find total power consumed by rechargeable battery. capacitors are uncharged. Find the charge on the capacitor Cl as a function of time t. (a) CIE [1 -e t/ RC2 'l where C = (d) CE e- where C = An infinitely long current carrying wire is bent as shown in figure, All the vertical sections of the wire are equally spaced. The magnetic field at point O is : a
  5. out 01 plane ot paper out of plane of paper In 16 3) out of plane of paper out of plane of paper X C 41. It is necessary to illuminate the bottc-• of a well by reflected solar beam when the incident ray is at an angle of 400 to the veilical. At what angle to the horizontal should a plane mirror sphere reflected. Find exerted by light sphere. (a) 4.19 x ICY' 14 N (c) 7.14 N Radiation coming be;) 10 (b) (d) from on 5.45 x 10 N None of these transitions n = 2 to be placed ? (a) 900. (c) 700 (b) 400 (d) 200 42. The two blocks shown in figure have equal masses and = pi k. = 0.3 for both blocks. Wedge W is fixed and block A is given initial speed of 1 m/s down the plane. How far will it move before coming to rest if inclines and strings are quite long ? [Take g = 10 m/s2] m 530 W 370 43. (a) 0.45 m (b) 0.9 m (c) + 4.8m (d) Question is irrevalant As shown in figure. a uniform solid sphere rolls on a horizontal surface at 20 m/s. It then rolls up the incline shown. What will be the value of h where the ball stops ? v = 20 m/s 45. C 46. 47. 1048. 49. n 1 of hydrogen atom falls on helium ions in n = 1 and n = 2 states. What are the possible transitions of helium ions as they absorb energy from the radiation ? (a) n = 2 to n = 3 (c) (a) and (b) both (d) None of these A spinning wheel initially has an angular velocity of 50 rad/s east; 20s later, its angular 'If the angular velocity is 50 rad/ s west. acceleration is constant, what are the magnitude and direction of the angular acceleration ? (a) 5 rad/s2 towards east (b) 2 rad/s2 towards west (c) 5 rad/s2 towards west (d) 2 rad/s2 towards east Find the energy released for the nuclear reaction 86Ra222 + 2He4. The KF of emitted a-patticle is 4.78 MeV. Assume the parent nucleus to be at rest : (a) 8 MeV (b) 4.78 Mev (c) 4.87 MeV (d) Information is insufficient The acceleration of an electron in first orbit of H-atom is : 33 (a) (h/ 27t)2 (h/ 27t)2 (c) 3 mr (h/ 2Tt)2 (b) 23 3 (d) (h / 21t)2 (a) 28.6 m (c) 6m 300 (b) 8.6 m (d) 18.6m Q44. A parallel beam of light having intensity 10m W/cm2 is incident on a sphere of radius 2cm 300/0 of the light has been absorbed by For an insulating uniformaly charged solid sphere of radius R and having charge Q the correct option is : 3
  6. N/A
  7. TES "62. The diamagnetic molecules are : (9) B2, of, N2 63. 1.0 g of a metallic carbonate left on ignition 0.56 g of its oxide. The atomic weight of the metal if its specific heat is 0.155 cal/ gec : (b) 20.0 (cf 80.0 (d) 25.0 64. Two lighter nuclei are fused together to form another nucleus and energy is released in the process because : (a) binding energy of lighter nucleus is more. (b) binding energy per nucleon of lighter nucleus is more (c) binding energy per nucleon is more for lighter nucleus. (d) energy is always released when two nucleus are combined 1865, 'Chemisorption' is also said : (a) physiosorption (b) van der Walls' adsorption (c) reversible adsorption (4) activated adsorption 66. The element with the electronic configuration 4f145dl 6s2 is a . (a) representative element (b) transition element (c)ßanthanide (d) actinide 6 71. 73. 75. (S) CICH2—CH2C1 NaCH=CHNa zn cH2 cH2 —CH2 cl cl MOCK = CH2 Intermediate of this reaction is . (a) carbocation (b) carbanion (S) carbon free radical (dj carbene Basic character of which of the following is (a) CH3—NH2 (c) NaNH2 (J CH3 CH3 cH3 78. T 80. 81. 82 d 67. Which of the following is used as a depressant Q 76. in froth floatation process ? (b) Pine oil (a) Amyl xanthate (c) Copper sulphate (d) Potassium cyanide 68. Which of the following shows bonds in silicones ? (c) Si—C—Si—C—Si 69. The type of hybridization and possible geometry of tetrafluorides of members of oxygen family are . (9) sp3d, trigonal bipyramidal (b) sp3, tetrahedral (c) dsp2, square planar (d) d2sp3, octahedral '70. Reaction of Br2 on ethylene in presence ofNaCl gives the compound as major product is : 77. The reaction of glucose with acetic anhydride and Tollen's reagent suggest that it is . (0) a pentahydroxy aldehyde (bf hydrate of carbon (c) a polyhydroxy ketone (d) an alcohol Which of the following is homogenous catalyst ? (a) Lindlaes catalyst (Y) Nickel boride (P-2) (cj Willkinson catalyst (d) Adam's catalyst Which of the following is not a functional isomer ofC3H60 ? (b) 1, 2-epoxy propane (a) 'Prop-2-en-l-ol (d) Prop-2-one (c) Propanol The systematic naming of the molecule is o (a) exo-7-methyl bicyclo (2, 2, 1) heptan-2-one (b) endo-7-methyl bicyclo heptan-2-one (c) exo-5-methyl bicyclo (2,2,1) heptan-2-one (d) endo-5-methyl bicylo (2,2,1) hetpan-2-one In the photo-electric effect, the number of photoelectrons emitted per unit time depends upon the : (a) energy of incident radiations (b) frequency of incident radiations (c) intensity of incident radiations (dj both frequency and intensity of incident radiations (j
  8. A/EEE MOCK r&s7-s 78. •rhe length in 02, 052 and O} - follows the order : 2- 2 2 (b) > 02 > O; (c) 02 > o; > o;- > o; (d) O; > O}- > > 02 (a) 2.50 (c) 1.2 (d) 1.3 86. @79. The number of moles of HCI (percentage purity 60% by weight) in a 200 mL of solution of 87• specific gravity 1.12 : (g) 3.68 mol ($3.1 mol (b) 2.24 mol (d) 1.12 mol Q80. A zinc rod weighins 25.0 gwas kept in 100 mL (188. of 1.0 (M) CuS04 solution. After a certain time the molarity of Cu2+ in the solution was 0.8. The molarity of SO}- is : (a) 1.0M (c) 2.0M (b) 0.5 M (d) 0.25 M Q 81. In a solid, oxide ions are arranged in ccp. One sixth of the tetrahedral voids are occupied by the cations A while one third of the octahedral voids are occupied by the cations B. The formula for the compound is : (a .AB03 cfAB02 (b) A2B304 (d) A3B204 'b 82. The composition of sample of wustite is Feo 9301 00. What percentage of the iron is present in the form of Fe (Ill) ? 89. 90. 91. 92. 93. Mark out the wrong expression . (a) Boyle's temperature TB = b/ aR (b) critical pressure .Pc = a/ 27b (c) critical temperature T- = 8a/ 27Rb (d) critical volume Vc = 3b The temperature at which nitrogen under 1.00 atm pressure has the same root mean square speed as that of carbondioxide at STP : (b) 270C (a) OOC (d) -e 2000C Solution of AIC13 in water is (b) basic (a) acidic (d) amphotetic (c) neutral Mark out the incorrect statement about liquid junction potential : (a) LJP is an additional source of potenlial difference across the interface of two electrolytes. (b) LJP arises due to differing ionic mobility in two different liquid (c) LJP is essential part of electrolyte concentration cell (d) Salt bridge promotes liquid junction potential From the following pairs, pick out the pair having a similar geometry (a) 14% (b) 15.05% (a) Nog, NO; (c) NF3, PF3 (b) NH3, NH; 3 C 83. One mole of 02 at 300K and 1 atm pressure is heated in a closed vessel so that temperature is 500K and pressure is 5 atm. Then it is cooled so that temperature is 300K and pressure is 1 atm. Change in internal energy of the gas is : (a) 2.2 (b) 2.5 IU 84. When AgN03 is treated with excess of KI, Agl precipitates out, which forms colloidal solution with : (a) positive charge (b) negative charge (c) some positive, some negative (d) no acquisition of charge 5. The freezing point of a solution composed of 10.0 g of KCI in 100 g of water is 450C. Calculate the van't Hoff factor; i, for this solutiom In a combination of N073, Br- and l- present in a mixture, Br- and I - interfere in the ring test for NO;. These are removed by adding a solution of : (a) AgN03 (b) Ag2S04 (c) Ag2C03 (d) none of the above An element (X) forms compounds of the formula XC13, X 20s and CagX2, but does not form XC15. Which of the following is the element X ? (b) Al Which one of the following reactions demonstrates that 1-1202 acts as an oxidizing agent in the basic medium :
  9. (a) + 2011- Mn02 + 2H20 2 + 2H20 + 02 (c) ,Na2C03 + 1-1202 Na20.2+ E120 +C02 (d) Mn02 + + 210 + 2H20 + 02 94. Ostwald's process for the manufacture of nitric acid involves : (a) oxidation of N2 to NO (b) oxidation of NI-13 to NO (c) combination ofN2 and 1-12 (d) passage of steam over red hot coke Cc 95. Which of the following represents the correct order of increasing PIC a values of the given acids ? (a) Hc104 < I-IN03 < F12C03 < (b) HN03 < Hc104 < < E12C03 (c) < H2C03 < HC104 < HN03 (d) HC104 < HN03 < < 1-12C03 Q 96. The heat of combustion of benzene at constant volume was found to be 3263.9 10 mol-I at 250C. Then heat of combustion of benzene at constant pressure is : (a) HOOC (c) OMC Oil (b) I OH 01 IC CIA 2 (d) OMC oci4a 99. 100. 101. 102. Which does not give turbidity with 'I-IBr ? (a) (c) OH (b) (d) OH cH3 OH CH20H Which of the follovving cannot be directly oxidized into benzoic acid ? CH2CH
  10. CMcc— (c) 02N C 103.2 COOI I N02 OH N02 OH (d) I vNH2 Oil ocH3 COOH COOH product 8105. C 106. 107. 108. 109. procluct, which of the following is not the possible product (in significant amount) ? O (a) Me3 I (c) cMe3 (b) (d) cMC3 Product is pt1Qle complex having structure : o (a) (b) The standard enthalpies of formation oj methane, carbondioxide and water are x, y and z respectively. Enthalpy of combusticn of methane is : The vapour pressure of pure benzene, C61-16. at 500C is 268 torr. How many mol of nonvolatile solute per mol of benzene is required to prepare a solution of benzene having a vapour pressure of 167.0 torr at 500C ? 00 (d) none of the above 104 I I o N N (a) 0.605 mol (c) 0.12 mol (b) 0.50 mol (d) 0.24 mol CFI During the polymerization, the addition of benzoquinone : (a) catalyse the polymerization (b) inhibits the polymerization (c) increases the polystyrene density (d) to increase elasticity A fist order reaction in aqueous solution was too fast to be detected by a procedure that could have followed a reaction having a half-life of at least 2.0 ns. The minimum value of k for this reaction is : (a) 3.5 x 108 (b) 1.2x 108 s (C) 1.9X 108 s-l (d) 2.7 x 108 s -l 1m the reaction of a A + b B + cc products : (i) if concentration of A is .doubled) keeping concentration of B and C constant, the rate of reaction becomes double. (ii) if concentration of B is halved, keeping concentration of A and C constant, the rate of reaction remains unaffected. (iii) if concentrationi0f C is made 1.5 times, the rate of reaction becomes 2.25 times. The order of reaction is : (b) 2.5 (d) 3.5
  11. AIEEE MOCK JEST-5 1 110. A hydrogen gas electrode has potential of (d) 27 (a) (c) 2 7 b 2. - 0.118 V when H 2 gas is bubbled at 298 K and 1 attn, in HCI solution. The pH ofHCl solution is : Which one of the following is wrong ? (3) The elements on the main diagonal of a symmetric marix are all zero (b) The elements on the main diagonal of a skew-symmetric matrix are all zero (c) For any square matrix A, — (A + A') is symmetric (d) For any square matrix A, (A —A') is skew-symmetric Let R be set of real numbers. If f : R R is defined by f(x) = ex, then f is . (a) surjective but not injective (b) injective but not surjective (f) bijective (d) neither surjective nor injectiv tan 3x never lies beÄ&teen : tan x 1 and 0 (b) and 3 1 1 and (d) —3 and 3 W, then x is : 12 - 12 The function f (x) = sin- (a)? continuous at x = 0 (b) discontinuous at x (c) differentiable at x (d) none of the above (cos x) is If the angle between two lines represented by 2K 2 + 5xY + 3y2 + 7 y + 4 = O is tan- m, then m is equal to : 1 (a) 7 (c) A line segment has length 63 and direction ratios < 3, — 2, 6 If the line makes an-obtuse then the components of the vector are : (b) 27, 18, 54 (9) 27, 18, 54 (cf- 27, 18, -54 (d) 27, - 18, 54 The number of terms with integral coefficients 1/2 600 in the expansion of (71/3 + 5 x) is : (a) 100 (b) 50 (d) none of these In a football championship, there were played 153 matches. Every two teams played one match with each other. 'The number of teams participating in the championship is 1134. If sin x + cos x = (a) .2nn + (Y 2nn+ 2nrt — 12' (c) 2nn—Æ, 2n7t 12 (d) none of the above 135. The geometric meanG of the product ofn series of data with geometric means Gl, G2, , n respectively, then : (C) Jä=-GlG2 . ...n. G n (d) none of the above (a) 14 (c) 18 (b) 22 (d) none of these 11. b 12. The equation I z —il +1 z + il = k, k > 0, can represent an ellipse, if is : (d) none of these If + x -2) x2 + + 2) x < 1 for all x eR, then X belongs to the interval : 2 (c) 1 2 (d) none of these
  12. MOCK TEST-5 13. A gentleman invites 13 guests to a dinner and places 8 of them at one table and remaining 5 at the other, the tables being round. The number of ways he can arrange the guests, is . 40 (c) 40 40 14. A ladder rests against a wall at an angle to the horizontal. Its foot is pulled away from the wall through a distance a, so that it slides a distance b down the wall making an angle ß with the horizontal. Then a is equal to : (a) b tan (a + ß) (b) b tan — (a — B? (c) a tan — (a —4 13) (d) none of these x 15. Range of the function f (x) is : 1+1 xl C 16. The distance between the point (1, 1) and the tangent to the cunte y = e + x2 drawn from the point x = O is : 20. 0(21. (2122. C 23. 24. j25. 131 A man and lus wite appear .for an interview for two posts. The probability of the manis selection is 1/5 and that of his wife's selection is 1/7. The probability that at least one of them is belected, is : (b) 12/ 35 (a) 9/35 (d) 11/35 (c) 2/7 If the co-ordinates of the vertex A of a A ABC are (1, 2) and equation of the perpendicular bisectors of AB and AC are 3x + 4y 1 = 0 and 4x + 3y — O, then the area of A ABC is : (b) 3 sq unit (a) 2 sq unit (d) none of these (c) 1 sq unit If from any point P on the circle x2 + Y2 + 2gx+ 2fy + c = O, tangents are drawn to the circle x2 + y 2 + 2gx+ 2fy + c sin 2 u + (g 2 + f 2) cos2 = O, then angle between the tangents is : (c) (d) none of these 1 (a) 1 2 The value of a for which the function f (x) = sin x — cos x — ax + b decreases" for x e R is given by : (p a2Vä (b) a 21 1 f x (42 — 2f' (t)) dt, then f' (4) is 18. 4 Area of the triangle formed by the tangents and circle the of of chord contact x2 + y 2 + 6x + 8y = O, if tangents are drawn from the point (1, 1), is : 340 sq unit (a) 41 360 (b) sq unit 41 320 sq unit (c) 41 (d) none of the above The eccentric angle of a point on the ellipse 2 = 1 whose distance from the centre of the ellipse is 2, is : x equal to : (a) 32 32 (c) 32 (b) (d) none of these (a) (c) Distance 63 It (b) between the ! 319. If Al is the area of the parabola y 2 = 4ax lying between vertex and the latus rectu and A2 is the area between the latus rec m and the double ordinate x = 24 then Al /A2 is equal to: (d) none of these line 20 + 3fc+ —j + 4 and the plane r •(i + 5j + k) = Sis : 10 unit 10 Ui (c) unit 3 (b) unit 3 (d) none of these
  13. 'K 11--S forces of magnitudes P, Q and R act at a point parallel to the sides BC', CA ancl AB respectively of a ttiangle ABC, then magnitude of their resultant is : 2 2 2 + R2 2QR cosA - 2RP cosB (b) s-. 21)Q cos c) (d) none of the above In a A ABC, Z B = 900 and b + a = 4, the area of the triangle is the maximum when ZC is : 32. 6 (a) 255 (b) 127 (c) 60 (d) none of the above An elevator starts with passengers and stops at n floors S n). The probability that no two passengers alight at the same floor, is 3 m (c) (b) n ncm (d) m 27. & 28. (a) (c) C (b) (d) none of these 33. 34. COS X t— COS X clx is equal to : 1 cos3 x 2 sin-I (cos3/0 x) + c (a) 3 sin-I (cos3/2 x) + c (b) 2 cos-l (cos3/2 x) + c (c) A rigid body is rotating at 5 rad/s about an axis AB, where A and B are points whose position vectors are 2 i + j + k and 8i — 2j + 3k respectively. The velocity of the particle of the body at the point whose position vector is 15 5 (b) (47 6j 31Q) 7 15 (4i 6 j — 312) (d) none of the above (d) none of the above The function f (O) = satisfies : — + 2f(0) cot 0 (a) — 2 f (0) cot o (b) 2f(0) = o (d) 0 dx d() 0 1 — cos 0 cos x 29. The sum of the digits in the unit place of all the numbers formed with the help of 3, 4, 5, 6 taken all at a time, is . CJ 35. 3136. 37. A rectangular hyperbola whose centre is C is cut by any circle of radius r in four points P, Q, R and S. Then cp2 + + + CS2 is (a) 432 (c) 36 (bp 108 (dj 18 30. A pulley carrying a total load W hungs is a loop of a chord which passes over two fixed pulleys and has unequal weights P and Q freely suspended from the ends, each segment of the chord vertical of W remains at rest, then W is equal to : (c) 312 (b) 2r2 equal to : (a) 3PQ E xr, then n is : 2PQ (b) (d) 128 The shortest distance between the lines = (5 +7 j + 310+ x (5i -16j+ 7k) and = (9i + 13j + 15 (3i + 8j - 5k)is . (a) 14 unit (b) 12 unit (c) 10 unit (d) 8 'unit Let f (x) = x —l x — x 2 1, x el— 1, ll. Then the number of points at which fCÅi) is discontinuous, is : (d) none of these

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