Question Booklet Series JELET-2022 Etta , BSc. Candid (Booklet Number) Duration: 2 Hours No, of MCQ : 100 Full Marks: 120 INSTRUCTIONS 1, All questions are of objective type having four answer options for each. 2. Category-I : Carry 1 mark each and only one option is correct. In case of incorrect answer or any combination of more than one answer, / mark will be deducted. 3. Category-II : Carry 2 marks each and one or more option(s) is/are correct. If all correct answers are not marked and no incorrect answer is marked, then score = 2 x number of correct answers marked + actual number of correct answers. If any wrong option is marked or if any combination including a wrong option is marked, the answer will be considered wrong, but there is no negative marking for the same and zero mark will be awarded. 4. Questions must be answered on OMR sheet by darkening the appropriate bubble marked A, B, C, or D. Question booklet series code (A, B, C, or D) must be properly marked on the OMR. 5. Use only Black/Blue ball point pen to mark the answer by complete filling up of the respective bubbles. 6. Write question booklet number and your roll number carefully in the specified locations of the OMR. Also fill appropriate bubbles. 7. Write your name (in block letter), name of the examination center and put your full signature in appropriate boxes in the OMR. The OMR is liable to become invalid if there is any mistake in filling the correct bubbles for question booklet number/roll number or if there is any discrepancy in the name/ signature of the candidate, name of the examination center. The OMR may also become invalid due to folding or putting stray marks on it or any damage to it, The consequence of such invalidation due to incorrect marking or careless handling by the candidate will be sole responsibility of candidate. 9. Candidates are not allowed to carry any written or printed material, calculator, pen, fog table, wristwatch, any communication device like mobile phones etc. inside the examination hall. Any candidate found with such items will be reported against and his/her candidature will be summarily cancelled, 10, Rough work must be done on the question paper itself, Additional blank pages are given in the question paper for rough work. 11.. Hand over the OMR to the invigilator before leaving the Examination Hall. ex a.e.s. li 2091009322JELET-2022 MATHEMATICS Category-I (Q1 to 30) (Carry 1 mark each, Only one option is correct. Negative marks: a? -ab -ac kab b? —bc)=Kab?c2, then K = be @) 2 @) 4 2. Letz=1+iten 2 then id 3n 3n fn (A) |z|=sec—, ait =_ ceo d™ in (A) Iz] seo“ a ZS Bs Foe eae 3n 2n Bn a Cc on ae oe = seo3", arga= 4% © lzl=-seeE, ae2=Z ©) Iz\ns00% age 4 3. fi +22—z+i=0, then|z|= 1 (A) 1 am “@ ® 5 | 1 or © 5 4. The locus of the point which moves in such a way that the difference of its distance from the point (3, 0) and (9, 0) is 4 units in a conic section whose eccentricity is 5 (A) 2 ®) 5 3 : 4 2 py 4 Oz © 3 lah gl | 5. LetA=|h bf}, then | é le f ¢ C-F ; @) PEF =e BC-F?_A Oona 72 Where B, C, F are respectivel ET & B.Sc. a3 er SHEERS TOIT ams tse BERN BEDE TEENa 9. 10. ET & BSc. JELET-2022 Consider a branch of the hyperbola x? ~ 2y*- 2/2 x42 y~6=0 with vertex A. Let B be one of the end points of its latus rectum. If c is the focus of the hyperbola, nearer to A, then, the area of the triangle ABC is B ; (A) - sq. unit @) 7 =Isq. unit 2 F [a 5 © 14, [2 sq. unit () fF +15q. unit i 3 2 f If 2}+2k, | |=5 and the angle between & and Bis e then, the area of the triangle formed by & and as two sides is (A) Bea unit (B) 15 sq. unit © =e sq. unit (D) 15V3 sq. unit A force of magnitude V6 acting along the line joining the points A (2, -1, 1) and BG, I, 2) displaces a particle from A to B. The work done by the force is & V6 unit (B) 6unit (© 66 unit (D) 36unit Let f (x) be twice differentiable fumetion such that {"(x) = ~f (x) and f(x) = g (), h(x) = [ @)F? + fe). If h (5) = 11, then h (10) is equal to (A) 22 (B) 0 ou () 4 A triangle ABC of area A is inscribed in the parabola y? = ax of the parabola is at A, and the base BC is a focal chord, (a> 0) such that the vertex ‘The differences of ordinates of Band Cis w@ 4 @ 24 a a A 3A OF © > ' i | I | |il. 12. 13. 14. ET & BSc. JELET-2022 ' Hi lim (+x) i (A) does not exists (B) iso (© ise OF ie Consider the function f(x) =|.x|, x ¢ £. Then (A) Rolle’s theorem is always applicable to fin [a, 6] (C®) (B) Rolle’s theorem is applicable to f in [a, b] when 0 26 2: © x 21. A man of 2 m height walks ata uniform speed of 6 kin/h, away from a lamp post of 6m high. The rate at which the length of his shadow increases is (A) 2kmh | (@) [kmh () 6km/h 3 kwh ET & BSc,22, 23. 25. 26. JELET-2022 The equation of curve passing throuigh the point (13) and having slope at tangent at any point (x, y) as cos? (2) is * x tta(2 atu Z (A) x=e () @)xe8 wo(2) ta(2 tetun(2 (©) x= i) @) x20 #4) Wy = 202%, then a dr : (A) y=oet toe* te (B) y=(A+Bre*+ ie 2 e (© y=(A+Bx)e*+ a (D) y=Acosx+B sinx + —- The digits 1, 2, 3,» 9 ate written in random order to form a nine digit number. The probability that this number is divisible by 36 is 2 w 5 org 1 4 Hi p) 4 © 5 @) 3 ‘The probability that at least one of A and B occurs is 0.6. If A and B occurs simuJtaneously with probability 0.3, then P (A') +P @))is 09 (B) 0.15 © wl (@) 12 1-[ then t= (ove) (-*) z+ 1-ve B) +0 (A) ate @) Tae alle-1 D Aga) © nies (@) l=) +0JELET-2022 j 27. A= ( 2 ) and Tis the unit matrix of order 2 then A? equal to % i ‘i YS 4A-31 @®) 3A-4I i (©) A-I () A+I 28. tea (5 | 32, (A) Aisnon-diagonalizable (B) Ais singular matrix (@f Ais diagonatizable g ©) ATA=1, 100 29, LetA=|1 0 1], then A?~A?—A +4, (I, is the identity matrix of order 3) is 010 GAS Vdentty watx of onder 3 (B) null matrix of order 3 100 (©) non-null matrix of order 3 () jo 1 0 000 0 bid re. 2 V2 ‘ 30. LetA=|0 -2 04Q=|-1 0 6 |. Lo 1. FAS) Oim 2 Then QTAQ is (A) a diagonal matrix (B) not a diagonal matrix (©) an orthogonal matrix (D), anull matrix = i ET & BSc,31. 32. 33. 34, 35. JELET-2022 MATHEMATICS Category-II (Q 31 to 40) (Carry 2 marks each, One or more options are correct. No negative marks.) TP2top Ore > anda ova pa then x ¥3 @) 7 = cos (6+ $) x © x+t=20050+8) ©) xyt L=2005 (0-4) y y 2 If the latus rectum of the hyperbola ofa subtend a right angle at the centre of the a hyperbola, then eccentricity of the ellipse is VS5+1 V5+2 (A) we ®) z (©) lessthan2 =~ (D) greater than 2 | The veotor ax(5x (A) coplanar with Zand 6 (B) coplanar with 6 and & (©) perpendicular to (D) perpendicular to Ifx+|y |= 2y, then y as a function of x is (A). defined for all real x (B) continuous at x= 0 (© differentiable for all x (D) such that a forx<0 a ( The equation (s) of the tangents to the ellipse aD =I parallel to the line y = x is (are) (B) y=x+3 (A) y=x+5 © yax-3 @) y=x-5:36. 37. 38. 39. 40. JELET-2022 Bit WHEY say? 0 Let f(x,y)=4 x7+y 0,x?+y?=0 (A) _ neither f, nor f, exists at (0, 0) but f is continuous at (0, 0) () £,(0,0)=1 but f, does not exist at (0, 0) (©) fis continuou at (0, 0) (D) £, f, exist at (0, 0) and both are 0 If —_—— dx = fi) +c, then fx) equals sin x cos x (A) V2 sin“ (sinx—cos x) (B)-v2 cos" (sin x - cos x) (©) sine (sin x—cos x) (D) cos" (sin x cos x) Ifxdy = y (dx + ydy), y(1) = 1, then y (-3) is (a) 3 : @) 2 © -1 @) 4 a 1 0 LetA=| 3 2-2 1 |.RankofAis 3041) 0 AFL (A) 2fora=0 (B) 3 fordx0, (©) 3ford=2 (D) 3ford=-1 Under which of the following conditions the system of equations ax + by + ¢z = 0, bx + cy +.az= 0, cx + ay + bz =0 have a non-zero solution ? (A) atb+e=0 (B) a=b=c (C) abe=1 (D) #+b+c%=041, 42. 43. JELET-2022 PHYSICS. Category-I (Q 41 to 65) (Carry 1 mark each, Only one option Is correct. Negative marks : +t ) A block of mass 1.0 kg moving on a smooth horizontal surface with speed 2 mis enters a rough surface, The retarding force (F,) on the block is given by ex 310m100m The kinetic energy of the block at x=100 m will be Giver, In 10=2.3) (A) 23 ©) (©) 115s (D) osss ‘A uniform disc of mass M and radius R can rotate in vertical plane about its horizontal axis. A point mass m is glued to the disc at point P, as shown in figure. If the system is released from rest, the angular velocity of the disc when the point mass reaches the bottom most point P, is 4mg 2m B) d/ et. ® Gea 4mg 4mg Dp) AS radi Teme ©) Garnpemeee A constant force F is applied to the block of mass m connected to the spring of spring constant k as shown in figure. Initially (t = 0), the block is at rest. The amplitude of k oscillation of m will be [cmisero-E)44, 45. 46. 47. 48. 49, JELET-2022" If the change in volume is 0.4 % due to a change in length is 1% when a stress is applied along the length of the rod, the Poisson ratio of the material is (A) 03 B) 06 © 08 (D) cannot be determined A large open tank has two holes in the wall, One is a square hole of side L at a depth y from the top and the other is a circular hole of radius R at a depth 2y from the top. The quantities of water flowing out per second from both holes are the same. Then R/L is equal to : ot w+ 72! 1 1 (A) 8) =z T ¥ x 2 Be adn ar 5 ‘A small sphere falls from rest in a viscous liquid. Heat is produced during its fall due to friction with the liquid. If R be the radius of the sphere, then the rate of production of heat at terminal velocity is (A) proportional to R? (B) proportional to RS (C)_ proportional to R3 (D) independent of R ‘A well lagged wire of length L and cross-sectional area S has its ends maintained at temperatures T, and T,, The thermal conductivity of the wire is given by K = B + T where T is the temperature and B and are constants. Then the rate of flow of heat along the wire is equal to SI , S ; @ 2a,-1ity-0 @ Star+TitB-o s F s D © FM-T)ifr=0,p=0 @) Sap ity=2 A one litre glass flask contains some mercury. It is found that at different temperatures, the volume of air in the empty space in the flask remains the same. What is the volume of mercury in the flask ? (The co-efficient of linear expansion of glass is 9 x 10-6 °C~" and the volume expansion of mercury is 1.8 x 10-4 °C-!) 7 (A) 50cm? (B) 150. cm? (© 450m? (D) 400 em ‘Two identical point masses are placed on y axis at y= a and y = ~2. ‘The variation of the ‘magnitude of the gravitational potential [V(x)] as a function of xis given by IVoo] 4 IV@) @) @) QU yy x i —_— Veo} f [Veo] © ©) Fe x aeJELET-2022 50, The angle of prism and refractive index of its material are A and cot A respectively Then cos, is (8,,: angle of minimum deviation) (A 56. A point source of monochromatic light $ is kept at the of radius 15 cm, The cylinder contains liquid of refractive in If the area of liquid surface through which the light emerges in 8 equal to (A) 0.23 B) <7 ( © 1.33 i 15 \ i ae ie eo ET & BSc. Te 4 4 ‘JELET-2022 57. A piece of ice floats in a liquid of density p,. Density of water is pw and py # py. When the ice melts completely, the level of liquid (A) will rise if p, < py (B) will rise if p, > py (©) will fall fp, > py (D) level remains unchanged 58. Two spherical planets P and Q have masses Mp and Mg, surface areas A and 4A respectively and same uniform density p, A spherical planet W also has uniform density P and its mass is (Mp + Mg). The escape velocities from the planets P, Q and W are Vp, Vg and Vy respectively. Then . (A) VwVq>Vp ©) Vo>Vy>Vp 59. A rod of length 1000 mm and co-efficient of linear expansion a = 10 °C"! is placed symmetrically between fixed walls separated by 1001 mm, The Young's modulus of the rod is 10!! N/ m2. If the temperature is increased by 30°C, then the stress developed in the rod is (A) 108 Pa (B) 2x 108Pa (©) 3x 108 Pa (D) 4x 108Pa 60. A cyclic process ABCA, shown in V-T diagram, is performed with a constant mass of an ideal gas. Which of the following graphs represents the corresponding prosses on a P-V diagram ? (A) © ET & BSc.SJELET-2022 The length, breadth’ and thickness of a strip are given by L = (10.0 + 0.1) em, 61. h= (1.00 + 0.01) cm, t= (0.1 + 0.001) cm, The most probable error in volume will be (A) 0.03 cm? (B) 0.111 cm (©) 0.012 em? (D) 0.12 em? 62. The area of the triangle having vertices at P (1, 3, 2); Q(2,-1, 1) and R (1, 2, 3) will be (A) Vi07 squnit (B) 2V107 squnit (©) 37-2 sq.unit @) $Ai07 squnit 63. The kinetic energy of a particle moving along a circle of radius R is ox where o is a constant and x is the distance covered. The force acting in the radial direction is proportional to A * @) # © (D) independent of x 64, The trajectory of a point particle in a projectile motion is given by the equation Y = 2x — 5x2, where ¥ is height and x is horizontal distance. With what velocity was the particle projected? (g=10 m/s?) (A) i+jm/s (B) 2i+jm/s (©) i+2j m/s (D) 3itjm/s 65. The equation of a wave is given by y= A sin @ (2-«] where the symbols A, o and v have their usual meanings, The dimension of p and q are respectively, @) LT (D) dimensionless, TH @ LT © LT ET & BSc, L.68. 69. 70. SELET-2022 A biconvex lens of focal length 15 cm is placed 10 cm in front ofa plane mirror, A small object O is kept at a distance of 30 cm in front of the lens as shown in the figure. Then which of the following statement(s) is /are true ? 30cm 10cm (A) The second image I, will be formed at a distance 10 cm to the left of the lens. (B) The final image at Iy is at a distance 16 cm from mirror. ‘The first image I, will behave as a virtual object for mirror. (D) The final image is real. Two monochromatic radiations, blue and violet of same intensity are incident on a photosensitive surface and cause photoelectric emission. If n, and n, represent frequencies of blue light and violet light respectively then (A) 7m < (B) Number of electrons emitted per second by the blue light will be more than that by the violet light. ‘Maximum kinetic energy of ejected electrons will be more for blue light. @) Work function of the material is different for blue and violet light. ‘A closed container of fixed volume has a mixture of one mole of hydrogen and one mole of helium in equilibrium at temperature T. ‘Assume the gases are ideal. Which of the following statement (s) is/are true 2 (a) (2) of the mixture isd (B) Average energy per mole ofthe ges mixture s 2RT (©) Degtee of freed ofthe gas mixture is 5 H The ratio of rms speed of the Helium molecules to that of hydogen molecules is 1:42 : , ET &BSe. 18 ae Ir & a JELET-2022 PHYSICS Category-II (Q 66 to 70) C (Carry 2 marks each. One or more options are correct. No negative marks) 6. A Face of mass 'm' moves rectilinearly under the force F = A - Bx where A> 0, B> 0 and x is the distance from the point where the particle was initially at rest. If” is the distance travelled by the particle till it comes to rest, then which of the following statement(s) is/are true ? 2A a) d= (A) B (B) acceleration of the particle at dis — 4 m (©) Speed of the particle ata distance x= ais of@ acceleration vs x graph is a straight line with slope A/B 61. Astone of mass ‘m' travels with a uniform speed Vo perpendicular to a stick of mass ‘m’ AAS Tength L at rest. The stone collides elastically “ith the stick at a distance ‘h’ from its agen aass. The stone and the stick move with ‘equal speed after collision. Assume that stone moves in the same direction after collision, Then which of the following statement(s) is/are true ? wy, me- F --- cM x er collision is > (A) The speed of the stick aft 1 «, Wo¥0 Jar velocity of the stick is served in this process 3) The angu! © ‘Angular momentum is not com L () h= O's ET & BSc.JELET-2022 CHEMISTRY Category-I (Q 71 to 85) (Carry 1 mark each. Only one option is correct, Negative marks : 71. » Electronic configuration of Cu* is (Atomic numberof Cu is 29) (A) [Arse as? BY [Ar}3e? as! (© [Arja!? : (D) 1s? 2s? 2p6 3s! 3p6 3d! 4s! 72. A strong electrolyte M,,A,._ yielding the ions M+ and A in solution, the relation between equivalent conductivity (A,,) and molar conductivity (A,,) is A, A, A A, (A) A, = B) A, =tm =a © = Age. Age ©) Ant Doda 73. At a definite temperature the molar concentrations of two monobasic acids HA and HA’ in their individual solutions are same. At that temperature if ionization constants of the acids HA and HA’ are x, and x, respectively and degrees of ionization of HA and HA’ are o, and a respectively, then hk, ! @ S=\ee O Fy Oe =a 74, To which of the following ions, Bohr model is applicable ? QA) ut /> @). Lit (© Lit (D) He \ 75. The metal hydroxide that dissolves both in aqueous KOH and ammonia, is : (A) BeOM, -. @) MeOH, © AlOM, f(z Om, 16. Thiosulphuric acid is : (A), H,S,0, @y H,S0, © @) #80, 7. The correct order of the acidity is : : (A) HCIO,>HCIO,>HCIO,>HCIO BF HCIO> HCIO, > HCIO, > HCI, (©) HCIO,>HCIO,> HCIO, > HCIO (D) HCIO, > HCIO > HCIO; > HCIO, ~~ Be is aes a ET & BSc, 19 BJELET-2022 78, The shape of the NH, molecules is : (A) pyramidal (©) triangular planar (B) tetrahedral (D) see-saw, How many isomers are possible with molecular formula C,HC!? 79. (A) 3 ® 4 > we 2 @) 5 80. Which of the following oxides is used as a white pigment a (A) ZnO ae HgO (Cc) Cud @) NiO If heat absorbed by a system and work done by the system are 120 J and 30 J 81. respectively by a process, then change of internal energy of the system is @ 1503 ®) 905 (© -1505 (D) -905 82. The element of the following that reacts with N, to form a nitride is : (A) Na @y kK (© Cs @) Li ion of a substance A reacts with y ml of a solution of a substance B 83. Let x ml of a solutic If molar concentrations of the solutions according to the reaction 2A + 3B —> products. of A and B are (M,) and (M,) respectively, then (A) 2xM, =3yM, (B) 3xM,=2yM, (©) 2xM,=3yM, 3xM, = 2yM, 84. If the density of a solution of a substance is z gomr? and gram molecular mass of the substance is y g, then the molality of the x (M) solution is @ —— bd Z-0.001xy z—xy x 0.01x (Cc) ——— D) ——— KS) 1000z—xy ©) Too0z-ay 85, If an electron is passed through a potential difference of V volts, then de Broglie m = mass of electron, wavelength of the moving electron is [h = Planck's constant, e = charge of an electron) h h h heV, Fimev A Ymev One © law ET & BSc. 20JELET-2022 CHEMISTRY Category-II (Q 86 to 90) (Carry 2, marks each. One or more options are correct. No negative marks) 86. Which of the chemical conversion(s) as given below show(s) the highest degree of redox change ? (A) Phosphoric acid to phosphine. = (B) Nitric acid to molecular nitrogen. Sulphuric acid to elemental sulphur, — (D) " Borax to diborane 87, A chemical change will be spontaneous at constant pressure and temperature under the set(s) of conditions ; (A) AH=~ve, AS=—ve, | AH |>/'TAS| (B) AH=+ve, AS=+ ve, | AH|<|TAS| (©) AH=—ve, AS =~ve, | AH|=|TAS| (BY AH=+ve, AS=+ve,| AH|>|TAS | 88. bea following statement (5) is / are true ? 4A” K, ofa chemical reaction increases with increase in temperature for an exothermic reaction, : (B) K, of a chemical reaction increases with decrease in temperature for an endothermic reaction. (©) K, of a chemical reaction increases with decrease in temperature for an exothermic reaction, (©) K, of a chemical reaction decrease with decrease in temperature for an endothermic reaction. 89, Which of the following compounds have covalent bonds ? wae ®) 10 (©) CH, ®) caco, 90. Which of the following aqueous solutions of metal chlorides is neutral 2 (A) AICI, (B)’ BeCl, (& Bacl, (D) RbCl ET & BSc, a De,JELET-2022 Fundamentals of Electrical & Electronics Engineering Category-I (Q 91 to 100) (Carry 1 mark each. Only one option Is correct. Negative marks: 4) 91. A series circuit consists of two elements has the following current and applied voltage i =4 cos (2000t +11.32° ) A and v= 200 sin (2000t + 50°) V. The circuit elements are (A)_ Resistance and Capacitance (B) Capacitance and Inductance Inductance and Resistance (D) Both resistances 92. Two incandescent light bulbs of 40W and 60 W rating are connected in series across the mains. Then (A) the bulbs together consume 100 W ws the bulbs together consume 50 W (C)_ the 60 W bulb glows brighter (D) the 40 W bulb glows brighter 93. The average value of v((t) in the given circuit will be + Vo(t) ‘AV, @ o @ ye SPD) Nn 94, In the comparator shown, v, is a sinusoidal input of peak value 6V. The period (in degrees) for which the output will be high is ve—F >——e Vo 3v—_ |, s (A) 180° 60° (© 120°. @) 150° 95. What Boolean function does the following circuit represents ? B a oe ; DD TS LE o AIF+(B+C).(D+E)]G (B) AtBC+DEF+G ) A[(B+C)+F(D+E)]G (D) ABG+ABC+F(DtE)r 96. 98. 100. JELET-2022 IfTg= 15 mA and Vcg = 3 V, then the value of Voc required is Ic = 1000 Vee {+ 1 @) 4v eos © 3153V.— @) IBV ADC shunt motor is started with an open circuited field. Then (A) The motor picks up fast and acquires full speed while drawing large current. (B) Motor does not pick up speed but draws a large current. Gore motor does not pick up speed but draws only a small current. The motor picks up speed fast and acquires full speed while drawing only a small current. A voltage v(t) = V,, sint is connected to a moving Iron instrument. The reading of the instrument will be 2V, A) Va oo % © & o Ao 2 ™ A25 KVA transformer is constructed to a turn ratio of Ny/N, = 10. The impedance of the primary winding is 2 + j5 Q and of the secondary windings is 0.5 + j0.8 ©. What will be the impedance when referred to primary? a (A) 52+j850 “ (B) 2.54j5.8Q 50+j80.Q (D) 0.025+J0.508 Q On the Torque -Speed curve of the Induction motor shown in the figure, four points of: operation are marked, as W, X, Y and Z. Which one represents the operation at a slip greater than 1 ?