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JEE Advance Exam 2021 : PCM : Electrostatics + Capacitance + Current electricity + Periodicity, Chemical Bonding, Coordination, Electrochemistry, Gaseous State and GOC (all effects) + AOD + PnC + BINOMIAL

43 pages, 104 questions, 2 questions with responses, 2 total responses,

Nisarg Bhavsar
Seventh-Day Adventist Higher Secondary School (SDA), Maninagar, Ahmedabad
Junior Kindergarten to 10th

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Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 Test Name : 12th AITS JEE Advanced [22.11.2020] Difficulty Level : Medium Test Type : Paid Q.1 Total Questions : 60 Total Marks : 249.00 Duration : 180.00 mins A block having mass m and charge q is connected by spring of force constant k. The block lies on a frictionless horizontal track and a uniform electric field E acts on system as shown. The block is released from rest when spring is unstretched (at x = 0). Then A. Maximum stretch in the spring is B. In equilibrium position, stretch in the spring is C. Amplitude of oscillation of block is D. Amplitude of oscillation is Answer : A,B,C, Solution : NA Q.2 The adjacent figure shows variation of electric potential with distance for a spherical symmetric charge distribution system and given as r = (r R) = (r R) Which of the following option is/are correct? r Page - 1/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 A. B. C. D. For spherical region r R total electrostatic energy stored is zero Within r = 2R, total charge is q. There will be no charge anywhere except at r = R Electric field is discontinuous at r = R Answer : A,B,C,D, Solution : NA Q.3 Three identical, parallel conducting plates A, B and C are placed as shown. Switches S1 and S2 are open, and can connect A and C to earth when closed. +Q charge is given to B. Then A. B. C. D. if S1 is closed with S2 open, a charge of amount Q will pass through S1 if S2 is closed with S1 open, a charge of amount Q will pass through S2 if S1 and S2 are closed together, a charge of amount 2Q/3 will pass through S2 all the above statements are correct Answer : A,B,C, Solution : NA Q.4 Three capacitors each having capacitance C = 2 F are connected with a battery of emf 30 V as shown in figure. When the switch S is closed : Page - 2/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 A. B. C. D. the amount of charge flown through the battery is 20 C the heat generated in the circuit is 0.6 mJ the energy supplied by the battery is 0.6 mJ the amount of charge flown through the switch S is 60 C Answer : A,C,D, Solution : The charges stored in different capacitors before and after closing the switch S are The amount of charge flown through the battery is q = 20 C Energy supplied by the battery is U = qV = (20 10 6) (30) J U = 0.6 mJ Energy stored in all the capacitors before closing the switch S is Ui = Cnet V2 = (30)2 = 0.6 mJ and after closing the switch Uf = CnetV2 = (2 10 6) (30)2 = 0.9 mJ Page - 3/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 Heat generated H = U (Uf Ui) = 0.3 mJ and charge flown through the switch is 60 Q.5 C. A, B & C are three large, parallel conducting plates horizontally. A & C are rigidly fixed and earthed. B is given some charge. Under electrostatics and gravitation forces B may be A. B. C. D. in equilibrium if it closer to A than to C in equilibrium midway between A and C in equilibrium if it is closer to C than to A B can never be in stable equilibrium Answer : A,D, Solution : NA Q.6 A charge Q is imparted to two identical capacitors in parallel. Separation of the plates in each capacitor is d. Suddenly, the first plate of the first capacitor and the second plate of the second capacitor starts moving to the left with speed v, then A. Charge on the two capacitor as a function of time are , B. Charge on the two capacitors as a function of time are C. Current in the circuit will increase as time passes D. Current in the circuit will be constant , Answer : A,D, Solution : NA Page - 4/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 Q.7 A conductor is made of an isotropic material (resistivity ) has rectangular cross-section. Horizontally dimension of the rectangle decreases linearly from 2x at one end to x at the other end and vertical dimension increases from y to 2y as shown in figure. Length of the conductor along the axis is equal to l. A battery is connected across this conductor then A. B. C. D. rate of generation of heat per unit length is maximum at the ends of conductor rate of generation of heat per unit length is maximum at middle cross-section drift velocity of conduction electrons is minimum at middle section at the ends of the conductor, electric field intensity is same Answer : C,D, Solution : NA Q.8 All capacitors were initially uncharged A. B. C. D. Battery current just after closing of switch S is 3.42 A Battery current just after closing of switch S is 0.962 A Battery current after long time of closing of switch S is 3.42 A Battery current after long time of closing of switch S is 0.962 A Answer : A,D, Solution : Page - 5/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 Just after closing of switch S = + = = 4.61 + 10 = 14.61 i= i= Q.9 R = 10 = 3.42 A = 0.962 Amp and E = 13 V and voltmeter and ammeter are ideal, then - A. Reading of ammeter is 2.4 A B. Reading of ammeter is 8.4 A Page - 6/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 C. Reading of voltmeter is 8.4 V D. Reading of voltmeter is 27 V Answer : B,D, Solution : Using Kirchoff law solve the circuit. Q.10 Essay : 10-12): A small charged ball of mass m = 6 kg and charge Q = 15 C is suspended by a string of length L = 1m in a uniform electric field = ( + ) 106 N/C as shown. The ball is in equilibrium at angle with vertical. (Take g = 10 m/s2 and sin 37 = 0.6) Angle at equilibrium is A. 30 B. 37 C. 53 D. 60 Answer : D, Solution : NA Q.11 Essay : 10-12): A small charged ball of mass m = 6 kg and charge Q = 15 C is suspended by a string of Page - 7/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 length L = 1m in a uniform electric field = ( + ) 106 N/C as shown. The ball is in equilibrium at angle with vertical. (Take g = 10 m/s2 and sin 37 = 0.6) Tension in the string at equilibrium position is A. 10 N B. 20 N C. 30 N D. 40 N Answer : C, Solution : NA Q.12 Essay : 10-12): A small charged ball of mass m = 6 kg and charge Q = 15 C is suspended by a string of length L = 1m in a uniform electric field = ( + ) 106 N/C as shown. The ball is in equilibrium at angle with vertical. (Take g = 10 m/s2 and sin 37 = 0.6) If the external electric field is switched off, maximum tension in the string during subsequent motion will be A. 60 N B. 84 N C. 108 N D. 120 N Answer : D, Solution : NA Page - 8/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 Q.13 Essay : 13-15): The V verses x plot for six identical metal plates of cross-sectioned area A is shown. The plates are placed with separation d Equivalent capacitance between 2 & 5isA. B. C. D. Answer : B, Solution : NA Q.14 Essay : 13-15): The V verses x plot for six identical metal plates of cross-sectioned area A is shown. The plates are placed with separation d Page - 9/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 Total charge on plate 2 is A. B. C. D. None of these Answer : A, Solution : NA Q.15 Essay : 13-15): The V verses x plot for six identical metal plates of cross-sectioned area A is shown. The plates are placed with separation d Ratio of charge on plate 2 to plate 5 is | Q2 : Q5 | is A. 2 : 1 B. 3 : 1 C. 1 : 1 D. None of these Answer : C, Solution : NA Q.16 A dust particle with mass m = 5.0 10 9 kg and charge q = 2.0 nC starts from rest at point 'a' Page - 10/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 and moves in a straight line to point 'b'. Its speed is v at point b. Value of v is ....... m/s Answer : 4, Solution : mv2 qVa = qVb + 2.0 10 9 9 109 100 = 2.0 10 9 9 109 + 100 5.0 10 9 v2 10 9 1800 + 100 = 18 10 9 100 5.0 10 9v2 1800 = 5.0 v2 = v2 360 6 = v2 6 6 10 6 = v2 12 =v Q.17 In the figure two conducting concentric spherical shells are shown. If the electric potential at the centre is 2000 V and the electric potential of the other shell is 1500 V, then the potential of Page - 11/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 the inner shell is......... 103 volts. Answer : 2, Solution : Q.18 A particle A having a charge q is fixed on a vertical (insulated) wall. A second particle B of mass m, charge Q is suspended by a silk thread of length l from point P on the wall that is at a distance l above the point A. The angle in degree made by the thread with vertical, when B is in equilibrium is 10x for Qq = 4 mgl2. Then find x Answer : 6, Solution : = where F = Page - 12/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 = AB = 2l sin Q.19 A D.C. supply of 120 V is connected to a large resistance X. A voltmeter of resistance 10 k placed in series in the circuit reads 20 V. This is an unusual use of voltmeter for measuring very high resistance. The value of X is 10 k (approx). Answer : 5, Solution : I= = 20 10 4 But 20 10 4 = or 20 10 4x + 20 = 120 x= = 5 104 = 50 k Q.20 Nine wires each of resistance 5 are connected to make a prism as shown in figure. Find the Page - 13/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 equivalent resistance of the arrangement across AB. Answer : 3, Solution : D and E at same potential C and F at same potential r=5 req : = = =3 Q.21 A. A, Page - 14/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 B. B, C. C, D. D, Answer : A,B,C, Solution : Q.22 A. B. C. D. A, B, C, D, Answer : A,B,C,D, Solution : Page - 15/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 Q.23 Page - 16/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 A. B. C. D. A, B, C, D, Answer : A,B,C,D, Solution : Q.24 A. B. C. D. A, B, C, D, Answer : A,B,C,D, Page - 17/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 Solution : Page - 18/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 Q.25 A. A, B. B, Page - 19/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 C. C, D. D, Answer : B,C, Solution : Q.26 A. B. C. D. A, B, C, D, Answer : A,B,C, Solution : Q.27 A. A, B. B, Page - 20/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 C. C, D. D, Answer : A,B,C, Solution : Q.28 A. B. C. D. A, B, C, D, Answer : A,B,C, Solution : Q.29 A. A, Page - 21/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 B. B, C. C, D. D, Answer : A,B,C, Solution : Q.30 Essay : 30-31): Page - 22/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 A. B. C. D. A, B, C, D, Answer : B, Solution : Q.31 Essay : 30-31): A. B. C. D. A, B, C, D, Answer : D, Solution : Page - 23/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 Q.32 Essay : 32-33): A. B. C. D. A, B, C, D, Answer : B, Solution : NA Q.33 Essay : 32-33): A. B. C. D. A, B, C, D, Answer : B, Solution : NA Page - 24/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 Q.34 Essay : 34-35): A. B. C. D. A, B, C, D, Answer : D, Solution : Q.35 Essay : 34-35): A. B. C. D. A, B, C, D, Page - 25/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 Answer : C, Solution : Q.36 Answer : 87, Solution : Page - 26/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 Q.37 Answer : 200, Solution : Q.38 Page - 27/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 Answer : 1632, Solution : Q.39 Page - 28/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 Answer : 5, Solution : Page - 29/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 Q.40 Answer : 2121, Solution : Q.41 If (1 + x + x2)n = a + a1x + a2 x2 + ......+ a2nxn, then the value of a + a3 + a6+.........is A. a1 + a4 + a7 +..... B. a2 + a5 + a8 +...... C. 3n 1 D. None of these Answer : A,B,C, Solution : (1 + x + x2)n = a + a1x + a2x2 +.......+a2nx2n Now x = w (1 + w + w2)n = a+a1w + a2w2 +......+a2nw2n.... (i) x = w2 (1+w+w2)n = a + a1w2 + a2w4 +.....+a2nw4n .....(ii) x=1 Page - 30/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 3n = a + a1 + a2 + ........+a2n ..............(iii) adding (i), (ii) & (iii) 3n = 3(a + a3 + a6 + ..................) a + a3 + a6 +..................=3n 1 .............(iv) (i) (ii) (w w2) (a1 a2 + a4 a5 +...) = 0.......(v) (iii) (iv) a1 + a2 + a4 + a5 +..........= 3n 3n 1 = 2 . 3n 1 ........(vi) (v) + (vi) 2(a1 + a4 + a7 +...........) = 2 . 3n 1 (vi) (v) 2(a2+ a5 + ..........) = 2.3n 1 Q.42 A. B. C. D. A, B, C, D, Answer : A,C,D, Solution : Page - 31/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 Q.43 A. B. C. D. A, B, C, D, Answer : B,C, Solution : Q.44 Page - 32/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 A. B. C. D. A, B, C, D, Answer : B,C,D, Solution : Q.45 A. B. C. D. A, B, C, D, Answer : D, Solution : Page - 33/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 Q.46 A. B. C. D. A, B, C, D, Answer : A, Solution : NA Q.47 A. B. C. D. A, B, C, D, Answer : A, Solution : Page - 34/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 Q.48 Two villages A and B are on the same side of a straight river. A pump set is to be installed by the river side at a point P. Then if the villages are situated at a distance c then A. minimum value of PA + PB is B. minimum value of PA + PB is C. minimum value of PA + PB is D. The required location must lie on the imaginary line joining village A and image of village B in the river. Answer : B,D, Solution : Take river as x axis, line joining origin and village A as x axis k2 = c2 (b a)2 image of A in the river, this is A' and BA' must be minimum value of PA + PB BA' = = = Page - 35/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 Q.49 A. B. C. D. A, B, C, D, Answer : A,B,D, Solution : Page - 36/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 Q.50 Essay : 50-51): A. B. C. D. A, B, C, D, Answer : A, Solution : Page - 37/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 Q.51 Essay : 50-51): A. B. C. D. A, B, C, D, Page - 38/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 Answer : A, Solution : Q.52 Essay : 52-53): If (x + y)n = , where Cr = nCr is equal to A. B. C. D. None of these Page - 39/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 Answer : A, Solution : NA Q.53 Essay : 52-53): If (x + y)n = If A. B. C. D. , where Cr = nCr n Cr = , then n is equal to 8 6 5 4 Answer : C, Solution : NA Q.54 Essay : 54-55): There is a convex polygon of n sides (n > 8). Number of quadrilateral having three, two and one side common with polygon are represented by A, B and C respectively, Also D represents the number of quadrilateral having vertices at the vertices of polygon and at least one side common with sides of polygon, then answer the following questions: The value of B is A. (n 5)n B. n(n 3) C. n(n 4) D. n(n 6) Answer : A, Solution : Page - 40/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 Number of selection of 4 vertices of the polygon out of which only three are consecutive (i.e., two sides common) = n n 5C1 = n(n 5). Q.55 Essay : 54-55): There is a convex polygon of n sides (n > 8). Number of quadrilateral having three, two and one side common with polygon are represented by A, B and C respectively, Also D represents the number of quadrilateral having vertices at the vertices of polygon and at least one side common with sides of polygon, then answer the following questions: The value of C is given by A. B. C. D. None of these Answer : B, Solution : Number of selection of 4 vertices of the polygon out of which only two are consecutive = n n 4C2 = . Q.56 Answer : 1, Solution : Page - 41/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 Q.57 Answer : 7, Solution : Q.58 Number of points of inflexion on the curve is equal to then 5 is equal to Answer : 15, Solution : Q.59 Page - 42/43 Edunova Educational Foundation https://www.edunova.ac.in, edunovadigital@edunova.ac.in 9327101002 Answer : 1, Solution : Q.60 Answer : 1, Solution : Page - 43/43

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