DATE : SUBJECT : PHYSICS, CHEMISTRY, MATHEMATICS

Transcription

1 PAPER- (B.E./B. TECH.) JEE (MAIN) JEE (MAIN) 8 CBT TEST PAPER (WITH SLUTIN & ANSWER KEY) DATE : SUBJECT : PHYSICS, CHEMISTRY, MATHEMATICS Resonance Eduventures Ltd. Registered & Corporate ffice: CG Tower, A-46 & 5, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)-45 Tel.No.: ,,, a: Website: contact@resonance.ac.in CIN: U8RJ7PLC49

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3 PAPER- (B.E. / B.TECH.) JEE (MAIN) NLINE PHYSICS Straight bjective Type This section contains multiple choice questions. Each question has 4 choices (), (), () and (4) for its answer, out of which nly ne is correct.. The relative uncertainty in the period of a satellite orbiting around the earth is. If the relative uncertainty in the radius of the orbit is negligible the relative uncertainty in the mass of the earth is : () () 6 () (4) Ans. () rom kepler's Law 4 T r GM M T = M T. At some instant a radioactive sample S having an activity 5 Ci has twice the number of nuclei as another sample S which has an activity of Ci. The half lives of S and S are : () 5 years and years, respectively () years and 5 years, respectively () years and years, respectively (4) years and years, respectively Ans. () Given : N = N n N = N 5 c i t n N = N c i t t N t N t t 4 Hence 5years and year. Two moles of helium are mied with an moles of hydrogen. If () () () (4) / Ans. () Cp fmi C f v mi f mi = 4 n f n f fmi n n 4 n 5 n n = mole CP for the miture then the value of n is C V Registered & Corporate ffice: CG Tower, A-46 & 5, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)-45 Tel.No.: ,,, a: CIN: U8RJ7PLC49 To Know more: sms RES at contact@resonance.ac.in Page

4 PAPER- (B.E. / B.TECH.) JEE (MAIN) NLINE Unpolarized light of intensity I is incident on a system of two polarizers, A followed by B. The intensity of emergent light is I/. If a third polarizer C is placed between A and B the intensity of emergent light is reduced to I/. The angle between the polarizers A and C is, then / 4 () cos = () cos = () cos = Ans. () A and B have same alignment of transmission ais. Lets assume c is introduced at angle I I cos cos cos 4 = cos = / 4 / 4 / (4) cos = 5. The de-broglie wavelength ( B ) associated with the electron orbiting in the second ecited state of hydrogen atom is related to that in the ground state ( G ) by : () B = G () B = G () B = G/ (4) B = G/ Ans. () B Pa mv G P mv G B B V z n So B B G n n G / B = G Length of rbit = n = r n n 6. In the given circuit the current through zener diode is : R 5 5V 5 R V Z = V ().ma ().5mA () 5.5mA (4) 6.7mA Ans. () 5 Current in R = I = 5 I = ma Current in R = I = 5 Current in zener diode = I I = I = ma ma ma Registered & Corporate ffice: CG Tower, A-46 & 5, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)-45 Tel.No.: ,,, a: CIN: U8RJ7PLC49 To Know more: sms RES at contact@resonance.ac.in Page

5 PAPER- (B.E. / B.TECH.) JEE (MAIN) NLINE The end correction of a resonance column is cm. If the shortest length resonating with the tuning fork is cm, the net resonating length should be : () cm () 4cm () 8cm (4) 6cm Ans. () Given : e = cm or first resonance e cm 4 or second resonance e = = cm 4 8. Two sitar strings A and B playing the note 'Dha' are slightly out of tune and produce beats of frequency 5Hz. The tension of the string B is slightly increased and the beat frequency is found to decrease by Hz. If the frequency of A is 45 Hz. the original frequency of B is : () 48 Hz () 4 Hz () 4 Hz (4) 4 Hz Ans. (4) requency of B is either 4Hz or 4Hz As tension in B is increased its frequency will increase. If frequency is 4Hz, beat frequency will increase If frequency is 4 Hz beat frequency will decrease, hence correct answer is 4Hz 9. A power transmission line feeds input power at V to a step down transformer with its primary windings having 4 turns giving the output power at V. If the current in the primary of the transformer is 5A and its efficiency is 9% the output current would be : () 45A () 5A () A (4) 5A Ans. () Ps Efficiency n =.9 = P V s I s =.9 V P I P.9 5 I s = = 45A P. A body of mass m starts moving from rest along -ais so that its velocity varies as = a s where a is a constant and s is the distance covered by the body. The total work done by all the forces acting on the body in the first t seconds after the start of the motion is : () 8ma 4 t () 4 ma4 t () 4ma 4 t (4) 8 ma4 t Ans. (4) ds v = a s dt s at a t S 4 a = m Work = ma a t = 4 4 ma t 8 Registered & Corporate ffice: CG Tower, A-46 & 5, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)-45 Tel.No.: ,,, a: CIN: U8RJ7PLC49 To Know more: sms RES at contact@resonance.ac.in Page

6 PAPER- (B.E. / B.TECH.) JEE (MAIN) NLINE Suppose that the angular velocity of rotation of earth is increased. Then as a consequence: () Weight of the object every where on the earth will decrease () Weight of the object every where on the earth will increase () Ecept at poles weight of the object on the earth will decrease (4) There will be no change in weight anywhere on the earth. Ans. () g' = g Rcos Where is latitude there will be no change in gravity at poles as = 9 At all other points as increases g' will decrease.. Both the nucleus and the atom of some element are in their respective first ecited states. They get deecited by emitting photons of wavelengths N, A respectively. The ratio is closest to : N () () 6 () (4) Ans. () N E a E a N where E a and E N are energies of photons from atom and nucleus respectively. E N is of the order of MeV and E a in few ev. A So N a 6. A plane electromagnetic wave of wavelength has an intensity I. It is propagating along the positive Y-direction. The allowed epressions for the electric and magnetic fields are given by : I I E cos y ct k; () c E cos y ct k; ˆ () c B Ei ˆ B Ei ˆ c c I E cos y ct k; ˆ I () c E cos y ct i; (4) c B Ei ˆ B Ek c c Ans. () If E is magnitude of electric field then E C I E I C E B C direction of E B will be along + ĵ. 4. A charge q is spread uniformly over an insulated loop of radius r. If it is rotated with an angular velocity with respect to normal ais then magnetic moment of the loop is : () q r () q r () 4 qr (4) q r Ans. () Registered & Corporate ffice: CG Tower, A-46 & 5, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)-45 Tel.No.: ,,, a: CIN: U8RJ7PLC49 To Know more: sms RES at contact@resonance.ac.in Page 4

7 PAPER- (B.E. / B.TECH.) JEE (MAIN) NLINE M q L m q M = mr m M = qr 5. A heating element has a resistance of at room temperature. When it is connected to a supply of V a steady current of A passes in it and temperature is 5 C more than room temperature. What is the temperature coefficient of resistance of the heating element? () 5 4 C () 4 C () 4 C (4).5 4 C Ans. () Resistance after temperature increases by 5 C = = = ( + 5) = 5 = 4 C 6. A coil of cross-sectional area A having n turns is placed in a uniform magnetic field B. When it is rotated with an angular velocity the maimum e.m.f. induced in the coil will be : () nba () nba () nba (4) nba Ans. () = BAn sint ma = BAn 7. A ray of light is incident at an angle of 6 on one face of a prism of angle. The emergent ray of light makes an angle of with incident ray. The angle made by the emergent ray with second face of prism will be : () () 9 () (4) 45 Ans. () = I + e A = 6 + e e = So angle with face = 9 6 Registered & Corporate ffice: CG Tower, A-46 & 5, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)-45 Tel.No.: ,,, a: CIN: U8RJ7PLC49 To Know more: sms RES at contact@resonance.ac.in Page 5

8 PAPER- (B.E. / B.TECH.) JEE (MAIN) NLINE A galvanometer with its coil resistance 5 requires a current of ma for its full deflection. In order to construct an ammeter to read up to a current of A the approimate value of the shunt resistance should be : ().5 ().5 ().5 (4).5 Ans. () I g R g = (I I g )S 5 S ~ S ~.5 or.5 I g G I I g S 9. An oscillator of mass M is at rest in the equilibrium position in a potential V = k( X). A particle of mass m comes from right with speed u and collides completely inelastically with M and sticks to it. This process repeats every time the oscillator crosses its equilibrium position. The amplitude of oscillations after collisions is : (M =, m = 5, u =, k = ) () () () (4) 5 Ans. () In first collision mu momentum will be imparted to system. In second collision when momentum of (M + m) is in opposite direction mu momentum of particle will make its momentum zero. on th collision m M +m M +m V mu = (M + m)v mu u v = M m 5 v = A u K A 5 M m A = ne mole of an ideal monatomic gas is taken along the path ABCA as shown in the PV diagram. The maimum temperature attained by the gas along the path BC is given by : P P B P A C () 5 P V 4 R () 5 P V 8 R V V V Registered & Corporate ffice: CG Tower, A-46 & 5, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)-45 Tel.No.: ,,, a: CIN: U8RJ7PLC49 () 5 P V 8 R To Know more: sms RES at contact@resonance.ac.in Page 6 (4) 5 P V 6 R

9 PAPER- (B.E. / B.TECH.) JEE (MAIN) NLINE Ans. () Equation of line BC P P = P V (V V ) P V P V 4P V V Temperature = R P V T = 5V R V dt dv = 5 4V V = V = 5 4 V P 5V 5 T = 5 V R 4 V 6 T = 5 P V 8 R. In a circuit for finding the resistance of a galvanometer by half deflection method a 6V battery and a high resistance of k are used. The figure of merit of the galvanometer produces a deflection of = 9 divisions when current flows in the circuit. The value of the shunt resistance that can cause the deflection of / is () 55 () () 55 (4) Ans. (4) I = R G G = K 9 I S GS S G R G S I RG S = R G I 7 S = S = 6 S I S R(S G) GS I G G I/ R R E E Registered & Corporate ffice: CG Tower, A-46 & 5, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)-45 Tel.No.: ,,, a: CIN: U8RJ7PLC49 To Know more: sms RES at contact@resonance.ac.in Page 7

10 PAPER- (B.E. / B.TECH.) JEE (MAIN) NLINE In the following circuit the switch S is closed at t =. The charge on the capacitor C as a function of time will be given by C eq CC C C C C S E R () C E[ ep( tr/c )] () C eq E ep( t/rc eq ) () C eq E [ ep( t/rc eq )] (4) C E[ ep( t/rc )] Ans. () t / Rc q = C eq E e eq Both capacitor will have same charge as they are connected in series. C eq E R. Let A ˆ i ˆj and B i ˆ ˆj by : 9 () () 9 Ans. () If C ai ˆ bj ˆ then A.C A.B a + b = (i) B.C A.B a b = (ii) Solving equation (i) and (ii) we get a =, b =. The magnitude of a coplanar vector C such that A.C B.C A.B is given () 5 9 (4) 9 C A particle eecutes simple harmonic motion and is located at = a, b and c at times t, t and t respectively. The frequency of the oscillation is : a c a b a b a c () cos () cos () cos (4) cos t b t c t c t b Ans. () Registered & Corporate ffice: CG Tower, A-46 & 5, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)-45 Tel.No.: ,,, a: CIN: U8RJ7PLC49 To Know more: sms RES at contact@resonance.ac.in Page 8

11 PAPER- (B.E. / B.TECH.) JEE (MAIN) NLINE a = Asint b = Asint c = Asint a + c = A[sint + sint ] = Asint cost a c = cost b = a c cos t b a c f = cos t b 5. A thin circular disk is in the y plane as shown in the figure. The ratio of its moment of inertia about z and z' aes will be : z z' o y () : 4 () : 5 () : (4) : Ans. () mr I z = ' I z = I mr ' I z z 6. Two identical conducting spheres A and B carry equal charge. They are separated by a distance much larger than their diameters and the force between them is. A third identical conducting sphere C is uncharged. Sphere C is first touched to A then to B and then removed. As a result the force between A and B would be equal to : () 4 () () 8 (4) Ans. () q q r kq = when A and C are touched charge on both will be q r Then when B and C are touched q q q q B = 4 q q k kqaqb kq ' = 4 r r 8 r 8 Registered & Corporate ffice: CG Tower, A-46 & 5, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)-45 Tel.No.: ,,, a: CIN: U8RJ7PLC49 To Know more: sms RES at contact@resonance.ac.in Page 9

12 PAPER- (B.E. / B.TECH.) JEE (MAIN) NLINE Two particles of the same mass m are moving in circular orbits because of force given by 6 (r) = r. The first particle is at distance r = and the second at r = 4. The best estimate for the ratio r of kinetic energies of the first and the second particle is closest to : () () 6 () 6 (4) Ans. () mv 6 r r r KE = mv = [6 + r4 ] 6 K 7 K K ~ 6 K 8. The percentage errors in quantities P, Q, R and S are.5%, %, % and.5% respectively in the P Q measurement of a physical quantity A =. The maimum percentage error in the value of A will be : RS () 6.5% () 7.5% () 6.% (4) 8.5% Ans. () A P Q R S A P Q R S = = A = 6.5% A 9. A carrier wave of peak voltage 4V is used for transmitting a message signal given to achieve a modulation inde of 8% will be : ().4V () 7V ().V (4) 8V Ans. () Am m = A A m =.8 4 =.V c. A small soap bubble of radius 4cm is trapped inside another bubble of radius 6cm without any contact. Let P be the pressure inside the inner bubble and P the pressure outside the outer bubble. Radius of another bubble with pressure difference P P between its inside and outside would be : ().4cm () cm () 4.8cm (4) 6cm Ans. () Registered & Corporate ffice: CG Tower, A-46 & 5, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)-45 Tel.No.: ,,, a: CIN: U8RJ7PLC49 To Know more: sms RES at contact@resonance.ac.in Page

13 P = P + PAPER- (B.E. / B.TECH.) JEE (MAIN) NLINE T 4T P = P + 4T 6 4 r r =.4cm r P P r 6 Registered & Corporate ffice: CG Tower, A-46 & 5, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)-45 Tel.No.: ,,, a: CIN: U8RJ7PLC49 To Know more: sms RES at contact@resonance.ac.in Page

14 PAPER- (B.E. / B.TECH.) JEE (MAIN) NLINE CHEMISTRY Straight bjective Type This section contains multiple choice questions. Each question has 4 choices (), (), () and (4) for its answer, out of which nly ne is correct.. or standardizing NaH solution, which of the following is used as a primary standard? () Sodium tetraborate () errous Ammonium Sulfate () alic acid (4) dil. HCl Ans. () alic acid is used as a primary standard for NaH standardizing.. Products A and B formed in the following reactions are respectively : NH CH C C6H5NH + HN A B S H N=N CCH N=N NH () and S H N=N CCH S H H N=N N () and S H N=NCCH S H N=N () and S H S H N=NCCH (4) S H and H S N H NH Registered & Corporate ffice: CG Tower, A-46 & 5, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)-45 Tel.No.: ,,, a: CIN: U8RJ7PLC49 To Know more: sms RES at contact@resonance.ac.in Page

15 PAPER- (B.E. / B.TECH.) JEE (MAIN) NLINE Ans. () NH CH C N N C CH N=N C CH HN S H S H S H (A) H N N=N NH S H (B). When X is fused with an alkali metal hydroide in presence of an oidizing agent such as KN ; a dark green product is formed which disproportioates in acidic solution to afford a dark purple solution. X is : () Mn () Cr () V (4) Ti Ans. () Mn + KH K Mn 4 (dark green) Acidic KMn4 solution (dark purple) 4. The major product B formed in the following reaction sequence is : Me CH (i) CH5MgBr (ii) H A HCl B () Cl Cl () Me Cl () Me (4) Me Ans. (4) CH C H (i) CH5MgBr (ii) H CH H HCl SN CH Cl Registered & Corporate ffice: CG Tower, A-46 & 5, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)-45 Tel.No.: ,,, a: CIN: U8RJ7PLC49 To Know more: sms RES at contact@resonance.ac.in Page

16 PAPER- (B.E. / B.TECH.) JEE (MAIN) NLINE In a compleometric titration of metal ion with ligand M (Metal ion) + L (Ligand) C (Comple) end point is estimated spectrophotometrically (through light absorption). If 'M' and 'C' do not absorb light and only 'L' absorbs, then the titration plot between absorbed light (A) versus volume of ligand 'L' (V) would look like : A () A () A () A (4) V (Ligand) V (Ligand) V (Ligand) V (Ligand) Ans. () Initially ligand consumed by metal due to formation of comple. So absorbed light (A) remain constant, after comple formation is completed, etra volume of ligand solution increases ligand concentration and also increases absorbed light. 6. The major product of the following reaction is : CH=CHCH HBr CH CH CH Br BrCHCH CH CH CHCH CH=CHCH () () () Br (4) Br Ans. () CH=CH CH CH CH CH Br CH CH CH HBr Br 7. Among the following, the incorrect statement is : () Cellulose and amylose has,4-glycosidic linkage. () Lactose contains -D-galactose and -D-glucose. () Maltose and lactose has,4-glycosidic linkage. (4) Sucrose and amylose has,-glycosidic linkage. Ans. (4) In amylose,4-glycosidic linkage is present. Registered & Corporate ffice: CG Tower, A-46 & 5, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)-45 Tel.No.: ,,, a: CIN: U8RJ7PLC49 To Know more: sms RES at contact@resonance.ac.in Page 4

17 PAPER- (B.E. / B.TECH.) JEE (MAIN) NLINE In the etraction of copper from its sulphide ore, metal is finally obtained by the oidation of cuprous sulphide with : () S () e () Cu (4) C Ans. () Cu S + Cu 6Cu + S 9. Among the oides of nitrogen : N, N 4 and N 5 ; the molecule(s) having nitrogen-nitrogen bond is/are : () N and N 4 () N 4 and N 5 () N and N 5 (4) nly N 5 Ans. () N N N N 4 N N. Which of the following conversions involves change in both shape and hybridisation? Ans. () () H H + () B B 4 () CH 4 C H 6 (4) NH NH 4 B B 4 B sp Triangle planar B sp Tetrahedral. The most polar compound among the following is : () () () (4) Ans. () In, the bond dipole vector of C bond is not subtractive. Registered & Corporate ffice: CG Tower, A-46 & 5, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)-45 Tel.No.: ,,, a: CIN: U8RJ7PLC49 To Know more: sms RES at contact@resonance.ac.in Page 5

18 PAPER- (B.E. / B.TECH.) JEE (MAIN) NLINE In Wilkinson's catalyst, the hybridization of central metal ion and its shape are respectively : () sp d, trigonal bipyramidal () d sp, octahedral () dsp, square planar (4) sp, tetrahedral Ans. () Wilkinson catalyst [RhCl(PPh ) ]. At K, a gas A is % dissociated to A(g). The standard free energy change at K and atm in Ans. () J mol is approimately : (R = 8.4 JK mol ; ln =.69 ; ln =.98) () 844 () 68 () 48 (4) 476 A (g) A(g).8.4 K p = (p) A (p) A = =. Gº =. 8.4 log. = 48 J/mole 4. Which of the following complees will show geometrical isomerism? () Potassium tris(oalato)chromate(iii) () Pentaaquachlorochromium(III)chloride () Aquachlorobis(ethylenediamine)cobalt(II) chloride (4) Potassium amminetrichloroplatinate(ii) Ans. () [Co(H )Cl(en) ]Cl en + H + H Co en Co en en Cl (Geometrical Isomer) Cl Registered & Corporate ffice: CG Tower, A-46 & 5, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)-45 Tel.No.: ,,, a: CIN: U8RJ7PLC49 To Know more: sms RES at contact@resonance.ac.in Page 6

19 PAPER- (B.E. / B.TECH.) JEE (MAIN) NLINE Which of the following statements is false? () Splitting of spectral lines in electrical field is called Stark effect. () requency of emitted radiation from a black body goes from a lower wavelength of higher wavelength as the temperature increases. () Photon has momentum as well as wavelength. (4) Rydberg constant has unit of energy. Ans. () and (4) [both are false] When temperature is increased, black body emit high energy radiation, from higher wavelength to lower wavelength. Rydberg constant has unit length (i.e. cm ) 6. When 9.65 ampere current was passed for. hour into nitrobenzene in acidic medium, the amount of p-aminophenol produced is : () 9. g () 98. g () 9.8 g (4).9 g Ans. () H C 6 H 5 N NH 4e + 4H + + C 6 H 5 N C 6 H(H)(NH) 4 M.W. 9 g + H (v.f.) = 4 W = ZIt = E I t M E W = W = 9.8 g 7. or which of the following processes, S is negative? () C(diamond) C(graphite) () N (g, atm) N (g, 5 atm) () N (g, 7 K) N (g, K) (4) H (g) H(g) Ans. () N (g, atm) N (g, 5 atm) T S = ncp ln T V + nr ln V V for isothermal process T = T and V = P P S < P = + nr ln P = nr ln 5 Registered & Corporate ffice: CG Tower, A-46 & 5, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)-45 Tel.No.: ,,, a: CIN: U8RJ7PLC49 To Know more: sms RES at contact@resonance.ac.in Page 7

20 PAPER- (B.E. / B.TECH.) JEE (MAIN) NLINE An unknown chlorohydrocarbon has.55 % of chlorine. If each molecule of the hydrocarbon has one Ans. (4) chlorine atom only ; chlorine atoms present in g of chlorohydrocarbon are : (Atomic wt. of Cl = 5.5 u ; Avogadro constant = 6. mol ) () 6. 9 () 6. () 6. (4) 6. C H y Cl % Cl =.55 Weight of Cl =.55 n =.55 Cl 5.5 No of Cl ion = = The incorrect statement is : () Cu + ion gives chocolate coloured precipitate with potassium ferrocyanide solution. () Cu + and Ni + ions give black precipitate with H S in presence of HCl solution. () erric ion gives blood red colour with potassium thiocyanate. (4) Cu + salts give red coloured bora bead test in reducing flame. Ans. () Due to common ion effect, sufficient S concentration not produce and not formed ppt of NiS.. The mass of a non-volatile, non-electrolyte solute (molar mass = 5 g mol ) needed to be dissolved in 4 g octane to reduce its vapour pressure to 75 %, is : () 7.5 g () 75 g () 5 g (4) 5 g Ans. (Bonus) o P P P s s = n N P 75P 75P = W = W 5 W = 5 g Registered & Corporate ffice: CG Tower, A-46 & 5, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)-45 Tel.No.: ,,, a: CIN: U8RJ7PLC49 To Know more: sms RES at contact@resonance.ac.in Page 8

21 PAPER- (B.E. / B.TECH.) JEE (MAIN) NLINE The incorrect geometry is represented by : () N trigonal planar () B trigonal planar () As 5 trigonal bipyramidal (4) H bent Ans. () N N sp Trigonal pyramidal. Assuming ideal gas behaviour, the ratio of density of ammonia to that of hydrogen chlroide at same temperature and pressure is : (Atomic wt. of Cl 5.5 u) ().46 ().64 ().46 (4).64 Ans. () d = P(M.w.) RT d d NH HCl (M.w.) NH = (M.w.) HCl = =.46. The correct match between items of List-I and List-II is : List-I List-II (A) Phenelzine (P) Pyrimidine (B) Chloroylenol (Q) uran (C) Uracil (R) Hydrazine (D) Ranitidine (S) Phenol () (A)-(S), (B)-(R), (C)-(Q), (D)-(P) () (A)-(R), (B)-(S), (C)-(P), (D)-(Q) () (A)-(R), (B)-(S), (C)-(Q), (D)-(P) (4) (A)-(S), (B)-(R), (C)-(P), (D)-(Q) Ans. () Phenelzine contains hydrazine Chloroylenol contains phenol Uracil is the pyrimidine base Ranitidine contains furan ring 4. The gas phase reaction N (g) N 4 (g) is an eothermic reaction. The decomposition of N 4, in equilibrium miture of N (g) and N 4 (g), can be increased by : () addition of an inert gas at constant pressure. () lowering the temperature () increasing the pressure (4) addition of an inert gas at constant volume. Ans. () N (g) N 4 (g) H = ( ) By addition of an inert gas at constant pressure, volume increases, so reaction moving in backward direction and decomposition of N 4 increases. Registered & Corporate ffice: CG Tower, A-46 & 5, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)-45 Tel.No.: ,,, a: CIN: U8RJ7PLC49 To Know more: sms RES at contact@resonance.ac.in Page 9

22 PAPER- (B.E. / B.TECH.) JEE (MAIN) NLINE Which one of the following is not a property of physical adsorption? () Higher the pressure, more the adsorption () Greater the surface area, more the adsorption () Lower the temperature, more the adsorption (4) Unilayer adsorption occurs Ans. (4) Physical adsorption is multilayer adsorption. 6. A group element 'X' reacts with chlorine gas to produce a compound XCl. XCl is electron deficient and easily reacts with NH to form Cl X NH adduct; however, XCl does not dimerize. X is : () B () Al () In (4) Ga Ans. () BCl Cl H B + Cl BCl [not dimerise due to (p-p) back bonding] NH Cl B Cl H N H 7. The major product of the following reaction is : Br NH KH SN H H H H () NH () NH () H N (4) H N Ans. () Br H H NH KH SN or NH H N Inversion takes place at the carbon containing bromine atom. Registered & Corporate ffice: CG Tower, A-46 & 5, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)-45 Tel.No.: ,,, a: CIN: U8RJ7PLC49 To Know more: sms RES at contact@resonance.ac.in Page

23 PAPER- (B.E. / B.TECH.) JEE (MAIN) NLINE If 5 % of a reaction occurs in second and 75 % of the reaction occurs in second, the order of this reaction is : () () () Zero (4) Ans. (4) Co second 75 % complete Co second Co 4 irst order reaction as half life is constant. 9. The major product of the following reaction is : Me Me H (i) HCCHCCl (ii) HS 4, heat () () Me Me () Me Ans. () CH H C CH C Cl H CH (4) H C= H H H CH H Electrophilic substitution C= H H, CH H Dehydration CH. Which of the following compounds will most readily be dehydrated to give alkene under acidic condition? () 4-Hydroypentan--one () -Hydroypentan--one () -Pentanol (4) -Hydroycyclopentanone Ans. () H will most readily be dehydrated to give conjugated alkene. Registered & Corporate ffice: CG Tower, A-46 & 5, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)-45 Tel.No.: ,,, a: CIN: U8RJ7PLC49 To Know more: sms RES at contact@resonance.ac.in Page

24 PAPER- (B.E. / B.TECH.) JEE (MAIN) NLINE MATHEMATICS PART C Straight bjective Type (lh/ks olrqfu"b izdkj) This section contains multiple choice questions. Each question has 4 choices (), (), () and (4) for its answer, out of which nly ne is correct. bl [k.m esa cgq&fodyih iz'u gsaa izr;sd iz'u ds 4 fodyi (), (), () rkk (4) gsa] ftuesa ls flqz,d lgh gsa. If = () y Ans. () cosec t dy dy / dt = d d / dt = and y = sec t ( t ), then dy (*) is equal to : d y () sec t n sec t cosec t n cosec t t t t t (4) y y = sec t cosec t = y. Let N denote the set of all natural numbers. Define two binary relations on N as R = {(, y) N N : + y = } and R = {(, y) N N : + y = }. Then () Both R and R are transitive relations () Range of R is {,,, 4}. () Range of R is {, 4, 8} (4) Both R and R are symmetric relations. Ans. () R = {(, 8), (, 6), (, 4), (9, )} R = {(8, ), (6, ), (4, ), (, 4)} Range of R = {,,, 4}. The coefficient of in the epansion of the product ( ) (( + + ) 6 + ( 4 ) 6 ) is : () 7 () 8 () 55 (4*) 6 Ans. (4) coefficient of = coefficient of in (( + + ) 6 + ( 4 ) 6 ) constant term ( + + ) 6 = 6 6 r r c ( ) r = 6 C + 6 C ( + ) + 6 C ( + ) +. coefficient of = ( ) = 8 = 6 Registered & Corporate ffice: CG Tower, A-46 & 5, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)-45 Tel.No.: ,,, a: CIN: U8RJ7PLC49 To Know more: sms RES at contact@resonance.ac.in Page

25 PAPER- (B.E. / B.TECH.) JEE (MAIN) NLINE 4. If the area of the region bounded by the curves, y =, y = and the lines y = and = t (t > ) is sq. unit, then t is equal to : (*) e () e () (4) 4 Ans. () d d = + nt = t = e 5. If the length of the latus rectum of an ellipse is 4 units and the distance between a focus and its nearest verte on the major ais is units, then its eccentricity is : () () Ans. (4) b a = 4 b = a b = a ( e ), a ( e) = = a( e) ( + e) = ( + e) e = () 9 (4) 6. The number of numbers between, and 5, that can be formed with the digits,,,, 4 (repetition of digits is not allowed) and are multiple of is : () 6 () () 4 (4) 48 Ans. () number can be formed y (,,, ) or (,,, 4) number of 4 digits number =! +! = 7. Two different families A and B are blessed with equal number of children. There are tickests to be distributed amongst the children of these families so that no child gets more than one ticket. If the probability that all the tickets go to the children of the family B is, then the number of children in each family is : () 6 () 5 () (4) 4 Ans. () Let n number of children are there in each family n = C.! n C.! n C n C = n = 5 Registered & Corporate ffice: CG Tower, A-46 & 5, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)-45 Tel.No.: ,,, a: CIN: U8RJ7PLC49 To Know more: sms RES at contact@resonance.ac.in Page

26 8. lim () Ans. () lim lim (7 ) equals : 9 (7 ) () = PAPER- (B.E. / B.TECH.) JEE (MAIN) NLINE 6 9. Let p, q and r be real numbers (p q, r ), such that the roots of the equation p q r are equal in magnitude but opposite in sign, then the sum of squares of these roots is equal to : () p + q p q () () (p + q ) (4) p + q + r Ans. () ( + p + q) r = ( + p) ( + q) + (p + q r) + pq pr qr = p + q = r..(i) + = ( + ) = [pq pr qr] = pq + r (p + q) = pq + (p + q) = p + q. Let, (),, ( i for i =,,., n) be in A.P. such that = 4 and =. If n is the least positive n n integer for which n > 5, then i is equal to : i (4) () () 8 Ans. () 4 +.d = d = < 5 n 4 n < 5 n > 4 n = 5 5 i 4 i 4 = 4 () 4 (4) 8 Registered & Corporate ffice: CG Tower, A-46 & 5, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)-45 Tel.No.: ,,, a: CIN: U8RJ7PLC49 To Know more: sms RES at contact@resonance.ac.in Page 4

27 PAPER- (B.E. / B.TECH.) JEE (MAIN) NLINE. The differential equation representing the family of ellipses having foci either on the -ais or on the y-ais, centre at the origin and passing through the point (, ) is : (*) y y y + 9 = () y y + (y) y y = () y y + y 9 = (4) + y y = Ans. () Equation of ellipse a + y b = Passes (, ) a + y 9 = () a = y dy 9 d a + y dy 9 d = () a = y y 9 By () & () D. equation is y y 9 y + 9 = y y y + 9 =. The sum of the intercepts on the coordinate aes of the plane passing trhough the point (,, ) and containing the line joining the points (,, ) and (,, ), is : () 4 () () 8 (4) 4 Ans. (4) Equation plane y z = ( + ) + (y + ) + 6 (z ) = y 6z + 8 = sum of intercepts = = 4. Let A = and B = A. Then the sum of the elements of the first column of B is : () () () 5 (4) Ans. (4) A = A = ; A = 6 A 4 = 4.. A = 4 Sum of the elements of first column = Registered & Corporate ffice: CG Tower, A-46 & 5, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)-45 Tel.No.: ,,, a: CIN: U8RJ7PLC49 To Know more: sms RES at contact@resonance.ac.in Page 5

28 PAPER- (B.E. / B.TECH.) JEE (MAIN) NLINE 4. Let A, B and C be three events, which are pair-wise independent and E denotes the complement of an event E. If P(A BC) = and P(C) >, then P [( A B ) C] is equal to : () P( A ) P(B) () P( A ) P(B ) () P( A ) + P(B ) (4) P(A) + P(B ) Ans. () P[(A B) C] P[( A B ) C] = P(C) = P(C) P(A C) P(B C) P(A B C) P(C) P(C) P(A)P(C) P(B)P(C) = P(C) = P (A) P(B) = P A P(B) or PB P(A) 5. If p (p q) is false, then the truth values of p and q are respectively : (), () T, T (), T (4) T, Ans. () P (~p ~q) p q ~ p ~ q p (~ p ~ q) T T T T T T T T T T 6. If the function f defined as f() = k,, is continuous at =, then the ordered pair (k, f()) is e Ans. () equal to : () (, ) () (, ) () (, ) (4), f() = k e ; f() is continuous at = f() = Lim = Lim k e! ( () ()...( (k ) Clearly k = and f() = e Registered & Corporate ffice: CG Tower, A-46 & 5, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)-45 Tel.No.: ,,, a: CIN: U8RJ7PLC49 To Know more: sms RES at contact@resonance.ac.in Page 6

29 PAPER- (B.E. / B.TECH.) JEE (MAIN) NLINE 7. If the angle between the lines, = y = z and 5 = 7y 4 p () 7 () 7 () Ans. () = y = z and 5 = y P / 7 = z 4 P 4 4 Angle between both lines is cos = 7 cos P = 56 P P 98 = z is cos 4 4 (4) 7 7 4, then p is equal to : P 98 = P + 8 P + 98 = P + 56P P = 96 P = 7 8. The locus of the point of intersection of the lines, y + 4 k = and k + ky 4 = (k is any non-zero real parameter), is : () an ellipse whose eccentricity is. () a hyperbola whose eccentricity is () a hyperbola with length of its transverse ais 8 (4) an ellipse with length of its major ais 8. Ans. () y + 4 k =...(i) k + ky 4 =...(ii) Eliminating k by (i) and (ii) y y 4 = 4 y = y 6 = Hyperbola e = 6 = and length of transverse ais = 8 9. A man on the top of a vertical tower observes a car moving at a uniform speed towards the tower on a horizonatal road. If it takes 8 min. for the angle of depression of the car to change from to 45 ; then after this, the time taken (in min.) by the car to reach the foot of the tower, is : () 9 ( ) () 8( + ) () 8 ( ) (4) 9 ( + ) Ans. (4) Let length of tower = h B AC' = AB = h and AC = AB cot º = h CC' = ( ) h Time taken by car form C to C' = 8 min time take by car to reach the foot of the tower = 8 min. = 9 ( + ) min A 45º º C C Registered & Corporate ffice: CG Tower, A-46 & 5, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)-45 Tel.No.: ,,, a: CIN: U8RJ7PLC49 To Know more: sms RES at contact@resonance.ac.in Page 7

30 PAPER- (B.E. / B.TECH.) JEE (MAIN) NLINE. If an angle A of a ABC satisfies 5 cosa + =, then the roots of the quadratic equaiton, = are : () sec A, cota () seca, tana () tana, cosa (4) sina, seca Ans. () 5cosA + = cosa = 5 clearly A (9º, 8º) Now roots of equation = are Roots seca and tana 5 4 and. If a circle C, whose radius is, touches eternally the circle, + y + 4y 4 = at the point (, ), then the length of the intercept cut by this circle C, on the -ais is equal to : () () 5 () (4) 5 Ans. (4) Centre of given circle = (, ) and radius = 4 4 = centre of required circle (5,) or ( 4,) length of intercept on -ais will be square in both circle so one required circle ( 5) + (y ) = + y 4y + = Length of intercept = = 5 = 5 g c. Let P be a point on the parabola, = 4y. If the distance of P from the centre of the circle, + y = is minimum, then the equation of the tangent to the parabola at P, is : () + y + = () + 4y = () + y = (4) y + = Ans. Let P (t, t ) equation normal at P to = 4y be y t = t ( t) it passes through (,) t = t ( t) t + t + = (t + ) (t t + ) = t = Point P is (,) equation of tangent to = 4y at (,) ( ) = (y + ) + y + = Registered & Corporate ffice: CG Tower, A-46 & 5, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)-45 Tel.No.: ,,, a: CIN: U8RJ7PLC49 To Know more: sms RES at contact@resonance.ac.in Page 8

31 PAPER- (B.E. / B.TECH.) JEE (MAIN) NLINE. If f() = t(sin sin t) dt then : () f () f() = cos sin () f() + f() f() = cos () f() + f() = sin (4) f() + f() = cos sin Ans. 4 f() = t(sin sint)dt f() = sin t dt f'() = (sin) + cos f'()= cos tdt f''() = (cos) (sin) t sintdt t dt sin tdt f'''() = ( sin) + cos (sin) (cos) f'''() + f'() = cos sin 4. The number of values of k for which the system of linear equations, (k + ) + y = k k + (k + ) y = k has no soution, is : () () () (4) 4 Ans. () or no solution k k = k k k (k + ) (k + ) = k k 5k + 6 = k =, k for k = both lines identical so k = only so number of values of k is tdt 5. tan K tan If d = tan tan KA tan + C, (C is a constant of integration), then the ordered A pair (K, A) is equal to () (, ) () (, ) () (, ) (4) (, ) Ans. () tan I = d tan tan sec d tan tan dt = t t, where tan = t sec d = dt t dt = = tan tan C = tan C / / t 4 = k =, A =. Registered & Corporate ffice: CG Tower, A-46 & 5, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)-45 Tel.No.: ,,, a: CIN: U8RJ7PLC49 To Know more: sms RES at contact@resonance.ac.in Page 9

32 PAPER- (B.E. / B.TECH.) JEE (MAIN) NLINE i 6. The least positive integer n for which =, is i () () 5 () 6 (4) Ans. (4) i i n n n = least positive integer value of n is. n 7. The sum of the first terms of the series , is : 6 () 9 + () 8 + () Ans. () = ( ) +.upto terms = 4...up to terms 4 8 = 4 = 4 + = (4) Let a = î + ĵ + ˆk, c = ĵ ˆk and a vector b be such that a b = c and a b =. Then b equals : () Ans. () a b c a a b a c a.b a a.ab a c a b î ĵ kˆ () i + j + kˆ bˆ = î + ĵ + kˆ b 5î ĵ kˆ b = b = () (4) Registered & Corporate ffice: CG Tower, A-46 & 5, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)-45 Tel.No.: ,,, a: CIN: U8RJ7PLC49 To Know more: sms RES at contact@resonance.ac.in Page

33 PAPER- (B.E. / B.TECH.) JEE (MAIN) NLINE 9. The mean and the standard deviation (s.d.) of five observations are 9 and, respectively. If one of the observations is changed such that the mean of the new set of five observations becomes, then their s.d. is : () () () 4 (4) Ans. () Standard deviations with be same so S.D is. Let M and m be respectively the absolute maimum and the absolute minimum values of the function, f() = in the interval [, ]. Then M m is equal to : () 9 () 4 () (4) 5 Ans. () f() = , [, ] f'() = f'() = 6( ) ( ) f() = f() = 9 f() = 5 f() = 4 M = 4, m 5 M m = 9 Registered & Corporate ffice: CG Tower, A-46 & 5, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)-45 Tel.No.: ,,, a: CIN: U8RJ7PLC49 To Know more: sms RES at contact@resonance.ac.in Page

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