JEE Main Exam (Paper & Solution) Part A PHYSICS

Transcription

1 JEE Main Exam 07 (Paper & Solution) Code A Date : Part A PHYSICS Q. A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains same, the stress in the leg will change by a factor of- () 9 () 9 Ans. [] Let volume of man is Lbh As all dimension increases by a factor (K 9) keeping the density constant Stress on his legs Initial stress Stress Final stress Stress weight area Vρg A K Vρg K A Vρg A Stress K Stress Where (K 9) So stress is changed by a factor 9. CAREER PIN () 8 () 8 Q. A body is thrown vertically upwards. Which one of the following graphs correctly represent the velocity vs time? v () v () v t () v t () Ans. [] v u gt (straight line graph) v t t t CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

2 Q. A body of mass m 0 kg is moving in a medium and experiences a frictional force F kv. Its initial speed is v 0 0 ms. If, after 0 s, its energy is mv 0, the value of k will be- 8 () 0 kg m () 0 kg s () 0 kg m () 0 kg m s Ans. [] kv a m dv kv dt m v 0 dv v v 0 k m 0 0 dt k v 0 m k 0 v k 000 v 0 According to question KE mv mv 0 8 v v k k k 0 Q. A time dependent force F 6t acts on a particle of mass kg. If the particle starts from rest, the work done by the force during the first sec. will be- ().5 J () J () 9 J () 8 J [JEE Advance, Chapter : Work-Power-Energy, Ex., Page No.5, Q. No.] Ans. [] 6 t a 6 t dv 6t dt v 6t 0 KE.5 W ΔKE Joule CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

3 Q.5 he moment of inertia of a uniform cylinder of length l and radius R about its perpendicular bisector is I. What is the ratio l/r such that the moment of inertia is minimum? () () () () Ans. [] R l Moment of inertia of cylinder about perpendicular bisector is I L R I M + For given mass and density M πr Lρ R M πlρ L M I M + πlρ For maxima or minima of I di 0 dl di L M M dl πl ρ L 6 M L ρ π 0 L 6 πr L R Lρ πl ρ L R CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

4 Q.6 A slender uniform rod of mass M and length l is pivoted at one end so that is can rotate in vertical plane (see figure). here is negligible friction at the pivot. he free end is held vertically above the pivot and then released. he angular acceleration of the rod when it makes an angle θ with the vertical is- z θ Ans. [] g () sin θ l g () sin θ l x g () cosθ l [JEE Advance, Chapter : Rotational motion, Ex., Page No., 6, Q. No.] z λ/ θ θ mg τ mg l sin θ l sin θ τ Iα l mg sin θ α g sin θ l α ml α x g () cosθ l Q.7 he variation of acceleration due to gravity g with distance d from centre of the earth is best represented by (R Earth's radius)- g g () g d () g R d () R d () R d CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

5 [JEE Main, Chapter : Gravitation, Ex., Page No.,, Q. No.0] Ans. [] R g g g g r GM when r > R r GM r R when r < R g r R r Q.8 A copper ball of mass 00 gm is at a temperature. It is dropped in a copper calorimeter of mass 00 gm, filled with 70 gm of water at room temperature. Subsequently, the temperature of the system is found to be 75ºC. is given by- (Given : room temperature 0ºC, specific heat of copper 0. cal/gmºc) () 800ºC () 885ºC () 50ºC () 85ºC Ans. [] otal heat gain otal heat loss (75 0) + 70 (75 0) ( 75) ºC Q.9 An external pressure P is applied on a cube at 0ºC so that it is equally compressed from all sides. K is the bulk modulus of the material of the cube and α is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. he temperature should be raised by- () P αk () P αk α () PK () PKα Ans. [] B P dv V dv P V B dv PV B CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

6 By heating we have to increase the volume by ΔV VγΔ V α Δ V αδ Δ Here B K Δ P αb P αb PV B PV B Q.0 C p and C v are specific heats at constant pressure and constant volume respectively. It is observed that C p C v a for hydrogen gas C p C v b for nitrogen gas he correct relation between a and b is- () a b () a b () a b () a 8 b [JEE Main, Chapter : KG, Ex., Page No.7, Q. No.5] [JEE Advance, Chapter : KG, Ex., Page No.5,Q. No.] Ans. [] C p C v R If C p and C v are molar specific heat But if C p and C v are specific heat i.e. gram specific heat then C MS g {Q CΔ Q MS g Δ C MS g } C S g M MS gp MS gv R R S gp S gv M R a R b 8 b a a b CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

7 Q. he temperature of an open room of volume 0 m increases from 7 C to 7 C due to the sunshine. he atmospheric pressure in the room remains 0 5 Pa. In n i and n f are the number of molecules in the room before and after heating, the n f n i will be : ().6 0 ().8 0 () () [JEE Advance, Chapter : KG, Ex., Page No.7, Q. No.5] Ans. [] PV nr PV n R i K f K n f n i Q. A particle is executing simple harmonic motion with a time period. At time t 0 it is at its position of equilibrium. he kinetic energy - time graph of the particle will look like : () KE 0 t () KE 0 t () KE 0 t () KE 0 t [JEE Main, Chapter : SHM, Ex., Page No.7, Q. No.] Ans. [] x A sin ωt CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

8 dx v Aω cos ωt dt KE ma ω cos ωt ma ω cos π t KE 0 t Q. An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency 0 GHz. What is the frequency of the microwave measured by the observer? (speed of light 0 8 ms ) () 0. GHz (). GHz () 7. GHz () 5. GHz Ans. [] According to theory of relativity f app v + c v c + c / c f c / c 0 GHz 0 GHz f app 7. GHz (for approach) 0 GHz Q. An electric dipole has fixed dipole moment p r, which makes angle θ with respect to x-axis. When subjected to an electric field E r E î, it experience a torque r τ kˆ. When subjected to another electric field E r E ĵ it experiences a torque r r. he angle θ is. () 0 () 5 () 60 () 90 Ans. [] E E p θ x CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

9 τ r PE sinθ kˆ E E ĵ p θ x τ r P E cosθ ( kˆ ) PE sin θ ( kˆ ) P Ecosθ ( kˆ ) PE sin θ tan θ θ 60 E cosθ Q.5 A capacitance of μf is required in an electrical circuit across a potential difference of.0 kv. A large number of μf capacitors are available which can withstand a potential difference of not more than 00 V. he minimum number of capacitors required to achieve this is : () () 6 () () [JEE Main, Chapter : Capacitance, Ex., Page No.7, Q. No.] Ans. [] n capacitor in a row m rows Potential on each capacitor V n 0 n 000 n C eq C m n m n m n 8 Minimum number of capacitor 8 CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

10 Q.6 In the given circuit diagram when the current reaches steady state in the circuit, the charge on the capacitor of capacitance C will be: E r C r Ans. [] () CE () CE r (r + r) r () CE [JEE Main, Chapter : Capacitance, Ex., Page No., Q. No.5] E r i r (r + r ) () CE r (r + r) r C r At steady state current through capacitor branch become zero. i E r + r Potential difference across capacitor ΔV ΔV ir ΔV E r r + r charge on capacitor C ΔV r CE r + r Q.7 In the above circuit the current in each resistance is : V V V Ω Ω Ω V V V () A () 0.5 A () 0.5 A () 0 A Ans. [] CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

11 V V V 0 Ω Ω Ω 6 V V 0 V Potential difference across each resistor is zero so current in each resistor also zero. Q.8 A magnetic needle of magnetic moment Am and moment of inertia kg m is performing simple harmonic oscillations in a magnetic field of 0.0. ime taken for 0 complete oscillations is : () 6.65 s () 8.89 s () 6.98 s () 8.76 s Ans. [] M Am I kg m, B 0.0 τ MB sin θ Ια MB θ (for small oscillations ) MB MB α θ ω π I I I MB π sec ime for 0 oscillation Δt 0 Δt 6.65 sec Q.9 When a current of 5 ma is passed through a galvanometer having a coil of resistance 5Ω, it shows full scale deflection. he value of the resistance to be put in series with the galvanometer to convert it into a voltmeter of range 0 0 V is () Ω ().05 0 Ω ().55 0 Ω () Ω Ans. [] I g max 5 ma, R g 5 Ω Range of voltmeter 0 volt I g R g R H ΔV ΔV I g (R g + R H ) Range ΔV max I g max (R g + R H ) (5 + R H ) R H 985 Ω R H Ω CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

12 Q.0 In a coil of resistance 00 Ω, a current is induced by changing the magnetic flux through it as shown in the figure. he magnitude of change in flux through the coil is : 0 Current (amp.) Ans. [] ime 0.5 sec () 00 Wb () 5 Wb () 50 Wb () 75 Wb [JEE Advance, Chapter : EMI, Ex., Page No., Q. No.] 0 Current (amp.) Emf ir ime 0.5 sec dφ ir dt ( dφ) ( ) idt R 0.5 ( Δφ) R idt 0 ( Δφ) R (area of i t curve) Δφ R ( 0.5 0) Δφ 00 (.5) Δφ 50 Wb Q. An electron beam is accelerated by a potential difference V to hit a metallic target to produce X-ray. It produces continuous as well as characteristic X-rays. If λ min is the smallest possible wavelength of X-ray in the spectrum, the variation of log λ min with log V is correctly represented in - log λ min log λ min () log V () log V CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

13 log λ min log λ min () log V () log V Ans. [] log λ min log V K.E. ev (K.E. kinetic energy of electron) E Pmax K.E. hc hc ev λ min V constant λmin e ln λ min + ln V ln constant ln λ min ln V + ln (constant) Straight line of ve slope Q. A diverging lens with magnitude of focal length 5 cm is placed at a distance of 5 cm from a converging lens of magnitude of focal length 0 cm. A beam of parallel light falls on the diverging lens. he final image formed as - () real and at a distance of 0 cm from convergent lens () virtual and at a distance of 0 cm from convergent lens () real and at a distance of 0 cm from the divergent lens () real and at a distance of 6 cm from the convergent lens Ans. [] 5 cm ƒ 5 cm ƒ 0 cm Image form by diverging is at the focus of diverging lens. Now image form by diverging act as a source for converging lens. For converging lens object real at a distance 0 cm from it which is at (ƒ). u ƒ, ƒ + ƒ, v + ƒ v u ƒ Final image real at a distance ƒ 0 cm from converging lens. CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

14 Q. In a Young s double slit experiment, slits are separated by 0.5 mm, and the screen is placed 50 cm away. A beam of light consisting of two wavelengths, 650 nm and 50 nm, is used to obtain interference fringes on the screen. he least distance from the common central maximum to the point where the bright fringes due to both the wavelengths coincide is - ().56 mm () 7.8 mm () 9.75 mm () 5.6 mm [JEE Advance, Chapter : Wave nature of light : Interference, Ex.6, Page No., Q. No.] Ans. [] d 0.5 mm, D.5 m, λ 650 nm, λ 50 nm β λ D d mm λ β D mm d Least distance where their maxima again coincides from central maxima is LCM of β & β 7.8 mm Q. A particle A of mass m and initial velocity v collides with a particle B of mass m which is at rest. he Ans. [] m collision is head on, and elastic. he ratio of the de-broglie wavelengths λ A to λ B after the collision is - λ () A λa λ () () A λ () A λ λ λ λ v v B v v v m m/ v + 0 m + m/ m/ m/ v Similarly m v 0 + v m + m/ m v v m/ v v Q λ m h v λ m v λ mv, λ m / m B m/ m m h. v v / v / v m/ B v B CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

15 Q.5 Some energy levels of a molecule are shown in the figure. he ratio of the wavelength r λ, is given by - λ E E λ λ E E () r () r () r () r [JEE Main, Chapter : Atomic Structure, Ex.5, Q. No.7] Ans. [] hc λ ( E) ( E) hc λ E.(i) hc λ ( E) E E + By (i) & (ii) hc λ r E λ hc E / E E + E E.(ii) Q.6 A radioactive nucleus A with a half life, decays into a nucleus B. At t 0, there is no nucleus B. At sometime t, the ratio of the number of B to that of A is 0.. hen, t is given by - log log. () t () t () t log (.) () t log. log log(.) Ans. [] A B A A 0 e λt ; B A 0 ( e λt ) ; 0. e λt e λt. λt ln (.) ln() t ln (.) t ln(.) t ln() log(.) log() B A A ( e 0 A λt λt 0e ) CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

16 Q.7 In a common emitter amplifier circuit using an n-p-n transistor, the phase difference between the input and the output voltages will be - () 5º () 90º () 5º () 80º Ans. [] In C-E amplifier phase difference between input-output voltage is 80º. Q.8 In amplitude modulation, sinusoidal carrier frequency used is denoted by ω c and the signal frequency is denoted ω m. he bandwidth (Δω m ) of the signal is such that Δω m << ω c. Which of the following frequencies is not contained in the modulated wave? () ω m () ω c () ω m + ω c () ω c ω m Ans. [] LSB USB ω c ω m ω c ω c + ω m because Δω m << ω c ω m is not present in modulated wave. Q.9 Which of the following statements is false? () Wheatstone bridge is the most sensitive when all the four resistances are of the same order of magnitude () In a balanced Wheatstone bridge if the cell and the galvanometer are exchanged, the null point is disturbed () A rheostat can be used as a potential divider () Kirchhoff s second law represents energy conservation Ans. [] (I) P Q (II) A G B P Q R S G R S In I st case for balance CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

17 P Q R S P R Q S In II nd case for balance P R Q S In both case Null point is same..(i).(ii) Q.0 he following observations were taken for determining surface tension of water by capillary method : diameter of capillary, D.5 0 m rise of water, h.5 0 m. Using g 9.80 m/s rhg and the simplified relation 0 N/m, the possible error in surface tension is closest to - () 0.5% ().5% ().% () 0% [JEE Advance, Chapter : Practical Physics, Ex., Page No.70, Q. No.7] Ans. [] D.5 0 m, ΔD m, h.5 0 m, Δh m g 9.80 m/s rhg 0 N/m r h g 0 r h constant Δ Δr Δh 0 r h Δ Δr Δh + r h Δ % error.5 % Δ D r ΔD Δr ΔD Δr D r CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

18 Q. Given C ( graphite) + (g) C (g) ; Part B CHEMISRY Δ r H 9.5 kj mol H (g) + (g) H (); Δ r H 85.8 kj mol C (g) + H () CH (g) + (g); Δ r H kj mol Based on the above thermochemical equations, the value of Δ r H at 98 K for the reaction C (graphite) + H (g) CH (g) will be ; () 7.8 kj mol ().0 kj mol () +7.8 kj mol () +.0 kj mol [JEE Main, Chapter : Chemical Energetic,Exercise- Q. No.] [JEE Advance, Chapter : Chemical Energetic,Exercise- Q. No.] Ans. [] C( graphite) + (g) C(g) ; Δ r H 9.5 kj... (i) H (g) + (g) H (); Δ r H 85.8 kj... (ii) C (g) + H () CH (g) + (g); Δ r H (iii) C ( graphite) + H(g) CH (g) ; Δ r H?... (iv) eq. (iv) eq. (i) + eq (ii) + eq. (iii) ( 85.8) kj/mol Q. gram of a carbonate (M C ) on treatment with excess HCl produces mole of C. he molar mass of M C in g mol is - () 8.6 ().86 () 86 () 8. Ans. [] M C + HCl C gm.086 PAC on carbon.086 x 8. x Q. ΔU is equal to - () Adiabatic work () Isothermal work () Isochoric work () Isobaric work CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

19 Ans. [] FL (According to first law of thermodynamics) ΔE q + w If q 0, ΔE w adiabatic process Q. he yndall effect is observed only when following conditions are satisfied - (a) he diameter of the dispersed particles is much smaller than the wavelength of the light used (b) he diameter of the dispersed particle is not much smaller than the wavelength of the light used (c) he refractive indices of the dispersed phase and dispersion medium are almost similar in magnitude (d) he refractive indices of the dispersed phase and dispersion medium differ greatly in magnitude. () (a) and (c) () (b) and (c) () (a) and (d) () (b) and (d) [JEE Advance, Chapter : Surface Chemistry, Key Concept, ptical Properties] Ans. [] Facts Q.5 A metal crystallises in the face centred cubic structure. if the edge length of its unit cell is 'a', the closest approach between two atoms in metallic crystal will be : () a () a () a () a [JEE Main, Chapter : Solid State, Solved Example, Q. No.] [JEE Advance, Chapter : Solid State, Solved Exercise-, Q. No.] Ans. [] nearest distance a a fcc CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

20 Q.6 Given E Cl / Cl E Cr7 / Cr Cr / Cr.6V, E + 0.7V, Mn / Mn +.V, E +.5V Among the following, the strongest reducing agent is - () Cr + () Cl () Cr () Mn + [JEE Main, Chapter : Electro Chemistry, Exercise-, Q. No.6] [JEE Advance, Chapter : Electro Chemistry, Exercise-5, Section [A], Q. No.] Ans. [] Less is the SRP, more is the reducing power & strongest is the reducing agent. Q.7 he freezing point of benzene decreases by 0.5 C when 0. g of acetic acid is added to 0 g of benzene. If acetic acid associates to form a dimer in benzene, percentage association of acetic acid in benzene will be (K f for benzene 5. K kg mol ) () 7.6% () 9.6% () 6.6% () 80.% [JEE Main, Chapter : Solution, Solved Example Q. No.0] [JEE Advance, Chapter : Solution, Exercise-5, Section [B], Q. No.] Ans. [] Δ f i K f m i i.57 i.57 β. 96 or 9.6 % / n / Q.8 he radius of the second Bohr orbit for hydrogen atom is (Planck's Const. h Js; mass of electron kg; charge of electron e C; permittivity of vaccum kg m A ) () 0.59 Å (). Å ().65 Å () 7.76 Å [JEE Main, Chapter : Atomic Structure, Exercise-, Q. No.] [JEE Advance, Chapter : Atomic Structure, Exercise-, Q. No.] Ans. [] n r 0.59 Å z () Å. Å CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

21 Q.9 wo reactions, R and R have identical pre-exponential factors. Activation energy of R exceeds that of R by 0 kj mol. If k and k are rate constants for reactions R and R respectively at 00 K, then ln(k /k ) is equal to. (R 8. J mol K ). () 6 () () 8 () [JEE Main, Chapter : Chemical Kinetics, Exercise-5, Section [B], Q. No.7] [JEE Advance, Chapter : Chemical Kinetics, Exercise-, Q. No.5] Ans. [] R R A A E a +0 E a k k (Ea + 0)/R k A e Ea /R k A e k ( Ea + Ea + 0) / R e k k 0/ R e 0 0 / e k 0000 / 9. e e k ln k Q.0 pk a of a weak acid (HA) and pk b of a weak base (BH) are. and., respectively. he ph of their salt (AB) solution is- () 7.0 ().0 () 7. () 6.9 [JEE Main, Chapter : Ionic Equilibrium, Exercise-, Q. No.8] [JEE Advance, Chapter : Ionic Equilibrium, Exercise-, Q. No.8] Ans. [] ph pk w + pka pk b Q. Both lithium and magnesium display several similar properties due to the diagonal relationship; however, the one which is incorrect, is : () Both form nitrides () Nitrates of both Li and Mg yield N and on heating () Both form basic carbonates () Both form soluble bicarbonates Ans. [] It is the best possible option but, it should be bonus because Li C is less basic and MgC is basic CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

22 Q. Which of the following species is not paramagnetic? () () B () N () C [JEE Main, Chapter : Chemical bonding, Exercise #, Q. No.9] [JEE Advance, Chapter : Chemical bonding, Exercise #, Q. No.] Ans. [] C is diamagnetic because all electrons are paired in it. Q. Which of the following reactions is an example of a redox reaction? () XeF 6 + H XeF + HF () XeF 6 + H Xe F + HF () XeF + F XeF 6 + () XeF + PF 5 [XeF] + PF 6 Ans. [] XeF + F XeF 6 + his reaction is a redox reaction Q. A water sample has ppm level concentration of following anions F 0 ; S 00 ; N 50 he anion / anions that make / makes the water sample unsuitable for drinking is / are () nly F () nly S () nly N () Both S and N Ans. [] F ion concentration above ppm causes brown mottling of teeth Q.5 he group having isoelectronic species is (), F, Na, Mg + (), F, Na +, Mg + (), F, Na +, Mg + (), F, Na, Mg + [JEE Main, Chapter : Periodic able, Exercise #, Q. No.5] [JEE Advance, Chapter : Periodic able, Exercise #, Q. No.] Ans. [], F, Na +, Mg + are isoelectronic species. hey all have 0e Q.6 he products obtained when chlorine gas reacts with cold and dilute aqueous NaH are () Cl and Cl () Cl and Cl () Cl and Cl () Cl and Cl [JEE Main, Chapter : p-block elements, Exercise #, Q. No. 9] [JEE Advance, Chapter : p-block elements (Halogens), Exercise #, Q. No. 9] Ans. [] Cl + NaH (cold/dilute) NaCl + NaCl + H CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

23 Q.7 In the following reactions, Zn is respectively acting as a / an (a) Zn + Na Na Zn (b) Zn + C ZnC () acid and acid () acid and base () base and acid () base and base Ans. [] Zn + Na Na Zn acid Zn + C ZnC Base Zn is an amphoteric oxide Q.8 Sodium salt of an organic acid 'X' produces effervescence with conc. H S. 'X' reacts with the acidified aqueous CaCl solution to give a white precipitate which decolourises acidic solution of KMn. 'X' is - () CH CNa () Na C () C 6 H 5 CNa () HCNa [JEE Advance, Chapter : Salt analysis, Exercise #, Q. No. 9] Ans. [] [X] Na C (xalate-ion) CaCl Conc. H S Na C + H C C Effervesce CaC + NaCl White ppt KMn + C H + C + Mn + Pink Colour xalate ion Colourless Q.9 he most abundant elements by mass in the body of a healthy human adult are : xygen (6.%), Carbon (.9 %), Hydrogen (0.0%) and Nitrogen (.6%). he weight which a 75kg person would gain if all H atoms are replaced by H atoms is () 7.5 kg () 0 kg () 5 kg () 7.5 kg Ans. [] Weight of 0 H in person kg 00 Now if H is replaced by H han person will gain weight by 7.5 kg CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

24 Q.50 n treatment of 00 ml of 0. M solution of CoCl.6H with excess AgN ;. 0 ions are precipitated. he complex is : () [Co(H ) 6 ]Cl () [Co(H ) 5 Cl]Cl.H () [Co(H ) Cl ]Cl.H () [Co(H ) Cl ].H Ans. [] CoCl.6H + AgN (excess) AgCl 00 ml, 0. M. 0 ion No. of moles 0.0 mol mol Q 0.0 mol of CoCl.6H produce 0.0 mol of AgCl mol of CoCl.6H produce mol of AgCl Correct complex is [Co(H ) 5 Cl]Cl.H Q.5 Which of the following compounds will form significant amount of meta product during mono-nitration reaction? NH NHCCH H CCH () () () () [JEE Advance, Chapter : Amines and Nitrogen Compounds, Example-] Ans. [] NH NH NH N NH HN N + + N [7%] [%] [5%] In aniline protonation of NH Group make it deactivating and meta directing. So meta product is significant. Q.5 Which of the following, upon treatment with tert-buna followed by addition of bromine water, fails to decolourize the colour of bromine? () Br () Br C 6 H 5 () Br () Br CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

25 Ans. [] [JEE Advance, Chapter : Halogen Derivatives, Exercise #, Q. No.6] CH CH C Θ CH CH Br Elimination reaction not possible Non Nucleophillic base CH C CH CH It do not give unsaturation test Q.5 he formation of which of the following polymers involves hydrolysis reaction? () Nylon 6, 6 () erylene () Nylon 6 () Bakelite [JEE Main, Chapter : Polymer, Exercise # 5, Q. No.] [JEE Advance, Chapter : Carbohydrate, Amino acid, Protein & Polymer, Example-] Ans. [] Nylon-6 is formed by monomer which is obtain by hydrolysis of CAPRLACAM NH C H /Δ NH (CH ) 5 CH Polymerisation NH (CH ) 5 C Amino caproic acid n Caprolactam Nylon-6 Q.5 Which of the following molecules is least resonance stabilized? () () N [JEE Main, Chapter : GC, Page 5, Q. No.] [JEE Advance, Chapter :GC, Exercise #, Q. No.5] Ans. [] () () N Aromatic Non Aromatic Aromatic is least stable as other are aromatic and is non aromatic.... Aromatic CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

26 Q.55 he increasing order of the reactivity of the following halides for the S N reaction is : CH CHCH CH CH CH CH Cl p H C C 6 H CH Cl Cl (I) (II) () (I) < (III) < (II) () (II) < (III) < (I) () (III) < (II) < (I) () (II) < (I) < (III) [JEE Main, Chapter : Haloalkane, page 8, Q. No.7] [JEE Advance, Chapter : Halogen Derivatives, Exercise #, Q. No.] (III) Ans. [] Rate of SN reaction stability of carbocation CH CHCH CH Θ CH CH CH CH + Cl Cl (I) º Carbocation CH CH CH Cl CH CH CH CH º Carbocation CH Cl CH CH rder of SN II < I < III Resonance Stabilize Q.56 he major product obtained in the following reaction is : Br H C 6 H 5 ( + ) C 6 H 5 BuK Δ Ans. [] () ( + )C 6 H 5 CH( t Bu)CH C 6 H 5 () ( )C 6 H 5 CH( t Bu)CH C 6 H 5 () ( ± )C 6 H 5 CH( t Bu)CH C 6 H 5 () C 6 H 5 CH CHC 6 H 5 [JEE Main, Chapter : Hydrocarbon, page 7, Q. No. ] [JEE Advance, Chapter : Hydrocarbon, Exercise #, Q. No. 9] Br H tbuk C 6 H 5 C 6 H 5 CH CH C 6 H 5 Δ C 6 H 5 It is example of E elimination as t butoxide is stronger base and heating is also used. CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

27 Q.57 Which of the following compounds will behave as a reducing sugar in an aqueous KH solution? HH C HH CH H C CH CH () H () CH H H H H HH C CH H HH C CH H () H () CCH H H H [JEE Main, Chapter : Carbohydrate, page 7, Q. No. 9] [JEE Advance, Chapter : Carbohydrate, Protein & Polymer, Exercise # 5, Q. No. ] Ans. [] HCH CH H Aq. HCH H C CH KH Hydrolysis H H H It is hemiacetal that is why it can behave as reducing sugar. CH H H Q.58 -Methyl-pent--ene on reaction with HBr in presence of peroxide forms an addition product. he number of possible stereoisomers for the product is : () wo () Four () Six () Zero [JEE Main, Chapter : Hydrocarbon, page 0, Q. No.50] [JEE Advance, Chapter : Hydrocarbon, Example-, Q. No.50] Ans. [] CH H C CH C CH CH CH HBr * CH CH CH CH CH Peroxide * Br Major Product wo new chiral center are formed so total stereoisomer his HBr/Peroxide gives antimarkownikov product as major product CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

28 Q.59 he correct sequence of reagents for the following conversion will be : H CH H CH CH CH () CH MgBr, [Ag(NH ) ] + H, H + /CH H () [Ag(NH ) ] + H, CH MgBr, H + /CH H () [Ag(NH ) ] + H, H + /CH H, CH MgBr () CH MgBr, H + /CH H, [Ag(NH ) ] + H Ans. [] H CH C H [Ag(NH ) ] + H Θ ollen s reagent oxidise Aldehyde in carboxylic acid C Θ H + /CH H C CH CH MgBr H CH CH Q.60 he major product obtained in the following reaction is : DIBAL H CH () CH () CH H CH H CH () CH () CH Ans. [] CH H CH DiBAL H CH CH CH DiBAL-H is selective reducing agent which reduce carboxylic acid and it s derivative up to aldehyde only [further reduction not possible] CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

29 Part C MAHS Q.6 he function f : R x, defined as f(x) + x () injective but not surjective () surjective but not injective () neither injective nor surjective () invertible [JEE Main, Chapter : Function, Page 55, Ex. 5A, Q. No. ] [JEE Advance, Chapter : Function, Page 0, Ex., ] Ans. [] y-axis, is / max. x-axis min. / x f(x) (odd) + x (symmetry about origin) dy ( + x ) x(0 + x) dx ( + x ) x ( + x min. ) 0 x, max. + Line parallel to x-axis cuts the graph more than one points hence function is many one. Range, codomain hence function is onto Q.6 If, for a positive integer n, the quadratic equation, x (x + ) + (x + ) (x + ) (x + n ) (x + n) 0n has two consecutive integral solutions, then n is equal to () 9 () 0 () () Ans. [] CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

30 x (x + ) + (x + ) (x + ) (x + (n )) (x + n) 0n After simplify nx + ( (n )x + ( (n )n) 0n nx + n x + x + nx + n n(n ) 0 0 0n 0 x n + nx + 0 Put n (where n I + ) x + x + 0 x + x (x + 6) (x + 5) 0 i.e. x 5, 6 (wo consecutive integral solutions) So, n Q.6 Let ω be a complex number such that ω + z where z. If 7 ω ω k, then k is equal to ω ω () z () () () z [JEE Advance, Chapter : Complex Number, Page 9, Ex. ] Ans. [] Apply operation C C + C + C 0 ( + ω ) ω k 0 ω ω 0 0 ω ω ω ω k (Because + ω + ω 0) open by C (ω ω ) k (ω ω) k ( ω ω) k ( + ω) k Given that ω + z z k k z CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

31 Q.6 If A, then adj (A + A) is equal to () () Ans. [] A A A + A 8 6 adj (A + A) () () 6 5 Q.65 If S is the set of distinct values of 'b' for which the following system of linear equations x + y + z x + ay + z ax + by + z 0 has no solution, then S is () an infinite set () a finite set containing two or more elements () a singleton () an empty set Ans. [] Δ 0 and at the one of Δ or Δ or Δ 0 Δ a 0 a b [a b] [ a] + [b a ] 0 a b + b a 0 a a + 0 a x + y + z x + y + z x + by + z 0 only one value of b, S is singleton set CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

32 Q.66 A man X has 7 friends, of them are ladies and are men. His wife Y also has 7 friends, of them are ladies and are men. Assume X and Y have no common friends. hen the total number of ways in which X and Y together can throw a party inviting ladies and men, so that friends of each of X and Y are in this party, is () 68 () 69 () 8 () 85 Ans. [] [JEE Main, Chapter :P & C, Page 6, Ex., Q. No. 9] X 7 friends Y 7 friends M L M L Case I : L from X side and M from Y side C C 6 Case II : M from X side and L from Y side C C Case III : L and M from X side and M and L from Y side ( C C ) ( C C ) (6 ) (6 ) 8 8 Case IV : M and L from X side and M and L from Y side ( C C ) ( C C ) ( ) ( ) otal number of ways Case I + Case II + Case III + Case IV Q.67 he value of ( C 0 C ) + ( C 0 C ) + ( C 0 C ) + ( C 0 C ) ( C 0 0 C 0 ) is () 0 () 0 9 () 0 0 () Ans. [] ( C + C C 0 ) ( 0 C + 0 C C 0 ) [ C + C C ] ( 0 ) 0 [ C C + C C + C C + C ( C + C )] 0 + ( 0 ) ( ) ( 0 ) CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

33 Q.68 For any three positive real numbers a, b and c, 9(5a + b ) + 5(c ac) 5b(a + c). hen () b, c and a are in A.P. () a, b and c are in A.P. () a, b and c are in G.P. () b, c and a are in G.P. [JEE Main, Chapter : Progression, Page 7, Ex., Q. No. 9] [JEE Advance, Chapter : Progression, Page 0, Ex., Q. No. 6 ] Ans. [] 5a + 9b + 5c 75ac 5ab 5bc 0 50a + 8b + 50c 50ac 0ab 0bc 0 (5a b) + (b 5c) + (5a 5c) 0 (5a b) 0, (b 5c) 0, (5a 5c) 0 5a b, b 5c 5a b 5c a b c k (let) 5 a k, b 5k, c k hen a, c and b are in A.P. Q.69 Let a, b, c R. If f(x) ax + bx + c is such that a + b + c and f(x + y) f(x) + f(y) + xy, x, y R, then 0 n f (n) is equal to () 65 () 90 () 55 () 0 Ans. [] As a + b + c So, f() f(x + y) f(x) + f(y) + xy Put x, y f() f() + 7 Put x, y f() f() + f() + Put x, y f() f() So, f (n) f() + f() + f() f(0) n Let S f(n) S f(n) f(n) n f(n) [6 + (n )] CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

34 f(n) 0 n n (n + 5) 0 f (n) n n n n cot x cos x Q.70 lim π ( π x x ) equals : () 6 () 8 () () [JEE Main, Chapter :Limit, Page 0, Ex., Q. No. 0] [JEE Advance, Chapter :Limit, Page 6, Ex., Q. No. 8] Ans. [] Put x π + h π π cot + h cos + h) lim π π + h h 0 tan h + sin h lim 8h h 0 tan h sin h lim h 0 8h by expansion method h 0 h h + + lim h + lim h h h h... h ! 5! 8h 5 h! + 8h ! CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

35 Q.7 If for x 0,, the derivative of 6x x tan is x g(x), then g(x) equals : 9x x x () 9x x () 9x () + 9x 9 () + 9x Ans. [] [JEE Advance, Chapter : Differentiation, Page 5, Ex., Q. No. 6] y tan tan tan 6x x 9x x (x (x x ) x x ) dy (x + x ) (differentiating w.r.t. x) dx + (x x ) x 6 x + x + 9x 9 x + 9x 9 x + 9x Q.7 he normal to the curve y(x ) (x ) x + 6 at the point where the curve intersects the y-axis passes through the point : (), (), (), (), Ans. [] y(x ) (x ) x + 6 at y axis, x 0 y( ) ( ) y Now y(x 5x + 6) x + 6 x + 6 y x 5x + 6 dy (x dx 5x + 6) (x + 6)(x 5) (x 5x + 6) 6 (6)( 5) at x 0, y 6 CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

36 equation of normal y (x 0) x + y passes, (by option) Q.7 wenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. hen the maximum area (in sq. m) of the flower-bed, is : () 0 () 5 () 0 ().5 [JEE Main, Chapter :Maxima & Minima, Page 96, Ex., Q. No. ] Ans. [] Given r + r + rθ 0 0 r θ r r θ r rθ Area r z r θ (0r 0 r r r dz (0 r) 0 r 5 dr ) d z at r 5, θ, < 0 (hence maxima) dr maximum area z r θ 5 5m CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

37 n Q.7 Let In tan x dx, (n > ). If I + I 6 a tan 5 x + bx 5 + C, where C is a constant of integration, then the ordered pair (a, b) is equal to : (), 0 (), (), 0 (), [JEE Main, Chapter : Indefinite Integration, Page, Ex., Q. No. ] [JEE Advance, Chapter : Indefinite Integration, Page 5, Ex., Q. No. ] Ans. [] I n tan n x dx I + I 6 (tan x + tan x) dx 6 tan x( + tan x) dx tan x sec x dx t dt put t tan x t 5 + C 5 tan 5 x + C 5 n comparison, we get a, b 0 5 π Q.75 he integral + π dx is equal to : cosx () () () () [JEE Main, Chapter :Definite Integration, Page, Ex. 5A, Q. No. 7] Ans. [] I π/ π/ π/ dx + cosx I by using f (x)dx f (a + b π/ dx + cos( π x) b a b a x)dx CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

38 π/ I + dx I π/ π/ π/ + cosx cosec x dx π/ π/ I (cot x) ( ) cosx π/ π/ dx cos x Q.76 he area (in sq. units) of the region {(x, y) : x 0, x + y, x y and y + x } is : () () () () Ans. [] y (0, ) (0, ) (, ) (, ) (, 0) x + x Required Area x dx x 0 x + / x / 9 + x x x x + x dx dy π Q.77 If ( + sin x) + (y + ) cos x 0 and y(0), then y is equal to : dx () () () () [JEE Main, Chapter : Differential Equation, Page 70, Ex. 5A, Q. No. 6] Ans. [] CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

39 dy ( + sin x) + (y + )cosx 0 dx dy (y + )cosx dx + sin x dy cosx dx y + + sin x log(y + ) log( + sin x) + log c c y + + sin x Given that y(0) c + c Equation of curve at y + + sin x π x y + + y y () Q.78 Let k be an integer such that the triangle with vertices (k, k), (5, k) and ( k, ) has area 8 sq. units. hen the orthocentre of this triangle is at the point : (), (), (), (), Ans. [] Area k 5 k k k ± 8 k(k ) + k(5 + k) + (0 + k ) ± 56 k k + 5k + k k ± 56 5k + k + 0 ± 56 5k + k 6 0 5k + k k + k 0k 6 0 D < 0 k(5k + ) (5k + ) 0 No solution (5k + ) (k ) 0 k (k is integer) Hence co-ordinate (, 6) (5, ) (, ) CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

40 E(, β) AD BC β 8 + β 8 β β, y (, ) A E (, β) C (5, ) D x B (, 6) x Q.79 he radius of a circle, having minimum area, which touches the curve y x and the lines, y x is : () ( ) () ( ) () ( + ) () ( + ) [JEE Advance, Chapter : Area under the curve, Ex. ] Ans. [] y (0, ) y x y x r (0, k) x CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

41 Circle touches the line By graph radius k Perpendicular distance from centre radius k 0 k 6 + k 8k k k 6k ± 56 () k 6 ± k 8 6 ± 8 k k 8 ± k 8 (k should be 0 < k < ) Radius k (8 ) ( ) Q.80 he eccentricity of an ellipse whose centre is at the origin is. If one of its directrices is x, then the equation of the normal to it at, is : () x y () x + y 7 () x + y () y x [JEE Main, Chapter : Ellipse, Page 58, Ex., Q. No. ] [JEE Advance, Chapter : Ellipse, Page, Ex., Q. No. ] Ans. [] x y Let the equation of ellipse + a b given that e x a / e and directrix or x CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

42 e a a Now, b a ( e ) b Equation of ellipse x y + diff. w.r.t. x x y dy + 0 dx dy dx (, / ) Equation of normal at, is y y (x x) dy dx y (x ) y x x y Q.8 A hyperbola passes through the point P(, ) and has foci at (±, 0). hen the tangent to this hyperbola at P also passes through the point : () (, ) () (, ) () (, ) () (, ) Ans. [] Let the equation of hyperbola x y a b given that foci (±ae, 0) (±, 0) ae Hyperbola passes through P(, ) b a a a (e ) CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

43 a a 8 a a a a a 9a (a 8) (a ) 0 a 8 and a b a (e ) b a (e ) b 8 b b (not possible) Equation of hyperbola x y tangent at P(, ) 0 x y By option it passes through (, ) Q.8 he distance of the point (,, 7) from the plane passing through the point (,, ), having normal x y + z x y + z + 7 perpendicular to both the lines and, is : () 0 8 () 5 8 () 0 7 () 0 7 [JEE Advance, Chapter : D, Page 0, Ex., Q. No. 7] Ans. [] î ĵ kˆ nˆ 5 î ĵ( 7) + kˆ Equation of plane 5(x ) + 7(y + ) + (z + ) 0 5x + 7y + z Perpendicular distance of the plane from (,, 7) is CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

44 Q.8 If the image of the point P(,, ) in the plane, x + y z + 0 measured parallel to the line, Ans. [] x y z is Q, then PQ is equal to : 5 () () () 6 5 () 5 P(,, ) given line R (,, 8) Q he equation of line PR x y + z k 5 let R(k +, k, 5k + ) it lies on the plane x + y z + 0 (k + ) + (k ) (5k + ) + 0 6k k R(,, 8) Image of P in the plane is (R is the mid-point of PQ) Q(, 6, ) PQ Q.8 Let a î + ĵ kˆ and b î + ĵ. Let c be a vector such that c a, ( a b) c and the angle between c and a b be 0º. hen a c is equal to : () () 5 () 8 () 8 5 [JEE Main, Chapter : Vector, Page 55, Ex. 5A, Q. No. 0] [JEE Advance, Chapter : Vector, Page 8, Ex., Q. No. 5] Ans. [] î ĵ kˆ a b 0 CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

45 a b î ĵ + kˆ a b given ( a b) c a b c sin 0º c c Now c a c + a a. c a. c 9 a. c Q.85 A box contains 5 green and 0 yellow balls. If 0 balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls drawn is : 6 () 6 () () 5 () 5 Ans. [] otal no. of balls 5 (5 green and 0 yellow balls) (Varience) σ npq where n No. of rial p Probability of happening of that event q Probability of not happening of that event 5 0 n 0, p, q So, σ σ CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

46 Q.86 For three events A, B and C, P (Exactly one of A or B occurs) P(Exactly one of B or C occurs) P(Exactly one of C or A occurs) and P(All the three events occur simultaneously) 6. hen the probability that at least one of the events occurs, is : 7 7 () () () () 7 Ans. [] [JEE Main, Chapter : Probability, Page 5, Ex., Q. No. 6] P(Exactly one of A or B occurs) P(A) + P(B) P(A B) P(Exactly one of B or C occurs) P(B) + P(C) P(B C) P(Exactly one of C or A occurs) P(C) + P(A) P(C A)... ()... ()... () Adding (), () and () [P(A) + P(B) + P(C) P(A B) P(B C) P(C A)] P(A) + P(B) + P(C) P(A B) P(B C) P(C A) 8 P(All the three events occurs simultaneously) P(A B C) 6 7 P(Atleast one of the events occurs) P(A B C) Q.87 If two different numbers are taken from the set {0,,,,, 0}, then the probability that their sum as well as absolute difference are both multiple of, is : 7 6 () () () () Ans. [] n(s) C 55 Favorable events (0, ) (0, 8) (, 6), (, 0) (, 8), (6, 0) So, required probability Fav. Events 6 otal Events 55 CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

47 Q.88 If 5(tan x cos x) cosx + 9, then the value of cosx is : () () 9 Ans. [] 5(tan x cos x) cosx + 9 sin x 5 cos x (cos x ) + 9 cos x 5[( cos x) cos x] cos x cos x + 9cos x 9cos x + cos x 5 0 9cos x + 5cos x cos x 5 0 cos x (cos x + 5) (cos x + 5) 0 cos x cosx cos x cosx Now cosx cos x cosx 9 cosx 7 9 () 9 7 () 5 Q.89 Let a vertical tower AB have its end A on the level ground. Let C be the mid-point of AB and P be a point on the ground such that AP AB. If BPC β, then tan β is equal to : 6 () () () () Ans. [] B x C x A β α γ x α β γ P tan α tan γ tanβ + tan α.tan γ CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph:

48 Q.90 he following statement (p q) [(~p q) q] is : () equivalent to ~p q () equivalent to p ~q () a fallacy () a tautology Ans. [] q p ~p (p q) (~p q) (~p q) q (p q) [(~p q) q] F F F F F F F F F It is a tautology. CAREER PIN Ltd., CP ower, IPIA, Road No., Kota (Raj.), Ph: