Part A - PHYSICS. CODE-S AIEEE 2013 (JEE Main) EXAMINATION CAREER POINT 1 / 59

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1 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Part A - PHYSICS Q. A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure. The electric potential at the point O lying at a distance L from the end A is - () Q 4π 0 Lln Ans. [] Sol. Electrostatics v 0 L () O Qln 4π 0 L O kdq Q dv x λ L L k λ dx V x kq L V l n L L kq V ln() L L x A () L Q 8π 0 L dq dx B (4) Q 4π 0 L CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

2 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Q. A sonometer wire of length.5 m is made of steel. The tension in it produces an elastic strain of %. What is the fundamental frequency of steel if density and elasticity of steel are kg/m and. 0 N/m respectively? () 00.5 Hz () 770 Hz () 88.5 Hz (4) 78. Hz Ans. [4] Sol. Methanical wave and string n L T A ρ T / A Q Y L/ L T A Y L L L L Hz Q. A projectile is given an initial velocity of ( î + ĵ) m/s, where î is along the ground and ĵ is along the vertical. If g 0 m/s, the equation of its trajectory is - () 4y x 5x () 4y x 5x () y x 5x (4) y x 5x Ans. [4] Sol. Students may find this question in CP Sheet at : Projectile motion (same as theory given on article. Page 80) Velocity at time t v î + ( 0t) ĵ dx So, v x dt x t.() dy and v y 0t dt y t 5t () so by equation () and () y x 5x CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

3 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Q.4 A uniform cylinder of length L and mass M having cross-sectional area A is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density σ at equilibrium position. The extension x 0 of the spring when it is in equilibrium is - (Here k is spring constant) Mg LAσ Mg LAσ () () + k M k M () Mg k Ans. [] Sol. Fluid Mechanics Mg LAσ (4) k M B kx 0 At equilibrium kx 0 + B Mg L kx 0 Mg A 6g Mg x 0 k LAρ M mg CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

4 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Q.5 The graph between angle of deviation (δ) and angle of incidence (i) for a triangular prism is represented by - () δ () δ O i O i () δ (4) δ O i O i Ans. [] Sol. Students may find this question in CP Sheet at : Prism, Level-, Ques. 4/Page no.48 By theory and experiment. δ O i Q.6 Diameter of a plano-convex lens is 6 cm and thickness at the centre is mm. If speed of light in material of lens is 0 8 m/s, the focal length of the lens is - () 0 cm () 0 cm () 5 cm (4) 0 cm CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

5 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Ans. [] Sol. mm (R ) 0mm R µ / (R ) + (0) R R + 9 6R R 6R 909 R 5.5 mm f 5.5 f 0 f 0 mm f 0. cm Q.7 The supply voltage to a room is 0 V. The resistance of the lead wires is 6Ω. A 60 W bulb is already switched on. What is the decrease of voltage across the bulb, when a 40 W heater is switched on in parallel to the bulb? (). V () 0.04 V () zero V (4).9 V CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

6 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Ans. [] Sol. Current Electricity Bulb 60W 0V 6Ω 0V (0 0) R bulb 40 Ω 60 V bulb V V, 40W Heater 807Ω Bulb 6Ω 0V (0) R heater 60 Ω 40 0 V heater V V CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

7 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Q.8 A beam of unpolarised light of intensity I 0 is passed through a polaroid A and then through another polariod B which is oriented so that its principal plane makes an angle of 45º relative to that of A. The intensity of the emergent light is - I () 0 4 I () 0 8 () I0 I (4) 0 Ans. [] Sol. Students may find this question Same as Level- Q.0/Page no.8 I Intensity of light emerge out from A 0 Again from Malus, law Intensity of light emerge out from B I 0 I cos 45º 0 4 Q.9 The amplitude of a damped oscillator decreases to 0.9 times its original magnitude in 5s. In another 0s it will decrease to α times its original magnitude, where α equals - () 0.79 () 0.6 () 0.7 (4) 0.8 Ans. [] Sol. SHM A A 0 e λt For first 5s 0.9 A 0 A 0 e 5 λ...() In another 0s αa 0 A 0 e 5 λ...() A 0 (e 5 λ ) (0.9) A 0 So, α 0.79 CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

8 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Q.0 Two coherent point sources S and S are separated by a small distance 'd' as shown. The fringes obtained on the screen will be - S d S Screen D () semi-circles () concentric circles () points (4) straight lines Ans. [] Sol. Level-4 (Sec-B) Q./Page no.5 Q. A metallic rod of length 'l ' is tied to a string of length l and made to rotate with angular speed ω on a horizontal table with one end of the string fixed. If there is a vertical magnetic field 'B' in the region, the e.m.f. induced across the ends of the rod is - 4Bωl () Bωl () Ans. [] () (4) 5Bωl Bωl CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

9 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Sol. Electro Magnetic Induction emf across length dx de vbdx (xω)bdx x l E Bω xdx x l ω l l dx x B x E Bω l l B ω [(l) (l) ] Bωl 5 Q. If a piece of metal is heated to temperature θ and then allowed to cool in a room which is at temperature θ 0, the graph between the temperature T of the metal and time t will be closest to - T T () θ 0 () θ 0 O t O t T T () (4) θ 0 O t O t CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

10 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Ans. [] Sol. Practical physics sheet, Page no.68, Q.5 By Newton's law of cooling dt K(T T0 ) dt T Tinitial dt T T 0 t 0 kdt T T 0 + (T i T 0 )e kt Q. This question has Statement-I and Statement-II. Of the four choices given after the statements, choose the one that best describes the two statements. Statement-I : Higher the range, greater is the resistance of ammeter. Statement-II : To increase the range of ammeter, additional shunt needs to be used across it. () If statement-i is true but statement-ii is false. () If statement-i is false but statement-ii is true. () If both statement-i and statement-ii are true, and statement-ii is the correct explanation of statement-i. (4) If both statement-i and statement-ii are true but statement-ii is not the correct explanation of statement-i Ans. [] Sol. Electric Instruments Statement-I false Statement-II True Q.4 Two charges, each equal to q, are kept at x a and x a on the x-axis. A particle of mass m and charge q 0 q is placed at the origin. If charge q0 is given a small displacement (y << a) along the y-axis, the net force acting on the particle is proportional to - () () y y () y (4) y Ans. [] CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

11 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Sol. Electrostatics q x a F θ θ q/ θ θ y F q x a F net F cos θ q kq (a + y ) a y + y kq y (a + y ) / if y << a, (a + y ) / a kq y F net a F net y CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

12 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Q.5 This question has Statement-I and Statement-II. Of the four choices given after the statements, choose the one that best describes the two statements. Statement-I : A point particle of mass m moving with speed v collides with stationary point particle of mass m M. If the maximum energy loss possible is given as f mv then f. M + m Statement-II : Maximum energy loss occurs when the particles get stuck together as a result of the collision. () If statement-i is true but statement-ii is false. () If statement-i is false but statement-ii is true. () If both statement-i and statement-ii are true, and statement-ii is the correct explanation of statement-i. (4) If both statement-i and statement-ii are true but statement-ii is not the correct explanation of statement-i Ans. [] Sol. Students may find this question in CP Sheet at : Given on page no.50, Article 6. Inelastic collision Loss in KE E mm (v 0) ( e ) m + M M mv ( e ) m + M So, it will maximum when e 0 for perfectly inelastic so st is wrong and is correct. CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

13 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Q.6 The I-V characteristic of an LED is - I V O () O V () R Y G B I () I Red Yellow Green Blue (R) (Y) (G)(B) I B G (4) Y R Ans. [] Sol. O Semi Conductor By theory V Q.7 Assume that a drop of liquid evaporates by decrease in its surface energy, so that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible? he surface tension is T, density of liquid is ρ and L is its latent heat of vaporization - () T ρl () T ρl Ans. [] Sol. Properties of matter Surface energy T A A 4πr 4π (r dr) 8π rdr m (4πr dr)ρ according to question T A ml T 8πr dr (4πr dr L)ρ T r ρl O ρl () T (4) V T ρl CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

14 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Q.8 Two capacitors C and C are charged to 0 V and 00 V respectively. It is found that by connecting them together the potential on each one can be made zero - () C + 5C 0 () 9C 4C () 5C C (4) C 5C Ans. [4] Sol. Capacitance C C 0V 00V Common potential V CV CV C + C 0C 00C 0 C 5C 0 Q.9 What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of R? () GmM R () GmM R () 5GmM 6R (4) GmM R Ans. [] Sol. Students may find this similar question in CP Sheet : Q.No.7, Page no.0, Level- (Gravitation) E K E K E K GMm R GMm R GMm R 5GMm 6R GMm + m R GMm + R + GMm 6R GMm 6R GM R CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

15 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Q.0 Given p-v diagram represents the thermodynamic cycle of an engine, operating with an ideal monoatomic gas. The amount of heat, extracted from the source in a single cycle is - p p 0 () p 0 v0 p 0 v 0 v v 0 () 4p 0 v 0 () p 0 v 0 (4) p 0 v 0 Ans. [4] Sol. Thermodynamics Q nc v T + nc p T 5 nrt0 + nr(t0 ) nrt0 + 5nRT 0 nrt0 P0 V 0 Q. A circular loop of radius 0. cm lies parallel to a much bigger circular loop of radius 0 cm. The centre of the small loop is on the axis of the bigger loop. The distance between their centres is 5 cm. If a current of.0 A flow through the smaller loop, then the flux linked with bigger loop is - (). 0 weber () weber () 9. 0 weber (4) 6 0 weber Ans. [] CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

16 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Sol. Electro Magnetic Induction i R r x A B We know that mutual inductance remain same whether we pass current in any coil we pass same current in bigger coil then φ Smaller BA cos 0º (R µ 0iR. πr / + x µ 0πiR r / (R + x 4π 0 7 ) ) π (0.) ( 0 ( wb / ) ) Q. A diode detector is used to detect an amplitude modulated wave of 60% modulation by using a condenser of capacity 50 pico farad in parallel with a load resistance 00 kilo ohm. Find the maximum modulated frequency which could be detected by it - () 5. MHz () 5. khz () 0.6 MHz (4) 0.6 khz Ans. [4] CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

17 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Sol. Communication 00 0 Ω 50 0 F Given : f f C m 0.6 the modulated frequency is given by f C πrc π π π π khz This is 60% of maximum frequency. 00 f max khz CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

18 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Q. An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass M. The piston and the cylinder have equal cross sectional area A. When the piston is in equilibrium, the volume of the gas is V 0 and its pressure is P 0. The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency - () A γp π MV 0 0 () π MV AγP 0 0 () AγP0 π V M 0 (4) V0MP π A γ 0 Ans. [] Sol. SHM Given in sheet thoery page 50 Article- x In Adiabatic process P 0 V 0 γ (P 0 + P) (V 0 V) γ By solving P γp0 V V 0 {neglect P V} so Restoring force F PA F γp or acceleration γ M 0 A MV0 So ω γp0 A MV 0 or f γp0 A π MV 0 CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

19 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Q.4 A hoop of radius r and mass m rotating with an angular velocity ω 0 is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will bet he velocity of the centre of the hoop when it ceases to slip? () rω0 Ans. [] Sol. Rotational dynamics m rω0 () rω 0 () 4 (4) rω0 at t 0 ω 0 Linear acceleration f/m α f.r I after time t f mr Friction force f v 0 + m f t f ω ω 0 t mr when body start pure rolling v rω f f t r ω0 t so t m mr So v m f mrω 0 rω 0 f mrω0 f CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

20 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Q.5 Two short bar magnets of length cm each have magnetic moments.0 Am and.00 Am respectively. They are placed on a horizontal table parallel to each other with their N poles pointing towards the South. They have a common magnetic equator and are separated by a distance of 0.0 cm. The value of the resultant horizontal magnetic induction at the mid-point O of the line joining their centres is close to (Horizontal component of earth's magnetic induction is Wb/m ) () Wb/m () Wb/m () Wb/m (4) Wb/m Ans. [4] Sol. Magnetism S M B H B B 0.m O 0.m S M N N N W E S B 0 B + B + B H µ 0 M 4π r 7 + µ 0 M 4π r + B H (0.) (0.) wb/m CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

21 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Q.6 The anode voltage of a photocell is kept fixed. The wavelength λ of the light falling on the cathode is gradually changed. The plate current I of the photocell varies as follows I I () () O λ O λ I I () (4) O λ O λ Ans. [] Sol. Students may find this question in CP Sheet at : level (4) Q. 9 (Photoelectric Effect) CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

22 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Q.7 Let [ε 0 ] denote the dimensional formula of the permittivity of vacuum. If M mass, L length, T time and A electric current, then - () [ε 0 ] [M L T A ] () [ε 0 ] [M L T A] () [ε 0 ] [M L T A] (4) [ε 0 ] [M L T 4 A ] Ans. [4] Sol. Unit & dimension, Error theory given on page no., Article.4. qq F 4πε qq ε 0 Fr ε 0 0 r C MLT T L T A T 4 L M Q.8 In a hydrogen like atom electron makes transition from an energy level with quantum number n to another with quantum number (n ). If n >>, the frequency of radiation emitted is proportional to - () / n () n () n Ans. [] Sol. Atomic Structure Students may find this question in CP Sheet at : Level Page No. n to (n ) c crz λ (n ) n ν RcZ n (n ) n (n ) (4) n CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

23 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT ν RcZ n n (n ) ν RcZ n 4 n ν n Q.9 In an LCR circuit as shown below both switches are open initially. Now switch S is closed S kept open. (q is charge on the capacitor and τ RC is Capacitive time constant). Which of the following statement is correct? V R C S S () At t τ, q CV ( e ) L () At t τ, q CV ( e ) () Work done by the battery is half of the energy dissipated in the resistor (4) At t τ, q CV/ Ans. [] Sol. Students may find this question in CP Sheet at : From Sheet (Capacitance) During charging of capacitor q q 0 [ e t/rc ] q CV[ e t/t ] q CV[ e ] CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

24 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Q.0 The magnetic field in a traveling electromagnetic wave has a peak value of 0 nt. The peak value of electric field strength is - () 9 V/m () V/m () V/m (4) 6 V/m Ans. [4] Sol. Students may find this question in CP Sheet at : From EMW Sheet E B 0 0 C E E 0 6 V/m CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

25 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Part B - MATHEMATICS Q. The real number k for which the equation, x + x + k 0 has two distinct real roots in [0, ] () lies between and 0 () does not exist () lies between and (4) lies between and Ans. [] Sol. Students may find this Question in CP Sheet at Q.; Level-; Page no. 44 f (x) x + x + k As f ' (x) 6x + (always +ve) so it is strictly so equation has only one root. Therefore no value of k. Q. The number of values of k, for which the system of equation : (k + ) x + 8y 4k, kx + (k + ) y k, has no solution, is - () () () infinite (4) Ans. [4] Sol. Students may find this Question in CP Sheet at Q., Level-4; Sec- B; Page no. 40 k + 8 k k + 0 (k + ) (k + ) 8k 0 k + 4k + 8k 0 k 4k + 0 (k ) (k ) 0 k, CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

26 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Then x 4k k 8 k + 0 x (k k + ) 0 x (k ) (k ) 0 k, x 0 at k No. of values of k is only one. Q. If P α 4 is the adjoint of a matrix A and A 4, then α is equal to - 4 () 5 () 0 () 4 (4) Ans. [4] Sol. P ( ) α (4 6) + (4 6) P 0 + α 6 P (α ) P adj. A P adj.a A (α ) 6 α 8 α Q.4 Let T n be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If T n+ T n 0 then the value of n is - () 0 () 8 () 7 (4) 5 CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

27 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Ans. [4] Sol. n+ C n C 0 (n + )! (n )!! n!!(n )! n(n )(n ) 6 n! 0!(n )! (n + ) 0 (n ) n n (n ) 0 n n 0 0 (n 5) (n + 4) 0 n 5 + n + (n ) 0 Q.5 At present, a firm is manufacturing 000 items. It is estimated that the rate of change of production P w.r.t. dp additional number of workers x is given by 00 dx x. If the firm employs 5 more workers, then the new level of production of items is - () 500 () 4500 () 500 (4) 000 Ans. [] Sol. dp (00 x) dx P 00x.. x / + c P 00x 8x / + c At x 0 c P 000 P 00x 8 x / P CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

28 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Q.6 ABCD is a trapezium such that AB and CD are parallel and BC CD. If ADB θ, BC p and CD q, then AB is equal to - () Ans. [] Sol. C p p + q p cosθ + q q 90º α q p + q sin θ (p + q )sin θ () (pcosθ + qsin θ) α B E A sin θ sin( π ( θ + α)) By Sine rule AB p + q θ D 80º (θ + α) () (p + q )sin θ pcosθ + qsin θ (4) p + q cosθ pcosθ + qsin θ AB p + q sin θ sin( θ + α) AB Then AB p + q sin θ sin θcosα + cosθsin α sin θ p q p + q + q sin θ + cosθ p p + q (p + q )sin θ So, AB qsin θ + pcosθ Q.7 All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 0 to each of the students. Which of the following statistical measures will not change even after the grace marks were given? () mode () variance () mean (4) median CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

29 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Ans. [] Sol. Students may find this Question in CP Sheet at Q.4; Level-; Page no. 4 If variance of x, x, x,... x n is σ then variance of x + k, x + k,... x n + k is also σ Q.8 A ray of light along x + y gets reflected upon reaching x-axis, the equation of the reflected ray is - () y x () y x () y x + (4) y x Ans. [4] Sol. y 0º (, 0) 0º x y 0 tan0º (x ) y (x ) y x. CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

30 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Q.9 The area (in square units) bounded by the curves y x, y x + 0, x-axis, and lying in the first quadrant is - () 8 7 () 4 () 9 (4) 6 Ans. [] Sol. Students may find this Question in CP Sheet at Q.4; Level-4; Sec. B; Page no. 97 (9, ) (0, 0) (, 0) 6 (9, 0) y x...() y x () solving () & () y y + 0 y y 0 (y ) (y + ) 0 y, y Point of intersection (9, ). 9 Area 0 x dx.6. (x / ) (7) CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

31 CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Q.40 If z is a complex number of unit modulus and argument θ, then arg + + z z equals - () θ () π θ () θ (4) π θ Ans. [] Sol. Arg + + z z Arg + + z z Arg + + z z z Arg z θ

32 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Q.4 If f (x)dx ψ(x), then x f (x ) dx is equal to - () x ψ (x ) x ψ(x )dx + C () [ ψ x (x ) x ψ(x ) dx] 5 () [ ψ x (x ) x ψ(x ) dx] + C + C (4) x ψ(x ) x ψ(x )dx + C Ans. [] Sol. Students may find this Question in CP Sheet at Q.; Level-; Page no. 4 x.x.f (x ) dx t. f (t) dt I II x t [ t. ψ (t) ψ (t)dt] + C [x. ψ (x ) ψ ( x ). dx ] + C [x. ψ (x) ] ψ(x ).x.dx + C [x ψ (x )] ψ(x ) x dx + C Q.4 Let A and B be two sets containing elements and 4 elements respectively. The number of subsets of A B having or more elements is - () 9 () () 56 (4) 0 Ans. [] Sol. n (A), n (B) 4 n (A B) 8 No. of subsets of (A B) containing atleast '' elements is 8 C + 8 C C C C C C 0 8 C 8 C CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

33 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Q.4 If the lines x y z 4 and k x y 4 k z 5 are coplanar, then k can have - () exactly two values () exactly three values () any value (4) exactly one value Ans. [] Sol. Students may find this Question in CP Sheet at Q.4; Level-4; Sec. A (Topic-D) L x y x y 4 L k L & L are coplanar. x x a a y b b z 4 k z 5 y z z c c k 0 k k 0 k ( + k) ( + k ) + ( k) 0 k k + k 0 k k 0 k + k 0 k(k + ) 0 k 0, k Exact two values. CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

34 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Q.44 The x-coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as (0,) (, ) and (, 0) is - () + () () + (4) Ans. [4] Sol. Students may find this Question in CP Sheet at Q.; Level- (Topic-Point) C(, 0) (, 0) R Q(, ) A (0, 0) P(0, ) B(0, ) I I I 0( ) + 0() + () 0(, , , + + ) + () + 0() + + x-coordinate +. CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

35 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Q.45 Consider : Statement-I : (p ~ q) (~ p q) is a fallacy. Statement-II: (p q) (~ q ~ p) is a tautology. () Statement-I is true; Statement-II is false. () Statement-I is false, Statement-II is true. () Statement-I is true; Statement-II is true; Statement-II is a correct explanation for Statement-I. (4) Statement-I is true; Statement-II is true; Statement-II is not a correct explanation for Statement-I. Ans. [4] Sol. Students may find this Question in CP Sheet at Q.5; Level-; Page no. 07 p ~p q ~q (p ~ q) (~p q) (p ~ q) (~ p q) T F T F F F F T F F T T F F F T T F F T F F T F T F F F Statement-I is correct. p q ~p ~q (p q) (~q ~ p) (p q) (~ q ~p) T T F F T T T T F F T F F T F T T F T T T F F T T T T T Statement-II is correct but not correct explanation. Q.46 If the equations x + x + 0 and ax + bx + c 0, a, b, c R, have a common root, then a : b : c is - () : : () : : () : : (4) : : CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

36 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Ans. [] Sol. Students may find this Question in CP Sheet at Q., Page no. x + x + 0.() D < 0 roots are imaginary ax + bx + c 0, a, b, c R.() Eq. () & () have one root common and roots of () are imaginary so both roots will be common a b a : b : c : : c Q.47 The sum of first 0 terms of the sequence 0.7, 0.77, 0.777,..., is - 7 () ( ) () ( ) () ( ) (4) ( ) 8 9 Ans. [] Sol. Students may find this Question in CP Sheet at Q.4, Level-, Page no terms 7 [ terms] 7 [ terms] terms terms CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

37 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT ( ) 0 8 Q.48 x + x The term independent of x in expansion of / / / x x + x x is - () 0 () 0 () 4 (4) 0 Ans. [] Sol. Students may find this Question in CP Sheet at Q.5, Level-, Page no.80 / (x ) + (x / / x x + x / 0 / x / / / )(x + ) / (x ) / + x / x x T r+ 0 C r (x / ) 0 r 0 C r x 0 r r / x r ( ) 0 r Term independent of x so 0 5r 0 r 4 T 5 0 C 4 ( ) 4 0 r 0 0 r 0 0 CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

38 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Q.49 If the vectors AB î + 4 kˆ and AC 5 î ĵ + 4 kˆ are the sides of a triangle ABC, then the length of the median through A is - () () 45 () 8 (4) 7 Ans. [] Sol. Students may find this Question in CP Sheet at Q.8, Level-4(Sec-A) ; (Topic-Vector) A AB î + 4kˆ B D C AC 5 î ĵ + 4kˆ AB + AC AD 8 î ĵ + 8kˆ AD AD 4 î ĵ + 4kˆ AD AD AD Q.50 If x, y, z are in A.P. and tan x, tan y and tan z are also in A.P., then - () 6x y z () 6x 4y z () x y z (4) x y 6z CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

39 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Ans. [] Sol. tan y tan x tan z tan y tan y x tan z y + yx + zy y x z y + yx + zy y x + zy xyz z y + xyz y x y (x + z) + y xyz x z 0 y (y) xyz y xz then x, y, z are in G.P. So, x y z x Q.5 The intercepts on x-axis made by tangents to the curve, y t dt, x R, which are parallel to the line 0 y x, are equal to - () ± () ± 4 () ± (4) ± Ans. [] Sol. x y t dt, x R ; parallel to y x, m 0 dy x x ± dx at x t y t dt t dt CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

40 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Equation of tangent at (, ) is y (x ) At y 0 x x at x y y t 0 0 dt t dt y ( t ) 0 y (0 (4)) Equation of tangent at (, ) is y + (x + ) At y 0 x + x Q.5 Distance between two parallel planes x + y + z 8 and 4x + y + 4z is () () () (4) Ans. [] Sol. Students may find this Question in CP Sheet at Q.8, Level-4 (Sec-A) (Topic : D) 4x + y + 4z x + y + 4z distance CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

41 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Q.5 The circle passing through (, ) and touching the axis of x at (,0) also passes through the point - () (5, ) () (, 5) () ( 5, ) (4) (, 5) Ans. [] Sol. Students may find this Question in CP Sheet at Q.8, Level-4 (Sec-B) (Topic : Circle) (,0) (, ) (,k) (x ) + (y k) k passes through (, ) ( ) + ( k) k k + k k 4k 8 k Eq. (x ) + (y + ) 4 Now check the option. x y Q.54 The equation of the circle passing through the foci of the ellipse +, and having centre at (0, ) is () x + y 6y 5 0 () x + y 6y () x + y 6y 7 0 (4) x + y 6y Ans. [] CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

42 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Sol. x y e b a Focus S and S (±ae, 0) 7 ±., ( ± 7, 0) radius, r C S C (0, ) S(± 7, 0) Eq. of circle is (x 0) + (y ) (4) x + y 6y x + y 6y 7 0 Q.55 If y sec (tan dy x), then at x is equal to - dx () () () (4) Ans. [] CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

43 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Sol. Students may find this Question in CP Sheet at Q.6, Level-, Page no.07, (Topic : Differentiation) x + x sec θ y sec (tan x) tan x θ y + x dy x dx + x dy dx x + x Q.56 tan A cot A The expression + cot A tan A can be written as - () tan A + cot A () sec A + cosec A () sin A cos A + (4) sec A cosec A + Ans. [4] Sol. tan A cot A + cot A tan A sin A cos A cos A + sin A sin A cos A sin A sin A cos A sin A cos A + cosa(sin A cosa) (cosa sin A)sin A sin A + cos A (cosa sin A)sin AcosA (cosa sin A)( + sin A cosa) (cosa sin A).sin A cosa + sin AcosA cosasin A (seca coseca + ) CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

44 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Q.57 Given : A circle, x + y 5 and a parabola, y 4 5 x. Statement-I : An equation of a common tangent to these curves is y x + 5. Statement-II : If the line, y mx + m 5 (m 0) is their common tangent, then m satisfies m 4 m + 0, () Statement-I is true; Statement-II is false. () Statement-I is false; Statement-II is true. () Statement-I is true; Statement-II is true; Statement-II is a correct explanation for Statement-I. (4) Statement-I is true; Statement-II is true; Statement-II is not a correct explanation for Statement-I. Ans. [4] Sol. x + y 5..() y 4 5 x..() 4a 4 5 Let, y mx + c..() 5 By () & () c ± ( + m ) By () & () c m a m 5 c 5 5 ( + m ) m m 4 + m 0 m t t + t 0 t + t t 0 t, m m t m ± c ± 5 By () y ± (x + 5 ) Eq. of common tangent. Now, m satisfy the given equation in statement-ii. CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

45 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Q.58 A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is () () 5 5 () 5 (4) 5 Ans. [] Sol. p and q ; n 5 P (r 4) P(r 4) + P(r 5) 5 C 4 p 4.q + 5 C 5 p π/ Q.59 Statement-I : The value of the integral b Statement-II : f (x)dx f (a + b x)dx. a b a dx + tan x π / 6 is equal to 6 π. () Statement-I is true; Statement-II is false. () Statement-I is false; Statement-II is true. () Statement-I is true; Statement-II is true; Statement-II is a correct explanation for Statement-I. (4) Statement-I is true; Statement-II is true; Statement-II is not a correct explanation for Statement-I. Ans. [] CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

46 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Sol. From Class notes result π / I π / 6 π / I π / π / dx dx I dx I π π / 6 tan x cot x π / π / 6 π π π tan x tan x dx Q.60 lim x 0 ( cosx)( + x tan 4x cos x) is equal to - () () () 4 (4) Ans. [] Sol. cos x lim x 0 4x x lim 0 + cos x 4x lim x 0 tan 4x 4 CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

47 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Part C - CHEMISTRY Q.6 Which of the following represents the correct order of increasing first ionization enthalpy for Ca, Ba, S, Se and Ar? () Ba < Ca < Se < S < Ar () Ca < Ba < S < Se < Ar () Ca < S < Ba < Se < Ar (4) S < Se < Ca < Ba < Ar Ans. [] Sol. Ba < Ca < Se < S < Ar. s-block metals have low value of IE. In a period, from left to right IE increases. Noble gases have highest IE. Q.6 A gaseous hydrocarbon gives upon combustion 0.7 g. of water and.08 g. of CO. The empirical formula of the hydrocarbon is - () C 6 H 5 () C 7 H 8 () C H 4 (4) C H 4 Ans. [] Sol. Students may find this question in CP Sheet (Class copy) C x H y + (x + y/4)o xco + y H O H O CO x : y 7 : 4 x : y 7 : 8 C 7 H mol 0.08 mol H mol 0.07 mol C Q.6 The rate of a reaction doubles when its temperature changes from 00 K to 0 K. Activation energy of such a reaction will be : (R 8.4 JK mol and log 0.0) () 58.5 kj mol () 60.5 kj mol () 5.6 kj mol (4) 48.5 kj mol Ans. [] CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

48 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Sol. Students may find this question in CP Sheet chapter-chemical Kinetics (Similar to) Q.4 Level-. k log 0 E a 0 k E 0. a E a 5.6 kj Q.64 The gas leaked from a storage tank of the Union Carbide plant in Bhopal gas tragedy was - () Ammonia () Phosgene () Methylisocyanate (4) Methylamine Ans. [] Sol. Students may find this question in CP Sheet chapter - N-Containing substance (Class copy) Methyl isocyanate (MIC) Q.65 An organic compound A upon reacting with NH gives B. On heating, B gives C. C in presence of KOH reacts with Br to give CH CH CH. A is - () CH CH COOH () CH CH COOH () CH COOH (4) CH CH CH COOH CH Ans. [] Sol. Students may find this question in CP Sheet chapter - Carboxylic acid (Example 8 Page No. 04) O O CH CH C OH Θ 4 CH CH C NH CH CH NH (A) (B) Q.66 Compound (A), C 8 H 9 Br, gives a white precipitate when warmed with alcoholic AgNO. Oxidation of (A) gives an acid (B), C 8 H 6 O 4. (B) easily forms anhydride on heating. Identify the compound (A). CH Br CH Br CH Br C H 5 () () () (4) CH Br CH CH Ans. [] (C) CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

49 Sol. CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Students may find this question in CP Sheet chapter - Halogen containing substance. CH Br CH Alc. AgNO [O] AgBr (ppt.) COOH COOH Q.67 A compound with molecular mass 80 is acylated with CH COCl to get a compound with molecular mass 90. The number of amino groups present per molecule of the former compound is - () 4 () 6 () (4) 5 Ans. [4] Sol. Students may find this question in CP Sheet chapter - Acid and its derivatives. O O R NH + CH C Cl R NH C CH H O O Due to reaction of one NH gp with CH C Cl difference in mass in 4. (increase) Mass of the compound having x-nh gp is given 80 After reaction mass of the product 90 Total increase in mass Total no. of NH gp present 5 4 Q.68 Which one of the following molecules is expected to exhibit diamagnetic behaviour? () O () S () C (4) N Ans. [, 4] Sol. C N * * x σ s σ s σs σ s πp πp * * σ s σ s σs σ s πp πp σp Both have zero unpaired electrons. Thus, they are diamagnetic. x y y z O C C O O CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

50 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Q.69 In which of the following pairs of molecules/ions, both the species are not likely to exist? () Ans. [] + H, He () H, + He () + H, He (4) H, He Sol. + H, He Both have zero bond order. Thus, they do not exist. Q.70 Which of the following complex species is not expected to exhibit optical isomerism? () [Co(NH ) Cl ] () [Co(en)(NH ) Cl ] + () [Co(en) ] + (4) [Co(en) Cl ] + Ans. [] Sol. [Co(NH ) Cl ] Ma b do not show optical isomerism because its both geometries have plane of symmetry. Q.7 The coagulating power of electrolytes having ions Na +, Al + and Ba + for arsenic sulphide sol increases in the order - () Ba + < Na + < Al + () Al + < Na + < Ba + () Al + < Ba + < Na + (4) Na + < Ba + < Al + Ans. [4] Sol. Students may find this question in CP Sheet chapter - Surface chemistry similar to Q.4, Level-. As S ve sol Coagulation power Magnitude of opp. charge Na + < Ba + < Al + Q.7 Consider the following reaction : xmno 4 + yc O 4 + zh+ xmn + z + yco + H O The values of x, y and z in the reaction are, respectively - (), 5 and 6 () 5, and 8 () 5, and 6 (4), 5 and 8 Ans. [] CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

51 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Sol. Students may find this question in CP Sheet chapter - Oxidation-Reduction same as Q.5, Level-. MnO 4 Mn + ; e gain 5...() C O 4 CO ; e loss...() () (To balance e ) () 5 + MnO4 + 5CO4 + zh Mn + z + 0CO + H O On balancing charge, z 6 x, y 5, z 6 Q.7 Which of the following exists as covalent crystals in the solid state? () Sulphur () Phosphorus () Iodine (4) Silicon Ans. [4] Sol. Students may find this question in CP Sheet chapter - Solid State (Class copy). Si has a regular covalent network structure. S 8, P 4 and I all are molecular solids. CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

52 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Q.74 A solution of ( ) chloro phenylethane in toluene racemises slowly in the presence of a small amount of SbCl 5, due to the formation of - () carbocation () free radical () carbanion (4) carbene Ans. [] Sol. Students may find this question in CP Sheet chapter-halogen derivative (Q.7 Level-4B, Page No. 66). SbCl 5 is a Lewis acid which forms carbocation on reaction with alkyl halide. CH CH Cl SbCl 5 CH CH Q.75 An unknown alcohol is treated with the "Lucas reagent" to determine whether the alcohol is primary, secondary or tertiary. Which alcohol reacts fastest and by what mechanism - () secondary alcohol by S () tertiary alcohol by S N N () secondary alcohol by S (4) tertiary alcohol by S N N Ans. [4] Sol. Students may find this question in CP Sheet chapter-alcohol (Q. Level-, Page No.7.) Lucas reagent is conc. HCl + anhy.zncl alcohols are most reactive because Reactivity Stability of carbocation formed HCl anhy.zncl Cl Θ R OH R R Cl White turbidity Q.76 How many litres of water must be added to litre of an aqueous solution of HCl with a ph of to create an aqueous solution with ph of? ().0 L () 9.0 L () 0. L (4) 0.9 L Ans. [] CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

53 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Sol. Students may find this question in CP Sheet chapter -Ionic Equilibrium (Class copy). HCl ; ph ; [H + ] 0 Final ph ; [H + ] 0 M V M V 0 ( lit.) 0 V V 0 lit. V water V V 9 lit. Q.77 The molarity of a solution obtained by mixing 750 ml of 0.5(M)HCl with 50 ml of (M)HCl will be - ().75 M () M () M (4).00 M Ans. [] Sol. Students may find this question in CP Sheet chapter-solution & Colligative properties similar to Q., Level- MV + M V M res. V + V ( ) + ( 50) M Q.78 A piston filled with 0.04 mol of an ideal gas expands reversibly from 50.0 ml to 75 ml at a constant temperature of 7.0ºC. As it does so, it absorbs 08 J of heat. The values of q and w for the process will be - (R 8.4 J/mol K) (ln 7.5.0) () q 08 J, w + 08 J () q + 08 J, w + 08 J () q + 08 J, w 08 J (4) q 08 J, w 08 J Ans. [] CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

54 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Sol. Students may find this question in CP Sheet chapter- Chemical Energetics similar to Q.6, Level- By I st law of thermodynamics, q E W At constt T, E 0 q W Heat absorbed 08 J q +08 J W 08 J Q.79 Experimentally it was found that a metal oxide has formula M 0.98 O. Metal M, is present as M + and M + in its oxide. Fraction of the metal which exists as M + would be - () 6.05% () 5.08% () 7.0% (4) 4.08% Ans. [4] Sol. Students may find this question in CP Sheet chapter-solid State similar to solved example 8. M 0.98 O M x (+)M y (+)O Atoms : x + y () Charge : x + y 0 x + y...() On solving, x 0.94, y 0.04 % M + y 00 x + y % 0.98 Q.80 For gaseous state, if most probable speed is denoted by C*, average speed by C and mean square speed by C, then for a large number of molecules the ratios of these speeds are - () C* : C : C :.8 :.5 () C* : C : C :.5 :.8 () C* : C : C.5 :.8 : (4) C* : C : C.8 :.5 : Ans. [] CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

55 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Sol. Students may find this question in CP Sheet chapter-gaseous State same as Q.7 Level-. RT U mp C * M U av. U rms 8RT πm RT M C C C* : C : C :.4 :.6 :.7 :. :. 8 : π Q.8 Arrange the following compounds in order of decreasing acidity : OH OH OH OH ; ; ; Cl CH NO OCH (I) (II) (III) (IV) () III > I > II > IV () IV > III > I > II () II > IV > I > III (4) I > II > III > IV Ans. [] Sol. Students may find this question in CP Sheet chapter-goc (Example 5, Page No. 5) OH OH OH OH ; I Cl +M +H CH (I) +I (II) III > I > II > IV ; NO (III) M I ; +M OCH I (IV) CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

56 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Q.8 The order of stability of the following carbocations : CH CH CH ; CH CH CH ; CH I II III () I > II > III () III > I > II () III > II > I (4) II > III > I Ans. [] Sol. Students may find this question in CP Sheet chapter-goc (Class copy). CH CH CH ; is - (I) Less conjugation less stable CH CH CH ; (II) Non conjugated least stable CH (III) More conjugation more stable III > I > II Q.8 The first ionisation potential of Na is 5. ev. The value of electron gain enthalpy of Na + will be - () 0. ev () +.55 ev ().55 ev (4) 5. ev Ans. [4] Sol. Na Na + + e ; ( H) IE +5. ev On reversing, (By Lavoiser Laplace law) Na + + e Na ; ( H) eg 5. ev Q.84 Four successive members of the first row transition elements are listed below with atomic numbers. Which 0 one of them is expected to have the highest E + + value? M / M () Fe(Z 6) () Co(Z 7) () Cr(Z 4) (4) Mn(Z 5) Ans. [] 0 Sol. The value of E + + for Co is +.97V which is highest among these elements. M / M CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

57 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Q.85 Stability of the species Li, Li and () Li < Li < Li + () Ans. [4] + Sol. Li < Li < Li * Li σ σ ; B.O. Li + σ s s σs * sσs σs s * s s * s + Li increases in the order of - Li < Li < Li + () Li < ; B.O. 0.5 Li σ σ σ σ ; B.O. 0.5 Bond order stability of molecules Because, Li has greater no. of anti-bonding e hence, + Li < Li (4) Li is less stable than Li < + Li. + Li < Li Q.86 Energy of an electron is given by E Z J. Wavelength of light required to excite an n electron in an hydrogen atom from level n to n will be : (h Js and c ms ) () m () m () m (4) m Ans. [] Sol. Students may find this question in CP Sheet chapter- Atomic Structure (Class copy). E E E E E E λ hc λ λ m. 0 7 m CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

58 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Q.87 Synthesis of each molecule of glucose in photosynthesis involves - () 8 molecules of ATP () 6 molecules of ATP () 8 molecules of ATP (4) 0 molecules of ATP Ans. [] Sol. Students may find this question in CP Sheet chapter-biomolecules. One CO requires ATP molecules, one glucose molecule gives 6 CO molecules. Each glucose molecule involves 8 ATP molecules in photosynthesis. Q.88 Which of the following is the wrong statement? () Ozone is violet-black in solid state () Ozone is diamagnetic gas () ONCl and ONO are not isoelectronic (4) O molecule is bent Ans. [No option correct] Sol. All statement are correct and we have to chose wrong statement. Q.89 Which of the following arrangements does not represent the correct order of the property stated against it? () Co + < Fe + < Cr + < Sc + : stability in aqueous solution () Sc < Ti < Cr < Mn : number of oxidation states () V + < Cr + < Mn + < Fe + : paramagnetic behaviour (4) Ni + < Co + < Fe + < Mn + : ionic size Ans. [] Sol. V + < Cr + < Mn + < Fe + V + [Ar] 4s 0 d ; unpaired e Cr + [Ar] 4s 0 d 4 ; unpaired e 4 Mn + [Ar] 4s 0 d 5 ; unpaired e 5 Fe + [Ar] 4s 0 d 6 ; unpaired e 4 CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59

59 CODE-S AIEEE 0 (JEE Main) EXAMINATION CAREER POINT Q.90 Given 0 Cr / Cr E V; 0 E + MnO4 / Mn.5 V 0 E + CrO7 / Cr. V; E 0 Cl/Cl.6 V Based on the data given above, strongest oxidizing agent will be - () Mn + () MnO 4 () Cl (4) Cr + Ans. [] Sol. Students may find this question in CP Sheet chapter-electrochemistry similar to Q.4, Level-. Highest SRP Bottom of E.C.S Strongest oxidising agent MnO 4 ` CAREER POINT, CP Tower, Road No., IPIA, Kota (Raj.) Ph.: / 59