SOLUTIONS & ANSWERS FOR JEE MAINS-2015 VERSION A

Size: px

Start display at page:

Download "SOLUTIONS & ANSWERS FOR JEE MAINS-2015 VERSION A"

Damon Jackson
5 years ago
Views:

1 SOLUIONS & ANSWERS FOR JEE MAINS-5 ERSION A [PHYSICS, CHEMISRY & MAHEMAICS] PAR A PHYSICS. wo stones are thrown up simultaneously from the edge of a cliff ---- S ut gt S ut gt (S S ) (u u )t upto 8 s From t 8 s to t s, S t 5t for st stone is t 5t 5t t ± 8 t ± 7 8 s for nd stone is t 5t ± 6 8 s. he period of oscillation of a simple pendulum is L π. Measured value of L is ---- g % L g L g g g g.7% 5 g %. Given in the figure are two blocks A and B of weight N and N, respectively. hese are being ---- N (y y )m 8 f B ωt of A ωt of B N t(s). A particle of mass m moving in the -direction with speed v is hit by another particle of mass m % p y mvĵ p mv î mv v vî m v y vĵ v vnˆ m v mv KE ( ) mv KE ( m) v 8.m. v mv KE KE KE 5 KE KE 56% 5. Distance of the centre of mass of a solid uniform cone from its verte is z. If the radius ---- h h C.G of solid cone for aped 6. From a solid sphere of mass M and radius R a cube of maimum possible volume is cut. Moment ---- MR π h/ h/

2 M πr ρ R λ (Θ R body diagonal) M M π Ι M' L M' R 6 6 MR π 7. From a solid sphere of mass M and radius R, a R spherical portion of radius is removed, as shown in the figure. aking ---- GM R M M 8 GM R R R GM GM R 8R GM' G( mm) R' R 8. GM 8R GM GM GM 8R 8R R 8. A pendulum made of a uniform wire of cross sectional area A has time period. When an additional mass M is added ---- M π M π L g A Mg π L g L L M π g g M L M L L L M L L L L L Y M A Mg Mg AY. Consider a spherical shell of radius R at temperature. he black body radiation ---- R U U p p nr πr R. A solid body of constant heat capacity J/ C is being heated by keeping it in ---- λn, λn dq msd dq d Entropy ms dq ms ms d msλn (nearest answer). Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an ---- τ γ πd avgn n ρ density avg τ p Qv rms ρ p ρ p ρ ---- () p γ constant nr γ. constant --- () γ From () & () τ

3 τ γ τ γ q γ. For a simple pendulum, a graph is plotted between its kinetic energy (KE) and potential energy ---- E E PE KE PE KE d d R and R < (R R ) kq i [ R r ] R R [ R r ] kq ; R where, r R 5 [ R r] R 5 ( R r ) R 5R 8R 6r (Note: R < R is also answer. R R R R R R R) 6. In the given circuit, charge Q on the µfcapacitor changes as C is varied from A train is moving on a straight track with speed m s. It is blowing its whistle at the frequency ---- % Q Charge f f c c v ( ) f f c c v ( ) f c v f c v f f f 7.7% % 7 5 f f 5 7. A long cylindrical shell carries positive surface charge σ in the upper half and negative surface charge ---- CE Q ( C) the dq is the is with decreasing dc 7. When 5 potential difference is applied across a wire of length. m ---- ρ.6 5 Ω m E j λnev µf C µf Ω m 8. In the circuit shown, the current in the Ω resistor ---- Electric field in the equatorial line is opposite to dipole moment direction. 5. A uniformly charged solid sphere of radius R has potential (measured with respect to ) A, from Q to P 5 Ω Ι A Ι Ι 6 6

4 A ( Q to P) 5 Ω µ 6 Ι A 6 7 Ι Ι ' A 7 Ι Ι Ι A (from Q to P). wo coaial solenoids of different radii carry current Ι in the same ---- F F F F. wo long current carrying thin wires, both with current Ι, are held by insulating ---- sin θ πλgl µ cos θ µ F Ι µ Ι. L π L sin θ πl sin θ µ Ι F sin θ π sin θ MgλLg cosθ F µ Ι tanθ Mg π sin θλlg. An inductor (L. H) and a resistor (R.5 kω) are connected in series to a battery ma t i Ι τ e 5.5. e 5 e 5 A 5.67 ma. A red LED emits light at. watt uniformly around it. he amplitude of the / m πr Ι P ε E c Ι ε E c πr P P E εcπr.5 /m. Monochromatic light is incident on a glass prism of angle A. If the refractive inde of the material r C sin µ r A r A sin µ θ > sin µ sina sin µ Ι sin θ πλgl µ cos θ 5. On a hot summer night, the refractive inde of air is smallest near the ground and A rectangular loop of sides cm and 5 cm carrying a current Ι of A ---- (b) and (d), respectively Stable PE minimum M. B is minimum (i.e. M & B in same direction) Fig. (b) Unstable PE maimum M. B is maimum i.e. M & B in opposite direction) Fig. (d) θ < cos µ sina sin µ Directed horizontally, is assumed as light horizontal on surface of Earth coming with grazing incidence enters at critical angle light bents upwards. Note: If light is coming from upper layer, it will not deviate. 6. Assuming human pupil to have a radius of.5 cm and a comfortable viewing distance ----

5 .λ d D 5.λ 5 d.5 ; D.5 µm 7. As an electron makes a translation from an ecited state to the ground state ---- KE, PE, E 8. Match List I (Fundamental Eperiment) with List II (its conclusion) and select ---- (A) (ii) (B) (i) (C) (iii). A signal of 5 khz frequency is amplitude modulated on a carrier wave of frequency khz khz and 5 khz. An LCR circuit is equivalent to a damped pendulum. In an LCR circuit the capacitor is charged ---- moles resin mol Ca 6 g mol Ca. Sodium metal crystallizes in a body centred cubic lattice with ο A r r a..86 ο A. Which of the following is the energy of a possible ecited state of hydrogen?----. e.6 e En n When, n, E n. e. he intermolecular interaction that is dependant on the inverse ---- ion-dipole interaction ion-dipole interaction 5. he following reaction is performed at 8 K----.5[ 86,6 R(8) λn(.6 )] Q ma L G R(8) λn.6 ο f G (NO).5[ 86,6 R(8) λn(.6 )] L < L τ < τ Discharge faster for case PAR B CHEMISRY. he molecular formula of a commercial resin used for echanging ions in water---- Q ma L t L L C 8H 7SO Na Ca (C 8H 7SO ) Ca Na t 6. he vapour pressure of acetone at C is 85 torr ο P PS W.M ο P W.M M B M B 6 7. he standard Gibbs energy change at K for the given reaction A B C ---- reverse direction because Q > K c [B][C] Q [A] G. K e R e

6 hus, K c < Q 8. wo Faraday of electricity is passed through a solution of CuSO.---- Ιnterhalogen compounds are more reactive than respective halogens. 6. Match the catalysts to the correct processes: g (A)-(ii), (B)-(i), (C)-(iv), (D)-(iii) Cu e Cu F deposits mole of Cu. Higher order (> ) reactions are rare due to:---- low probability of simultaneous collision of all the reacting species low probability of simultaneous collision of all the reacting species. g of activated charcoal was added to 5 ml of aceti acid solution (.6 N) in a flask mg Amount of acetic acid adsorbed 5[.6.] 6 mg Amount adsorbed per gram charcoal mg 8 mg ο. he ionic radii (in A) of N, O and F are ---- icl Zielglar-Natta polymerisation PdCl Wacker process CuCl Deacon s process O 5 Contact process 7. Which one has the highest boiling point?---- Xe he boiling points of Xe 65 K Kr.7 He. K Ne 7. K 8. he number of geometric isomers that can eist for square planar ---- Square planar comple of the type [MABCD] have geometrical isomers.. he color on KMnO is due to:----.7,. and.6 L M charge transition For iso-electronic species, ionic radii decreases with increase in atomic number.. Ιn the contet of the Hall-Heroult process for the etraction of Al---- Na AlF 6 serves as the electrolyte Molten Al O serves as the electrolyte.. From the following statements regarding H O, choose the incorrect statement:---- Ιt can act only as an oidising agent. Ιt can act both as an oidising and reducing agent.. Which one of the following alkaline earth metal sulphates has its hydration enthalpy---- BeSO Be, due to its small size, has high hydration enthalpy. 5. Which among the following is the most reactive? ---- ΙCl L M charge transition 5. Assertion: Nitrogen and Oygen are the main components ---- he assertion is incorrect, but the reason is correct During lightning, atmospheric nitrogen combines with oygen to form oides of nitrogen. 5. Ιn Carius method of estimation of halogens, 5 mg of an organic compound % of B Which of the following compounds will ehibit geometrical isomerism? phenyl--butene C6H CH CH CH CH 5 ( phenyl butene) Ιt shows geometrical isomerism. 5. Which compound would give 5-keto-- methylheanal upon ozonolysis? ----

7 CH NH NaNO / HCl -5 C N Cl CH CH CH Ozonolysis O CH C CH CH CH CHO CH CH CH (D) CuCN / KCN CN CH N 57. Which polymers is used in the manufacture of paints and lacquers? he synthesis of alkyl fluorides is best accomplished by---- Swartz reaction Swartz reaction is used to synthesise alkyl fluoride. 55. Ιn the following sequence of reactions:---- C 6H 5CHO CH COOH Glyptal Glyptal is used in paints and lacquers. 58. Which of the vitamins given below is water soluble?---- itamin C itamin C is water soluble. 5. Which of the following compounds is not an antacid? ---- KMnO SOCl Phenelzine Phenelzine is an antidepressant drug. COCl (A) CHO 6. Which of the following compounds is not colored yellow? Ιn the reaction NH (B) H / Pd BaSO (C) NaNO CuCN/KCN D E N 5 C ---- Zn [Fe(CN) 6] Zn [Fe(CN) 6] is a blush white compound. PAR C MAHEMAICS 6. Let A and B be two sets containing four and two elements respectively CH CN CH Number of subsets of A B 8 Number of subsets of A B having no element having one element 8 having two elements 8 C 8 herefore, number of subsets of A B having at least elements 8 ( 8 8) Choice (a) 6. A comple number z is said to be unimodular if z ---- circles of radius

8 z z z z ( z z )( z z ) ( z z ) ( z, ) z z z z z z z zz zz z z z z z z ( z ) z ( z )} ( z ) ( z ) z z 6. Let α and β be the roots of equation Given a n α n β n a a 8 8 α β α β 8 a ( α β ) 8 8 α ( α ) β ( β ) ( α β ) But α and β are roots of the quadratic α 6α and β 6β Required epression 8 8 α 6α β 6β ( ) ( ) ( α β ) 6( α β ) ( α β ) 6. If A is a matri satisfying the a b equation AA Ι,---- (, ) a AA Ι a b b a b a b (a b ) ( ) b a b a ( given) a b a b a b solving we get a and b choice (d) 65. he set of all values of λ for which the system of linear equations---- contains two elements λ λ λ ( λ) {λ ( λ) } { λ } { ( λ)} λ( λ) ( λ) ( λ) λ λ λ(6 λ λ) 8 λ λ 8 λ λ λ 5λ λ λ 5λ λ is a root Division gives λ λ (λ ) (λ ) λ,, 66. he number of integers greater than 6 that can be formed, using---- digit numbers greater than 6 may start with 6, 7 or 8 ways Number of digit numbers 7 All possible 5 digit numbers 5! otal required numbers 7 Choice (b) 67. he sum of coefficients of integral powers of in the binomial---- ( 5 ) Put y ( y) 5 5 C 5 C y 5 C y.. () sum of coefficient lowest integral power is 5 C 5 C 5 C.. put y and and adding 5 [ 5 C 5C...] required coefficient If m is the A. M. of two distinct real numbers λ and n---- λm n

9 λ n m λ, G, G, G, n are in G. P n λr n r λ n G λ λ n G λ λ n G λ λ G G G n n n λ λ λ λ λ λ nλ n λ λn nλ{λ nλ n } nλ(λ n) nλ m λm n Choice (b) 6. he sum of first terms of the series n th term... n terms ( n ) n n ( n ) ( n ) We want n... { } { 5 7 } 8 6 Choice (b) ( cos )( cos ) lim tan { } ---- ( cos )( cos ) lim tan ( sin ) lim tan sin lim tan 7. If the function g() ---- k, g() m, < 5 g() should be continuous at k m k m () k, g () m, < 5 g() is differentiable at k m k m () From () and () 5m m 5 k 5 8 k m choice (a) 7. he normal to the curve, y y ---- y meets the curve again in the fourth quadrant y y represent the two lines y and y o y (, ) y Normal at (, )

10 Normal at (, ) to the curve meets the curve again at a point in the th quadrant 7. Let f() be a polynomial of degree four he integral ( ) f Since lim f() must be of the form a b c f () a b c a b c () a b c 8a b c () Also, since f( ) lim a b c lim c c Substituting in () and () a b 8a b a a b a 6 b f() 6a 8b c 6 8 ( ) d ( ) d ---- ( ) C d t d dt 5 d dt 5 Substituting dt t t t ( ) C log 75. he integral d ---- log log( 6 ) log Let Ι d log log( 6 ) log d log log( 6 ) () b b We know f ( ) d f( a b ) Ι a log () () Ι Ι log d log 6 a ( ) log( 6 ) log log 6 d ( ) d () d 76. he area (in sq. units) of the region described by- --- y

11 Required An ( ) dy y y dy y y y Let y() be the solution of the differential equation---- We require only integer points lying an the interior of the triangle. when points of which two are deleted as (, ) and (, ) lie on the boundary points. when 8 points etc when points and when No points Locus of the image of the point (, ) in the line--- - circle of radius Observe that the two lines y and y intersect at the point (, ) dy (log) y log() d dy y d log log log Ι. F e e ( log ) log solution is y log log d (, ) L y L y a line L y log log.. d C ylog [log ] C when c when e y. [e loge e] C y C y (e) 78. he number of points, having both co-ordinates as integers Consider the triangle it is right angled and the hypotenuse is part of the line y. he family of lines L y k( y ) pass through the point (, ) Distance of the image of (, ) in L is at a distance ( ) ( ) from (, ) Locus of the image is the circle centered at (, ) and whose radius equals 8. he number of common tangent to the circles---- S : y 6y S : y 6 8y 6 C (, ) r 5 5 C (, ) r 6 8 C C 5 C C r r No: common tangent

12 8. -he area (in sq. units) of the quadrilateral formed by the tangents at the end points--- 7 B P O (, ) A y z λ (λ, λ, λ ) lies on plane λ λ λ 6 λ λ point of intersection (5,, ) Distance from (,, ) to (5,, ) he equation of the plane containing, the line 5y z ; ---- y focus (, ) a 5 5 Co-ordinate of P is, y Equation of tangent at P is y : B (, ) y : A, Ans OAB.. Required Ans Let O be the verte and Q be any point on the parabola---- y 6z 7 he plane can be taken as ( 5y z ) λ ( y z 5) i.e., ( λ ) ( 5 λ)y ( λ)z 5λ Since this plane is parallel to the plane y 6z, λ 5 λ λ 6 λ Required plane is 7 y z i.e. y 6z Let a, b and c be three non- zero vectors such that no two of them are collinear---- y o P Q Let the point Q be, 8 hen by section formula, coordinate of P is y coordinate of P is Clearly, Locus of P is y 8. he distance of the point (,, ) from the point of intersection---- (a b) c b c a (a. c) b (b. c) a b b b c b c cosθ b c cosθ a. c and - (. c) sinθ 8 c 86. If identical balls are to be places in identical boes, then the probability that a

13 Since the boes are identical probability of selecting a bo (in which we are to put balls) is p, q p he given problem is: Probability that the selected bo should contain eactly balls which is the same as Probability of eactly success in trials (putting the balls in boes) C Choice (a) 87. he mean of the data set comprising of 6 observations is 6. If one Correct Correct mean If the angles of elevation of the top of a tower from three collinear points A, B and C---- : h tan y z h z z z z z ( )z y ( )z : z (Choice a) h z z 8. Let tan y tan tan ---- tan y tan tan tan ( ) tan tan Choice (a). he negation of ~s (~r s) is equivalent ---- s (r ~ s) Negation of ~s (~r s) s (r ~ s) (s r) (s ~ s) s r h 5 6 A B y C z tan 6 h h z y z h y ( ) z z z

J E E (M ain)-2015 PAPER 1 CHEMISTRY, MATHEMATICS & PHYSICS. Important Instructions:

J E E (M ain)-2015 PAPER 1 CHEMISTRY, MATHEMATICS & PHYSICS. Important Instructions: Note: For the benefit of the students, specially the aspiring ones, the question of JEE(Main), 05 are also given in this booklet. Keeping the interest of students studying in class XI, the questions based