NARAYANA I I T / N E E T A C A D E M Y. CPT 4 XII-P LJ JEE-ADVANCE-2016-P2-Model

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1 NARAYANA I I T / N E E T A C A D E M Y CPT XII-P LJ JEE-ADVANCE-06-P-Model Time: 3 hr. IMPORTANT INSTRUCTIONS Max Marks: 86 PHYSICS: Sectio Questio Type +Ve - Ve No.of Total Marks Marks Qs marks Sec I(Q.N : 6) Questios with Sigle Correct Choice Sec II(Q.N : 7 ) Questios with Multiple Correct Choice (Partial Markig +) Sec III(Q.N : 5 8) Questios with Comprehesio Type ( Comprehesios + = Q) 3 0 CHEMISTRY: Sectio Total 8 6 Questio Type +Ve Marks - Ve Marks No.of Qs Sec I(Q.N : 9 ) Questios with Sigle Correct Choice Sec II(Q.N : 5 3) Sec III(Q.N : 33 36) MATHEMATICS: Sectio Questios with Multiple Correct Choice (Partial Markig +) Questios with Comprehesio Type ( Comprehesios + = Q) Total marks Total 8 6 Questio Type +Ve Marks - Ve Marks No.of Qs Sec I(Q.N : 37 ) Questios with Sigle Correct Choice Sec II(Q.N : 3 50) Sec III(Q.N : 5 5) Questios with Multiple Correct Choice (Partial Markig +) Questios with Comprehesio Type ( Comprehesios + = Q) Total marks Total 8 6

2 PHYSICS SECTION I (SINGLE CORRECT ANSWER TYPE) This sectio cotais 6 multiple choice questios. Each questio has optios (A), (B), (C) ad (D) for its aswer, out of which ONLY ONE optio ca be correct. Markig scheme: +3 for correct aswer, 0 if ot attempted ad i all other cases.. A car is movig i a circular horizotal track of radius 0 m with a costat speed of 0 m/s. A plumb bob is suspeded from the roof of the car by a light rigid rod. The agle made by the rod with the vertical is (Take g = 0 m/s ) (A) zero (B) 30 o (C) 5 o (D) 60 o. A isect crawls up a hemispherical surface very slowly. The coefficiet of frictio betwee the surface ad the isect is /3. If the lie joiig the cetre of the hemispherical surface to the isect makes a agle with the vertical, the maximum possible value of is give (A) cot 3 (B) ta 3 (C) sec 3 (D) cosec 3 3. A strig of egligible mass goig over a clamped pulley of mass m supports a block of mass M as show i the figure. The force o the pulley by the clamp is give by (A) Mg (B) mg (C) (M m) m g (D) (M m) M g. A block of mass m is at rest uder the actio of force F agaist a wall as show i figure. Which of the followig statemet is icorrect? (A) f = mg [where f is the frictioal force] (B) F = N [where N is the ormal force] (C) F will ot produce torque Space for rough work

3 (D) N will ot produce torque 5. A block of mass m is placed o a curve surface with a vertical cross sectio give by 3 y x / IF the coefficiet of frictio is 0.5, the maximum height above the groud at which the block ca be placed without slippig is (A) m (B) m (C) m (D) m A particle is projected with a certai velocity at a agle above the horizotal from foot of a o iclied plae of icliatio 30. If the particle strikes the plae ormally the is equal to (A) (C) 30 ta 3 o o 3 (B) 30 ta o o 60 (D) 30 ta 3 SECTION II (MULTIPLE CORRECT ANSWER TYPE) This sectio cotais 8 multiple choice questios. Each questio has optios (A), (B), (C) ad (D) for its aswer, out of which ONE OR MORE tha ONE optio ca be correct. Markig scheme: + for correct aswer, 0 if ot attempted ad - i all other cases 7. A simple pedulum of legth L ad mass (bob) M is oscillatig i a plae about a vertical lie betwee agular limits ad. For a agular displacemet ( ), the tesio i the strig ad the velocity of the bob are T ad v respectively. The followig relatios hold good uder the above coditios (A) T cos Mg (B) T (C) The magitude of the tagetial acceleratio of the bob (D) T Mg cos Mv Mg cos L a g si 8. A referece frame attached to the earth (A) is a iertial frame by defiitio (B) caot be a iertial frame because the earth is revolvig aroud the su (C) is a iertial frame because Newto s laws are applicable i this frame (D) caot be a iertial frame because the earth is rotatig about its ow axis T Space for rough work 3

4 I the figure small block m is kept o plack of mass M ad a force F is applied o plack as show i diagram the which of the followig statemets is/are correct. (A) the acceleratio of m w.r.t. groud is F m (B) the acceleratio of m w.r.t. groud is zero (C) the time take by m to separate from M is (D) the time take by m to separate from M is m F M F 0. From the give diagram, choose the correct optio (all the strigs & pulleys are massless) (A) acceleratio of block a is zero (B) acceleratio of B is g (C) acceleratio of block A is o zero (D) tesio i the strig coectig A is zero. A block of mass m is placed o a wedge. The wedge ca be accelerated i four maers marked as (), (), (3) ad () as show. If the ormal reactios i situatio (), (), (3) ad () are N, N, N 3 ad N respectively ad acceleratio with which the block slides o the wedge i situatio are b, b, b 3 ad b respectively the: (A) N 3 > N > N > N (B) N > N 3 > N > N (C) b > b 3 > b > b (D) b > b 3 > b > b Space for rough work

5 Two blocks of masses m ad m (m > m ) are coected by a massless threads, that passes over a massless smooth pulley. The pulley is suspeded from the ceilig of a elevator. Now the elevator moves up with uiform velocity V 0. Now, select the correct optios. (A) magitude of acceleratio of m with respect to groud is (m m )g greater tha m m (B) magitude of acceleratio of m with respect to groud is equal (m m )g to m m (C) Tesio i the thread that coects m ad m is equal to mmg m m (D) tesio i the thread that coects m ad m is greater tha mmg m m 3. I the figure show, two blocks, oe of mass 5kg ad the other of mass kg are coected by light ad iextesible strig. Pulleys are light ad frictioless. Choose the correct statemet (A) the acceleratio of 5kg mass is 5g ms (B) the acceleratio of kg mass is 5g ms (C) tesio i the strig is g N (D) tesio i the strig is 0g. From a iclied plae two particles P, Q are projected with same speed at same agle, oe up ad other dow the plae as show i figure. Which of the followig statemet(s) is/are correct? (A) The particles will collide the plae with same speed (B) the times of flight of each particle are same (C) both particles strike the plae perpedicularly (D) the particles will collide i mid air if projected simultaeously Space for rough work 5

6 SECTION III (PARAGRAPH TYPE) This sectio cotais groups of questios. Each group has multiple choice questios based o a paragraph. Each questio has choices A), B), C) ad D) for its aswer, out of which ONLY ONE is correct. Markig scheme: +3 for correct aswer, 0 if ot attempted ad 0 i all other cases. Paragraph For Questios 5 ad 6: Two smooth blocks are placed at a smooth corer as show. Both the blocks are havig mass m. We apply a force F o the small block m. Block A presses the block B i the ormal directio, due to which pressig force o vertical wall will icrease, ad pressig force o the horizotal wall decrease, o as we icrease F. ( 37 with horizotal). As soo as the pressig force o the horizotal wall by block B becomes zero, it will lookse the cotact with the groud. If the value of F is further icrease, the block B will accelerate i upward directio ad simultaeously the block A will move toward right 5. What is miimum value of F, to lift block B from groud: (A) 5 mg (B) 5 mg (C) 3 mg (D) mg 3 6. If acceleratio of block A is a rightward, the acceleratio of block B will be: (A) 3a upwards (B) a upwards 3 Paragraph For Questios 7 ad 8: 6 (C) 3a upwards 5 Space for rough work (D) a upwards 5 A frame of referece that is accelerated with respect to a iertial frame of referece is called a o-iertial frame of referece. A coordiate system fixed o a circular disc rotatig about a fixed axis with a costat agular velocityis a example of o-iertial frame of referece. The relatioship betwee the force F rot experieced by a particle of mass m movig o the rotatig disc ad the force F i experieced by the particle i a iertial frame of referece is Frot Fi m(v rot ) m( r). where v rot is the velocity of the particle i the rotatig frame of referece ad

7 r is the positio vector of the particle with respect to the cetre of the disc. Now cosider a smooth slot alog a diameter of a disc of radius R rotatig couter-clockwise with a costat agular speed about its vertical axis through its ceter. We assig a coordiate system with the origi at the ceter of the sic, the x-axis perpedicular to the slot ad the z-axis alog the rotatio axis ( k). A small block of mass m is getly placed i the slot at r(r / )i ˆ at t = 0 ad is costraied to move oly alog the slot The distace r of the block at time t is R t t (A) e e (B) R cos t R e (C) t e t 8. The et reactio of the disc o the block is t t (A) m R(e e ) ˆj mgkˆ (B) (C) m R cos tj ˆ mgkˆ (D) (D) R cos t t t ˆ ˆ m R(e e ) j mgk m R si tj ˆ mgkˆ CHEMISTRY SECTION I (SINGLE CORRECT ANSWER TYPE) This sectio cotais 6 multiple choice questios. Each questio has optios (A), (B), (C) ad (D) for its aswer, out of which ONLY ONE optio ca be correct. Markig scheme: +3 for correct aswer, 0 if ot attempted ad i all other cases. 9. The percetage by volume of C 3 H 8 i a gaseous mixture of C 3 H 8, CH ad CO is 0. Whe 00 ml of the mixture is burt i excess of O, the volume of CO produced is (A) 90 ml (B) 60 ml (C) 0 ml (D) 0 ml 0. What will be the ormality of a solutio obtaied by mixig 0.5 N ad 0.60 N NaOH i the ratio : by volume? (A) 0. N (B) 0.5 N (C).05 N (D) 0.5 N. Which oe of these solutio has the highest ormality? (A) 8 kr KOH per 00 ml (B) 0.5 M H SO (C) 6 gr of NaOH per 00 ml (D) N H 3 PO. 0. N solutio of a dibasic acid ca be prepared by dissolvig 0.5 gr of the acid i water ad dilutig to 00 ml. the M. Wt of the give acid is (A) 5 (B) 90 (C) 35 (D) 80 Space for rough work 7

8 The vapour desity of a tribasic acid is x. The equivalet mass of that acid is (A) x 3 (B) x 3 (C) x 3 (D) x 3. The equivalet weight of divalet metal is 3.8. The weight of a sigle atom is 3 (A) g 3 (B) g (C) 63.6 g (D) 63.6 / g SECTION II (MULTIPLE CORRECT ANSWER TYPE) This sectio cotais 8 multiple choice questios. Each questio has optios (A), (B), (C) ad (D) for its aswer, out of which ONE OR MORE tha ONE optio ca be correct. Markig scheme: + for correct aswer, 0 if ot attempted ad - i all other cases 5. Which of the followig is/are correct for 7 g/l of H O solutio? (A) volume stregths is 5.6 at 73 K ad atm (B) molarity of solutio is 0.5 M (C) ml of this solutio gives.8 ml O at 73 K ad atm (D) the ormality of solutio is M 6. Whe a equimolar mixture of Cu S ad CuS is titrated with Ba(MO ) i acidic medium, the fial products cotais Cu +, SO ad M +. If the molecular weight of Cu S, CuS ad Ba(MO ) are M, M ad M 3 respectively the: M M (A) equivalet wt. of Cu S is (B) equivalet wt. of CuS is 8 6 M3 (C) equivalet wt. of Ba(MO ) is (D) Cu S ad CuS both have same equivalets i mixture 5 7. Silver metal i ore is dissolved by potassium cyaide solutio i the presece of air by the reactio g 8KCN O HO KAg(CN) KOH (A) the amout of KCN required to dissolve 00 g of pure Ag is 0 g (B) the amout of oxyge used i this process is 0.7 g (C) the amout of oxyge used i this process is 7.0 g (D) the volume of oxyge used i this process is 7.0 g 8. The desity of 3 M sodium thiosulphate is.5 g/ml, idetify the correct statemets amout the followig: (A) % by weight of sodium thiosulphate is 37.9 (B) the mole fractio of sodium thiosulphate is (C) the molarity of Na + is 0.53 ad SO 3 is.5 (D) all of these 8 Space for rough work

9 Which of the followig samples of reducig agets is/are chemically equivalet 5 ml of 0. N KMO to be reduced to M + ad water (A) 5 ml of 0. M FeSO to be oxidized to Fe 3+ (B) 50 ml of 0. M H3AsO3 to be oxidized to H3AsO (C) 5 ml of 0. M SO 3 to be oxidized to SO (D) 5 ml of 0. M SCl to be oxidized to SCl 30. 0mL of H O is reacted completely with acidified K Cr O 7 solutio. 0mL of K CrO 7 was required to oxidize the H O completely. Also,.0 ml of the same K Cr O 7 solutio required 5.0 ml of a.0 M H C O solutio to reach equivalece poit. Which of the followig statemets is/are correct? (A) the H O solutio is 5M (B) the volume stregth of H O is 56 V (C) the volume stregth of H O is V (D) if 0 ml of 5M/8 H O is further added to the 0 ml of above H O solutio the volume stregth of the resultig solutio is chaged to 6.8 V 3. A sample of a mixture of CaCl ad NaCl weighig. gm was treated to precipitate all the Ca as CaCO 3, which as the heated ad quatatively coverted to. g of CaO. Which of the followig is correct (A) mixture cotais 50% Nacl (B) mixture cotais 60% CaCl (C) mass of CaCl is. g (D) mass of CaCl. g 3. If 00 ml of M H SO solutio is mixed with 00 ml of 9.8% (w/w) of H SO solutio (d = g/ml) the: (A) cocetratio of solutio remais same (B) volume of solutio becomes 00 ml (C) mass of H SO i the solutio is 98 gm (D) mass of H SO i the solutio is 9.6 gm SECTION III (PARAGRAPH TYPE) This sectio cotais groups of questios. Each group has multiple choice questios based o a paragraph. Each questio has choices A), B), C) ad D) for its aswer, out of which ONLY ONE is correct. Markig scheme: +3 for correct aswer, 0 if ot attempted ad 0 i all other cases. Space for rough work 9

8.09.07 MATHEMATICS SECTION I (SINGLE CORRECT ANSWER TYPE) This sectio cotais 6 multiple choice questios.

10 MATHEMATICS SECTION I (SINGLE CORRECT ANSWER TYPE) This sectio cotais 6 multiple choice questios. Each questio has optios (A), (B), (C) ad (D) for its aswer, out of which ONLY ONE optio ca be correct. Markig scheme: +3 for correct aswer, 0 if ot attempted ad i all other cases. 37. If a, a. a are positive real umbers whose product is a fixed umber c, the the miimum value of a a... a a is (A) (c) (B) ( )c (C) c (D) ( )()c 0 Space for rough work

11 38. Let be a positive iteger such that si cos The (A) = 6 (B) =,, 3, 8 (C) = 5 (D) = x 39. Number of solutios of si x 0 (A) (B) (C) 7 (D) 0 0. The umber of distict real roots of the equatio 8 8 cos x si x, 0 x is (A) (B) 8 (C) 3 (D) 6 ta5x ta x. The geeral solutio of is ta 5x ta x (A) ; Z (B) ; Z (C) (D) ; Z 6 si x cosx. Geeral solutio of is 5 (A) (B) (C) ( ) (D) SECTION II (MULTIPLE CORRECT ANSWER TYPE) This sectio cotais 8 multiple choice questios. Each questio has optios (A), (B), (C) ad (D) for its aswer, out of which ONE OR MORE tha ONE optio ca be correct. Markig scheme: + for correct aswer, 0 if ot attempted ad - i all other cases 3. Let the sum of the series upto terms be S , =,, 3,. The S caot be... greater tha (A) / (B) (C) (D). Let a sequece {a } be defied by a... ; The (A) a (B) a (C) a a (D) a a (3 )(3 )(3 3) 3( ) Space for rough work

12 If si cos, the the possible values of are (A) 0 (B) (C) (D) 3 6. Cosider the equatio cot x log x, 0 x the the true statemets amog the followig are (A) the equatio has o real root (B) the equatio has two distict real roots (C) the equatio has a uique root (D) a root of the equatio lies betwee 0 ad 7. Let, [0, ] be such that 3 cos ( si ) si ta cot cos, ta( ) 0 ad si. The caot satisfy (A) 0 (B) (C) 3 (D) x x x f (x) si x si 3 si... si (0 x ) 3 ( ) (A) mi. value is (B) max. value is ( ) ( ) ( ) (C) rage is, (D) miimum value is ( ) 8. If 9. The iequatio 5 5 (A) is satisfied i, si x 5si x 0 5 (B) is satisfied i, 6 ( 5) ( ) (C) is satisfied i, (D) is satisfied for all x for which si x The sum of the umerical series..., upto term is (A) 3 3 (B) 3 3 (C) less tha (D) less tha / SECTION III (PARAGRAPH TYPE) This sectio cotais groups of questios. Each group has multiple choice questios based o a paragraph. Each questio has choices A), B), C) ad D) for its aswer, out of which ONLY ONE is correct. Space for rough work

13 Markig scheme: +3 for correct aswer, 0 if ot attempted ad 0 i all other cases. Paragraph For Questios 5 ad 5: Two cosecutive umbers from,, 3.. are removed. The A.M of the remaiig umbers is The value of is (A) 8 (B) 9 (C) 50 (D) 5 5. The removed umbers are (A) 6, 7 (B) 8, 9 (C) 7, 8 (D) 9, 0 Paragraph For Questios 53 ad 5: Cosider the equatio ta cos x a ta cos x a 0, a beig a parameter. (Give ta =.56) 53. If a = the the umber of distict real roots of the equatio is (A) 0 (B) (C) (D) ifiite 5. If a the the umber of distict real roots of the equatio is (A) 0 (B) (C) 3 (D) If you have ay geuie questio paper problems please cotact the followig subject cocered persos. PAPER SETTER PHYSICS CHEMISTRY MATHEMATICS DEL-KS MR. VIKAS KAUSHIK DR. MOHIT SAXENA MR. DHARMENDRA SINGH TEST DATE CPT-5 (06 Paper - Model) Previous to previous Week 50% Previous week 50% PHYSICS CHEMISTRY MATHEMATICS Projectile o iclied place, FBD, equilibrium, costrait relatio, coected body problems Frictio ad pseudo force; Dyamics of circular motio ************** Gaseous state Gas laws upto ideal gas equatio, Ideal ad real gases, kietic theory of gases Vaderwaal equatio Cocept of equivalet weight, molarity, ormality, acid base titratio, Redox titratio, back titratio, double titratio, eudiometry Trigoometric Equatios Sequece ad Series Space for rough work 3

04 - LAWS OF MOTION Page 1 ( Answers at the end of all questions )

04 - LAWS OF MOTION Page 1 ( Answers at the end of all questions ) 04 - LAWS OF MOTION Page ) A smooth block is released at rest o a 45 iclie ad the slides a distace d. The time take to slide is times as much to slide o rough iclie tha o a smooth iclie. The coefficiet