JEE MAIN 2021 TEST-6 Chemistry, Physics, Mathematics PDF

T E S T-6 CHEMISTRY , PHYSICS, MATHEMATICS Time : - 3 Hours Max. Marks:- 300 Date :................. INSTRUCTIONS : 1. The test is o...

T E S T-6 CHEMISTRY , PHYSICS, MATHEMATICS Time : - 3 Hours Max. Marks:- 300 Date :................. INSTRUCTIONS : 1. The test is of 3 hours duration. 2. The Test Booklet consists of 90 questions. The maximum marks are 300. 3. There are three parts in the question paper A, B, C consisting of Chemistry, Physics and Mathematics having 30questions in each part of equal weightage. 20 questions will be MCQs and 10 questions (ATTEMPT ANY FIVE QUESTIONS OUT OF 10)will have answer to be filled as numerical value. Marking Scheme for MCQs Correct Answer Four mark (+4), Incorrect Answer Minus one mark (–1), Unanswered No mark (0) Marking Scheme for questions for which answer is a Numerical value Correct Answer Four mark (+4), Incorrect Answer No mark (0), Unanswered No mark (0) 4. There is only one correct response for each question. Filling up more than one response in each question will be treated as wrong response and marks for wrong response will be deducted accordingly. SYLLABUS CHEMISTRY : SOME BASIC CONCEPTS IN CHEMISTRY, STATES ALCOHOLS, PHENOLS & ETHERS, ATOMIC STRUCTURE, CHEMICAL BONDING AND MOLECULAR STRUCTURE. PHYSICS : ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENTS, ELECTROMAGNETIC WAVES MATHEMATICS : LIMITS, CONTINUITY AND DIFFERENTIABILITY, DIFFERENTIATION, APPLICATION OF DERIVATIVES The art of being wise is the art of knowing what to overlook. Today a reader, tomorrow a leader Name :.................................................................................................................... Address :................................................................................................................................................................................................................................................. Phone/Mobile No................................................................................................. Roll No...................................................................................................................  PART A – CHEMISTRY (1) 4, 6 (2) 2, 3 SECTION - 1 (Q.1 - Q.20) (3) 0, 1 (4) 1, 2 Each question has FOUR options (1), (2), (3) Q.7 The correct order in which the C–O bond and (4). ONLY ONE of these four options is length in CO, CO3–2 and CO2 is :- correct. (1) CO3–2 < CO2 < CO Q.1 The molality of 1 M solution of NaCl (specific gravity 1.0585 g/ml) is :- (2) CO2 < CO3–2 < CO (1) 1.0585 (2) 1.0 (3) CO < CO3–2 < CO2 (3) 0.10 (4) 0.0585 (4) CO < CO2 < CO3–2 Q.2 The mass of Mg3N2 produced if 48 gm of Mg Q.8 In the crystalline solid MSO4. nH2O of molar metal is reacted with 34 gm NH3 gas is mass 250 g mol–1, the percentage of anhydrous Mg + NH3 Mg3N2 + H2 salt is 64 by weight. The value of n is (1) (200/3) gm (2) (100/3) gm (1) 2 (2) 3 (3) (400/3) gm (4) (150/3) gm (3) 5 (4) 7 Q.3 Which of the following energy change is less Q.9 The H–N–H angle in ammonia is 107.6º, while than third balmer transition in He+ ion : the H–P–H angle in phosphine is 93.5º. (1) First excitation energy of He+ ion Relative to phosphine, the p-character of the (2) Third separation energy of Li+2 ion lone pair on ammonia is expected to be (3) Fourth excitation energy of H-atom (1) Less (2) More (4) Ionisation energy of Be+3 ion (3) Same (4) Cannot be predicted Q.4 Which of the following relation is incorrect :- Q.10 Consider the van der Waals constants, a and b, (1) 1 mol N–3 ions have 10 mol electrons for the following gases. Gas Ar Ne Kr Xe (2) 1 mol O–2 ions have 6.023 × 1022 electrons 6 2 a / (atm dm mol ) 1.3 0.2 5.1 4.1 (3) 1 mole CH4 has 10 mol protons 2 3 1 b / (10 dm mol ) 3.2 1.7 1.0 5.0 (4) 1 mole water has 10 mol protons Q.5 Which of the following diagrams shows correct Which gas is expected to have the highest change in the polarity of bond ? critical temperature? O— H D ecrease C l— H O— H D e crease C l— H (1) Kr (2) Ne (3) Ar (4) Xe D ecrease Incre ase In cre ase D ecrease D ecrease D ecrease Q.11 The electrons are more likely to be found : S— H F— H S— H F— H a (x) (1) (2) b x O— H In crease C l— H O— H D ecrease C l— H –x D ecrease Incre ase In crease Incre ase c D ecrease D ecrease (1) in the region a and b S— H F— H S— H F— H (2) in the region a and c (3) (4) (3) only in the region c Q.6 Calculate the minimum and maximum number (4) only in the region a of electrons which have magnetic quantum Q.12 Which of the following statement is wrong:- number m = +1 and spin quantum number. (1) B. P. of O-nitrophenol is greater than s = –½ in chromium (Cr) :- p-nitrophenol. SPACE FOR ROUGH WORK 2  (2) In SO3 p – d bond is present Q.20 6.02 × 1020 molecules of urea are present in (3) In S3O9 no. of bridge oxygen is 3. 200mL of its solution. The concentration of (4) All of these urea solution is Q.13 At identical temperature and pressure, the rate (1) 0.001 M (2) 0.01 M (3) 0.005 M (4) 0.10 M of diffusion of hydrogen gas is times that SECTION - 2 (Q.21 - Q.30) of a gaseous hydrocarbon having molecular This section contains TEN (10) questions. formula CnH2n – 2. What is the value of n? ATTEMPT ANY FIVE (05) QUESTIONS. (1) 1 (2) 4 (3) 3 (4) 8 The answer to each question is Q.14 For which of the following species, Bohr's NUMERICAL VALUE. If the numerical theory is not applicable value has more than two decimal places (1) Be+3 (2) Li+2 truncate/round-off the value upto TWO (3) He+2 (4) H decimal places. Q.15 When 2 L of CO2 is heated with graphite, Q.21 If Aufbau rule is not obeyed and instead volume of gases collected is 3 L, calculate electronic filling occurs orbit by orbit till number of moles of CO produced at STP? saturation is reached. The percentage change in (1) 1 / 22.4 (2) 2 / 22.4 sum of all (n + ) values for unpaired electrons (3) 3 / 22.4 (4) 4 / 22.4 in an atom of iron is 10x.What is the value of x. Q.22 6.2 g of a sample containing Na2CO3, NaHCO3 Q.16 For the configuration and non-valatile inert impurity on heating loses which rule is violated ? 5%of its weight due to formation of H 2O and (1) Aufbau principle (2) (n + ) Rule CO2 as in reaction (3) Pauli 's Rule (4) Hund's Rule Q.17 Correct order of bond angle is :- 2NaHCO3 Na2CO3 + H2O + CO2. (1) OF2 < H2O < NH3 < Cl2O Residue is dissolved in water and formed 100 (2) OF2 < NH3 < Cl2O < H2O ml solution and its 10 ml portion requires 4.5 ml of 0.2 M aqueous solution of BaCl 2 for (3) OF2 < Cl2O < H2O < NH3 complete precipitation of carbonates. If number (4) Cl2O < OF2 < H2O < NH3 of moles of Na2CO3 in the original sample Q.18 Which bond angle  gives maximum dipole were 'q' then the value of '100 q' is : moment for triatomic molecule XY2 : Q.23 How many of the following has more than 10 (1) = 90° (2) = 120° bonds. (3) = 180° (4) Both 2 and 3 (a) P4O6 (b) K2Cr2O7 (c) KMnO4 Q.19 Following P vs V curve is plotted : P (d) I2Cl6 (e) K2MnO4 (f) K2CrO4 T1 (g) C5H8 T2 T3 Q.24 How many molecules are having zero dipole V moment. PCl3F2, P(CH3)3(CF3)2, BF3, CHCl3, What is the relation between T1, T2 and T3 ? P(CH3)2(CF3)3, PF3Cl2, CH4, CCl4. (1) T1 = T2 = T3 (2) T1 > T2 > T3 Q.25 A photon is emitted in -line of Balmer series (3) T1 < T2 < T3 (4) None of the above of He+ ion. This photon is absorbed by an SPACE FOR ROUGH WORK 3  electron present in ground state of hydrogen (1) 5 V (2) 10 V atom. Calculate the value of z, where (3) 15 V (4) 20 V Q.32 A conducting rod AC of length 4 is rotated , = De Broglie wavelength about a point O in a uniform magnetic field associated with electron in final orbit of directed into the paper. AO =  and OC = 3. hydrogen atom. (in Å). Then which is incorrect :- Q.26 An electron is continuously accelerated in vacuum tube by applying potential difference. A C O If its de-broglie wavelength is decreased by 4%. Determine the approx % change in kinetic (1) | VA – VO | = energy of the electron. Report your answer by adding '1' if kinetic energy increases and (2) | VO – VC | = subtracting '1' if kinetic energy decreases. Q.27 20ml of O2 contracts to 17ml when subjected to (3) | VA – VC | = silent electric discharge in an ozoniser. What (4) | VC – VO | = further contraction would be observed if the partially ozonised oxygen is treated with oil of Q.33 In the circuit shown in figure,. cinnamon (which absorbs ozone). All volumes Switch S is closed at time t = 0. The current are reported at the same temperature and through C & L would be equal after a time 't' pressure. equal to :- Q.28 The binding energy of electrons in a metal is L R 250 kJ/mol. The threshold frequency of metal C R will be..... × 1014 sec–1. Q.29 The ratio of bond orders in CO32– ion NO3– ion is. V S Q.30 Atomic number of an element is 24. The (1) CR (2) CR ln 2 number of unpaired electrons present in its (3) (4) LR dipositive ion is Q.34 In L-C-R, A.C. series circuit, L = 9 H, R = 10.PART B – PHYSICS & C = 100µF. Hence Q-factor of the circuit is – SECTION - 1 (Q.31 - Q.50) (1) 25 (2) 45 Each question has FOUR options (1), (2), (3) (3) 35 (4) 30 and (4). ONLY ONE of these four options is Q.35 The total number of turns and cross-section correct. area in a solenoid is fixed. However, its length Q.31 The network shown in figure is a part of a L is varied by adjusting the separation between complete circuit. If at a certain instant the windings. The inductance of solenoid will be current 'i' is 5 A and is decreasing at the rate of proportional to : 103 A/sec. then VA – VB is :- (1) 1/L2 (2)1 / L 1 5m H (3) L (4) L2 + – i A B Q.36 A 20 Henry inductor coil is connected to a 10 15V ohm resistance in series as shown in figure. The SPACE FOR ROUGH WORK 4  time at which rate of dissipation of energy is 1. If it is removed from the magnetic field (joule's heat) across resistance is equal to the in 1s, the induced charge in the coil is – rate at which magnetic energy is stored in the (1) 1 C (2) 0.01 C inductor is : (3) 0.1 C (4) 0.001 C i 10 Q.40 A plane electromagnetic wave travels in free space along the x-direction. The electric field E 20 H component of the wave at a particular point of space and time is E = 6 V m–1 along y- (1) (2) ln 2 direction. Its corresponding magnetic field component, B would be : (3) 2 ln 2 (4) (1) 6 × 10–8 T along z-direction (2) 6 × 10–8 T along x-direction Q.37 An electromagnetic wave is represented by the (3) 2 × 10–8 T along z-direction electric field sin [t + (6y – 8z)]. (4) 2 × 10–8 T along y-direction Taking unit vectors in x, y and z directions to Q.41 When a 60 mH inductor and resistor are be the direction of propagation is : connected in series with an AC voltage source, the voltage leads the current by 60°. If the (1) (2) inductor is replaced by a 0.5 mF capacitor, the voltage lags behind the current by 30°. What is (3) (4) the frequency of the AC supply? Q.38 In the given arrangement, the loop is moved (1) (2) with constant velocity v in a uniform magnetic field B in a restricted region of width a. The (3) (4) time for which the emf is induced in the circuit Q.42 The magnetic field of a plane electromagnetic is :- wave is given by : a b where B0 = 3 × 10–5 T and B1 = 2 × 10–6 T. v The rms value of the force experienced by a b> a stationary charge Q = 10–4 C at z = 0 is closest to : (1) 0.9 N (2) 0.1 N (1) (2) –2 (3) 3 × 10 N (4) 0.6 N Q.43 A very long solenoid of radius R is carrying (3) (4) current I(t) = kte–t (k > 0), as a function of Q.39 A coil of surface area 200 cm2 having 25 turns time (t  0), counter clockwise current is taken is held perpendicular to the magnetic field of to be positive. A circular conducting coil of radius 2R is placed in the equatorial plane of intensity 0.02 Wb/m2. The resistance of the coil the solenoid and concentric with the solenoid. SPACE FOR ROUGH WORK 5  The current induced in the outer coil is (4) move parallel to the wire correctly depicted, as a function of time, by Q.47 The power factor of the circuit as shown in figure is I I X C= 4 0  t t=0 t=0 t 220V ~ R 1= 4 0  50H z (1) (2) XL= 1 0 0 R2= 4 0 t=0 t=0 (1) 0.2 (2) 0.4 t t (3) 0.8 (4) 0.6 (3) (4) Q.48 If value of R is changed then : Q.44 An electromagnetic wave of intensity 50 Wm–2 enters in a medium of refractive index 'n' 10V 10 V R without any loss. The ratio of the magnitudes Supply of electric fields, and the ratio of the magnitudes of magnetic fields of the wave (1) voltage across L remains same. before and after entering into the medium are (2) voltage across C remains same. respectively, given by : (3) voltage across L-C combination remains same. (1) (2) (4) voltage across L-C combination changes. (3) (4) Q.49 The primary winding of a transformer has 100 turns and its secondary winding has 200 turns. Q.45 A 10 m long horizontal wire extends from The primary is connected to an ac supply of North East to South West. It is falling with a 120 V and the current flowing in it is 10 A. The speed of 5.0ms–1, at right angles to the voltage and the current in the secondary are : horizontal component of the earth's magnetic (1) 240 V, 5 A (2) 240 V, 10 A field, of 0.3 × 10–4 Wb/m2. The value of the (3) 60 V, 20 A (4) 120 V, 20 A induced emf in wire is : Q.50 In the circuit shown in figure neglecting source (1) 2.5 × 10–3 V (2) 1.1 × 10–3 V resistance the voltmeter and ammeter reading (3) 0.3 × 10–3 V (4) 1.5 × 10–3 V will respectively be : Q.46 A square conducting loop is placed near an V infinitely long current carrying wire with one edge parallel to the wire as shown in the figure. R =30 X L=25  X C = 25  If the current in the straight wire is suddenly A halved, which of the following statements will be true? 240V “The loop will.......” (1) 0V, 3A (2) 150V, 3A (1) stay stationary (3) 150V, 6A (4) 0V, 8A (2) move towards the wire I (3) move away from the wire SECTION - 2 (Q.51 - Q.60) SPACE FOR ROUGH WORK 6  This section contains TEN (10) questions. generated by the beam if the protons are ATTEMPT ANY FIVE (05) QUESTIONS. moving at a speed v = 2m/sec. The answer to each question is Q.55 Figure shows a circuit in vertical plane kept in NUMERICAL VALUE. If the numerical uniform horizontal magnetic field B. L value has more than two decimal places truncate/round-off the value upto TWO B decimal places.  Q.51 In the circuit shown below, the ac source has g voltage V = 20 cos (t) with  = 2000 rad/sec. k The amplitude of the current will be nearest to: 50 µ F //////// 5m H , 4 The slider is movable while remaining part is fixed. The slider has mass m = 1 kg. Electrical resistance of circuit is equal to zero. Take B = 10 T, l = 1m, L = 1 H, g = 10 m/s 2. In the 6 absence of spring maximum distance travelled Q.52 A very long straight conducting wire, lying by slide is X1 and in the presence of spring along the z-axis, carries a current of 2A. The maximum distance travelled by slider is X2. integral is computed along the straight For k = 102 N/m it is found that then line PQ, where P has the coordinates (2cm, 0, 0) and Q has the coordinates (2cm, 2cm, 0). find the value of n. The integral can be expressed as N×10–7 in SI units. Find N Q.56 In the circuit, E = 10 volt, R1 = 5.0 ohm, R2 = Q.53 Branched chain AB (fig.) has the following 10 ohm and L = 5.0 henry. Calculate the parameters : L1 = 0.1 H, L2 = 0.4 H, current i just when the switch S is pressed. R1 = 10ohms. At some point of time, the current I1 = 0.2 A begins to increase at a rate of 5 A/s, and the current I2 = 0.5 A decreases at a rate 1.25 A/s, find the resistance R2. L1 I1 R1 Q.57 A current increases uniformly from zero to one ampere in 0.01 second, in a coil of inductance 10mH. The induced e.m.f. (in V) will be- A B Q.58 The ratio of contributions made by the electric R2 I2 L2 field and magnetic field components to the intensity of an electromagnetic wave is :: X : Y Q.54 Protons moving in a straight, cylindrically.Find the minimum sum of X and Y. symmetrical beam have a charge density  = Q.59 A 40 µF capacitor is connected to a 200 V, 50 A /r, where r is the distance from the beam’s Hz ac supply. The rms value of the current in axis and A is a constant equal to 4/µ 0. Find the the circuit is, nearly (y/2) amp. Find the value magnetic field (in tesla) at r = (3/4) m of y. SPACE FOR ROUGH WORK 7 Q.60 In LC circuit the inductance L = 40 mH and tan–1(1/2). Water is poured into it at a constant capacitance C = 100 µF. If a voltage rage of 5 cubic meter per minute. The rate (in V(t) = 10sin (314 t) is applied to the circuit,if m/min.), at which the level of water is rising at the maximum value of current in the circuit is : the instant when the depth of water in the tank is 10m; is :-. Find the value of X. (1) 2/ (2) 1/5 (3) 1/10 (4) 1/15 PART C – MATHEMATICS Q.65 The height of a right circular cylinder of SECTION - 1 (Q.61 - Q.80) maximum volume inscribed in a sphere of Each question has FOUR options (1), (2), (3) radius 3 is and (4). ONLY ONE of these four options is (1) (2) correct. (3) (4) Q.61 Let f : [0, 2] R be a twice differentiable function such that f ''(x) > 0, for all x  (0, 2). Q.66 If f (1) = 1, f ' (1) = 3, then the derivative of If f (f ( f (x))) + ( f (x))2 at x = 1 is : f (x) = f (x) + f (2 – x), then f is : (1) 12 (2) 33 (1) decreasing on (0, 2) (3) 9 (4) 15 (2) decreasing on (0, 1) and increasing on (1, 2) Q.67 Applying mean value theorem on f (x) = logx ; (3) increasing on (0, 2) x  [1, e] the value of c = ……… (4) increasing on (0, 1) and decreasing on (1, 2) (1) log (e – 1) (2) e – 1 (3) 1 – e (4) 2 Q.68 If the point (1,3) serves as the point of inflection of the curve y = ax3 + bx2 then the Q.62 If value of ‘a’ and ‘b’ are - (1) a = 3/2 & b = – 9/2 (2) a = 3/2 & b = 9/2 (3) a = –3/2 & b = – 9/2 (4) a = – 3/2 & b = 9/2 is continuous at x = 0, then the ordered pair (p,q) is equal to : Q.69 Let f (x) = (1) (5/2, 1/2) (2) (–3/2, –1/2) (3) (–1/2, 3/2) (4) (–3/2, 1/2) Q.63 If m is the minimum value of k for which the Which of the following properties does f have function f (x) = x is increasing in the on the interval (0, 6) ? interval [0, 3] and M is the maximum value of f I. n f(x) exists ; II. f is continuous in [0, 3] when k = m, then the ordered pair III. f is monotonic (m, M) is equal to : (1) I only (2) II only (1) (2) (3) III only (4) none Q.70 The approximate value of 52.01 is …….., (3) (4) where, (loge 5 = 1.6095). Q.64 A water tank has the shape of an inverted right (1) 25.4125 (2) 25.2525 circular cone, whose semi-vertical angle is SPACE FOR ROUGH WORK 8  (3) 25.5025 (4) 25.4024 Then f increases in the interval - (a) (–, –2) (b) (–2, –1) (c) (1, 2) (d) (2, ) Choose the correct option – Q.71 If f (x) = , (1) a ,b , d (2) a, b, c (3) a, b, c, d (4) a, c then correct statement is - Q.77 If , (1) f (x) is discontinuous at x = 0 for any value of a (2) f (x) is continuous at x = 0 when a = 8 then f '(1) equals - (3) f (x) is continuous at x = 0 when a = 0 (1) 2/9 (2) –2/9 (4) none of these (3) 0 (4) does not exist Q.72 If a variable tangent to the curve x 2y =c3 makes intercepts a, b on x and y axis respectively, Q.78 Let f (x) = then the value of a2b is - (1) 27c3 (2) c3 where [x] denotes the greatest integer function. Then (3) c3 (4) c3 (1) f (x) is continuous and differentiable in Q.73 The difference between the greatest and the for all a, provided b = 2. least value of is (2) f (x) is continuous and differentiable in (1) (2) if f(a) = 4 , b = 2. (3) f (x) is continuous and differentiable in (3) (4) if a = 4 and b = 0. Q.74 If , then equals (4) for no choice of a and b, f(x) is (1) (2) differentiable in. Q.79 If f (4) = g (4) = 2 ; f ' (4) = 9 ; g' (4) = 6 then (3) (4) none of these is equal to Q.75 The length of the subnormal of the curve y2 = 8ax (a > 0) is - (1) (2) (1) 2a (2) 4a (3) 0 (4) none of these (3) 6a (4) 8a Q.80 A helicopter is flying along the curve given by Q.76 Let f(x) =. SPACE FOR ROUGH WORK 9  y – x3/2 = 7, (x  0). A soldier positioned at the If f (x) = (a – 1) x3 + (2b + 3) x2 + 2x + 1, and point (1/2, 7) wants to shoot down the f (g (x)) = 6x – 7 where g (x) is a linear helicopter when it is nearest to him. Then this function then find the value of g' (2012). nearest distance is : Q.88 Let f : R R be defined as f (x) = x + cos x + 2 and g (x) be the inverse function of f (x). (1) (2) Find (g'(3) + g''(3)). Q.89 Let f : R R+ be a differentiable function (3) (4) satisfying f ' (x) = 2f (x) x R. Also f (0) = 1 and g (x) = f (x). cos2x. If n1 represent number of SECTION - 2 (Q.81 - Q.90) This section contains TEN (10) questions. points of local maxima of g (x) in [–, ] and ATTEMPT ANY FIVE (05) QUESTIONS. n2 is the number of points of local minima of The answer to each question is g (x) in [–, ] and n3 is the number of points NUMERICAL VALUE. If the numerical in [–, ] where g (x) attains its global value has more than two decimal places minimum value, then find the value of truncate/round-off the value upto TWO (n1 + n2 + n3). decimal places. Q.90 A polynomial y = f (x) of degree 4 increases in Q.81 is the interval (–, 1) (2, 3) and decreases in the interval (1, 2) (3, ) and satisfies f(0) = Q.82 f '(x) = g (x) and g'(x) = – f (x) for all real x and 1 and f ' (0) = 6. Find the value of f (2). f (5) = 2 = f ' (5) then f2(10) + g2(10) is - Q.83 Let f : R R be a function such that f (x) = x3 + x2 f ' (1) + x f '' (2) + f '''(3), x R. Then f (2) = (–A). Find the value of A. Q.84 The tangent to the curve, passing through the point (1, e) also passes through the point (A/3, 2e). Find the value of A. Q.85 The maximum value of the function f (x) = 3x3 – 18x2 + 27x – 40 on the set S = {x  R : x2 + 30  11x} is (120 + A). Find the value of A. Q.86 Let f (x) = if x 3, when x = 3 such that f (x) is continuous for all x R then the value of  is Q.87 Let the equation (a – 1) x2 = x (2b + 3) be satisfied by three distinct values of x, where a, b R. SPACE FOR ROUGH WORK 10