MPC-28-02-11th (PQRS & J) Code-A

FINAL TEST Class : XI PAPER CODE : A Time : 3 hour Max. Marks : 180 INSTRUCTIONS 1. The question paper contains 16 pages and 2-parts. Part-A contains 36 objective question and Part-B c o n t a i n s 6 "Match the Column" questions. All questions are compulsory. Please ensure that the Question Paper you have received contains all the QUESTIONS and Pages. If you found some mistake like missing questions or pages then contact immediately to the Invigilator. PART-A (i) Q.1 to Q.24 have only one correct alternative and carry 3 marks each. There is NEGATIVE marking and 1 mark will be deducted for each wrong answer. (ii) Q.25 to Q.36 have one or more than one correct alternative(s) and carry 5 marks each. There is NO NEGATIVE marking. Marks will be awarded only if all the correct alternatives are selected. PART-B (iii) Q.1 to Q.6 are "Match the Column" type which may have one or more than one matching options and carry 8 marks for each question. 2 marks will be awarded for each correct match within a question. There is NEGATIVE marking. 0.5 Marks will be deducted for each wrong match. Marks will be awarded only if all the correct alternative(s) is/are selected. 2. Indicate the correct answer for each question by filling appropriate bubble in your OMR answer sheet. PART-A For example if only 'B' choice is correct then, the correct method for filling the bubble is A B C D PART-B For example if Correct match for (A) is P, Q; for (B) is P, R; for (C) is P and for (D) is S then the correct method for filling the bubble is P Q R S For example if only 'B & D' choices are correct then, the correct method for filling the bubbles is A B C D The answer of the question in any other manner (such as putting , cross , or partial shading etc.) will be treated as wrong. (A) (B) (C) (D) USEFUL DATA Atomic Mass: Al = 27, Mg = 24, Cu = 63.5, Mn = 55, Cl = 35.5, O = 16, H = 1, P = 31, Ag = 108, N = 14, Li = 7, I = 127, Cr = 52, K=39, S = 32, Na = 23, C = 12, Br = 80, Fe = 56, Ca = 40, Zn = 65.4, Ba = 137, Co = 59, Hg = 200, Pb = 207, He = 4, F=19, Ar = 40 Radius of nucleus =10–14 m; h = 6.62 ×10–34 Js; me = 9.1 ×10–31 kg, RH = 109637 cm–1. Take g = 10 m/s2 where ever required. PART-A Select the correct alternative. (Only one is correct) [24 × 3 = 72] There is NEGATIVE marking and 1 mark will be deducted for each wrong answer. x 1 Q.1 The function f (x) = x3 1 can be written as the sum of an even function and an odd function. The even function is (A) x 4 1 x6 1 (B) x 4 1 x6 1 (C) x4 1 x6 1 (D) x 4 1 x6 1 Q.2 For a positive integer n, let fn () = (2 cos  + 1) (2 cos   1) (2 cos 2   1) (2 cos 22   1) (2 cos 2n  1   1). Which one of the following does not hold good? (A) f2 (/6) = 0 (B) f3 (/8) =  1 (C) f4 (/32) = 1 (D) f5 (/128) = Q.3 For a > 0 and 0 < b < , if sin x + cos x = a sin(x + b) then the value of arc sin(sin ab) equals 2 (A) 3  (B) 3  (C) 6  (D) – 6 Q.4 Let a, b, c, d and e be five consecutive terms of an arithmetic sequence such that a + b + c + d + e = 30. Then which of the following can be determined? (A) a (B) b (C) c (D) d Q.5 The sum of the zeroes, product of the zeroes and the sum of the coefficients of the quadratic function f (x) = ax2 + bx + c are equal. Their common value must be equal to (A) the coefficient of x2 (B) the coefficient of x (C) the y-intercept of the graph of y = f (x) (D) the mean of the x-intercept of the graph of y = f (x) ROUGHWORK Q.6 If sin a + sin b = and cos a + cos b = 1 then the value of cos(a – b) equals 1 (A) 3 1 (B) 2 2 (C) 3 (D) 1 Q.7 The line y = 1 – x cuts the curve ky = x2 + x in points P and Q. If POQ is a right angle (where 'O' is the origin) then 'k' equals (A) (B) 1 (C) 2 (D) 1/2 Q.8 Number of 4 letter collections that can be had using the letters of the word ASSISTING, equals (A) 10 (B) 41 (C) 60 (D) none Q.9 A box weighing 6 kg is being pulled with an acceleration of 0.5 m/s2 over a rough surface with the help of a string as shown in the diagram. If the coefficient of kinetic friction involved is 0.5, then the tension in the string is (A) 30 N (B) 60 N (C) more than 6 N but less than 60 N (D) 10 N Q.10 The diagram shows a square carrom board without any pockets. A coin is pushed from the corner, which is the origin, with velocity 2i + 3j. Assume gravity and friction to be absent. The coin collides with edges of the carrom board elastically. What is the velocity vector of coin after the 3rd collision? (A) 2i + 3j (B) 2i – 3j (C) –2i + 3j (D) –2i – 3j ROUGHWORK Q.11 In the diagram shown, no friction at any contact surface. Initially, the spring has no deformation. What will be the maximum deformation in the spring? (A) 4F/3K (B) 8F/3K (C) 4F/K (D) None Q.12 Three identical uniform rods of the same mass M and length L are arranged in xy plane as shown in the figure. A fourth uniform rod of mass 3M has been placed as shown in the xy plane. What should be the value of the length of the fourth rod such that the center of mass of all the four rods lie at the origin? (A) 3L (B) 2L (C) L( 1)/3 (D) L ( 2 1)/3 Q.13 A small block of mass m is rigidly attached at 'P' to a ring of mass m and radius r. The system is released from rest at  = 0° and rolls without sliding. The speed of centre of mass when block reaches the bottom is (A) (B) rg (C) 2 (D) none Q.14 One mole of an ideal monoatomic gas is enclosed in a chamber at 300 K. The gas undergoes a process in which pressure is proportional to the volume. At the end of the process, the volume of the gas is doubled. The change in the internal energy of the gas is [R is gas constant] (A) 450 R (B) 700 R (C) 1350 R (D) data insufficient ROUGHWORK Q.15 A potential energy versus position curve U(x) is shown in the figure. What is the maximum value of the mechanical energy of the particle, if the particle is to be trapped within the region shown in graph? (A) 3 J (B) 5 J (C) 6 J (D) 8 J Q.16 Two conducting movable smooth pistons are kept inside a non conducting, adiabatic container with initial positions as shown. Gas is present in the three parts A, B & C having initial pressures as shown. Now the pistons are released and are allowed to attain equilibrium position slowly. Then the final equilibrium position length of part A will be (A) L/8 (B) L/4 (C) L/6 (D) L/5 Q.17 Energy required to ionise 2 mol of gasesous He+ ion present in its ground state is (Z of He = 2) (A) 54.4 eV (B) 108.8 NA eV (C) 54.4 NA eV (D) 108.8 eV Q.18 Total number of structural isomers of C3H4Br2 are (A) 4 (B) 5 (C) 6 (D) 7 Q.19 I O, S, F are in order of increasing electron affinity II Li, B, C are in order of decreasing 2nd ionisation energy III Cs+, I–, Rb+ are in order of increasing hydration energy IV NH , NH3, NH – are in order of increasing Lewis basic nature 4 2 (A) I & II are correct (B) II & III are correct (C) I, II & IV are correct (D) I, II & III are correct ROUGHWORK Q.20 Write the IUPAC name of sec-amyl isopropyl propargyl carbinol (A) 5-ethyl-4-(methylethyl) hept-2-en-4-ol (B) 4-(1-ethylpropyl)-5-methyl hex-2-yn-4-ol (C) 5-ethyl-4-(methylethyl) hept-1-en-4-ol (D) 5-ethyl-4-(methylethyl) hept-1-yn-4-ol Q.21 40 ml gaseous mixture of CO, CH4 and argon was exploded with 10 ml of oxygen. On cooling, the gases occupied 36.5 ml. After treatment with KOH the volume reduced by 9 ml and again on treatment with alkaline pyrogallol, the volume further reduced. Percentage of argon in the original mixture is (A) 22.5 (B) 77.5 (C) 27.5 (D) 72.5 Q.22 Correct IUPAC name of ethoxy methane is (A) ethyl methyl ether (B) methoxy ethane (C) dimethyl ether (D) diethyl ether Q.23 A bottle of an aqueous H2O2 solution is labelled as '28 V' H2O2 and the density of the solution in gm per ml is 1.25. Choose the correct option (A) Molality of H2O2 solution is 2 'm' (B) Molarity of H2O2 solution is 5M (C) Molality of H2O2 solution is 2.15 'm' (D) Molarity of H2O2 solution is 1.25 M * * * * * * Q.24 (C H3)2 CH  C H  CH2 C H3  CH  CH2 C H3  CH2  CH  C H2 I II III The carbon-carbon bond length (marked as *) will be in following order (A) II > I = III (B) II > III > I (C) III > II = I (D) I = II = III ROUGHWORK Select the correct alternative(s). (One or more than one is/are correct) [12 × 5 = 60] There is NO NEGATIVE marking. Marks willbe awarded onlyifall the correct alternative(s) is/are selected. Q.25 The equation (log1 2 4x)  2   log2    8 has     (A) one integral solution (B) two rational solutions (C) no prime solution (D) one real solution Q.26 Which of the cubic polynomials given below do not have their roots in arithmetic progression? (A) x3 + 3x2 – 2x – 1 (B) x3 + 3x2 – 2x – 2 (C) x3 + 3x2 – 2x – 3 (D) x3 + 3x2 – 2x – 4 f  1 x  Q.27 A function f : R  R is such that  1 x  = x for all x  – 1. Then which of the following statements are true?   f  1 x  (A) f  f (x) = x (B)  1 x  = f (– x), x  1   f  1  (C)  x  = – f (x), x  0 (D) f (– x – 2) = – f (x) – 2   Q.28 Which of the following function(s) is/are odd? (A) k (x) = cos(tan–1x) (B) g (x) = tan(cot1x) (C) h (x) = sin(tan–1x) (D) f (x) = tan(cos1x) ROUGHWORK Q.29 Which of the following statements is/are true in case of specific heat of an ideal gas? (A) specific heat of an ideal gas is zero when it undergoes an adiabatic process (B) specific heat of an ideal gas is infinite when it undergoes an isothermal process (C) the difference between specific heats at constant pressure and constant volume is the same for all ideal gases (D) the ratio of specific heats at constant pressure and constant volume is the same for all ideal gases Q.30 Three identical blocks each of mass m = 1 kg and volume 3 × 10–4 m3 are suspended by massless strings from a support as shown. Underneath are three identical containers containing same amount of water are placed over the scales. In Fig. A, the block is completely out of the water, in Fig. B, the block is completely submerged but not touching the beaker, and in Fig. C, the block rests on the bottom of the beaker. The scale in Fig. A reads 14 N. (A) The tension in the string in Fig. B is 10 N (B) The tension in the string in Fig. B is 7 N (C) The reading of the scale in Fig. B is 17 N (D) The reading of the scale in Fig. C is 24 N Q.31 A particle of mass m is going along surface of smooth hemisphere of radius R in vertical plane. At the moment shown its speed is v. Choose correct option. (A) mg – Ncos = m(gsin2 – mv2 v cos ) (B) N– mgcos = R mv2 R v2 (C) mg – Nsin = R (D) Nsin = m(gsincos – ROUGHWORK sin) R Q.32 Consider a cart of mass M on a frictionless surface that can hold a full tank of water with mass M. A fire-hose sprays water with a constant dm ejectionspeed Vw at a constant mass rate r = dt and at an angle  relative to the horizontal. (A) The acceleration at any time t of the cart while it is spraying water is given by Vwr cos M  rt (B) The speed of the cart as a function of time  t  M  is Vwrt cos    r  M  rt (C) The speed of the cart as a function of time  t  M  is V cos ln(M  rt)    r  w (D) The externalhorizontalforce that must beapplied to keepthecart stationerywhile sprayingwater is rVwcos Q.33 Choose the incorrect statement(s) (A) For a particular orbital in hydrogen atom, the wave function may have negative value but radial probability distribution function though may have zero value but can never have negative value (B) 3dx2 y2 orbital has two angular nodes and one radial node (C) yz and xz planes are nodal planes for dxy orbital (D) all the above three are incorrect statements Q.34 Choose the correct statement(s) regarding given compound CH3–CH=CH–CH2–NO2 (A) Compound will show geometrical isomerism (B) Compound will show tautomerism (C) Compound will show functional isomerism (D) Compound will show metamerism ROUGHWORK Q.35 Select the correct option(s) (A) 3p – 2p, 2p – 2p, 2s – 2s are in order of increasing extent of overlapping (B) The species XeF4, SiF62–, IF +, SF6 have same type of hybridisation (C) H3BO3, H3PO3, H3PO4 all have 3 OH bonds (D) H2S, H2Se, H2Te, H2O are in increasing order of their boiling points Q.36 Statement I: Fe2+, Cd2+, Cu+ all are paramagnetic Statement II: TiO, VO, CrO, FeO are in decreasing order of basic strength Statement III: In B2H6 all the atoms are in same plane Statement IV: MgSO4, CaSO4, SrSO4, BaSO4 are decreasing order of solubility (Atomic Number : Fe = 26, Cu = 29, Cd = 48) (A) Statements I & II are correct (B) Statements II & III are incorrect (C) Statements II & IV are correct (D) Statements I & III are incorrect ROUGHWORK PART-B MATCH THE COLUMN [6 × 8 = 48] There is NEGATIVE marking. 0.5 Marks will be deducted for each wrong match. INSTRUCTIONS: Column-I and column-II contains four entries each. Entries of column-I are to be matched with some entries of column-II. One or more than one entries of column-I mayhave the matching with the same entry of column-II and one entry ofcolumn-I mayhave one or more than one matching withentries of column-II. Q.1 Column-I Column-II (A) In the given figure AC = 2x, BC = 2x + 1 (P) 0 and  ACB = 30°. If the area of  ABC is 18 then the value of x, is equal to (Q) 1 (B) Number of real solution(s) of the equation log2x – 1(x3 + 3x2 – 13x + 10) = 2 is (R) 2 (C) Number of intervals given below are not the subsets of the (S) 4 the domain of the function f (x) = x  4 (a) (– , – 1) (b) (– 7, 0) (c) [, 4) (d) [3, 10] (e) (8, ) (D) If f (t) = sint    then the smallest positive value of 't' for    2  which f (t) attains its minimum value is ROUGHWORK Q.2 Column-I Column-II (A) The complex number 1 – 4i is a zero of the function (P) 2 f (x) = x4 – 4x3 + 18x2 – 28x – 51. If the product of the other three zeroes is written as  + i, (Q) 3  where ,   R then the ratio  equals (R) 4   2 k (B) If A =  3    1 k and B =  2  cos(k) (S) None of P, Q and R k0  k0  then the value of AB equals (C) x-coordinate of the centre of the circle touching the line 3x + y + 2 = 0 at the point (–1, 1) and passing through the point (3, 5) is (D) Given that the sum of the solutions of the equation sin x · tan x – sin x + tan x – 1 = 0 over [0, 2] = k, where k  N then the value of k equals Q.3 In the diagram strings, springs and the pulley are light and ideal. The system is in equilibrium with the strings taut, match the column. Masses are equal. Column I Column II Just after (A) string W breaks (P) | a A| = 0 (B) spring X breaks (Q) | a B| = 0 (C) string Y breaks (R) | a C| = 0 (D) spring Z breaks (S) | a B| = | a C| ROUGHWORK Q.3 Entries in column I consists of diagrams of thermal conductors. The type of conductor & direction of heat flows are listed below. Entries in column II consists of the magnitude of rate of heat flow belonging to any of the entries in column I. If temperature difference in all the cases is (T1 – T2), then match column Column I Column II (A) (P) 6k 0R(T1  T2 ) (B) (Q) k0R (T  T ) 3ln 2 1 2 (C) (R) k0R(T1 – T2) (D) (S) 4k0R (T  T ) ln 2 1 2 ROUGHWORK Q.5 5 mole of an ideal gas is filled in container A, fitted with a massless, frictionless piston. With this container A two more empty containers B and C are connected through the stop cocks as shown. Stop cock I is opened for considerable time and then closed. Thereafter, stop cock II is opened for considerable time and then closed. Column I Column II (A) Number of moles of gas in container B are (P) 4/5 (B) Number of moles of gas in container C are (Q) 1/2 (C) The ratio of height of pistion after closing stop cock II and (R) 1/3 before opening the stop cock I is (D) The ratio of mean free path of molecules in container C and (S) 2/3 that in container B is ROUGHWORK Q.6 Chile salt peter, a source of NaNO3 also contains NaIO3. The NaIO3 can be used as a source of iodine, produced in the following reactions IO– + HSO–   I– + SO2– ...(1) I– + IO–   I2 + H2O ...(2) One litre of chile salt peter solution containing 396 g of NaIO3 is treated with stoichiometric quantity of NaHSO3. Now a substantial amount of same solution is added to reaction mixture to bring about the reaction (2). Column I Column II (A) n–factor of IO– in reaction (2) (P) 6 (B) Number of moles of HSO– used in reaction (1) (Q) 1.2 (C) Moles of I2 produced (R) 2 (D) Equivalents of IO– used in reaction(2) (S) 5 ROUGHWORK