PART A - PHYSICS 1. In series LCR circuit voltage drop across resistance is 8 volt and across capacitor is 1 volt. Then : Voltage of the source will b

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1 XII - LAKSHYA UNIT TEST (LUT) Test No. 581 Physics : AC complete, Ray Optics upto Spherical mirrors Chemistry : Chemical Kinetics,P block (16) Mathematics : Vetors, D Geometry Question Booklet Serial No Date : 9/1/16 Maximum Marks : 6 Time Allotted : Hours Please read the instructions carefully. 1. Immediately fill the particulars on this page of the Test Booklet with Blue/Black ball point pen. Use of pencil is strictly prohibited.. The answer sheet is kept inside this test booklet. When you are directed to open the test booklet, take out the answer sheet and fill in the particulars carefully.. The test is of hours duration.. The test booklet consists of 9 questions. The maximum marks are There are three parts in the question paper A,B,C consisting of physics, chemistry and mathematics having questions in each part of equal weightage. Each question is allotted (four) marks for correct response. 6. Candidates will be awarded marks as stated above in instruction No.5 for correct response of each question. 1/ (one fourth) marks will be deducted for indicating incorrect response of each question. No deduction from the total score will be made if no response is indicated for an item in the answer sheet. 7. There is only one correct response for each question. Filling up more than one response in any question will be treated as wrong response and marks for wrong response will be deducted accordingly as per instruction 6 above. 8. Use Black Ball Pen only for writing/marking responses on side-1 and side- of the Answer sheet. Use of pencil is strictly prohibited. 9. No candidate is allowed to carry any textual material, printed or written, bits of papers, paper, mobile phone, any electronic device, etc. except the admit card inside the examination hall/room. 1. Rough work is to be done on the space provided for this purpose in the test booklet only. This space is given at the bottom of each page. 11. On completion of the test, the candidate must hand over the answer sheet to the invigilator on duty in the room/hall. However, the candidates are allowed to take away this test booklet with them. 1. Do not fold or make any stray marks on the answer sheet. Advice : 1. It is recommended to select easy questions and optimize your score.. Students are advised not to spend too much time on a particular question.

2 PART A - PHYSICS 1. In series LCR circuit voltage drop across resistance is 8 volt and across capacitor is 1 volt. Then : Voltage of the source will be leading current in the circuit Voltage drop across each element will be less than the applied voltage power factor of circuit will be / None of these. Rms value of the saw tooth voltage of peak value V as shown is T T V V V V. A bulb is rated at 1 V, 1 W, it can be treated as a resistor. Find out the inductance of an inductor (called choke coil) that should be connected in series with the bulb to operate the bulb at its rated power with the help of an ac source of V and 5 Hz. H 1 H H H. A 5 Hz ac source of volts is connected across R and C as shown in figure. The voltage across R is 1 volt. The voltage across C is 8 V 16 V 1 V not possible to determine unless values of R and C are given 5. The e.m.f E = cos 1t volts is applied to an L R circuit containing inductance mh and resistance. The amplitude of current is 7 A 1. A A.8 A 7 1

3 6. If i 1 = sin t and i = cos t, then i is 5 sin ( t + 5 ) 5 sin ( t + 7 ) 5 sin ( t + 5 ) 5 cos ( t + 5 ) 7. A circuit element is placed in a closed box. At time t =, a constant current generator supplying a current of I amp is connected across the box. Potential diff. across the box varies according to graph as shown in the figure. The element in the box is a resistance of a battery of emf 6V an inductance of H a capacitance 8. In the given circuit the average power developed is 5 watt watt 15 watt watt 9. In a series LCR circuit with an AC source R =, C = 5 F, L = 1 H, E rms = 5 V and = Hz. The potential difference across the capacitor is 5 V V 5 V V

4 1. The alternating current I in an inductance coil varies with time according to graph given in figure. Which one of the following graphs, below. Gives the variation of voltage with time? 11. An LCR series circuit with 1 resistance is connected to an AC source of V and angular frequency radians per second. When only the capacitance is removed, the current lags behind the voltage by 6º. When only the inductance is removed, the current leads the voltage by 6. Then the current and power dissipated in LCR circuit are respectively 1A, watt 1A, watt A, watt A, watt 1. An alternating voltage E = sin (1 t) V is connected to a 1 F capacitor through an ac ammeter. The reading of ammeter will be 1 ma 5 ma ma ma 1. A 1 volt AC source of frequency 5 Hz is connected to a L C R circuit with L = 8.1 mh, C = 1.5 F and R = 1, all connected in series. The potential difference across the resistance is 1 V V V V 1. In an a.c. circuit V and I are given by V = 1 sin (1 t) volts I = 1 sin (1 t + / ) ma the power dissipated in the circuit is 1 watt 1 watt.5 watt 5. watt 15. A step down transformer reduces V to 11 V. The primary draws 5 ampere of current and secondary supplies 9 ampere. The efficiency of transformer is % % 9% 1%

5 16. The tuning circuit of a radio receiver has a resistance of 5, an inductor of 1 mh and a variable capacitor. 1 MHz radio wave produces a potential difference of.1 mv. The values of the capacitor to produce resonance is (Take = 1).5 pf 5. pf 5 pf 5 pf 17. The power dissipated in the adjacent circuit is V R V 5R V 5R V 1R 18. In a transformer N p = 5, N s = 5. Input voltage is V and frequency is 5Hz. What are the output voltage and frequency V, Hz 1 V, 5 Hz V, 5 Hz 15 V, Hz 19. In given circuit, when a dielectric slab is introduce between the plates of the capacitor, intensity of bulb increases decreases may increase or decrease can't say. In adjacent circuit the instantaneous current equation is sin 1t sin 1t sin t 1t +

6 1. An alternating voltage E = 6 sin t + 8 cos t is applied to a series resonant circuit as shown. The correct statements are ~ The capacitance C is 1.5 mf The resonant current in the circuit is A Power dissipated in the circuit is watt Quality factor of the current is.9. The reading of the ammeter and voltmeters are (Both the instruments are ac meters and measures rms value) A, 11 V A, V A, 55V 1A, V. In series R L C circuit, the rms voltage across the resistor and inductor are respectively V and 7 V. If the Equation for the applied voltage is E = 5 sin t, then the peak voltage across the capacitor is E5 sint 1 V 1 V V V. In an LCR circuit the capacitance is made 1/th then what should be the change in inductance that the circuit remains in resonance again? 8 times 1/ times times times 5. A resistance of ohm is connected to a source of an alternating potential V = sin (1 t ). The time taken by the current to change from its peak value to rms value is. sec.5 sec 5 1 sec.5 1 sec 6. In the following circuit the readings of AC voltmeters and ammeters will be respectively V, A 15V, A 15V, 6ª V, 8A 5

7 7. A resistors R, an inductor L, a capacitor C and voltmeter V 1, V and V are connected to an oscillator in the circuit as shown in the adjoining diagram, when the frequency of oscillator increases, then at resonant frequency the reading of voltmeter V is equal to V 1 V V ~ that of voltmeter V 1 that of voltmeter V both the voltmeter V 1 & V none of these 8. In a series LCR circuit the frequency of a 1 V AC voltage source is adjusted in such a fashion that the reactance of the inductor measures 15 and that of the capacitor 11. If R =, the potential difference across the series combination of L and C will be 8 V 1 V V 5 V 9. A 1 V, AC source of frequency 5 Hz is connected to an LCR circuit with L = 8.1 mh, C = 1.5 F, R = 1 all connected in series as shown in figure. What is the quality factor of circuit? In a series LCR circuit, the voltage across resistance, capacitance and inductance is 1 V each. If the capacitor is removed, the voltage across the inductance will be 1 V 1 V 1 V V 6

8 PART B - CHEMISTRY 1. In a certain reaction 1% of the reactant decomposes in the 1 st hour, % in nd hour, % in third hour and so on. What are the dimensions of rate constant? hour 1 mol lit 1 sec 1 lit mol 1 sec mol sec 1. The instantaneous rate of disappearance of the MnO ion in the following reaction is.56 1 Ms 1. MnO + 1I + 16H + Mn + + 5I + 8H O The rate of appearance of I is M s M s.56 1 M s M s 1. Which of the following represents zero order reaction? t 1/ t 1/ Conc. of reactant Conc. of reactant t 1/ t 1/ Conc. of reactant Conc. of reactant. For a reaction, A B + C, it was found that at the end of 1 minutes from the start the total optical rotation of the system was 5 and when the reaction is complete, it was 1. Assuming that only B and C are optically active and dextro rotatory, the rate constant of this first order reaction would be.69 min 1.69 min min min 1 5. The kinetic datas for the reaction: A + B AB are as given below: [A] [B ] Rate mol L 1 mol L 1 mol L 1 min Hence the order of reaction w.r.t. A and B are, respectively, 1 and and 1 1 and 1 and 6. Which reaction characteristics are changing by the addition of a catalyst to a reaction at constant temperature Activation energy Equilibrium constant Reaction rate both A and C 7

9 7. For the first order reaction A (g) B (g) + C (g), the initial pressure is P A = 9 mm Hg, the pressure after 1 minutes is found to be 18 mm Hg. The rate constant of the reaction is sec 1. 1 sec sec sec 1 8. The rate law of a reaction, A + B Product is rate = K[A] n (B] m. On doubling the concentration of A and halving the concentration of B, the ratio of new rate to the earlier rate of reaction will be n m n m 1 mn m + n 9. For the formation of phosgene from CO(g) and chlorine (g) as CO(g) + Cl (g) COCl (g) the possible mechanism is Cl Cl (fast) Cl + CO COCl (fast) COCl + Cl COCl + Cl (slow). The rate law expression can be written as Rate = k [CO] [Cl ] Rate = k [CO] 1/ [Cl ] Rate = k [CO] [Cl ] / Rate = k [CO] [Cl ] 1/. At 7 C, the presence of a catalyst causes the activation energy of a reaction to decrease by.66k.cal. The rate of the reaction will be increased by times 1 times 1 times 1 times 1. At 5 K, the half life period of a gaseous reaction at an initial pressure of 8KPa is 5 Sec. When the pressure is KPa, the half life period is 175 Sec. The order of the reaction is Zero 1. For the first order decomposition of N O 5 can be written as N O 5 (g) NO (g) + O (g) ; rate = K[N O 5 ] N O 5(g) NO (g) + 1 O (g) ; rate = K 1 [N O 5 ] Then the correct expression K = K 1 K > K 1 K > K 1 K = K 1. A B : K A = 1 15 e /T C D : K C = 1 1 e 1/T Then temperature at which K A = K C is 1 K. K 8 1 K K.. In a first order reaction, the concentration of reactant decreases from 8 mol/dm to 5 mol/dm in 1 sec. The rate constant in sec 1 is : [log =.] For a first order reaction, the ratio of times to complete 99.9% and half of the reaction is

10 6. Which of the following hydrides has lowest boiling point? H O H S H Se H Te 7. Which one of the following oxoanious does not contain S S bond? S O S O S O 5 S O 7 8. Which of the following compound gives a foul odour when damp: Al S Na NO NH Cl AlCl 9. Which compound on heating alone does not from O : KClO KMnO KNO NH NO 5. The number of S S bonds in sulphur trioxide trimer (S O 9 ) is: Aqueous solution of Na S O on reaction with Cl gives Na S O 6 NaHSO NaCl NaOH 5. Which of the following statements regarding sulphur is incorrect? S molecule is paramagnetic The vapour at C consists mostly of S 8 rings. At 6C the gas mainly consists of S molecules. The oxidation state of sulphur is never less than + in its compounds. 5. Which one of the following on heating will give mixture of SO and SO? ZnSO CuSO Na SO FeSO 5. Copper turnings when heated with concentrated sulphuric acid will give SO SO H S O 55. Sodium thiosulphate is prepared by reducing Na SO solution with H S boiling Na SO solution with S in alkaline medium neutralising H S O solution with NaOH boiling Na SO solution with S in acidic medium 56. Two substances A (t 1/ = 5min) and B (t 1/ = 15 min) are taken in such a way that initially [A] = [B]. The time after which both the concentration will be equal is (assuming reactions are of 1 st order) : 5 min 15 min min concentration can never be equal 9

11 57. For Starting with pure A ratio of rate of production of B to C is Independent of time Independent of temperature depends upon initial concentration of A none 58. The activation energies of two reactions are E a1 and E a with E a1 > E a and their rate constants K 1 and K respectively at temp T 1. If the temperature of the reacting system is increased from T 1 to T predict which of ' ' the following alternative is correct (if K 1 and K are rate constant at T ) ' ' K1 K K K 1 ' ' K1 K K K 1 ' ' K1 K K K 1 ' ' K1 K K K The rate constant for the forward reaction A(g) B(g) is s 1 at 1 K. If 1 5 moles of A and 1 moles of B are present in a 1 litre vessel at equilibrium then rate constant for the backward reaction at this temperature is L mol 1 s L mol 1 s L mol 1 s consider the following first order competing reaction: k 1 k X A B and Y C D if 5% of the reaction of X was completed when 96% of the reaction of Y was completed, the ratio of their rate constant (k /k 1 ) is

12 PART C - MATHS 61. Two adjacent sides of a parallelogram ABCD are given by AB = i ˆ+1j ˆ+11k ˆ and AD = ˆi +j ˆ+k ˆ. The side AD is rotated by an acute angle in the plane of a parallelogram so that AD becomes AD. If AD makes right angle with side AB, then the cosine of the angle is given by If a b and a b c then b is a a c a c a c a a a c a c a c a 6. A unit vector coplanar with i j k, i j k and perpendicular to j k i j k 6 6. If a & b are non zero non collinear vector, then i j k i j k 6 i j k is [ a b iˆ ] iˆ + [ a b ˆj ] ˆj + [ a b kˆ ] k ˆ is equal to ab ab a b ba 65. The point of intersection of the lines joining points (1, 1, 1), (, 1, ) and points (, 1, ), ( 1,, 6) is (,, 1) (,, ) (, 1, ) None of these 66. Let a ˆ i k ˆ, b ˆi ˆj k ˆ and c iˆ ˆj 7k ˆ then a vector r such that r b c b and r a is iˆ 8ˆj ˆi j 8k iˆ 8ˆj kˆ iˆ 8ˆj 67. Let a, b, & c be three vectors having magnitudes 1, 1 and respectively. If a ( a b, then acute angle between a & c is 6 11

13 68. The value of a so that the volume of parallelepiped formed by ˆi aj ˆ kˆ, ˆj akˆ & aiˆ k ˆ becomes minimum is The equation of sphere whose centre has position vector ˆi 6 ˆj k ˆ & touches the plane r ( ˆi ˆj kˆ ) 1 is, r (ˆi 6 ˆj kˆ ) r (ˆi 6ˆj kˆ ) r (ˆi 6 ˆj kˆ ) None of these 7. The distance of the point (1,, ) form the plane x y + z = 5 measured parallel to the line 1 5 x y z 1 6 is 71. The length of the perpendicular form origin to the plane passing through the point a and containing the line r b c is a b c a b c a b b c c a a b b c a b c a b c b c c a c a a b 7. The angle between diagonals of cube is 1 1 cos 1 1 cos cos 1 1 None of these 7. If (,, ) is a point on the line x + y + z = = x y + z 1 then + is In three dimensional space, (x 1)(x ) = represents Pair of lines Sphere Pair of parallel planes Empty set 75. In D, the angle between plane x + y = and the line x + y = is 1

14 76. The shortest distance from the point (1,, 1) to the surface of the sphere x + y + z = is, The equation of the sphere concentric to the spherex + y + z x 6y 8z 5 = and which pass through the origin is x + y + z x 6y 8z = x + y + z x 6y 8z = 5 x +y + z x 6y 8z = 1 x + y + z = 78. The equation of sphere having P( & Q( b ) as a diameter is, + r a r b r a + r b a b r a + r b a r a + r b 79. The equation x + y + z x + 6y 8z + 9 = represents Sphere Plance Empty set None of these 8. If the direction cosines of two lines one such that l + m + n =, l + m n = then angle between them is Equation of the plane parallel to the planes x + y + z 5 = and x + y + z 7 = and equidistant from them is x + y + z 6 = x + y + z = x + y + z 8 = x + y + z = 8. If the planes x = cy + bz, y = az + cx, z = bx + ay pass through a line, then a + b + c + abc is 1 8. Let pairs ( a, &( c, each determine a plane, then planes are parallel if ( a ( b ( a ( b ( a ( c ( a ( c 8. If a& b are unit vectors such that If b is unit vector, then ( a bb ) b ( a b ) is 1 a b a b, then angle between a& b is a b ab a a b 1

15 86. If a is a vector of magnitude 5, collinear with vector 15 b 6 i ˆ 8 ˆ j k ˆ and makes an acute angle with the positive direction of z axis, then a is equal to ˆi ˆj kˆ ˆi ˆj kˆ 1 ˆi 16 ˆj 15kˆ None of these 87. If ( a c a ( b c ), where a, b & c are any three vectors such that a b, b c, then a & c are Perpendicular Parallel Inclined at an angle of Inclined at an angle of A vector which is linear combination of the vectors ˆi ˆj 5kˆ and 6 ˆi 7 ˆj kˆ is perpendicular to vector ˆi ˆ j k ˆ is ˆi 11 ˆj 8kˆ iˆ 11ˆj 8kˆ 9ˆi ˆj kˆ 9 ˆi ˆj kˆ 89. If a, b, c are three unit vectors inclined to each other at an angle, then maximum value of 9. Let P be interior point to acute angle triangle ABC. If PA +PB +PC is a null vector, then point P with respect to ABC is Centroid Orthocenter Incentre Circumcentre 5 6 1

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