VIBRANT ACADEMY SAMPLE PAPER (MEGA COURSE)
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1 VIBRANT ACADEMY (Idia Private Limited A-(A, Road No., Idraprastha Idustrial Area, Kota-005 (Raj. Tel.(07 866, 8666, 06 Fax 05 Website SAMPLE PAPER (MEGA COURSE Time Hours Maximum Marks 80 Please read the istructios carefully. You are allotted 5 miutes specifically for this purpose. INSTRUCTIONS A. Geeral. This booklet is your Questio Paper cotaiig 60 questios.. The questio paper cotais blak pages for your rough work. No additioal sheets will be provided for rough work.. Blak papers, clipboards, log tables, slide rules, calculators, cellular phoes, pagers ad electroic gadgets i ay form are ot allowed to be carried iside the examiatio hall. 5. Fill i the boxes provided below o this page ad also write your Name ad Form No.. 6. The aswer sheet, a machie-readable Objective Respose Sheet (ORS, is provided separately. 7. DO NOT TAMPER WITH / MUTILATE THE ORS OR THE BOOKLET. 8. Do ot ope the questio-paper booklet before beig istructed to do so by the ivigilators. B. Questio paper format Read the istructios prited o the back page C. Markig scheme (page o. of this booklet. Name of the cadidate Form Number I have read all the istructios ad shall abide by them. I have verified all the iformatio filled i by the cadidate Sigature of the Cadidate Sigature of the ivigilator USEFUL DATA Atomic weights Al = 7, Mg =, Cu = 6.5, M = 55, Cl = 5.5, O = 6, H =, P =, Ag = 08, N =, Li = 7, I = 7, Cr = 5, K=9, S =, Na =, C =, Br = 80, Fe = 56, Ca = 0, Z = 65.5, Ti = 8, Ba = 7, U = 8, Co= 59, B =, F = 9, He =, Ne = 0, Ar = 0, Mo = 96, g = 0 m/s
2 PART I MATHEMATICS Sigle Correct Choice Type This sectio cotais 0 multiple choice questios. Each questio has choices (A, (B, (C ad (D for its aswer, out of which ONLY ONE is correct.. Let x = ta > x > x... are positive real umbers satisfyig si (x + x + six six + = 0 for. The lim x equals x = ta > x > x... si (x + x + six six + = 0 lim x (A 8 (B 6 (C 0 (D. Let a, b ad c be distict real umbers such that a b = b c = c a, the (a + b (b + c (c + a is equal to... a, b c a b = b c = c a (a + b (b + c (c + a (A (B (C (D Noe (. Let f( deote the square of the sum of the digits of atural umber, whee f ( deote f(f(, f ( deote f(f(f( ad so o. The value of f f 0 0 (0 f (0 f 00 0 (0 (0 f(, f (, f(f(, f (, f(f(f( f f 0 0 (A (B 0 (C 0 (D 0 (0 f (0 f 00 0 (0 (0. Number of ordered triplets (a, b, c where a, b, c 0, such that a + b + 5 c is a multiple of is (a, b, c a, b, c 0, a + b + 5 c (A 000 (B 500 (C 50 (D 5 5. Fid the umbers of positive itegers from to 000, which are divisible by at least, or , 5 (A 7 (B 66 (C 78 (D 767 Vibrat Academy (I Pvt. Ltd. "A-(A" Road No., Idraprastha Idustrial Area, Kota (Raj. Ph [A-]
3 MATHEMATICS 6. Let x ad y be umbers i the ope iterval (0,. Suppose there exists a positive umber a, differet from such that log x a + log y a = log xy a. Which of the followig statemets are ecessarily true (I (log a x + log a y = log a x log a y (II x = y (III log a = log x x a x y (0, a ( log x a + log y a = log xy a (I (log a x + log a y = log a x log a y (II x = y (A I oly (III (C I ad II oly log a = log x x a (B II oly (D I, II ad III 7. If (/, / ad ta = si + cos the the value of ta is (/, / ta = si + cos ta (A (B + (C + (D 8. If si x + a cos x = b the the value of a si x cos x is equal to si x + a cos x = b a si x cos x (A a b (B a b (C a b (D a b 9. Let (a, b ad (a, b are the pairs of real umbers such that 0, a, b, ab costitute a arithmetic progressio. The value of the product (a b a b, is (a, b (a, b 0, a, b, ab (a b a b (A 5 (B 50 (C 75 (D I ABC, AB =, BC = ad AC = /. I MNP, MN =, NP = ad MNP = ABC. The side MP equals ABC AB =, BC = AC = / MNP MN =, NP = MNP = ABC MP (A (B 7/ (C (D 7 / Vibrat Academy (I Pvt. Ltd. "A-(A" Road No., Idraprastha Idustrial Area, Kota (Raj. Ph [A-]
4 . Let X deotes the value of the product ( + a + a + a +... ( + b + b + b +... where a ad b are the roots of the quadratic equatio x x = 0 ad Y deotes the umerical value of the ifiite series MATHEMATICS (log b where b = 000 the the value of (XY equals X ( + a + a + a +... ( + b + b + b +... a b x x = 0 Y (log b b = 000 (XY (A 5 (B 5 (C 6 (D 5. Let f(x = 0 deotes a cubic whose roots are cot A, cot B, cot C. If the triagle ABC is such that oe of its agle is 90º the which oe of the followig holds good f(x = 0 cot A, cot B, cot C ABC 90º (A r + R = s (B r + R = s + (C + r + R = s (D r + R = s. Cosider a circle x + y + ax + by + c = 0 lyig compltely i first quadrat. If m ad m are the maximum ad miimum values of y/x for all ordered pairs (x, y o the circumferece of the circle the the value of (m + m is x + y + ax + by + c = 0 m m (x, y y/x (m + m (A a b c c (B b ab c ab (C c b (D b ab ac. Let A(a, 0 ad B(b, 0 be fixed distict poits o the x-axis, oe of which coicides with the origi O(0, 0, ad let C be a poit o the y-axis. Let g be a lie through the origi O(0, 0 ad perpedicular to the lie AC. The locus of the poit of itersectio of the lies g ad BC if C varies alog the y-axis, is (provided c + ab 0 A(a, 0 B(b, 0 x- O(0, 0 C, y- g O(0, 0 AC C, y- g BC ( c + ab 0 (A x a y x y x y x y x (B y (C x (D y b a b b a b a Vibrat Academy (I Pvt. Ltd. "A-(A" Road No., Idraprastha Idustrial Area, Kota (Raj. Ph [A-]
5 5. For which positive itegers is the ratio, (A odd oly ( k k k k k k k k a iteger (B eve oly ( (C = + 6k oly, where k 0 ad k I ( = + 6k, k 0 k I (D = + k, iteger k 0 ( = + k, k 0 6. Let be a lie y = mx + c which itersect the curve y = x 6x + x i poits A(x, y, B(x, y, C(x, y ad D(x, y Statemet- The sum x (x + x + x (x + x x is idepedet of the gradiet of the lie. because Statemet- The sum x (x + x + x (x + x x vaishes y = mx + c y = x 6x + x A(x, y, B(x, y, C(x, y D(x, y - x (x + x + x (x + x x - x (x + x + x (x + x x (A Statemet- is true, Statemet- is true ad Statemet- is correct explaatio for Statemet- (B Statemet- is true, Statemet- is true ad Statemet- is NOT the correct explaatio for Statemet- (C Statemet- is true, Statemet- is false (D Statemet- is false, Statemet- is true 7. Let poits A, B, C are represeted by (a cos i, a si i i =,, ad cos ( + cos ( + cos ( = Statemet- Orthocetre of ABC is at oigi because Statemet- ABC is equilateral triagle A, B, C (a cos i, a si i i =,, cos ( + cos ( + cos ( = - ABC - ABC (A Statemet- is true, Statemet- is true ad Statemet- is correct explaatio for Statemet- (B Statemet- is true, Statemet- is true ad Statemet- is NOT the correct explaatio for Statemet- (C Statemet- is true, Statemet- is false (D Statemet- is false, Statemet- is true Vibrat Academy (I Pvt. Ltd. "A-(A" Road No., Idraprastha Idustrial Area, Kota (Raj. Ph [A-5]
6 8. A triagle formed by lies deoted by the equatio 5x x y + 6xy y = 0 will always be 5x x y + 6xy y = 0 (A acute agled ( (B obtuse agled ( (C right agled ( (D oe ( 9. Oe diagoal of a square is the portio of the variable lie x + ( y = ; > 0 ; which is itercepted 7 betwee the axes. If the area of the square is the the umber of vartices of the square whose both the coodiates are itegers, is x + ( y = ; > 0 ; 7 (A oe ( (B two ( (C four ( (D oe ( 0. If x, y, z R + the the miimum value of x y z xyz is x y z x, y, z R + xyz (A (B (C (D Vibrat Academy (I Pvt. Ltd. "A-(A" Road No., Idraprastha Idustrial Area, Kota (Raj. Ph [A-6]
7 PART II CHEMISTRY Sigle Correct Choice Type This sectio cotais 0 multiple choice questios. Each questio has choices (A, (B, (C ad (D for its aswer, out of which ONLY ONE is correct.. Total umber of structural isomers possible from molecular formula C H 0 O is C H 0 O (A (B 5 (C 6 (D 7. mole of A(g ad 0 mole of B(g are allowed to react i a closed vessel. Accordig to give reactio A (g 0 B(g A(g + B(g C(g Calculate volume of C(g produced at atm ad 7 K after completio of reactio, if % yield of the reactio is atm 7 K C(g (A 8. L (B 6. L (C. L (D 0. L. Molecular species i which cetral atom does ot use its d orbital i hybridizatio x y d x y (A PCl 5 (B XeO 6 6 (C SF 6 (D IF 7. Which of the followig is icorrect for M aqueous solutio of KOH, if desity of solutio is. g/ml KOH M. g/ml (A molal KOH(aq solutio ( KOH( (B.% w/v KOH (aq solutio (.% w/v KOH ( (C 0.07% w/w KOH (aq solutio (0.07% w/w KOH ( (D 5.6% w/v KOH (aq solutio (5.6% w/v KOH ( 5. The correct stability order for the followig species is (A II > IV> I > III (C I > II > III > IV (B II > I > III > IV (D I > III > II > IV 6. The orbit agular mometum of a electro i a Bohr's orbit of He + is.65 0 kg-m /sec. Calculate radius of the orbit (h = J-sec He kg-m /sec (h = J-sec (A 0.59 Å (B.805 Å (C.76 Å (D.058 Å Vibrat Academy (I Pvt. Ltd. "A-(A" Road No., Idraprastha Idustrial Area, Kota (Raj. Ph [A-7]
8 CHEMISTRY 7. Select icorrect match i give chemical reactio (A Z + HCl ZCl + H (o metal displacemet reactio ( (B CaH + HO Ca(OH + H (Metal displacemet reactio ( (C Cl + HO HCl + HOCl (Disproportioatio reactio ( (D Al(OH AlO + HO (Redox Thermal decompositio reactio ( 8. The graph represetig two radial ode is (A 9. (B (C (D Decreasig order of heat of hydrogeatio (I (II (A I > II > III 0. (III (B II > I > III (C III > II > I Which is favourable coditio for the formatio of NH NH N(g + H(g NH(g H = ve (A Low pressure ad low temperature (. (D II > III > I (B High pressure ad high temperature ( (C High pressure ad low temperature ( (D Low pressure ad high temperature ( Which of the property does ot follow followig order N > P > As N > P > As (A Atomic size ( (B Ioizatio eergy ( (C Electroegativity ( (D Basic ature of their hydride (. Select the reactio for which Kp > Kc at 800K. 800K (A N(g + H(g NH(g (C NO(g NO (g Kp > Kc (B PCl5 (g PCl(g + Cl(g (D H(g + I(g HI(g Vibrat Academy (I Pvt. Ltd. "A-(A" Road No., Idraprastha Idustrial Area, Kota (Raj. Ph [A-8]
9 CHEMISTRY. Which of the followig is aromatic (A. (B (C (D A mixture of 0.00 mole of KBrO ad 0.0 mole of KBr was treated i acidic medium ad bromie formed ad this bromie reacted with excess of KI ad I liberated ad this I reacted with NaSO. The volume of 0. M NaSO solutio required to cosume the liberated iodie will be 0.00 KBrO 0.0 KBr KI I, NaSO I 0. M NaSO (A 50 ml 5. (B 0 ml 6. (B HPO rch If iitial rate of effusio ratio rhbr i iitial mixture is CH (D 60 ml 'P' (C HSO (D HClO for CH & HBr is.5, at certai temperature the mole fractio of CH rch r HBr HBr CH.5 (A (C 90 ml H O 'P' pyro-oxy-acid, 'P' ca't be ( (A HSiO (B 0. (C 0.66 (D 0.50 I which of the followig fuctioal group isomerism ot possible (A Carboxylic acid ( (C Ether ( 8. (B aldehyde ( (D Alkylhalide ( For differet gases P, Q, R ad S values of Vader waal costat "a" are give as P, Q, R Gas ( S "a" Vader waal costat "a" ( P Q R S "a" (atm. L mol the which of the followig gas is required miimum liquefactio pressure (A Q 9. (C P (D S (C SO (D SiO Molecule with highest dipole momet is (A CO 0. (B R (B SO The equivalet weight of MSO is M/ (M = Molecular weight, whe it is coverted to MSO M/ (M = (A MO (B MO (C MO (D MO Vibrat Academy (I Pvt. Ltd. "A-(A" Road No., Idraprastha Idustrial Area, Kota (Raj. Ph [A-9]
10 PART III PHYSICS Sigle Correct Choice Type This sectio cotais 0 multiple choice questios. Each questio has choices (A, (B, (C ad (D for its aswer, out of which ONLY ONE is correct.. A helical sprig is iitially ustretched. It is first stretched by a legth x ad the agai by a further legth x. The works doe i the two cases are W ad W respectively. The x x W W (A W = W (B W = W (C W = W (D W = W. Power applied to a particle varies with time as P = (t 5t + watt, where t is i secod. Fid the chage i its K.E. betwee time t = ad t = sec. P = (t 5t + t t = t = (A 8 J (B 00 J (C J (D J. The equatios of motio of a projectile are give by x = 6t ad y = 96t 9.8t. The agle of projectio is x = 6t y = 96t 9.8t (A si (/5 (B si (/5 (C si (/5 (D si (/. I the arragemet show, all surfaces are frictioless. The rod R is costraied to move vertically. The vertical acceleratio of R is a ad the horizotal acceleratio of the wedge W is a. The ratio a /a is equal to R R a W a a /a (A si (B cos (C ta (D cot 5. A rod PQ of legth is restig o two mutually perpedicular axes as show i the figure. If the tip P begis to slide dow with a costat speed of m/ s, the speed of tip Q whe = 0 will be PQ P m / s Q = 0 (A m/ s. (B m/s. (C m/s. (D m/s. Vibrat Academy (I Pvt. Ltd. "A-(A" Road No., Idraprastha Idustrial Area, Kota (Raj. Ph [A-0]
11 PHYSICS 6. Mercury stads at a height h i a barometer. A small hole is made at a height h (less tha h. The mercury comes out of the hole with a speed v equal to h h (h v (A (C gh (B g(h h gh (D mercury does ot dome out 7. A uiform disc of mass M ad radius R is supported vertically by a pivot at its periphery as show. A particle of mass M is fixed to the rim ad raised to the highest poit above the cetre. The system is the released from rest ad it ca rotate about its pivot freely. The agular speed of the system whe the attached object is directly beeath (below the pivot is M R M (A g R (B 8g R (C 8 g R (D g 8R 8. A block is restig o a horizotal plate i the xy plae ad the coefficiet of frictio betwee block ad plate is. The plate begis to move with velocity u = bt i x directio. At what time will the block start slidig o the plate. xy µ x- u = bt b (A g (B bb g (C b (D g b 9. A small sphere is give vertical velocity of magitude v 0 = 5 m/s ad it swigs i a vertical plae about the ed of massless strig. The agle with the vertical at which strig will break, kowig that it ca withstad a maximum tesio equal to twice the weight of the sphere, is [g = 0 m/s ] v 0 = 5 m/s (A cos (B cos (C 60 (D 0 Vibrat Academy (I Pvt. Ltd. "A-(A" Road No., Idraprastha Idustrial Area, Kota (Raj. Ph [A-]
12 PHYSICS 50. I the arragemet show, ed A of light iextesible strig is pulled with costat velocity v. The velocity of block B is A v B (A v/ (C v/ (B v (D data isufficiet 5. The momet of iertia of a uiform flat disc about its ow axis is I. The radius of the disc is a. A quadrat of the disc is cut off ad separated. The momet of the remaiig part of the disc about the same axis will be I a (A I (B 8 I (C I (D I 5. Two vertically arraged sprigs of equal legth support a horizotally suspeded weightless rod. Sprig costat k = 0 N/m ad k = 50 N/m, the distace betwee them is d = m. At what distace from a sprig with stiffess k should we hag a mass so that the rod will be i a horizotal positio (Figure. k = 0 N/m k = 50 N/m d = m k (A 0.75 m (B 0.65 m (C 0.5 m (D 0.75 m 5. A thi wire of legth whe heated to a certai temperature icreases its legth by %. A sheet of the same material of area is heated to the same temperature the icreases i area will be % (A % (B.5% (C % (D.5% Vibrat Academy (I Pvt. Ltd. "A-(A" Road No., Idraprastha Idustrial Area, Kota (Raj. Ph [A-]
13 5. I a wire of youg's modulus Y, the logitudial strai produced is the the strai eergy per uit volume stored i the wire will be Y (A Y (B Y (C Y (D Y 55. Suppose that thermal eergy released by coolig water of volume m by C is used to raise temperature of air by C at costat volume. What is volume of air that ca be heated by C (Give cal =. J ; S air = J/gm C ; S water = cal/gm C ; d air =. kg/m ; d water = gm/cc m C C C (A 500 m (B.5 m (C m (D 5 m A wheel of radius R rolls o the groud with a uiform velocity v. The acceleratio of lowermost poit of the wheel with respect to groud is R v (A R v (B v (C R v R (D Zero 57. A uiform rod of mass M has a impulse applied at right agles to oe ed. If the other ed begis to move with speed V, the magitude of the impulse is M V (A MV (B MV (C MV (D MV 58. A particle of mass m movig alog the x-axis as a potetial eergy U(x = a + bx where a ad b are positive costats. It will execute simple harmoic motio with a frequecy determied by the value of U(x = a + bx x- m a b (A b aloe ( b (B b ad a aloe ( b a (C b ad m aloe ( b m (D b,a ad m aloe ( b, a m 59. The average degree of freedom per molecule of a gas is 6. The gas performs 5 J work, while expadig at costat pressure. The heat absorbed by the gas is 6 5 J (A 75 J (B 00 J (C 50 J (D 5 J 60. I a SHM what fractio of the total eergy is potetial whe the displacemet is of the amplitude (A (B (C (D Vibrat Academy (I Pvt. Ltd. "A-(A" Road No., Idraprastha Idustrial Area, Kota (Raj. Ph [A-]
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
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