INSTRUCTIONS:IIT /PMT VERY SIMILAR TEST. EVERY CORRECT ANSWER WILL REWARD U 3 MARKS AND EVERY WRONG ANSWER WIL DEDUCT YOURS 1 MARK. SO BE CARE FULL. SECTION-A | IIT-JEE (PHYSICS)INSTRUCTIONS:Q.1If force, acceleration and time are taken as fundamental quantities, then the dimensions of length will be:(A) FT2(B) F1 A2 T1 (C) FA2T(D) AT2Q.2The dimensions ML1 T2 can correspond to :(A) moment of a force or torque(B) surface tension(C) pressure(D) co-efficient of viscosity.(useful relation are = , S = F/l , F = 6 r, where symbols have usual meaning)Q.3Which of the following can be a set of fundamental quantities(A) length, velocity, time(B) momentum, mass, velocity(C) force, mass, velocity(D) momentum, time, frequencyQ.4Kinetic energy (K) depends upon momentum (p) and mass (m) of a body as K pa mb(A) a =1; b =1(B) a =2; b = –1(C) a =2; b=1(D) a =1; b =2Q.5If area (A) velocity (v) and density () are base units, then the dimensional formula of force can be represented as.(A) Av(B) Av2(C) Av2(D) A2vQ.6The pressure of 106 dyne/cm2 is equivalent to(A) 105 N/m2(B) 106 N/m2 (C) 107 N/m2(D) 108 N/m2Q.7If 1 unit of mass = 4 kg; 1 unit of length = m and 1 unit of time = 5 sec, then 1 Joule = x units of energy in this system where x = (A) 100 units(B) 0.01 units(C) 200 units(D) 0.02 unitsQ.8In a certain system of units, 1 unit of time is 5 sec, 1 unit of mass is 20 kg and unit of length is 10 m. In this system, one unit of power will correspond to (A) 16 watts(B) watts(C) 25 watts(D) none of theseQ.9In a book, the answer for a particular question is expressed as b = here m represents mass, a represents accelerations , l represents length. The unit of b should be(A) m/s(B) m/s2(C) meter(D) / sec.Q.10If the resultant of two forces of magnitudes P and Q acting at a point at an angle of 60° is Q, then P / Q is(A) 1(B) 3 / 2(C) 2(D) 4Q.11The resultant of two forces F1 and F2 is P. If F2 is reversed, then resultant is Q. Then the value of (P2 + Q2) in terms of F1 and F2 is(A) 2(F12 + F22)(B) F12 + F22(C) (F1 + F2)2(D) none of theseQ.12A man moves towards 3 m north then 4 m towards east and finally 5m towards 37° south of west. His displacement from origin is(A) (B) 0 m(C) 1 m(D) 12 mQ.13Three forces P, Q & R are acting at a point in the plane . The angle between P & Q and Q & R are 150º & 120º respectively, then for equilibrium, forces P, Q & R are in the ratio (A) 1 : 2 : 3(B) 1 : 2 : (C) 3 : 2 : 1(D) : 2 : 1Q.14A man rows a boat with a speed of 18km/hr in northwest direction. The shoreline makes an angle of 15° south of west. Obtain the component of the velocity of the boat along the shoreline.(A) 9 km/hr(B) 18 km/hr(C) 18 cos15°km/hr(D) 18 cos75° km/hrQ.15A bird moves from point (1, 2, 3) to (4, 2, 3) . If the speed of the bird is 10 m/sec, then the velocity vector of the bird is :(A) 5(B) 5(C) (D) Q.16The motion of a body is given by the equation = 6.0 3 v(t) ; where v (t) is the speed inm/s & t in sec., if the body has v = 0 at t = 0 then(A) the terminal speed is 2.0 m/s (B) the magnitude of the initial acceleration is 6.0 m/s² (C) the speed varies with time as v(t) = 2 (1 e-3t) m/s (D) the speed is 1.0 m/s when the acceleration is half the initial value. [JEE ’1995]Q.17A ball is dropped vertically from a height d above the ground it hits the ground and bounces up vertically to a height d/2. Neglecting subsequent motion and air resistances, its velocity v varies with the height h above the ground as[JEE'2000 (Scr)](A) (B) (C) (D) [JEE'1996]Q.18A small block slides without friction down an inclined plane starting from rest. Let Sn be the distance travelled from time t = n - 1 to t = n. Then is[JEE' 2004 (Scr)](A) (B) (C) (D) Q.19In 1.0 sec. a particle goes from point A to point B moving in a semicircle of radius 1.0 m. The magnitude of average velocity is :[JEE '99](A) 3.14 m/sec (B) 2.0 m/sec (C) 1.0 m/sec (D) zeroQ.20The co-ordinates of a particle moving in a plane are given by x (t) = a cos (t) and y (t) = b sin (t) where a, b (< a) & are positive constants of appropriate dimensions.(A) the path of the particle is an ellipse (B) the velocity & acceleration of the particle are normal to each other at t = /(2)(C) the acceleration of the particle is always directed towards a focus(D) the distance travelled by the particle in time interval t = 0 o t = /(2) is a .[JEE '1999]Q.21A ball is dropped vertically from a height d above the ground it hits the ground and bounces up vertically to a height d/2. Neglecting subsequent motion and air resistances, its velocity v varies with the height h above the ground as[JEE'2000 (Scr)](A) (B) (C) (D) Q.22A particle starts from rest. Its acceleration a) versus time (t) is as shown in the figure. The maximum speed of the particle will be [JEE' 2004 (Scr)](A) 110 m/s (B) 55 m/s (C) 550 m/s (D) 660 m/sBCOA45o45oQ.23 Find the resultant of three vectors and shown in the following figure. Radius of the circle is R.(a)2R(b) (c) (d) 24 If the angle between and is(a)60°(b)0°(c)120°(d)90° 25 At what angle must the two forces (x + y) and (x – y) act so that the resultant may be (a)(b)(c)(d) 26 . Let the angle between two nonzero vectors and be 120° and resultant be (a) must be equal to (b) must be less than (c) must be greater than (d) may be equal to 27. Fig. shows ABCDEF as a regular hexagon. What is the value of 150oPQR12(a) (c)(b) (d)P, Q and Q.28 There are three coplanar forces acting at a point and are in equilibrium. Given P = 1.9318 kg wt, 0.9659, the value of R is ( in kg wt)[CET 1998](a)0.9659OFAEDCB(b)2(c)1(d) Q.29 A man can swim with velocity v relative to water. He has to cross a river of width d flowing with a velocity u (u > v). The distance through which he is carried down stream by the river is x. Which of the following statement is correct (a)If he crosses the river in minimum time (b)x can not be less than (c)For x to be minimum he has to swim in a direction making an angle of with the direction of the flow of water(d)x will be max. if he swims in a direction making an angle of with direction of the flow of waterQ.30 . A stone tied to a string of length L is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of the change in its velocity as it reaches a position where the string is horizontal is [IIT-JEE 1998; CBSE PMT 2004](a)(b)(c)(d) SECTION-B | IIT-JEE (Maths)DifferentiationA function f is differentiable in the interval 0 ≤ x ≤ 5 such that f(0) = 4 and f(5)=-1. if , then there exists some ‘c’ in 0 < c < 5 such that equals :(a) (b) (c) (d) NoneAll the points on the curve at which the tangent is parallel to the x-axis lie on the curve.(a) y2 = 4ax(b) y2 = 4a2 sin (c) x2 = 4ay(d) x2 + y2 = a2The set onto which the derivative of the function f(x) = x (log x – 1) maps the ray [1, ) is :(a) [0, )(b) [1, )(c) (0, )(d) None of theseLet (x) = f(x) + f(1 - x) and in 0 ≤ x ≤ 1, then :(a) (x) decreases in (0, 1/2)(b) (x) increases in (0, 1)(c) (x) decreases in (0, 1)(d) None of theseThe value of as n is equal to :(a) 4 e(b) 2 e(c) (d) If f(x) = | x – a| + | x + b|, x R, Rb > a > a. Then :(a) (b) (c) (d) In the interval 0 < x < 2, the function f(x) = | sin 2x | is not differentiable at :(a) (b) (c) (d) For the function f() = 1, which of the following statements are true :(a) f( - 0) = - 1(b) f( + 0) = 1(c) f(x) is continuous at x = (d) f(x) is differentiable at x = .If f(x) = sin x, g(x) = x2 and h(x) = logex if f(x) = h(g(f(x))) then equals :(a) – 2 cosec2x(b) 2 cosec3x(c) 2 cotx2 – 4x2 cosec2 x2(d) Suppose f and g are functions having second derivatives and everywhere, if f(x) . g(x) = 1 for all x and and are never zero then equals :(a) (b) (c) (d) If and then is equal to :(a) (b) (c) (d) Passage – 1The successive derivative of certain functions follow a pattern. We can find the derivative of any order by following this pattern. Methods of induction can also be used in finding nth derivative of functions.The nth derivative of long x must be :(a) (b) (c) (d) The nth derivative of sinx must be :(a) (b) (c) (d) In n leaves remainder 3 when divided by 4 then value of nth derivative of tan-1 x at x = 0 must be :(a) 0(b) n!(c) (n – 1)!(d) – (n – 1)! (0 < x < 1) is(a) 0(b) (c) (d) None of theseif y = sin1 , x > 0, then is equal to(a) 1(b) 0(c) (d) None of theseDerivative of tan w.r.t. is(a) sec2 x(b) sec2 (c) (d) None of theseLet f(x +y) = f(x) + f(y) x, y R. Suppose that f(6) = 5 and f(0) = 1, then f(6) is equal to(a) 1(b) 30(c) 25(d) None of theseIf x sin (a + y) = sin y, then is equal to(a) (b) (c) (d) If y = , then is equal to(a) (b) (c) (d) None of theseIf y2 = ax2 + b, then is equal to(a) (b) (c) (d) None of theseIf x = at2, y = 2 at, then is equal to(a) 0(b) (c) (d) None of theseIf x = f(t) and y = g(t), then is equal to(a) (b) (c) (d) None of theseIf y = a sin mx + b cos mx, then is equal to(a) m2y(b) m2y (c) m(d) None of theseIf then y6 = (a) (b) (c) (d) None of these is equal to(a) (b) (c) (d) None of theseDifferential coefficient of a function f(g(x)) w.r.t. the function g(x) is(a) f (g(x))(b) f(g(x)) g(x)(c) (d) None of these is equal to(a) (b) (c) cosec x(d) None of theseIf y = emx, then yn, n N, is(a) emx(b) mnemx(c) mn emx(d) None of theseIf f(x) = tan1 x and g(x) = tan1 , the(a) f (x) = g(x)(b) Df = Dg(c) f(x) = g(x)(d) None of theseSECTION-C | IIT-JEE (CHEMISTRY)SolutionsWhich of the following is not correct for an ideal solution :(a) Raoult’s law is obeyed for entire concentration range(b) Hmix = 0(c) Vmix = 0(d) Smix = 0What is the normality of 1 M H3PO2 solution :(a) 0.5 N(b) 1.0 N(c) 2.0 N(d) 3.0 N1 mole of heptane (V.P. = 82 mm Hg) was mixed with 4 moles of octane (V.P. = 31 mm Hg). The V.P. of resulting ideal solution is :(a) 46.2 mm Hg(b) 40.0 mm Hg(c) 41.2 mm Hg(d) none of theseThe vapour pressure of a pure liquid A is 70 mm at 27°C. If forms an ideal solution with another liquid B. The mole fraction of B is 0.2 and total pressure of the solution is 84 mm at 27°C. The vapour pressure of pure liquid B at 27°C is :(a) 14(b) 56(c) 70(d) 140A strong electrolyte A gives 3 ions and B is a non-electrolyte. If 0.1 M solution of B produces an osmotic pressure of P, then 0.05 M solution of A will produce an osmotic pressure of :(a) 1.5 P(b) 3.0 P(c) 0.5 P(d) 0.75 PWhich solution will exert highest osmotic pressure :(a) 1 M glucose solution(b) 1 M urea solution(c) 1 M alum solution(d) 1 M NaCl solutionWhich of the following salts will have the same value of the Van’t Hoff factor as that of K4[Fe(CN)6] :(a) Al2(SO4)3(b) NaCl(c) Na2SO4(d) Al(NO3)3When HgI2 is added to the aqueous solution of KI :(a) boiling point does not change(b) freezing point is elevated(c) boiling point is elevated(d) freezing point is loweredThe elevation in boiling point of a solution of 10 g of binary electrolyte (Molar mass 100) in 100 g of water is Tb. The value of Kb for water is :(a) (b) Tb(c) 10 Tb(d) 2TbThe molal freezing point constant for water is 1.86 K kg mol-1. Therefore, the freezing point of 0.1 M NaCl solution in water is expected to be :(a) 0.186°C(b) – 0.186°C(c) – 0.372°C(d) 0.372°CAssuming the salts to be completely ionized in solution, which of the following solution has highest osmotic pressure :(a) 1% CsCl(b) 1% RbCl(c) 1% KCl(d) Same for allMole fraction of glycerol in a solution of 36 g of water and 46 g of glycerol is :(a) 0.46(b) 0.20(c) 0.36(d) 0.401 kg aqueous solution of CaCO3 contains 10 g of CaCO3. Concentration of solution is :(a) 10 ppm(b) 100 ppm(c) 1000 ppm(d) 10000 ppmElevation in boiling point is 0.52°C when 60g of a compound X was dissolved in 100 g of water Molar mass of X is (Kb(water) 0.52°C kg mol-1) :(a) 120(b) 60(c) 600 (d) 180The Van’t Hoff factor for 0.1 M Ba(NO3)2 solution is 2.74. The degree of dissociation is :(a) 91.3%(b) 87%(c) 74%(d) none of theseBenzoic acid undergoes dimerisation in benzene solution. The Van’t Hoff factor (i) is related to the degree of association () of the acid as :(a) i = 1 - (b) i = 1 + (c) (d) Glucose is added to 1 L of water ( = 1 g cm-3) to such an extent that the ratio of becomes 10-3. The mass of glucose added is :(a) 180 g(b) 18 g(c) 1.8 g(d) 0.18 gGlucose solution is 25% by weight of solution, Its percentage concentration by weight of solvent is :(a) 20%(b) 25%(c) 33.3%(d) none of theseAt a given temperature total vapour pressure (in mm) of a mixture of volatile components A and B is given by P = 120 – 75 XB. Hence, vapour pressure of pure A and B respectively (in mm) are :(a) 120, 75(b) 120, 195(c) 120, 45(d) 75, 45In the following equilibrium N2O4(g) 2NO2(g), NO2 is 50% of the total volume. Hence, Van’t Hoff factor (i) is :(a) 1.5(b) 1.25(c) 1.33(d) none of these21. Co-ordination number of Na+ in NaCl is a) 4 b) 3 c) 6 d) 522. Which has no rotation symmetry? a) Hexagonal b) Orthorhombic c) Cubic d) Triclinic23. The hardest substance among the following: a) BeC b) Graphite c) Ti d) SiC24. The number of molecules in a unit cell of fluorite is a) 2 b) 4 c) 6 d) 825. The coordination number of calcium fluoride type structure is a) 8:4 b) 4:8 c) 4:4 d) 8:826. The structure of sodium chloride is a) hexagonal b) octahedral c) rhombohedral d) tetrahedral27. Which of the following will not adopt CsCl structure a) CsBr b) CsCN c) CsC d) CsF28. The arrangement of first two layers, one above the other , in hcp and ccp arrangements is a) exactly same in both cases b) partly same and partly different c) different from each other d) nothing definite29. The number of atoms present in a unit cell of a monoatomic substance of a simple cubic lattice , body – centered cubic respectively a) 8,9, and 14 b) 1,2 and 4 c) 4,5 and 6 d) 2,3 and 530. Antiflourite structure is derived from fluorite structure by a) Heating fluorite crystal lattice b) Subjecting fluorite structure to high pressure c) Inter changing the position of cations and anions in the lattie d) None of these. SECTION-D | PMT (BIOLOGY) Meiosis can be observed inmegasporemicro mother cellmicrosporeanther wall the number of microsporangia present in anther is1234 filiform apparatus is located attip of microsporangiumtip of filamenttip of megasporangiumpericarpSexual reproduction in plants was reported byCamereriusHofmeisterStrasburgerNawaschinTriple fusion means, fusion oftwo polar bodies and male gametestwo eggs with male gametestwo male gametes and one eggtwo male gametes and one egg and secondary nucleusAngiosperms are characterized byfertilisationwithout gametesdouble fertilizationsimple fertilizationparthenocarpyWhich of the following is the reproductive organ of plants?FlowerPistilStamenAntherAssertion - Reason questionsDirection.if both assertion and reason are correct and reason is true explanation of assertion.if both assertion and reason aretrue but reason is not correct explanation of assertionIf assertion is true but reason is falseif assertion is false but reason is true.Two sperms in a pollen tube often change their shape.R. the sperms are released in the synergids as intact cells but only their nuclei migrate.A. a condensed rhizome is corm.R. Zinjiber stem is rrhizome.The volume of semen released per ejaculation is ..... in man2-4 ml2-8 ml1-2 ml6-7 mlThe head of the sperm serves two functionsassembly and activatinggenetic and activatinggenetic and cleavagegenetic and energySpermioteleosis is another name ofmaturation of ovumspermatogenesisspermiogenesisdegeneration of spermsOvary is attached with the back to body wall bymesorchiummesosalpinxmesovariumovarian ligamentMenarche is the stage whenfirst delivery occursfirst menstrual cycle startswhen first ejaculation occursfirst month of menopauseOne oogonium forms1 ovum and 3 polar bodies1 ovum and 1 polar body 1 ovum without centriole and 3 polar bodiessingle ovumSemen consist of an enzymeseminasehyaulonidasevasciulaseligaseThe phase of menstrual cycle when fertilization is possiblefollicularleutealbleeding phasenone of theseParturition is controlled byoxytocinFSHrelaxinOestrogenProbable fertility period of menstrual cycle is from ..... day to ..... day5 - 89 - 1213 - 1617 - 2050 primary spermatocytes give rise to220 spermatocytes50 spermatocytes200 spermatozoa50 spermatozoaDuring a woman's life she produces about 4000 eggs365 - 800 eggs40 eggs400 - 500 eggsThis is a method of birth controlIUDsGIFTHTFIVF-ETAssertion -Reason (For direction refer to those given in Ques. 23)During ovulation the oocyte has released one polar body.R. When oocyte is in fallopian tube it is in second metaphase state.Temporary and 100% effective method to control birth in males istubal ligationvasectomyoral contraceptivesmating rhythm controlSperm maturation in man occurs invasa differentiaepididymisrete testisvasa efferentiaSperm releases lysozyme because itaids to fertilizationdissolves oocyte membraneincrease sperm motilitydelays fertilizationEstrogen level is highest on 14th day12th day21st day5th dayAmphimixis is a) reaction of antifertilizin and fertilizin b) formation of reception cone by ovum c) fusion of male and female pronuclei d) penetration of sperms into ovum