20mpc-a(31.12.12).pmd

PART A–MATHEMATICS
The product of n positive numbers is unity. Then 0 ≤ x ≤ 2π , then the number of values of x is If the straight line x–2y+1=0 intersects the circle Let P (x)=1+2x+3x2+.(n+1)xn be a polyno-
x2+y2=25 in points P and Q, then the coordinates
mial such that n is even. Then the number of real of the point of intersection of tangents drawn at P and Q to the circle x2+y2=25 are
The locus of the middle points of parallel chords of a parabola y2=4ax is a straight line
(3) parallel to a bisector of the angles between All the possible four digit numbers are formed using (4) perpendicular to a bisector of the angles be- the digits 0, 1, 2, 3 so that no number has repeated digits. The number of even numbers among them is A tea party is arranged for 16 persons along two sides of a large table with 8 chairs on each side.
Four men want to sit on one particular side and two on other side. The number of ways in which they 37n+2+16n+1+30n is divided by 7 is
Space for rough work
Complete solution ste of tan2(sin–1x)>1 is
17. The most general values of θ satisfying the equa- 12. The number of diagonals in a octagon are (2) n π +(–1)n 6
13. A straight line passes through the intersection point of the lines x+2y=1 and y=2. The locus of the foot of the perpendicular on it drawn from origin is 18. Sum of the last 30 coefficients in the expansion of (1) x2+y2+3x–2y=0 (2) x2 – y2+3x–2y=0 (1+x)59, when expanded in ascending powers of x, is (3) x2+y2 –3x+5y=0 (4) x2 – y2 –3x+5y=0 19. The probability that in a random arrangement of the letters of the word ‘FAVOURABLE’, the two ‘A’ do latus-rectum is one-fourth of minor-axis is 15. The product of the lengths of the perpendiculars drawn from foci on any tangent to the hyperbola Space for rough work
If in a frequency distribution, the mean and median Directions : Question number 26 and 27 are Assertion-
are 21 and 22 respectively, then its mode is approxi- 22. Let P={(x, y) : x2+y2=1, x, y∈R}, then P is 23. If H , H , H , ., H be 20 harmonic means be- (1) Statement-A is true, statement-B is true and correct explanation for statement-A.
(2) Statement-A is true, statement-B is true but not the correct explanation for statement-A.
(3) Statement-A is true, statement-B is false.
24. If A(cosa, sina), B(sina, –cosa), C(1, 2) are the ver- tices of a ∆ ABC, then as a varies the locus of its 3 , then x2–5x+6>0.
If α < x < β , ax2+bx+c=0 and a have opposite
(1) Statement-A is true, statement-B is true and correct explanation for statement-A.
(2) Statement-A is true, statement-B is true but not the correct explanation for statement-A.
(3) Statement-A is true, statement-B is false.
Space for rough work
Directions : Question no. 28 to 30 are based on the fol-
PART B–PHYSICS
A boat having a speed of 5 km/hr. in still water, If a, b, c are complex number which can be represent in crosses a river of width 1 km along the shortest the form x+0i and z be a complex number which can be possible path in 15 minutes. The speed of the river represent in the form of x+iy such that a2+b2+c2=1,
32. An ideal gas can be expanded from an initial state to a certain volume through two different processes , (1) PV2 = K and (2) P = KV2 , where K is a positive constant. Then, choose the (1) Final temperature in (1) will be greater than in (2) (2) Final temperature in (2) will be greater than in (1) (3) Final temperature of the gases in both the pro- (4) Total heat given to the gas in (1) is greater are superposed. The two waves will produce : (1) constructive interference at (x – x )=2 λ (2) constructive interference at (x –x )= 23 (3) destructive interference at (x –x )=1.5 λ (4) destructive interference at (x –x )= 11 Space for rough work
34. A mass m is suspended separately from two springs 37. A satellite of mass 5M orbits the earth in a of different force constants. Their time periods are circular orbit. At one point in its orbit, the satellite found to be T and 2T respectively. If the same mass explodes into two pieces, one of mass M and the is suspended from the two springs connected in other of mass 4M. After the explosion the mass series, then the time period of the combination M ends up travelling in the same circular orbit, but in opposite direction. Then, motion of the mass 35. If the displacement of a body is given to be proportional to the cube of time elapsed, then the magnitude of the acceleration of the body is (4) will not be possible to decide due to insuffi- 38. A uniform rod of mass m is hinged at a point L/4 from one end of the rod and is at rest. An impulse I is imparted on the other end of the rod perpendicular to it. The angular speed of the rod just after the application of the impulse is The graph shown gives the temperature along x axis that extends directly through a wall 39. Two identical stars, each of mass M revolve around consisting of three layers A, B and C. The air temperature on one side of the wall is 150°C and isolated and distance between stars is L. The on the other side is 80°C. Thermal conduction amount of work that is required to dismantle the through the wall is steady. Then the thermal Space for rough work
43. A water tank resting on the floor has two small holes vertically one above the other. The holes are h and h distance above the floor. How high does water stand in the tank if the jets from the holes hit Suppose 0.5 mole of an ideal gas undergoes an isothermal expansion when energy is added to it as heat Q. Graph shows the final volume Vf 44. Vertical ranges of two projectiles fired with same 41. On an X temperature scale, water freezes at – speed with complementary angles with horizontal are 40 m and 90 m. Their horizontal range is temperature scale, water freezes at – 70.0° Y and boils at – 30.0° Y. The value of temperature on X-scale equal to the temperature of 50.0° Y 45. The density of steel at 0 °C is 8.0 g/cc. At what Co-efficient of linear thermal expansion of steel is 10–5 / °C .
42. A composite string is made up by joining two strings of different masses per unit length → µ and 4 µ. A transverse wave pulseY=A sin (5 t+40 x) , where 46. A pipe open at the top end is held vertically with 't' is in seconds and 'x' is in metres, is sent along some of its lower portion dipped in water. At a the lighter string towards the joint which is at x = certain depth of immersion, the air column in the 0. The equation of the wave pulse reflected from pipe resonates with a tuning fork of frequency 680 Hz. The speed of sound in air is 340 m/s. The pipe is now raised up by a distance 'x' until it resonates in the "next overtone" with the same Space for rough work
47. Length of a rod is measured with a scale and the A block of mass 2kg is lying on a floor. The coeffi- cient of static friction is 0.54. The value of fric- tional force, if applied horizontal force is 2.8 N, is If the mean absolute error is used to build the confidence interval, then the length of the rod, with due regard to significant figures will be Two pendulums have time-period T and 5T/4. They start S.H.M. at the same time from the mean position. What will be the phase difference between them after the bigger pendulum has completed one oscillation 48. The correct statement out of the following is (1) A particle may have angular momentum even though the particle is not moving in a circle A solid rubber ball is carried from the surface to (2) Zero net torque on a body means absence of the bottom of a 200 meter deep pond as a result (3) If the net force acting on a system is zero then of which its volume decreases by 0.1%. The density of pond water is 1.0×103 kg/m3. Then the bulk (4) If the net force acting on a system is zero then (1) 103 N/m2
(2) 2×102 N/m2
(3) 109 N/m2
(4) 2×109 N/m2
Water rises in a capillary upto a height of 4 cm.
If it is titled to 30° from the vertical, then the length Assume friction to be
completely absent
The water proofing agent makes the angle of Inside a hollow sphere of mass M and radius R, a rod of length R 2 and mass M is released from displacement of spheres with respect to earth in the time in which the rod becomes horizontal is One end of a horizontal pipe is closed with the help of a valve and the reading of a barometer attached to the pipe is 3 × 105 pascal. When the valve in the pipe is opened then the reading of barometer falls to 105 pascal. The velocity of water flowingthrough the pipe will be in m/s(1) 0.2 Space for rough work
Directions : Question number 56 and 57 are Assertion-
Directions : Question no. 58 to 60 are based on the fol-
If a ball is rolling on a surface without slipping, no In the case of rolling without slipping point of con- tacts are at rest relative to each other.
(1) Statement-A is true, statement-B is true and correct explanation for statement-A.
A mass of 8 kg is placed on a fixed inclined plane as shown.
(2) Statement-A is true, statement-B is true but A force F is applied at an angle θ=60° with horizontal.
not the correct explanation for statement-A.
58. What should be the value of F so that the mass 8kg (3) Statement-A is true, statement-B is false.
placed on fixed inclined plane as shown does not When a large soap bubble and a small soap bubble are connected by a capillary tube, the large bubble expands and while the small bubble shrinks.
59. What is the normal reaction on the body in the above The excess pressure inside a bubble is inversely pro- (1) Statement-A is true, statement-B is true and correct explanation for statement-A.
(2) Statement-A is true, statement-B is true but not the correct explanation for statement-A.
(3) Statement-A is true, statement-B is false.
60. If the force F calculated in the question number 58 is applied such that it becomes parallel to the in- (2) accelerate upward along inclined plane (4) have non-uniform acceleration along the in- Space for rough work
PART C–CHEMISTRY
65. What is correct regarding electronaffinity? The number of occupied orbitals with magnetic quan- (1) it is zero for all alkali metals & Noble gases tum number m=0 in electronic configuration (2) it regularly decreases from top to bottom in a (3) it regularly increases from left to right in a 62. The energy of an electron in the Bohr’s first orbit of (4) electronaffinity of nitrogen is less than that of H–atom is –13.6 eV. The possible energy value (s) of the excited state (s) for electrons in Bohr’s orbit 66. 2.4 g of pure Mg (at. mass=24) is dropped in 100 mL of 1M HCl. Which of the following statements (1) 1.12 L of hydrogen is produced at S.T.P.
63. The ionization potential of hydrogen is 13.6 eV/atom.
The energy required to produce H+ ions from 250
(3) 0.05 mol of Mg ions are formed in solution 67. 4.0 g of argon (at. mass=40) in a bulb at a tem- perature of T K had a pressure P atm. When the 64. What inference can be made from following graph? bulb was placed in hotter bath at a temperature 50° more then the first one, 0.8 g of gas had to be removed to get the original pressure. T is equal to(1) 510 K 68. The density of NH OH solution is 0.6 g/mL. It sation po
contains 34% by weight of NH OH. Calculate the Atomic number
(3) Element B has stable configuration as compared Space for rough work
and ∆S are –283 kJ and –87 J K–1 mol–1 respec-
tively. It was intended to carry out this reaction at 1000, 1500, 3000 and 3500 K. At which of these temperatures would this reaction be thermodynami- Kinetic energy
Which of the following statements is correct? (1) Most probable velocity at T K is greater than (2) Fraction of molecules having most probable HNO + I → HIO + NO + H O; stoichiometric number of moles of HNO and I reacting will (3) Area under the curve T K is different from area (1) Ordinary water is electrolysed more rapidily 75. For which of the following reaction is ∆S° < 0 ? (2) D O freezes at lower temperature than H O (3) Reaction betwen H and Cl is much faster than (4) Bond dissociation energy for D is greater than 76. When KMnO acts as an oxidant and ultimately forms [MnO ]2–, MnO , Mn O , and Mn2+, then number of Which of the following species is linear? electrons transferred in each case respectively is 77. The values of the standard reduction potentials of 72. One mole of a non-ideal gas undergoes a change of state (2 atm, 3 L, 95 K) → (4 atm, 5 L, 245 K) with a change in internal energy ∆U=30.0 L atm. The change in enthalpy in the process in L atm is Which one of the following is most easily reduced (4) not defined because pressure is not constant Space for rough work
78. Which of the following statements regarding 82. If 50 ml of 0.2 M KOH is added to 40 ml of 0.5 M HCOOH, the pH of the resulting solution is (K = 1.8 x 10–4)
83. When equal volumes of following solutions are mixed, 79. Which of the following methods give alkene having precipitation of AgCl (K = 4 × 10–10) will occur (1) 10–4 M Ag+ & 10–4 M Cl–
(2) 10–5 M Ag+ & 10–5 M Cl–
(3) 10–6 M Ag+ & 10–6 M Cl–
(4) 10–9 M Ag+ & 10–9 M Cl–
–CH –
(D+ is catalyst), compound A is
(4) Heat of hydrogenation will be same in (1) & (2) 80. 1.1 mole of A are mixed with 2.2 mole of B and the C=CH–C
mixture is then kept in one litre flask till the equilib- (2) CH – –
rium, 0.2 mole of C are formed. The equilibrium – –OC H
– –OC H
85. Which of the following can not exhibit geometrical The equilibrium constant (K ) for the decomposition α3/2p1/2
Space for rough work
Directions : Question number 86 and 87 are Assertion-
Directions : Question no. 88 to 90 are based on the fol-
Wurtz reaction involves the condensation fo two molecules of alkyl halides in the presence of sodium and dry ether In this reaction small amount of alkene is also formed as Isomers differ in the position of carbonyl group.
(1) Statement-A is true, statement-B is true and CH —CH —CH —CH +CH =CH +(CH —CH )by prod- correct explanation for statement-A.
(2) Statement-A is true, statement-B is true but Tertiary alkyl halides do not give Wurtz reaction. Frankland not the correct explanation for statement-A.
reaction is similar but has certain advantages over Wurtz (3) Statement-A is true, statement-B is false.
reaction. It is useful in the synthesis of symmetrical al- kanes. Frankland reaction is shown by primary, secondary During conversion of a metal oxide into metal through reduction, number of gram equivalent of 88. Which of the following alkanes is not obtained from The mass of metal oxide is equal to mass of the 89. Which among the following compounds will give (1) Statement-A is true, statement-B is true and correct explanation for statement-A.
(2) Statement-A is true, statement-B is true but 90. A mixture of ethyl iodide and methyl iodide is sub- not the correct explanation for statement-A.
jected to the Wurtz reaction. Products formed are (3) Statement-A is true, statement-B is false.
Space for rough work
31-12-12
S.C.O. 343-345, Top Floor, Sector 34-A, Chandigarh. Ph : 2624337, 2623155
XII Cum competition course for IIT-JEE/AIEEE-2013
Test - 20 (Level-I)
31-12-12
S.C.O. 343-345, Top Floor, Sector 34-A, Chandigarh. Ph : 2624337, 2623155
XII Cum competition course for IIT-JEE/AIEEE-2013
Test - 20 (Level-I)
Time : 3 hrs.
Max. Marks : 360
Complete Syllabus of XI
INSTRUCTIONS
1. The question booklet contains 90 questions.
There are three parts in the question paper
Part A—Mathematics (120 marks) — 30 Questions Part B—Physics (120 marks) — 30 Questions Part C—Chemistry (120 marks) — 30 Questions 2. For each correct answer, four marks will be awarded and for each wrong answer one
3. Use blue/black ball point pen only for writing particulars/marking responses on Side-1 and Side-2 of the answer sheet. Use of pencil is strictly prohibited 4. Do not use white-fluid or any other rubbing material on answer sheet.
5. Rough work should be done only on the space provided for this purpose in the 6. Before handing over the answer sheet to the invigilator, candidate should check his/ M.L. Syal
Principal

Source: http://www.helixinstitute.in/20MPCA.pdf