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Practice Question YOUR MATHS SEARCH ENDS HERE Time – 3 hrs

Instructions to take test:

1.Appear test in 1 sitting.

2.Complete test in stipulated time.

3.Do not open any help book

PHYSICS

  1. The switch Sw is shifted from position 1 to position 2 as shown in the figure. Heat generated in the circuit is

(a) independent of V1 but dependent on V2 (b) independent of V2 as well as V1 (c) dependent on V1 but independent of V2 (d) dependent on V2 as well as V1.

  1. Find equivalent capacitance across AB (all capacitances in)

(a) (b) 9 (c) 48(d)none.

  1. A ring of radius m carries a charge of 10C uniformly distributed on it, at a distance ofm from the centre on its axis, the electric field is E. If we take a point charge of magnitude 10C, at what distance from it, the electric field would be E. (a) (b) 23/4 m (c) 25/4 m (d) 27/4 m.
  2. A dipole of dipole moment 10-9 Cm is kept at the origin of coordinates. At which of the following points can the electric field be. (a) (3, 0) (b) (-6, 0) (c) (0, 3) (d) (0, -6)
  3. St1: The potential difference between the plates of a charged parallel plate capacitor can be increased without the help of a battery. St2: The charge on an isolated capacitor is conserved and capacitance can be changed (a) St1: is true, St2: is true and St2: is correct explanation for St1. (b) St1: is true, St2: is true and St2: is NOT correct explanation for St1. (c) St1: is true, St2: is false (d) St1: is false, St2: is true.
  4. A parallel plate capacitor is charged and then disconnected from the source of potential difference. If the plates of the condenser are then moved farther apart by the use of insulated handle, which one of the following is true? (a) The charge on the capacitor increases (b) the charge on the capacitor decreases (c) the capacitance of the capacitor increases (d) the potential difference across the plate increases.
  5. A photographic flash unit consists of a Xenon – field flash energized by the discharge of a capacitor, previously charged by a 1000 V source-. The average power delivered to the tube is 2000 W in a time of 0.04 s. The capacitance of the capacitor can be estimated as (a) 40 ×10-6 F (b) 80 × 10-6F (c) 160 × 10-6 F (d) none.
  6. In the figure shown, the potential difference between point A and B is: (a) 10 V (b) 30 V (c) 7.5 V (d) none.
  1. The electric field near the surface of a charged spherical conductor is 100 V/m. The conductor is at a potential of 100 V. The charge on the conductor is (a) 9C (b) 1.11 × 10-8 C (c) 9 × 10-8C (d) 1.11 ×10-6C.
  2. Figure shows V – T graph of a cyclic process. Which of the following PV graph represents the same process?
  1. A sphere uniformly charged with a charge density p has a radius R. A spherical cavity of radius is made in it such that centre of original sphere lies on its circumference. What is the electric field at point P.

(a) (b) (c) (d).

  1. If one mole of an ideal monoatomic gas (= 5/3) is mixed with one mole of ideal diatomic gas ( = 7/5), the value offor the mixture will be (a) 1.4 (b) 1.5 (c) 1.53 (d) 3.07.
  2. The space between the plates of a parallel plate capacitor is filled with two dielectrics of thickness d1 and d2 and relative permittivitiesandrespectively. If a single dielectric of the total thickness d1 + d2 is to replace the two, effectively to get the same capacitance then its relative permittivity should be (a) (b) (c) (d).
  3. Consider a ring of radius R uniformly charged with charge Q. On the axis of the ring, energy per unit volume due to electric field is. The distance of this point from the centre of the ring is (a) R (b) R (c)R (d)R.
  4. A point charge + Q is positioned at the center of the base of a square pyramid as shown. The flux through one of the four identical faces of the pyramid is (a) (b) (c) (d) none.
  1. 2 charges Q and – Q are kept at a distance 2a from each other. The electric field at their midpoint is E. At what distance from the midpoint on the perpendicular bisector would the electric field reduce to E/2? (a) (b) (c) (d) a.
  2. The potential across a 3F capacitor is 12 V when it is not connected to anything. It is then connected in parallel with an uncharged 6F capacitor. At equilibrium, the charge q on the 3F capacitor and the potential difference V across it are (a) q = 12C, V = 4V (b) q = 24C, V = 8 V (c)q = 36C, V = 12 V (d) q = 12C, V = 6V.
  3. In a Carnot’s cycle, the highest temperature is times the lowest temperature. Also the heat given to the system during the cycle istimes total work done during the cycle. What is the value of? (a) 2 (b) 1.5 (c) 3 (d) 2.4.
  4. 3 parallel infinite sheets carry charge of,2 and - 5per unit area on them. What is the electric field in region I, II, III and IV?
  1. A diatomic ideal gas is heated at constant volume until its pressure is doubled. It is again heated at constant pressure until its volume is doubled. The molar heat capacity for the whole process is kR where k is: (a) 23/5 (b) 19/5 (c) 19/6 (d) 13/4.
  2. Find the electric field due to a circular arc of radius R and charge / lengthat the origin. The arc in xy plane and extends fromto w.r.t. x – axis (a) (b) (c) (d).
  3. A gas contains only rigid diatomic molecules at temperature T. If I is the moment of inertia of the molecule, then mean square angular velocity of the molecule is: (a) (b) (c) (d).
  4. The flux of the electric field out of a sphere of radius R enclosing a point chargeN/m2/C. What is the flux of this electric field through a disc of radius R held perpendicular to the line joining the point charge at a distance of from it? (a) (b) (c) (d) .
  5. The plates of a parallel plate capacitor are charged upto 100 volt. A 2 mm thick plate is inserted between the plates, then to maintain the same potential difference, the distance between the capacitor plates is increased by 1.6 mm. The dielectric constant of the plate is (a) 5 (b) 1.25 (c) 4 (d) 2.5
  6. If the ms velocity of oxygen molecule at certain temperature is 0.5 km/s, the rms velocity for hydrogen molecule at the same temperature will be (a) 2 km/s (b) 4 km/s (c) 9 km/s (d) 16 km/s.
  7. If temperature versus density graph is a rectangular hyperbola, the process is (consider ideal gas) (a) Isobaric (b) Isochoric (c) Adiabatic (d) Isothermal.
  8. A cycle A B C is drawn on PV diagram as shown.

  1. A Carnot’s engine whose sink is at a temperature of 300 K has an efficiency of 40%. By how much should the temperature of the source be increased so as to increase the efficiency to 60%. (a) 250 K (b) 275 K (c) 300 K (d) 325 K.
  2. A vessel contains 64 gm of oxygen and 16 gm of hydrogen at STP. Chemical reaction is induced in the mixture by passing an electric spark till one of the gases is consumed completely. The temperature is restored to original value after reaction. The final pressure in the vessel will be (a) 0.5 atm (b) 0.4 atm (c) 0.33 atm (d) 0.75 atm.
  3. Two concentric conducting spherical shells carry charge Q each. The inner shell is earthed. The charge that flows into the earth is (a) Q (b) (c) (d) .

CHEMISTRY

  1. Molarity if aqueous NaOH solution will be, if mole fraction of NaOH in the solution is 0.5 [Given: density of pure NaOH = 4 gm/ml] (a) 76.92 (b) 35.71 (c) 68.96 (d) 26.46.
  2. 1.5 gm mixture of SiO2 and Fe2O3 on very strong heating leave a residue weighing 1.46 gm. The reaction responsible for loss of weight is Fe2O3(s) →Fe3O4(s) + O2(g) What is the percentage by mass of Fe2O3 in original sample (a) 80% (b) 20% (c) 40% (d) 60%.
  3. St1: Density of air (containing N2 and O2 gas) is greater than that of sample of air (containing N2O2 & SO2 gas) at same T and P. St2: Molecular mass of added gas is greater N2 & O2 both. (a) St1: is true, St2: is true and St2: is correct explanation for St1. (b) St1: is true, St2: is true and St2: is NOT correct explanation for St1. (c) St1: is false, St2: is true (d) St1: is true, St2: is false.
  4. St1: Two vander waal gases have same value of ‘a’ but different value of ‘b’, then the gas having smaller value of ‘b’ is more compressible. St2: b is measure of repulsive forces. (a) St1: is true, St2: is true and St2: is correct explanation for St1. (b) St1: is true, St2: is true and St2: is NOT correct explanation for St1. (c) St1: is false, St2: is true (d) St1: is true, St2: is false.
  5. A flask contains H2 gas & few drop of water at T.K. The pressure inside the flask is 830 mm of Hg. If the temperature of flask reduced by 10% of its initial value at constant volume. The new pressure in the task will be [Vapour pressure of water at these two temperature are 30 & 25 mm of Hg] (a) 747 (b) 745 (c) 720 (d) 737.
  6. Select the correct statement(s): (a)For a real gas compressibility factor Z =, where Vreal may or may not be equal to volume of container in which real gas is present (b) If Boyle’s temperature of a gas is 100 K, then it can be liquefied at 400 K. (c) At Boyle’s temperature for fixed amount of gas if pressure is doubled, the volume become half (Assuming pressure is still low) (d) If 1 mole of an ideal gas occupy 20 litre at 273 k in low pressure region, volume occupied by 1 mole of real gas must be less than 20 litre under similar conditions.
  7. Under identical conditions of temperature and pressure, the mean free path will be maximum for: (a) Gas with larger molecular size (b) Gas with smaller molecular size (c) Gas with greater mean speed (d) Gas present in larger container.
  8. Identify the option representing correct set of true/false statement: St1: TiO3 can behave as conductor or insulator depending upon temperature. St2: CrO2 has electrical properties like metals. St3: AgBr can show both frenkel as well as Schottky defects. (a) All the Statements are correct (b) Only Statement – III is correct (c) Only Statement – I is incorrect (d) Only statement – II is correct.
  9. Which of the statements regarding defects in crystal is not correct? (a) Impurity defects in silicon by doping Arsenic causes electronic defects (b) LiCl crystals appear yellow because of metal excess defects (c) Formation of Wustite is because of metal deficient defect (d) AgBr crystal can show both dislocation defect & Schottky defect.
  10. An element crystallizes in FCC with edge – length equal to 1600 pm. Calculate maximum radius of an atom which can fill the tetrahedral void without distorting the lattice. (a) 45pm (b) 90pm (c) 180pm (d) 90Å.
  11. Which of the following order is correct for the radii of the species? (a) ClΘ > S2- (b) FΘ > (c) (d) Fe+3 > Fe+2.
  12. What is correct name of linkage isomer of [Cr (H2O)5(NO2)]Br2. (a) Pentaaquanitrito – ‘O’ chromium (III) bromide. (b) Pentaaquanitro chromium (iii) bromide (c)Pentaaquonitro chromium (iii) bromide (d) Pentaaquanotrito - ‘O’ chromium (ii)bromide.
  13. Which of the following molecule has 3c – 2eΘbond (a) BeH2 (b) AlCl3 (c) AlBr3 (d) none.
  14. The correct order of Electronegativity is: (a) F > O > N (b) N > O > F (c) O > N > F (d) N = O> F.
  15. For which of the complex, the E.A.N. of the central atom of the complex obeys sidwick E.A.N. rule. (a) [Ti (-C5H5)2 (-C5H5)2] (b) [Fe (NO)2 (CO)2] (c) [Ag (CN)2]- (d) none.
  16. Which of the following is the correct increasing size? (a) Cl- < Ca2+ < S2 < Al3+ (b) Mg2+ < K+ < Li+ < Al3+ (c) Mg2+ < Na+ < F- < O2- <N3- (d) F- < Na+ < Mg2+ < O2-.
  17. The hybridization of central atom of cationic part and anionic part of the solid N2O5molecule are respectively. (a) sp2 and sp3 (b) sp and sp2 (c) sp2 and sp2 (d) sp2 and sp.
  18. St1: The square planar complex, [Mabcd]n+ type shows geometrical isomerism. St2: Restricted rotation around the single bond is present within the above complex. (a) St1: is true, St2: is true and St2: is correct explanation for St1. (b) St1: is true, St2: is true and St2: is NOT the correct explanation for St1. (c) St1: is true, St2: is false. (d) St1: is false, St2: is true
  19. St1: The second ionization energy of N is greater than O. St2: N – atom has half filled p – orbitals. (a) St1: is true, St2: is true and St2: is correct explanation for St1. (b) St1: is true, St2: is true and St2: is NOT the correct explanation for St1. (c) St1: is true, St2: is false. (d) St1: is false, St2: is true
  20. Two Pz orbitals from two atoms can form a - bond when they approach along. (a) x – axis (b) z – axis (c) y – axis (d) none.
  21. IUPAC Name of CH3 – CH2 --CHO is (a) N – ethyl aminoethanal (b) N – formyl aminoethane (c) N – ethyl methanamide (d) ethanaminal.
  22. Correct statement about the compound I, II, III are

(a) I and II are identical (b) I and II are diastereoisomer (c) I and III are enantiomer (d) I and II are enantiomers.

  1. How many stereoisomers are possible for the following

(a) 16 (b) 4 (c) 6 (d) 8.

  1. Monomer used to prepare Orion is (a) CH2 =CHCN (b) CH2 =CH –Cl (c) CH2 =CHF (d)CH2 =CCl2.
  2. How many alkene on catalytic hydrogenation give iso – pentane as a product? (a) 2 (b) 3 (c) 4 (d) 5.
  3. Which of the following will not decolourize bromine water?

Total diols formed after final reaction are (a) 6 (b) 5 (c) 4 (d) 8.

  1. H
  1. End product of the following sequence of reaction is

MATHEMATICS

  1. If the domain for the function f(x)= is, then which of the following best describes all possible values of c? (a) c > 1 (b) c = 1 (c) c < 1 (d) c1.
  2. The value of is equal to (a) -2 (b) 0 (c) 3 (d) does not exist.
  3. The two root r1 and r2 of the equation x2 + px + q = 0 satisfy the linear equations r1 + 2r2 = 2 and 2r1 – 3r2 = 5. The ordered pair (p, q) is (a) (5, -4) (b) (-5, 4) (c) (5, 4) (d) (-5, -4).
  4. Let (x) = x3 – 6x2 + Bx + C has 1 + 5i as a zero and B, C are real numbers, then value of (B + C) is (a) – 70 (b) 70 (c) 24 (d) 138.
  5. Suppose that ‘a’ is a non – zero real number for which sin x + sin y = a and cos x + cos y = 2a. The value of cos (x – y), is (a) (b) (c) (d).
  6. Let f(x) = x|x| - 4x – 1 for all x R, then f(x) is (a) continuous and derivable for all x R. (b) continuous for all x R but non – derivable only at x = 0 (c) neither continuous nor derivable at x = 0 (d) continuous for x R but non – derivable at two points.
  7. If f(x) = is continuous at x = 0, then value of a, b are (a) 2/3, e2/3 (b) 1/3, e1/3 (c) 2/3, 1/3 (d) none.
  8. The value of sin-1 is equal to (a) (b) (c) (d).
  9. The sum equals (a) (b) (c) (d) 1.
  10. Let f be a differentiable function such that, then the value of f’()is (a) (b) (c) (d) .
  11. Given that where m and n are relatively prime natural numbers, then the sum of m and n is equal to (a) 10 (b) 11 (c) 12 (d) 13.
  12. If then the value of cos2 x = where a, b, cN and ‘c’ is prime. The value of (a + b + c) is (a) 7 (b) 8 (c) 9 (d) 10.
  13. Let If f(x) is continuous at x =, then the value of k is (a) (b) (c) (d).
  14. is equal to (a) (b) (c) (d) .
  15. If, then a (a) (b) (c) (0, 1) (d) {0, 1}.
  16. Let h(x) = which one of the following describes the choice for the real number a so that h(x) exists? (a) a must be equal to 8 for the limit to exist. (b) There is no choice for a that will make the limit exist. (c) a must be positive real number for the limit to exist (d) a can be any real number for the limit to exist.
  17. The midpoint of the interval in which x2 – 2 is satisfied, is (a) (b) -2 (c) (d) .
  18. Let f(x) =. If f(x) is continuous for all x R, then number of integers in the range ofis (a) 0 (b) 4 (c) 5 (d) 6.
  19. The value ofcan be written as, where m and n are relatively prime positive integers. Then the value of (m + n) is (a) 28 (b) 47 (c) 66 (d) 85.
  20. Number of values of x [0,] where f(x) = [4 sin x – 7] is non – derivable is (a) 7 (b) 8 (c) 9 (d) 10.
  21. If ln(x + y) = 2xy, then y’(0) = (a) 1 (b) -1 (c) 2 (d) 0.
  22. Let f(x) =, then f(x) is equal to (a) 1 (b) 2 (c) 3 (d) non – existent.
  23. Let P(x) = x10 + a2x8 + x3x6 + a4x4 + a2x2 be a polynomial with real coefficient. If P(1) = 1 and P(2) = -5, the minimum number of distinct real zeroes of P(x) is (a) 5 (b) 6 (c) 7 (d) 8.
  24. The value of expression equals (a) (b) (c) (d) 1.
  25. If y = y(x) and it follows the relation x cos y + y cos x =, then y”(0) (a) 1 (b) -1 (c) (d) -.
  26. If x3 + mx2 + 2mx + 3 = 0 and x2 + 3x + 2 = 0 has a root in common then, m is equal to (a) 2 (b) 1 (c) 0 (d) -1.
  27. Which one of the following function is non – differentiable for atleast one real value of x? (a) (b) g(x) = cos |x| + sgn + sgn (-x) (c) h(x) = (d) k(x) = sgn (x2 + 3x + 4).
  28. The equation x2 + bx + c = 0 has distinct roots. If 2 is subtracted from each root, the results are reciprocals of the original roots. The value of (b2 + c2 + bc) equals (a) 7 (b) 9 (c) 10 (d) 11.
  29. He value of is equal to (a) 1 (b) 2 (c) 0 (d) -2.
  30. Let f(x) = Number of points where f(x) is discontinuous in is (a) 3 (b) 4 (c) 5 (d) 6.

Answer

1.a 2.b 3.c 4.a 5.a 6.d 7.c 8.a 9.b 10.c 11.d 12.b 13.d 14.b 15.c 16.b 17.a 18.a 19.d 20.c 21.b 22.d 23.a 24.a 25.a 26.a 27.d 28.a 29.b 30.b 31.b 32.a 33.c 34.a 35.b 36.c 37.b 38.a 39.b 40.b 41.b 42.a 43.d 44.a 45.b 46.c 47,b 48.c 49.d 50.b 51.c 52.d 53.a 54.c 55.a 56.b 57.d 58.a 59.c 60.a 61.a 62.c 63.b 64.a 65.d 66.a 67.a 68.a 69.c 70.c 71.c 72.b 73.d 74.c 75.c 76.d 77.a 78.b 79.b 80.a 81.a 82.a 83.a 84.a 85.c 86.a 87.c 88.a 89.c 90.b