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IPU Sample Papers

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Re: IPU Sample Papers
Guru Gobind Singh Indraprastha University is a public, professional university located in Delhi, India.It is affiliated to UGC.
List of few questions of IP University Engineering test is given below 1. Following two wave trains are approaching each other. y1 = a sin 200 π t y2 = a sin 208 π t The number of beats heard per second is : A. 8 B. 4 C. 1 D. 0 2. One of the geostationary satellites of India is vertically above A. New Delhi B. Mumbai C. Allahabad D. None of these 3. Light of wavelength 2400 x 1010 m in air will become light of wavelength in glass (µ = 1.5) equal to A. 1600 x 1010 m B. 7200 x 1010 m C. 1080 x 1010 m D. none of these 4. The ratio of secondary to primary turns is 4:5. If power input is P, what will be the ratio of power output (neglect all losses) to power input ? A. 4:9 B. 9:4 C. 5:4 D. 1:1 5. Lenz's law applies to A. electrostatics B. lenses C. electromagnetic induction D. cinema slides 6. If a proton and antiproton come close to each other and annihilate, how much energy will be released ? A. 1.5 x 1010 J B. 3 x 1010 J C. 4.5 x 1010 J D. none of these 7. If Sn is doped with As, what will be the result ? A. ntype semiconductor B. ptype semiconductor C. intrinsic semiconductor D. none of these 8. A charge is placed at the centre of a cube, what is the electric flux passing through one of its faces? A. (1/6) x (q/ε0) B. q/ε0 C. 6q/ε0 D. None of these 9. What is the degree of freedom in case of a mono atomic gas ? A. 1 B. 3 C. 5 D. None of these 10. The ratio of secondary to primary turns is 4:5. If power input is P, what will be the ratio of power output (neglect all losses) to power input ? A. B. C. D. 11. Speed of recession of galaxy is proportional to its distance A. directly B. inversely C. exponentially D. none of these 12. If a substance goes in a magnetic field and is pushed out of it, what is it ? A. Paramagnetic B. Ferromagnetic C. Diamagnetic D. Antiferromagnetic 13. Which is not a scalar quantity? A. Work B. Power C. Torque D. Gravitational Constant 14. Minimum energy required to excite an electron in a Hydrogen atom in ground state is : A. 13.6 eV B. 13.6 eV C. 10.2 eV D. 3.4 eV 15. If Gravitational Constant is decreasing in time, what will remain unchanged in case of a satellite orbiting around earth ? A. Time period B. Orbiting radius C. Tangential velocity D. Angular velocity 16. If a transparent medium of refractive index µ = 1.5 and thickness t = 2.5 x 105 m is inserted in front of one of the slits of Young's Double Slit experiment, how much will be the shift in the interference pattern ? The distance between the slits is 5.0 x 103 cm and that between slits and screen is 100 cm. A. 5 cm B. 2.5 cm C. 0.25 cm D. 0.1 cm 17. How does light propagate in optical fibres? A. Total internal reflection B. Refraction C. Reflection D. None of these 18. Dispersion of light is due to A. wavelength B. intensity of light C. density of medium D. none of these 19. Which of the following conclusions is correct regarding a stationary body? A. No force is acting on the body B. Vector sum of forces acing on the body is zero C. The body is in vacuum D. The forces acting on the body do not constitute a couple 20. Energy released in stars is due to A. Fission B. Fusion C. Combustion D. Chemical reaction 21. 13 days is the halflife period of a sample. After how many days, the sample will become 1/16th of the original substance ? A. 52 B. 3.8 C. 3 D. none of these 22. Absolute zero is the temperature at which A. water solidifies B. all gases become liquid C. motion of molecules becomes minimum D. everything solidifies 23. Motion of liquid in a tube is described by A. Bernaulli's Theorem B. Poiseuille Equation C. Stoke's Law D. Archimedes' Principle 24. Molecular motion shows itself as A. Temperature B. Internal Energy C. Friction D. Viscosity 25. Which is this gate ? A. AND B. NAND C. OR D. NOR 26. Energy bands in solids are a consequence of A. Ohm's Law B. Pauli's Exclusion Principle C. Bohr's Theory D. Heissenberg's Uncertainty Principle 27. A boy of mass M stands on the floor of an elevator moving downwards with an acceleration a which is less than g. The force exerted by the boy on the floor of the elevator is A. Mg x Ma B. g + a C. Mg – Ma D. Mg + Ma 28. A body A of mass m1 exerts a force on another body B of mass m2. If the acceleration of B be a2, then the acceleration (in magnitude ) of A is A. m2/m1 (a2) B. m1m2 a2 C. m1/m2 (a2) D. (m1 + m2) a2 29. What does not change when sound enters from one medium to another ? A. Wavelength B. Speed C. Frequency D. none of these 30. Resolving power of a microscope depends upon A. wavelength of light used, directly B. wavelength of light used, inversely C. frequency of light used D. focal length of objective 31. An astronaut of weight Mg is in a rocket accelerating upward with an acceleration of 4g. The apparent weight of the astronaut will be A. 5Kg B. 4Kg C. Mg D. zero 32. One proton beam enters a magnetic field of 104 m/s normally, sp. charge = 1011 C/kg, velocity = 109 m/s. What is the radius of the circle describe by it ? A. 0.1 m B. 100 m C. 10 m D. none of these 33. If a black body radiates 20 calories per second at 227°C, it will radiate at 727°C A. 10 calories per second B. 80 calories per second C. 320 calories per second D. none of these 34. If a carnot engine is working with source temperature equal to 227°C and its sink temperature is at 27°C, its efficiency will be A. 20% B. 10% C. 67% D. 50% 35. If the frequency of an oscillating particle is n, then the frequency of oscillation of its potential energy is A. n B. 2n C. n/2 D. 4n 36. If an electron oscillates at a frequency of 1 GHz, it gives : A. Xrays B. Microwaves C. Infrared rays D. None of these 37. Earth's atmosphere is richest in A. Ultraviolet rays B. Infrared rays C. Xrays D. Microwaves 38. Cathode rays consist of A. Photons B. Electrons C. Protons D. α particles 39. A body of mass m1 is moving with a velocity V. It collides with another stationary body of mass m2. They get embedded. At the point of collision, the velocity of the system A. increases B. decreases but does not become zero C. remains same D. becomes zero 40. One projectile moving with velocity V in space, gets burst into 2 parts of masses in the ratio 1:2. The smaller part becomes stationary. What is the velocity of the other part ? A. 4V B. V C. 4V/3 D. 2V/3 41. A thief steals a box of weight W & jumps from the third floor of a building. During jump, he experiences a weight of A. W B. 3W C. 1.5W D. zero 42. Two electron beams are moving parallel in space but in opposite directions; then A. they will attract each other B. they will repel each other C. no interaction will take place D. none of these 43. Two wires with resistances R and 3R are connected in parallel, the ratio of heat generated in 2R and R is A. 1 : 3 B. 2 : 1 C. 1 : 4 D. 4 : 1 44. A wire is drawn such that its radius changes from r to 2r, the new resistance is A. 2 times B. 4 times C. 8 times D. 1/16 times 45. In solids, interatomic forces are A. totally repulsive B. totally attractive C. combination of (a) and (b) D. none of these 46. When horse starts running all of a sudden, the rider on the horse back falls backward because A. he is taken aback B. he is afraid C. due to inertia of rest, the upper part of his body remains at rest D. due to inertia of motion, the lower part of his body comes in motion 47. What should be the minimum velocity at the highest point of a body tied to a string, so that the string just does not slack ? A. √ (Rg) B. √ (5Rg) C. (R/g)3/2 D. √ (2Rg) 48. If a person standing on a rotating disc stretches out his hands, the speed will: A. increase B. decrease C. remain same D. none of these 49. EMF is most closely related to A. mechanical force B. potential difference C. electric field D. magnetic field 50. Planetary system in the solar system describes A. conservation of energy B. conservation of linear momentum C. conservation of angular momentum D. none of these 51. Lenz's law is based upon A. energy B. momentum C. angular momentum D. inertia 52. Faraday's second law states that mass deposited on the electrode is directly proportional to A. atomic mass B. atomic mass x velocity C. atomic mass/valency D. valency 53. Unit of power is A. kilowatt hour B. kilowatt per hour C. kilowatt D. erg 54. Power can be expressed as A. F.v B. 1/2 (Fv2) C. F.t D. F x v 55. Units of coefficient of viscosity are A. Nms1 B. Nm2 s1 C. Nm2 s D. Nms2 56. Dimensions of torque are A. MLT2 B. ML2T2 C. M2L2T2 D. ML2T2 57. A body of weight mg is hanging on a string, which extends its length by l. The work done in extending the string is A. mg l B. mg l/2 C. 2 mg l D. none of these 58. The water droplets in free fall are spherical due to A. gravity B. viscosity C. surface tension D. intermolecular attraction 59. A ball of mass 1Kg is accelerating at a rate of 1ms2. The rate of change of momentum is A. 1 Kg ms2 B. 2 Kg ms2 C. 3 Kg ms2 D. 4 Kg ms2 60. A body orbitting around earth at a mean radius which is two times as great as the parking orbit of a satellite. The period of the body is A. 4 days B. 2√ 2 days C. 16 days D. 64 days 61. Gamma rays are A. high energy electrons B. low energy electrons C. high energy electromagnetic waves D. high energy positrons 62. Which is the most abundant metal in the earth's crust? A. Fe B. Al C. Ca D. Na 63. Which one does not give a precipitate with excess of NaOH? A. ZnSO4 B. FeSO4 C. AgNO3 D. HgCl2 64. What volume of CO2 will be liberated at NTP of 12 gm of carbon is burnt in excess of oxygen? A. 11.2 litres B. 22.4 litres C. 2.24 litres D. 1.12 litres 65. Which base is found only in nucleotides of RNA? A. Adenine B. Uracil C. Guanine D. Cytosine 66. Ascorbic acid is the chemical name of A. Vitamin B6 B. Vitamin A C. Vitamin C D. Vitamin D 67. A hydrocarbon has carbon and hydrogen. Its molecular weight is 28. Its possible formula would be A. C3H6 B. C2H4 C. CH4 D. C4H8 68. The first Noble Prize in chemistry was given to A. Faraday B. Cnrizzaro C. Mendeleevs D. Moseley 69. Four different colloids have the following gold number. Which one has its most effective action? A. 10 B. 30 C. 20 D. 40 70. Which is an example of thermosetting polymer? A. Polythene B. PVC C. Neoprene D. Bakelite 71. The number of unpaired electrons in ferrous ion is A. 3 B. 2 C. 4 D. 5 72. Strongest reducing agent is A. K B. Mg C. Al D. Ba 73. Which of the following is manmade element? A. Ra B. U C. Np D. C – 4 74. Which of the following statements is/are correct? A. Boiling point of alkylhalide is greater than its corresponding alkane B. In water, solubility of CH3OH > C2H5OH > C6H5OH C. Aniline is a weaker base than NH3 D. All of the above 75. Which amine of the following will not answer Carbylamine reaction? A. Ethylamine B. Methylamine C. Dimethylamine D. Phenylamine 76. Tollen's reagent can be used to detect A. (CH3)2 – CHOH B. CH3 – CO.CH3 C. CH3CH2CHO D. CH3OCH3 77. Glycerol on heating with Potassium bisulphate yields A. Acetone B. Glyceraldehyde C. Acrolein D. Propanol 78. Salicylic acid on heating with sodalime gives A. Benzene B. Calcium salicylate C. Benzoic acid D. Phenol 79. Which one of the following will not give iodoform test? A. Ethanol B. Ethanal C. 2propanone D. None of these 80. The rusting of iron is catalysed by A. Fe B. O2 C. Zn D. H+ 81. 100 ml of a liquid A was mixed with 25 ml of a liquid B to give nonideal solution of AB mixture. The volume of this mixture will be A. 75 ml B. 125 ml exact C. fluctuating between 75 ml and 125 ml D. close to 125 ml but not to exceed 125 ml 82. IUPAC name of a compound having the formula (CH3)3 C  CH = CH2 is A. 3, 3  dimethyl  l  butene B. 1, 1  dimethyl  3  butene C. 1,1, 1  dimethyl  2  propene D. 3, 3, 3  dimethyl  1  l propene 83. Which of the following compounds will be optically active? A. (OH3)2 – CHOH B. CH3  CH2  CH2  CH3 C. CH3 – CHCl.COOH D. (CH3)3.C.Cl 84. The major components of brass are A. Zn and Sn B. Cu and Zn C. Fe and Ni D. Zn and Fe 85. Lunar castic is A. Silver Chloride B. Silver Nitrate C. Sodium Hydroxide D. Potassium Nitrate 86. When hot iron is exposed in hot water vapour, the compound formed is A. FeO B. Fe2O4 C. Fe3O4 D. Fe2 (OH)2 87. Which of the following halide is not oxidised by MnO2? A. F B. Cl  C. Br  D. I  88. The outermost electronic configuration of the most electronegative element is A. ns2np3 B. ns2np4 C. ns2np5 D. ns2np6 89. Shape of CO2 is A. tetrahedral B. trigonal C. bent D. linear 90. The catalyst used in the manufacture of H2SO4 by contact process is A. Al2O3 B. Cr2O3 C. V2O5 D. MnO2 91. The composition of the common glass is A. Na2O.CaO.6SiO2 B. Na2O.Al2O3.2SiO2 C. CaO.Al2O3.2SiO2 D. Na2O.CaO.Al2O3.6SiO2 92. In a borax lead test, the brown colour is due to A. Chromium B.Cobalt C. Manganese D. Iron 93. Which of the following is not a fertiliser? A. Urea B. Superphosphate of lime C. Benzene Hexachloride D. Potassium 94. Which one of the following belongs to representative group of elements in the Periodic Table? A. Lanthanum B. Argon C. Chromium D. Aluminium 95. Which one of the following is not an isotope of Hydrogen? A. Tritium B. Deuterium C. Orthohydrogen D. None of the above 96. In the reaction I2 + 2S2O3 2  = 2I  + S4O6 2 , equivalent weight of iodine will be equal to A. its molecular weight B. 1/2 of its molecular weight C. 1/4 the molecular weight D. twice the molecular weight 97. Which of the following is the most powerful oxidising agent? A. F2 B. Cl2 C. Br2 D. I2 98. From the following values of dissociating constants of four acids, which value represents the strongest acid? A. 2 x 10 2 B. 0.02 x 10 1 C. 3 x 10 3 D. 2.0 x 104 99. In which of the following cases, does the reaction go the farthest for completion? A. K = 103 B. K = 10 2 C. K = 10 D. K = 1 100. The reaction which proceeds in the forward direction is A. Fe2O3 + 6HCl → 2FeCl3 + 3H2O B. NH3 + H2O + NaCl → NH4Cl + NaOH C. SnCl4 + Hg2Cl2 → SnCl2+ 2HgCl2 D. 2CuI + I2 + 4K+ → 2Cu2+ + 4KI 101. The substance capable of being drawn into fine wire is called A. malleable B. tensile C. ductile D. mild 102. The idea that most of the mass of an atom is concentrated in a very small core, i.e., nucleus is given by A. Amedo Avogadro B. Rutherford C. Bohr D. Henery Mosley 103. Which of the following does contain a coordinate covalent bond? A. N2H5 + B. BaCl2 C. HCl D. H2O 104. Which of the following contains both covalent and ionic bonds? A. CCl4 B. CaCl2 C. NH4Cl D. H2O 105. Keeping in view the periodic law and the periodic table, suggest which of the following elements should have the maximum electronegative character? A. Oxygen B. Nitrogen C. Fluorine D. Astatine 106. The electronic configuration of element atomic number 37 is A. (2, 8) 3s23p63d104s24p65s1 B. (2, 8) 3s23p63d104s25s64p5 C. (2, 8) 3s23p64s23d95s14p5 D. none of these 107. The pH of 0.1 M solution of a weak acid is 3. What is the value of ionisation constant for the acid? A. 0.1 B. 10 3 C. 10 5 D. 10 7 108. Pure Aniline is a A. brown coloured liquid B. colourless liquid C. brown coloured solid D. colourless solid 109. Sulphide ores are generally concentrated by A. roasting B. froth floatation C. reducing by carbon D. tempering 110. One mole of CO2 contains A. 6.02 x 1023 atoms of C B. 6.02 x 1023 atoms of O C. 18.1 x 1023 molecules of CO2 D. 3 gm atom of CO2 111. The Avogadro Number or a mole represents A. 6.02 x 1023 ions B. 6.02 x 1023 atoms C. 6.02 x 1023 molecules D. 6.02 x 1023 entities 112. What is the weight of one molecule of a monoatomic element X whose atomic weight is 36? A. 6.0 x 10 23 gm B. 6.02 x 1023 gm C. 36 x 1023 gm D. 36 x 10 23 gm 113. When α particles are set through a thin metal foil, most of them go straight through the foil because A. α particles are much heavier than electrons B. α particles are positively charged C. α particles move with high velocity D. α particles move with low velocity 114. The reaction, which proceeds in the forward direction, is A. Fe2O3 + 6HCl → 2FeCl3 + 3H2O B. NH3 + H2O + NaCl → NH4Cl + NaOH C. SnCl4 + Hg2Cl2 → SnCl2 + 2HgCl2 D. 2CuI + I2+ 4K → 2Cu+ + 4KI 115. The first order constant for the decomposition of N2O5 is 6.2 x 10 4 sec –1. The halflife period for this decomposition in second is A. 1117.7 B. 111.7 C. 223.4 D. 160.9 116. When the same amount of zinc is treated separately with excess of H2SO4 and excess of NaOH, the ratio of volumes of H2 evolved is A. 1 : 1 B. 1 : 2 C. 2 : 1 D. 9 : 4 117. Calcium does not combine directly with A. oxygen B. nitrogen C. hydrogen D. carbon 118. Carbon differs from other elements of its subgroup due to A. availability of dorbitals for bonding B. its limitation to a coordination number four C. its tendency to catenate D. its unique ability to form multiple bonds 119. Iodine reacts with cold dil. NaOH to give A. NaI + H2O + O2 B. NaI + NaIO + O2 C. NaI + NaIO + H2O D. NaI + NaIO3 + H2O 120. The number of isomers for the atomic compound of the formula C7H8O is A. 2 B. 3 C. 4 D. 5 121. Which of the following is not true in linear programming problem? A. A column in the simplex table that contains all of the variables in the solution is called pivot or key column. B. A basic solution which is also in the feasible region is called a basic feasible solution. C. A surplus variable is a variable subtracted from the left hand side of a greater than or equal to constraint to convert it into an equality. D. A slack variable is a variable added to the left hand side of a less than or equal to constraint to convert it into an equality. 122. The equation of the circle whose diameter lies on 2x + 3y = 3 and 16x  y = 4 and which passes through (4, 6) is A. x2 + y2 = 40 B. 5(x2 + y2)  4x  8y = 200 C. x2 + y2  4x  8y = 200 D. 5(x2 + y2)  3x  8y = 200 123. Let n(A) = 4 and n(B) = 5. The number of all possible injections from A to B is A. 120 B. 9 C. 24 D. none 124. If aN = {ax : x ∈ N} and bN ∩ cN = dN, where b, c ∈ N are relatively prime, then A. c = bd B. b = cd C. d = bc D. none of the above 125. A square root of 3 + 4i is A. √3 + i B. 2  i C. 2 + i D. none of the above 126. Which of the following is not applicable for a complex number? A. Inequality B. Division C. Subtraction D. Addition 127.  maximum amp (z)  minimum amp (z)  is equal to A. sin 1 (3/5)  cos 1 (3/5) B. π/2 + cos 1 (3/5) C. π  2 cos 1 (3/5) D. cos 1 (3/5) 128. If e, e' be the eccentricities of two conics S and S' and if e2 + e'2 = 3, then both S and S' can be A. hyperbolas B. ellipses C. parabolas D. none of the above 129. A stick of length 'l' rests against the floor and a wall of a room. If the stick begins to slide on the floor, then the locus of its middle point is A. an ellipse B. a parabola C. a circle D. a straight line 130. The eccentricity of the ellipse which meets the straight line x/y + y/2 = 1 on the axis of x and the straight line x/3  y/5 =1 on the axis of y and whose axes lie along the axes of coordinates is A. 2√6/7 B. 3√2/7 C. √6/7 D. none of the above 131. A and B are positive acute angles satisfying the equations 3 cos2 A + 2 cos2 B = 4 and 3 sin A/sin B = 2 cos B/cos A, then A + 2B is equal to A. π/3 B. π/2 C. π/6 D. π/4 132. At a point 15 metres away from the base of a 15 metres high house, the angle of elevation of the top is A. 90o B. 60o C. 30o D. 45o 133. If tan(π cos θ) = cot(π sin θ), 0 < θ < 3π/4, then sin(θ + π/4) equals A. 1/√2 B. 1/2 C. 1/(2√2) D. √2 134. In a triangle ABC, ∠ B = π/3, ∠ B = π/4, and D divides BC internally in the ratio1 : 3. Then (sin ∠ BAD)/(sin ∠ CAD) equals A. √2/3 B. 1/√3 C. 1/√6 D. 1/3 135. The straight line 5x + 4y = 0 passes through the point of intersection of the lines A. x + y  2 = 0, 3x + 4y  7 = 0 B. x  y = 0, x + y = 0 C. x + 2y  10 = 0, 2x + y + 5 = 0 D. none of the above 136. The number of common tangents of the circles x2 + y2  2x  1 = 0 and x2 + y2  2y  7 = 0 is A. 4 B. 1 C. 3 D. 2 137. If the product of the roots of the equation αx2 + 6x + α2 + 1 = 0 is 2, then α equals A. 2 B. 1 C. 2 D. 1 138. If the roots of a1x2 + b1x + c1 = 0 and a2x2 + b2x + c2 = 0 are same, then A. a1/a2 = b1/b2 = c1/c2 B. a1 = b1= c1, a2 = b2 = c2 C. a1 = a2, b1 = b2, c1 = c2 D. c1 = c2 139. The roots of the equation (3  x)4 + (2  x)4 = (5  2x)4 are A. two real and two imaginary B. all imaginary C. all real D. none of the above 140. The value of (1)n is A. 10 B. 0 C. 1 D. 1 141. If the 10th term of a G.P. is 9 and 4th term is 4, then its 7 th term is A. 9/4 B. 4/9 C. 6 D. 36 142. 1  1/2 + 1/3  1/4 + ....... to ∞ equals A. log 2 B. e C. e 1 D. none of the above 143. 9/1! + 19/2! + 35/3! + 57/4! + 85/5! + ....... = A. 16e 5 B. 7e  3 C. 12e  5 D. none of the above 144. How many different arrangements can be made out of the letters in the expansion A2B3C4, when written in full? A. 9!/(2! + 3! + 4!) B. 9!/(2! 3! 4!) C. 2! + 3! + 4! (2! 3! 4!) D. 2! 3!  4! 145. The numbner of straight lines that can be drawn out of 10 points of which 7 are collinear is A. 23 B. 21 C. 25 D. 24 146. 1/n! + 1/[2! (n  2)!] + 1/[4! (n  4)!] + ..... is A. (2n  1)/n! B. 2n/[(n + 1)!] C. 2n/n! D. 2n  2/[(n  1)!] 147. The term independent of x in (x2  1/x)9 is A. 1 B. 49 C. 1 D. none of the above 148. The 9th term of an A.P. is 499 and 499th term is 9. The term which is equal to zero is A. 501th B. 502th C. 500th D. none of the above 149. If A = 3 2 4 4 , B = 2 0 2 1 then (A + B)1 A. is a skew symmetric matrix B. A 1 + B 1 C. does not exist D. none of the above 150. If AB = A and BA = B, then B2 is equal to A. B B. A C. 1 D. 0 151. If the determinant a b 2aα + 3b b c 2bα + 3c 2aα + 3b 2bα + 3c 0 = 0, then A. a, b, c are in H.P. B. α is a root of 4ax2 + 12bx + 9c = 0 or a, b, c are in G.P. C. a, b, c are in G.P. only a, b, c are in A.P. 152. The value of K so that (x  1)/3 = (y  2)/2K = (z  3)/2 and (x  1)/3K = (y  1)/1 = (z  6)/ 5 may be perpendicular is given by A. 7/10 B. 10/7 C. 10 D. 10/7 153. The equation of the plane containing the line r = i + j + λ ( 2i + i + 4k ) is A. r . ( i  2j + k ) = 0 B. r . ( i + 2j  k ) = 0 C. r . ( i + 2j  k ) = 3 D. none of the above 154. The mean of discrete observations y1, y2, ........ yn is given by 155. For a poisson distribution whose mean is λ, the standard deviation will be A. λ2 B. 1/λ C. √λ D. λ 156. If a, b, c, d are constants such that a and c are both negative and r is the correlation coefficient between x and y, then the correlation coefficient between (ax + b) and (cy + d) is equal to A. (a/c)r B. c/a C.  r D. r 157. A person draws a card from a pack of 52 playing cards, replaces it and shuffles the pack. He continues doing this until he draws a spade, the chance that he will fail in the first two draws is A. 1/16 B. 9/16 C. 9/64 D. 1/64 158. In tossing 10 coins, the probability of getting exactly 5 heads is A. 193/256 B. 9/128 C. 1/2 D. 63/256 159. Four tickets marked 00, 01, 10, 11 respectively are placed in a bag. A ticket is drawn at random five times, being replaced each time, the probability that the sum of the numbers on tickets thus drawn is 23, is A. 100/256 B. 231/256 C. 25/256 D. none of the above 160.The value of tan2 x dx is equal to A. π/4 B. 1 + (π/4) C. 1  (π/4) D. none of the above 161. Let f[x + (1/x)] = [x2 + (1/x2)](x ≠ 0), then f(x) is equal to A. x2  1 B. x2  2 C. x2 D. none of the above 162. Let f(x) = [tan(π/4  x)]/cot2x, x ≠ π/4. The value which should be assigned to f at x = π/4, so that it is continous everywhere is A. 1 B. 1/2 C. 2 D. none of the above 163. If f1(x) and f2(x) are defined on domains D1 and D2 respectively, then domain of f1(x) + f2(x) is A. D1 ∩ D2 B. D1 ∪ D2 C. D1  D2 D. D2  D1 164. The derivative of sin x3 with respect to cos x3 is equal to A.  tan x3 B.  cot x3 C. cot x3 D. tan x3 165. If y = f(x) is an odd differentiable function defined on (∞, ∞) such that f'(3) = 2, then f'(3) equals A. 4 B. 2 C. 2 D. 0 166. The line (x/a) + (y/b) = 1 touches the curve y = bex/a at the point A. (a, ba) B. (a, a/b) C. (a, b/a) D. none of the above 167. The least value of 'a' for which the equation (4/sin x) + [1/(1  sin x)] = a has atleast one solution on the interval (0, π/2) is A. 4 B. 1 C. 9 D. 8 168. The area bounded by the curve y2 = 8x and x2 = 8y is A. 32/7 B. 24/5 C. 72/3 D. 64/3 169. The integrating factor of the differential equation [(dy/dx)(x log x)] + y = 2 log x is given by A. log (log x) B. ex C. log x D. x 170. If y = tan 1[(sin x + cos x)/(cos x  sin x)], then dy/dx is equal to A. 1/2 B. 0 C. 1 D. none of the above 171. The length of tangent from (5, 1) to the circle x2 + y2 + 6x  4y  3 = 0 is A. 81 B. 29 C. 7 D. 21 172. The equation of the straight line which is perpendicular to y = x and passes through (3, 2) will be given by A. x  y = 5 B. x + y = 5 C. x + y = 1 D. x  y = 1 173. If the imaginary part of (2z + 1)/(iz + 1) is  2, then the locus of the point representing z in the complex plane is A. a circle B. a straight line C. a parabola D. none of the above 174. The sum of 40 terms of an A.P. whose first term is 2 and common difference 4, will be A. 3200 B. 1600 C. 200 D. 2800 175. If a, b, c are in A.P., then a/bc, 1/c, 2/b are in A. A.P. B. G.P. C. H.P. D. none of the above 176. The term independent of x in [x2 + (1/x2)] is A. 1 B. 1 C. 48 D. none of the above 177. The equation of a line through (2, 3) parallel to yaxis is A. y = 3 B. y = 2 C. x = 2 D. x = 3 178. The value of (ax3 + bx + c) dx depends on A. the value of b B. the value of c C. the value of a D. the value of a and b 179. The range of the function f(x) = (1 + x2)/x2 is equal to A. [0, 1] B. [1, 0] C. (1, ∞) D. [2, ∞] 180. Two vectors are said to be equal if A. their magnitudes are same B. direction is same C. they meet at the same point D. they have magnitude and same sense of direction Contact: Guru Gobind Singh Indraprastha University Sector 16 C, Kakrola, New Delhi, Delhi 110078 011 2530 2170 Map:
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