#1
31st July 2014, 01:15 PM
| |||
| |||
Last year papers of Guru Gobind Singh Indraprastha University Engineering CET
Will you please share with me the last year papers of Guru Gobind Singh Indraprastha University Engineering CET?
|
#2
1st August 2014, 09:07 AM
| |||
| |||
Re: Last year papers of Guru Gobind Singh Indraprastha University Engineering CET
As you want to get the Last year papers of Guru Gobind Singh Indraprastha University Engineering CET so here it is for you: Some content of the file has been given here: 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 geo-stationary satellites of India is vertically above A. New Delhi B. Mumbai C. Allahabad D. None of these 3. Light of wavelength 2400 x 10-10 m in air will become light of wavelength in glass (µ = 1.5) equal to A. 1600 x 10-10 m B. 7200 x 10-10 m C. 1080 x 10-10 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. electro-magnetic induction D. cinema slides 6. If a proton and anti-proton come close to each other and annihilate, how much energy will be released ? A. 1.5 x 10-10 J B. 3 x 10-10 J C. 4.5 x 10-10 J D. none of these 7. If Sn is doped with As, what will be the result ? A. n-type semiconductor B. p-type 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 10-5 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 10-3 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 half-life 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 10-4 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. X-rays B. Micro-waves C. Infra-red rays D. None of these 37. Earth's atmosphere is richest in A. Ultra-violet rays B. Infra-red rays C. X-rays D. Micro-waves 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, inter-atomic 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. Nms-1 B. Nm2 s-1 C. Nm-2 s D. Nms-2 56. Dimensions of torque are A. MLT-2 B. ML2T-2 C. M2L2T-2 D. ML-2T-2 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. inter-molecular attraction 59. A ball of mass 1Kg is accelerating at a rate of 1ms-2. The rate of change of momentum is A. 1 Kg ms-2 B. 2 Kg ms-2 C. 3 Kg ms-2 D. 4 Kg ms-2 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 electro-magnetic 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 man-made 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. 2-propanone 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 non-ideal solution of A-B 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. Ortho-hydrogen 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 co-ordinate 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 half-life 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 sub-group due to A. availability of d-orbitals for bonding B. its limitation to a co-ordination 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 yi fi A. fi yi fi B. n yi C. i yi B. n 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 = be-x/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 |
#3
1st August 2014, 09:07 AM
| |||
| |||
Re: Last year papers of Guru Gobind Singh Indraprastha University Engineering CET
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 y-axis 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 1. If the ground state energy of H-atom is 13.6 eV, the energy required to ionize an H-atom from second excited state is : A. 1.51 eV B. 3.4 eV C. 13.6 eV D. 12.1 eV 2. The binding energy per nucleon is maximum in case of: A. 2He4 B. 26Fe56 C. 56Ba14 D. 92U23 3. The energy of a photon of wavelength λ is : A. hc λ B. hc/λ C. λ /hc D. hλ /c 4. Radio waves of constant amplitude can be generated with : A. rectifier B. filter C. FET D. oscillator 5. Great bear is a A. Star B. Galaxy C. Constellation D. Planet 6. Monoclinic crystal lattice has dimensions A. α = β = γ B. α = β = 90°, γ ≠ 90° C. α ≠ β ≠ γ D. None of these 7. Which of the following relations is correct ? A. E2 = pc2 B. E2 = p2c C. E2 = p2c2 D. E2 = p2/c2 8. During nuclear disintegration, the following is true A. mass in conserved B. energy is conserved C. kinetic Energy is conserved D. momentum is conserved 9. The nucleus forces are A. charge-dependent B. spin-dependent C. charge-symmetric D. long range 10. During radio-active decay, the negative charged particle is emitted because of A. X-rays B. β emissions C. Transmutation of neutron into proton D. None of these 11. Particle in β - decay is A. Neutron B. Proton C. Electron D. Photon 12. Energy in stars is produced by A. fusion B. fission C. radioactive decay D. artificial transmutation 13. Atomic packing fraction in bcc lattice is A. 1/√ π B. √ π C. π /√ 2 D. None of these 14. The count of α - particles decreases from 28,800 to 1,800 in 48 hours, the half-life of this radioactive element will be A. 4 hours B. 8 hours C. 12 hours D. 16 hours 15. Binding energy will be maximum in the case of A. He3 B. He2 C. H2 D. He4 16. Binding energy per nucleon in heavy nuclei is of the order of A. 8 MeV B. 8 eV C. 80 eV D. 80 MeV 17. Complete the series He6 ---> e + Li6 + ? A. nutrino B. anti-nutrino C. proton D. neutron 18. Line spectrum can be obtained from A. Sun B. Candle C. Mercury Vapour Lamp D. Electric Bulb 19. What is radius of 1st Bohr's orbit in a Hydrogen atom ? A. 0.53 x 10-10 cm B. 0.53 x 10-8 cm C. 2.73 x 10-10 cm D. 2.73 x 10-12 cm 20. What is the energy of an electron of Hydrogen in its ground state ? A. -13.6 eV B. 0 C. infinity D. 13.6 eV 21. What is the rest mass of a photon ? A. 0 B. 13.6 eV C. 1 MeV D. 3.1 x 10-27 kg 22. Two lenses of powers 12D and - 2D are placed together, the combined focal length will be A. 1 cm B. 10 cm C. 100 cm D. 1000 cm 23. The critical angle is maximum when light travels from A. water to air B. glass to air C. glass to water D. air to water 24. A rider on a horse back falls forward when the horse suddenly stops. This is due to A. inertia of horse B. inertia of rider C. large weight of the horse D. losing of the balance 25. Fundamental particle in an electro-magnetic wave is A. photon B. electron C. phonon D. proton 26. The wavelength is least in case of A. γ -rays B. X-rays C. infrared D. ultraviolet 27. The speed of electro-magnetic radiation in vacuum is A. µ0 ε0 B. √ (µ0 ε0) C. 1/µ0 ε0 D. 1/√ (µ0 ε0) 28. Power factor in LC oscillations is A. 0 B. 1 C. 1/4 D. 1/√ 2 29. 220 V is changed to 2,200 V through a step-up transformer. Th current in primary is 5 A, what is the current in the secondary ? A. 5 A B. 50 A C. 0.5 A D. 500 A 30. When a bar is placed near a strong magnet, it is repelled, then the material of the bar is A. Dimagnetic B. Ferromagnetic C. Paramagnetic D. Anti-ferrimagnetic 31. Electron enters into a magnetic field at an angle of 60°, its path will be A. straight line B. circle C. parabola D. helix 32. One electron is moving in electric and magnetic fields, it will gain energy from: A. electric field B. magnetic field C. both of these D. none of these 33. Force acting on a conductor of length 5 m carrying current 8 amperes kept perpendicular to the magnetic field of 1.5 tesla is A. 10 N B. 100 N C. 15 N D. 50 N 34. If E = at - bt3 , the neutral temperature is A. -2a/b B. -2b/a C. √ (a/3b) D. -b/2a 35. The charge carriers in an electrolyte are A. negative ions B. positive ions C. both A and B D. none of these 36. When 4 equal resistors are connected in series with a battery and dissipate a power of 10 W, what will be the power dissipated through any of them if it is individually connected across the same battery? A. 40 W B. 10/3 W C.90W D.10W 37. Cell of emf 1 volt is connected across a potentiometer, balancing length is 600 cm. What will be the balancing length for 2.5 volts ? A. 400 cm B. 600 cm C. 1500 cm D. 1200 cm 38. A Wire of resistance R is stretched to twice its original length, what is its new resistance ? A. 4 R B. R/9 C. 3 R D. R/3 39. The charge carriers in super-conductors are A. electrons B. protons C. phonons D. photons 40. 8 drops of mercury are combined to form a bigger single drop. The capacitance of a single big drop and of the single small drop will be in the ratio A. 2 : 1 B. 1 : 8 C. 8 : 1 D. 1 : 2 41. A dipole is placed in a uniform electric field, its potential energy will be minimum when the angle between its axis and field is A. 0 B. π C. π /2 D. 2π 42. Charge of 2 c is placed at the centre of a cube of volume 8 cc, what is electric flux passing through one face ? A. 1/(3ε0) B. (1/2) ε0 C. 2/ε0 D. 3/ε0 43. 1 MeV is A. 1.6 x 10- 19 J B. 1.6 x 10- 13 J C. 1.6 x 10- 16 J D. 1.6 x 10- 9 J 44. Fundamental frequency of a sonometer wire is n, if the tension is made 3 times and length and diameter are also increased 3 times, what is the new frequency ? A. n/3√ 3 B. 3n C. √ 3 n D. 3√ 3 n 45. What is the number of beats heard by the driver of a taxi which is approaching a wall at a speed 30 km/hr and emitting a sound of frequency 300 Hz ? Velocity of sound = 330 m/s. A. 10 B. 15 C. 20 D. 25 46. A person is standing on a railway platform and a train is approaching, what is the maximum wavelength of sound he can hear ? Given wavelength of whistle = 1 m; speed of sound in air = 330 m/s; speed of the train = 36 km/hr. A. 1 m B. 32/33 m C. 33/32 m D. 12/13 m 47. Velocity of sound in open-ended tube is 330 m/s, the frequency of waves is 1.1 kHz and the length of tube = 30 cm, which harmonic will it emit ? A. 2nd B. 3rd C. 4th D. 5th 48. If both sprong constants K1 and K2 are increased to 4K1 and K2 respectively, what will be the new frequency, if f was the original frequency? A. f B. 2f C. (1/2) f D. 4f 49. The radii of two drops are in the ratio 3 : 2, their terminal velocities are A. 9 : 4 B. 2 : 3 C. 3 : 2 D. 2 : 9 50. When a body is raised to a height R (which is the radius of earth), the change in its P.E. will be A. mgR B. 2 mgR C. mgR/2 D. 4 mgR 51. If the length of a simple pendulum is tripled, what will be its new time period? (T = original time period) A. 0.7 T B. 1.7 T C. T/2 D. T 52. A pendulum of length 2m left at P. When it reaches Q, it looses 10% of its total energy due to air resistance. The velocity at Q is A. 6m/s B. 1m/s C. 2m/s D. 8m/s 53. A lift is falling freely under gravity, what is the time period of a pendulum attached to its ceiling ? A. zero B. infinity C. one second D. two second 54. What is the ratio of the moment of inertia of two rings of radius r and nr respectively about an axis perpendicular to their plane and passing through their centres? A. 1 : n2 B. 1 : n C. 1 : 2n D. n2 : 1 55. Beta-particle is emitted from the nucleus of mass number A, with velocity V, what is the recoil speed of the nucleus? A. Me V/(A - Me) B. 4V/(A + 4) C. V D. V/(A - 4) 56. If an alpha particle collides head-on with the nucleus, what is the impact parameter ? A. zero B. infinity C. 10-10m D. 1010m 57. If momentum decreases by 20%, kinetic energy will decrease A. 40% B. 36% C. 18% D. 8% 58. If two balls are projected at angles 60° and 45° and the total heights reached are same, what is the ratio of their initial velocities ? A. √ 3 : √ 2 B. √ 2 : √ 3 C. 3 : 2 D. 2 : 3 59. Which one is a vector quantity ? A. heat B. couple C. energy D. volume 60. Gravel is dropped on to a conveyor belt at a rate of 0.5Kg s-2. The extra force in Newton required to keep the belt moving at 2 ms-2 is A. 1 B. 2 C. 4 D. 5 61. An element with atomic number 20 is A. an alkali metal B. an alkaline earth metal C. a halogen D. a noble gas 62. When supercooled water suddenly freezes, the free energy of the system A. increases B. decreases C. remains same D. becomes zero 63. The density of neon is highest at A. STP B. 0oC, 2 atm C. 273°C, 1 atm D. 273°C, 2 atm 64. Cadmium in a nuclear reactor acts as A. nuclear fuel B. neutron absorber C. a moderator D. neutron liberator to start the chain 65. The end product of 4π series A. 82Pb203 B. 92Pb207 C. 82Pb208 D. 82Bi204 66. Haemoglobin is a co-ordination compound in which the central metal atom is A. iron B. cobalt C. sodium D. manganese 67. The element californium belongs to the family of A. actinide series B. alkaline earth family C. lanthanide series D. alkali metal family 68. The coloured discharge tube for advertisements contain A. argon B. xenon C. helium D. neon 69. Which of the following is the strongest base? A. PH3 B. AsH3 C. NH3 D. SbH3 70. Canizzaro reaction is not given by A. Triethylacetaldehyde B. Acetaldehyde C. Benzaldehyde D. Formaldehyde 71. Which of the following statements is not true for alcohols? A. Lower alcohols have fiery pungent and strong smell B. As molecular mass increases, boiling point also increases C. Lower alcohols are water insoluble and their solubility increases with molecular weight D. Lower alcohols are water insoluble and their solubility decreases with molecular weight 72. Formaldehyde when heated with CH3CH2CH2MgBr gives A. Primary alcohol B. Secondary alcohol C. Tertiary alcohol D. Acetone 73. A compound of molecular formula C3H8O on oxidation gives a compound of formula C3H6O2. The original compound is A. Primary alcohol B. Secondary alcohol C. Aldehyde D. Tertiary alcohol 74. The increasing order of size of F-, Cl - , Br -, I - is A. I - < Br - < Cl - < F - B. I - < Cl - < Br - < F - C. F - < Cl - < Br - < I - D. Br - < Cl - < F - < I - 75. Which of the following series contains only nucleophiles? A. NH3, H2O, AlCl3 B. NH3, ROH, H2O C. H2O, H3O+, SO3 D. None of these 76. The formula of acetonitrite is A. CH3COCH B. CH3CN C. CH3CH2CN D. CH3CONH2 77. The IUPAC name of CH3CONH2 is A. Propionaldehyde B. Acetamide C. Ethanamide D. Ethylamine 78. The rate of reaction increases with temperature because A. threshold energy increases B. kinetic energy of molecules increases C. effective collision increases D. none of the above 79. If the graph of concentration of A versus time for completion of reaction is a straight line, then the order of the reaction is A. zero B. second C. first D. third 80. The decomposition of hydrogen peroxide 2H2O2 → 2H2O + O2 is A. zero order reaction B. first order reaction C. second order reaction D. third order reaction 81. The half-life period of a first order process is 1.6 min -1. It will be 90% complete in A. 0.8 min B. 3.2 min C. 5.3 min D. 1.6 min 82. Which of the following is an electrophile? A. AlCl3 B. CN - C. NH3 D. CH3OH 83. Molarity of a solution is the number of A. moles of solute per litre of solution B. moles of solute per 100 gm of the solution C. gram molecular weight of solute dissolved per litre of the solution D. gram equivalents of solute dissolved per litre of solution 84. The hybridisation in PF3 is A. sp3 B. sp2 C. dsp3 D. d2sp3 85. Which of the following is present in DNA? A. Deoxyribose B. Starch C. Riboflavin D. None of these 86. Propyne when treated with H2SO4 in presence of HgSO4 gives A. Acetone B. Propionaldehyde C. Acetaldehyde D. Propanoic acid 87. The general formula for alkyne is A. CnH2n + 2 B. CnH2n C. CnH2n - 2 D. CnHn 88. Mesotartaric acid is optically inactive due to the presence of A. molecular symmetry B. molecular asymmetry C. external compensation D. two asymmetric carbon atoms 89. Which of the following electronic configuration in the outermost shell is characteristic of alkali metals? A. (n - 1) s2p6ns2s1 B. (n - l) s2p6d10ns1 C. (n - l) s2p6ns1 D. ns2p6d1 90. Lead chloride is soluble in A. cold water B. hot water C. HCl D. acetic acid 91. When a copper wire is placed in a solution of silver nitrate, the solution acquires blue colour. This is due to the formation of A. a soluble complex of copper with AgNO3 B. Cu+ ions C. Cu2+ ions D. Cu2+ by reduction of Cu 92. The pyrites are heated with hydrochloric acid. The solution so obtained will give blood red colour with A. K4Fe(CN)6 B. KCN C. K3Fe(CN)6 D. KSNC 93 The ignition mixture in alumino thermite process contains a mixture of A. magnesium powder and BaO2 B. magnesium powder, aluminium powder and BaO2 C. magnesium and aluminium powders D. magnesium and aluminium oxides 94. One of the most important use of quick lime is A. as a purgative B. drying gases and alcohols C. in bleaching silk D. dyeing cotton 95. In preparing Cl2 from HCl, MnO2 acts as a/an A. dehydrating agent B. reducing agent C. catalytic agent D. oxidising agent 96. Seaweed is an important source of A. chlorine B. iodine C. fluorine D. bromine 97. Nitrates of all metals are A. unstable B. stable C. coloured D. soluble 98. Ostwald’s method is used for manufacture of A. HNO3 B. NO2 C. NO D. P2O5 99. Magnesium reacts with acids producing hydrogen and corresponding magnesium salts. In such reactions, magnesium undergoes A. oxidation B. reduction C. neither oxidation nor reduction D. simple dissolution 100. An acidic buffer solution can be prepared by mixing solution of A. ammonium chloride and HCl B. H2SO4 and Na2SO4 C. acetic acid and sulphuric acid D. ammonium acetate and acetic acid 101. Which of the following is not a Lewis acid? A. BF3 B. AlCl3 C. SnCl4 D. CCl4 102. Equal weights of methane and oxygen are mixed in an empty container at 25°C. The fraction of total pressure exerted by oxygen is A. 1/2 B. 1/3 C. 2/3 D. 1/3 x (273/298) 103. HI was heated in a sealed tube at 440oC till the equilibrium was reached. HI was found to be 22% decomposed. The equilibrium constant for dissociation is A. 0.282 B. 1.99 C. 0.0199 D. 0.0796 104. The molar heat of vaporisation ∆ Hvap for water is 2079 cal mol -1, therefore, molar heat of condensation of water is A. + 2079 cal mol -1 B. - 2079 cal mol -1 C. greater than 2079 cal mol -1 D. smaller than 2079 cal mol -1 105. Which of the following is an insulator? A. Diamond B. Graphite C. Aluminium D. Silicon 106. The purest coal is A. Anthracite B. Bituminous C. Peat D. Lignite 107. Among N 3-, O 2-, F -, and Na+, which one has largest size? A. N 3- B. O 2- C. F - D. Na+ 108. Ni, Pt, Pd belong to which group of the periodic table? A. 12th B. 14th C. 8th D. 10th 109. A mixture of 200 ml of dry hydrogen and oxygen in equal proportion at STP is exploded in an audiometer. What will be the nature of components in the audiometer immediately after the explosion? A. 50 ml of steam only B. 50 ml of steam and 50 ml of hydrogen C. 50 ml of steam and 50 ml of oxygen D. 100 ml of steam and 50 ml of oxygen 110. If 9.8 gm of hexane bums completely in oxygen, how many moles of CO2 is produced? A. 6 B. 0.6 C. 0.9 D. 1.2 111. Which one of the following nitrates does not give NO2 on heating? A. NaNO3 B. Pb(NO3)2 C. AgNO3 D. Cu(NO3)2 112. Which has lowest 1st I.P.? A. N B. Be C. B D. C 113. The oxidation states of phosphorus vary from A. - 3 to + 5 B. - 1 to + 1 C. - 3 to + 3 D. - 5 to + 1 114. The molecular velocity of any gas is A. proportional to the absolute temperature B. proportional to the square of the absolute temperature C. proportional to the square root of the absolute temperature D. independent of the absolute temperature 115. Which of the following is an endothermic reaction? A. 2H2 + O2 → 2H2O B. N2O2 → 2NO C. 2NaOH + H2SO4 → Na2SO4 D. C2H5OH + 3O2 → 2CO2 + +2H2O 3H2O 116. A solution of sodium sulphate in water is electrolysed between inert electrodes. The product at the cathode and anode are respectively A. H2, O2 B. O2, H2 C. H2, Na D. O2, SO2 117. Bauxite mineral containing iron as impurity is purified by A. Baeyer’s process B. Electrolytic process C. Hoope's process D. Serpeck's process 118. Butter of tin is represented by A. SnCl2.3H2O B. SnCl2.5H2O C. SnCl2.6H2O D. SnCl2.8H2O 119. Which group activates the benzene ring towards electrophilic substitution? A. bezo group B. amino group C. acetyl group D. carbyl group 120. Phenol is less acidic than A. ethanol B. propenol C. p-nitrophenol D. none of the above 121. The lines 3x - 4y + 4 = 0 and 6x - 8y - 7 = 0 are tangents of the same circle. The radius of this circle is A. 1/2 B. 1/4 C. 3/4 D. 2 122. The three dice are thrown simultaneously, then the probability of getting a score of 7 is A. 1/6 B. 5/216 C. 1/36 D. none of the above 123. Set A has 3 elements and set B has 4 elements. This number of injections (one to one mapping) that can defined from A to B is A. 24 B. 144 C. 12 D. none of the above 124. If θ is the angle between vectors a and b and | a x b | = | a.b |, then θ is equal to A. 0o B. 180o C. 135o D. 45o 125. The number log20 3 lies in A. (3/4, 4/5) B. (1/3, 1/2) C. (1/2, 3/4) D. (1/4, 1/3) 126. For x1, x2, y1, y2 ∈ R, if 0 < x1 < x2, y1 = y2 and z1 = x1 + i y1, z2 = x2 + i y2 and z3 = 1/2(z1 + z2), then z1, z2, and z3 satisfy A. | z1 | < | z3 | < | z2 | B. | z1 | > | z2 | > | z3 | C. | z1 | < | z2 | < | z3 | D. | z1 | = | z2 | = | z3 | 127. The complex number which satisfies the equation z + √2 | z + 1 | + i = 0 is A. 2 - i B. -2 - i C. 2 + i D. -2 + i 128. The equation of the line with slope -3/2 and which is concurrent with lines 4x + 3y - 7 = 0 and 8x + 5y - 1 = 0 is A. 2y - 3x - 2= 0 B. 3x + 2y - 2 = 0 C. 3x + 2y - 63 = 0 D. none of the above 129. The parabola y2 = 4ax passes through the point (2, -6), then the length of its latus rectum is A. 9 B. 16 C. 18 D. 6 130. The equation of the conic with focus at (1, -1) directrix along x - y + 1 = 0 and with eccentricity √2 is A. xy = 1 B. 2xy + 4x - 4y - 1 = 0 C. x2 - y2 D. 2xy - 4x + 4y + 1 = 0 131. If the radical axis of the circles x2 - y2 + 2gx + 2fy + c = 0 and 2x2 + 2y2 + 3x + 8y + 2c = 0 touches the circle x2 + y2 + 2x + 2y + 1 = 0, then A. g = 3/4 or f = 2 B. g ≠ 3/4 and f = 2 C. g = 3/4 or f ≠ 2 D. none of the above 132. If tan θ + sec θ = √3, θ < π, then θ is equal to or least positive value of θ is A. 5π/6 B. 2π/3 C. π/6 D. π/3 133. The roots of the equation 4x2 + 2√5x + 1 = 0 are A. cos 18o, cos 36o B. sin 18o, cos 18o C. sin 18o, cos 36o D. sin 36o, sin 18o 134. From the bottom of a pole of height h, the angle of elevation of the top of a tower is α. The pole subtends an angle β at the top of a tower. The height of the tower is A. [h sin α sin(α - β)]/sin β B. [h sin α cos(α + β)]/cos β C. [h sin α cos(α - β)]/sin β D. [h sin α sin(α + β)]/cos β 135. If sin(π cos θ) = cos(π sin θ), then the value of cos(θ + π/4) is A. 2/√2 B. 1/√2 C. -1/√2 D. 1/2/√2 136. If 4 ≤ x ≤ 9, then A. (x - 4) (x - 9) ≤ 0 B. (x - 4) (x - 9) ≥ 0 C. (x - 4) (x - 9) < 0 D. (x - 4) (x - 9) > 0 137. The circle x2 + y2 + 4x - 7y + 12 = 0 cuts an intercept on y-axis equal to A. 7 B. 4 C. 3 D. 1 138. If α and β are the roots of the equation x2 - p(x + 1) - q = 0, then the value of [(α2 + 2α + 1)/(α2 + 2αv + q)] + [(β2 + 2β + 1)/(β2 + 2β + q)] is A. 1 B. 0 C. 3 D. 2 139. For x ∈ R, if mx2 - 9mx + 5m + 1 > 0, then m lies in the interval A. [-61/4, 0] B. [4/61, 61/4] C. [0, 4/61] D. - [-4/61, 0] 140. If a, b, c are positive real numbers, then the number of real roots of the equation ax2 + b| x | + c = 0 is A. 0 B. 2 C. 4 D. none of the above 141. If ax = by = cz and a, b, c are in G.P., then x, y, z are A. G.P. B. A.P. C. H.P. D. none of the above 142. Let cos x = b. For what b do the roots of the equation form an A.P.? A. √3/2 B. 1/2 C. -1 D. none of the above 143. Coefficient of x4 in the expansion of (1 - 3x - x2)/ex is A. 5/24 B. 4/25 C. 24/25 D. 25/24 144. If C (10, 4) + C (10, 5) = C (11, r), then r equals A. 6 B. 5 C. 4 D. 3 145. In a steamer, there are stalls for 12 animals and there are cows, horses, and calves (not less than 12 of each) ready to be shipped. The total number of ways in which the shipload can be made is A. 12C3 B. 12P3 C. 312 D. 123 146. The coefficient of xn in the binomial expansion of (1 - x) -2 is A. 2n/2! B. n + 1 C. n D. 2n 147. The largest coefficient in the expansion of (1 + x)24 is A. 24C13 B. 24C11 C. 24C24 D. 24C12 148. The sum of first n terms of two A.P. are 3n + 8, 7n + 15, then the ratio of their 12th term is A. 7/16 B. 8/15 C. 4/9 D. 3/7 151. If the system of equations x = a(y + z), y = b(z + x), z = c(x + y) (a, b, c ≠ -1) has a non-zero solution, then the value of [a/(1 + a)] + [b/(1 + b)] + [c/(1 + c)] is A. -1 B. 0 C. 1 D. 2 152. Two lines with direction cosines < l1, m1, n1 > and < l2, m2, n2 > are at right angles if A. l1 l2 + m1 m2 + n1 n2 = 1 B. l1 l2 + m1 m2 + n1 n2 = 0 C. l1/l2 = m1/m2 = n1/n2 D. l1 = l2, m1 = m2, n1 = n2 153. Given the line L : [(x - 1)/3] = [(y + 1)/2] = [( z - 3)/-1] and the plane π : x - 2y = 0. Of the following assertions, the only one that is always true is A. L is perpendicular to π B. L lies in π C. L is parallel to π D. none of the above 154. Quartile deviation for a frequency distribution A. Q = 1/4 (Q2 - Q1) B. Q = 1/3 (Q3 - Q1) C. Q = 1/2 (Q3 - Q1) D. Q = (Q3 - Q1) 155. For a symmetrical distribution, Q1 = 20 and Q3 = 40. The value of 50th percentile is A. 20 B. 30 C. 40 D. none of the above 156. The area bounded by the curve y = x3, the x-axis and the ordinates x = -2 and x = 1 is A. -9 B. -15/4 C. 15/4 D. 17/4 157. A random variable X has the following probability distribution: X: 0 1 2 3 4 5 6 7 8 p(X = x): a 3a 5a 7a 9a 11a 13a 15a 17a then the value of a is A. 7/81 B. 5/81 C. 2/81 D. 1/81 158. Dialing a telephone number, an old man forgets the last two digits remembering only that these are different, dialed at random. The probability that the number dialed correctly is A. 1/90 B. 1/100 C. 1/45 D. none of the above 159. Three identical dice are rolled. The probability that the same number will appear on each of them is A. 1/18 B. 3/28 C. 1/36 D. 1/6 160. The value of n ∈ I for which the function f(x) = sin nx/[sin(x/n)] has 4π as its period is A. 5 B. 4 C. 3 D. 2 161. Lt (log cosx)/x is equal to x → 0 A. 0 B. 1 C. ∞ D. none of the above 162. Lt [ex - (1 + x)]/x2 is equal to x → 0 A. 1/2 B. 1 C. 0 D. 1/4 163. For the curve x = t2 - 1, y = t2 - t, tangent is parallel to x-axis where A. t = 1/√3 B. -1/√3 C. t = 0 D. 1/2 164. The function f(x) = Kx3 - 9x2 + 9x + 3 is monotonically increasing in each interval, then A. K > 3 B. K < 3 C. K ≤ 3 D. none of the above 165. The area of the region bounded by the curve y = x - x2 between x = 0 and x = 1 is A. 5/6 B. 1/2 C. 1/3 D. 1/6 166. If f(x) dx = 1, x f(x) dx = a, x2 f(x) dx = a2, then (a - x)2 f(x) dx equals A. 4a2 B. 0 C. 2a2 D. none of the above 167. The area between the curve y = 1 - | x | and x-axis is A. 1/3 B. 2 C. 1/2 D. 1 168. The equations ax + by + c = 0 and dx + ey + f = 0 represents the same straight line if and only if A. a/d = b/e B. c = f C. a/d = b/e = c/f D. a = d, b = e, c = f 169. If a + b + c = 0, | a | = 3, | b | = 5, | c | = 7, then the angle between a and b is A. π/6 B. 2π/3 C. 5π/3 D. π/3 170. The differential coefficient of log tan x is A. 2 sec3 2x B. 2 cosec3 2x C. 2 sec x D. 2 cosec x 171. The differential coefficient of f(log x) where f(x) = log x is A. x/(log x) B. (log x)/x C. (x log x)-1 D. none of the above 172. The number of solutions of the equation tan x + sec x = 2 cos x lying in the interval [0, 2π] is A. 0 B. 1 C. 2 D. 3 173. In a triangle ABC, the angle B is greater than the angle A. If the values of the angles A and B satisfy the equation 3 sin x- 4 sin3 x - k = 0, 0 < k < 1, then the value of C is A. π/3 B. π/2 C. 2π/3 D. 5π/6 174. If one root of 5x2 + 13x + k = 0 is reciprocal of the other, then A. k = 0 B. k = 5 C. k = 1/6 D. k = 6 175. The number of quadratic equations, which are unchanged by squaring their roots is A. 2 B. 4 C. 6 D. none of the above 176. If x2 -3xy + λy2 + 3x - 5y + 2 = 0 represents a pair of straight lines, then the value of λ is A. 1 B. 4 C. 3 D. 2 177. If each element of a determinant of third order with value A is multiplied by 3, then the value of newly formed determinant is A. 3A B. 9A C. 27A D. none of the above 178. If A, B, and C are non-empty set subsets of the sets, then (A - B) ∪ (B - A) equals A. (A ∩ B) ∪ (A ∪ B) B. (A ∪ B) - (A ∩ B) C. A - (A ∩ B) D. (A ∪ B) - B 179. A and B are two independent events. The probability that both A and B occur is 1/6 and the probability that neither of them occurs is 1/3. The probability of the occurence of the event A is A. 2/3 B. 5/6 C. 1/2 D. none of the above 180. The number of divisors of 9600 including 1 and 9600 is A. 60 B. 58 C. 48 D. 46 Contact Details: Guru Gobind Singh Indraprastha University Sector 16 C, Dwarka, New Delhi, Delhi 110078 011 2530 2170 India Map Location: [MAP]https://www.google.co.in/maps?q=Guru+Gobind+Singh+Indraprastha+University,+ Delhi+&hl=en&ll=28.595242,77.018259&spn=0.011474,0 .021136&sll=15.399724,75.073196&sspn=0.006299,0.01 0568&t=m&z=16&iwloc=A[/MAP] |
|