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Aieee4

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Published in: AIEEE
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Parteek S / Jaipur

4 years of teaching experience

Qualification: Pursuing Graduation

Teaches: Mental Maths, Chemistry, English, Logic, Mathematics, Economics, NSTSE, AIEEE, BITSAT, IIT JEE Mains, WBJEE

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  1. A IEEE-Y MOCK chdeVQ C J. A particle is moving in x-y plane whose by is given of motion equation Find the maximum distance it has travel along X axis. Assume the particle has been projected from origin . (a) 4 unit (b) 2Jä unit (c) 6 unit (d) 8/46 unit 2. Is it possible that potential difference across the battery should be greater than emf of it and if yes then in which case ? (a) Not possible (bf Possible when the 'battery is discharging (c) Possible when the battery is charging (d) None of the above 3. A 150 g mass has a velocity v = (2i + 6j) m/s at a certain instant. What is its kinetic energy? 3.0 J (a) 2.0kJ (dj -3000 Id (c) 3.0 kJ 4. In the relation force = pressure xarea, force is a c) vector quantity, so (a) pressure and area both must be vector (b) any one can beyector an&scalar (c) pressure isvector (d) area is vector 5. An electromagnetic •wave going through 7. 8, 9. 10. 11. (a) Monoat6mi&gas ha' 6degrees of freedom q)) Polyatomic gas has 6 deg-recs of freedom at high temperature (c) Polyatomic gas has 8 degrees of freedom at high temperature (d) All of the above are light Regarding conductance, mark the con-ect option : (a) Ats unit is mho and not siemen (b) Its value doen't change -with temperature (g) Its -value is different for different materials (dj All of the above What is the effect of increasing the wavelength of light 'that falls on the emitter in a photoelectric effect apparatus ? (p) Cut off frequency decreases (bj The stopping potential decreases (c) The time delay fov emission of photoelectron increases (d) None of the above Internal energy of gas (ideal) depends only on (a) pressure q 6. vacuum is E sin(Lx - B = sin(kx Then : (bf ok Bok (d) nohéofthe above Dégree/of freedom means the number of possiblc ways in which the system can have engrgy, for example translation, rotational) vibra rional energy etc. Mark the correct one : (b) remperature (c) volume (d) temperature and pressure In a coaxial, straight cable, the central conductor and the outer conductor carry equal currents in opposite directions. The magnetic field is zero . (a) outside the cable (b) inside the inner conductor (c) inside the outer conductor (d) in between the conductors An electronic circuit element is made of 23 mg of silicon. The electric curfent through it adds energy at the rate of 9.2 x 10-3 J/s. if your design doesn't allow any heat transfer out of the element, at what rate does its temperature increase? The specific heat of silicon is 705 J/kg-K. (a) 0.68 K/s (9 0.57 (b) 4K/s
  2. If the two ends of a p -n jonccion arejoined by a wite ; (a) there will not be a steady current in the circuit (b) there will be a steady current from the it-side to the p-side 18. (c) there will a steady current from the p-side to n-side (d) there may or tnay not be a current depending upon the resistance of the connecting wire 13. The atmospheric temperature is below OOC and its value is then ice starts forming on the surface of lake. Find the Erne ih which dlickness of ice formed gets h m. Let us consider K is the thermal conductivity of ice, p is the density of ice, L f is the latent heat of fusion : 2 (a) 21
  3. as another photon moving in the same direction as the incident photon. Neglecting the light emitted by the excited hydrogen atom, determine how many wavelengths can be observed in transmitted beam ? (b) Infinite 23. Mark the incorrect option : (a) Free neutron can transform itself into proton 9) Free proton can transform itself into neutron (c) In ß-emission the electron is originating from nucleus (d) All of the above 24. On a Carnot refrigerator, work of 230 J has C 25. been done as it extracts 346 J from cold reservoir at 300 K. Find the coefficient of performance and the temperature of hot reservoir to which it is supplying energy ? (a) 1.5, SOO K (b) 1.0, 800K (9 1.5, 550K (d) 1.0, 550K Rain is falling vertically with a speed of 30 m/s. A person walks with a speed of 20 m/s in horizontal direction. At what angle with the vertical, the person should hold the umbrella? (a) tan (c) tan (b) cos-1 2 (d) sm | 2 28. 29. d 30. 31. 32. 33. Find the cunent in the thee resistors figure : (a) 1 A in each (c) 0.5 A in each (d) 0 A In each A point object in front of a plane mirror Iras velocity — 2i 3j+ 4ü•nd mirror has velocity 3i 23 + 4k: The øXLædS is along the normal of the plane minoi. Find thevelocity of the image ? (a) 8i (b) + 33 + In thermal conduction at steady state : (a) the molecules of the body transfer heat from one position to ano ther, without their actual net motion (b) temperature of each cross-section is constant (c) temperature of different cross-sections are different (9 all of the above Motion of artificial earth satellites around the earth is powered by : (a) liquid fuel (b) solar energy (c) atomic energy (d) none of the above A mercury barometer stands at 762 mm, A gas bubble, whose volume is 33 cm3 when it is at the bottom of a lake 45.7 m deep, rises to the surface. 'What is its volume at the surface of the 26. Mårk the incorrect option : (a) When an uncharged capacitor is connected across the baitery, just after the connections has been made,ii behaves as short circuit (b) When capacitor i' fully charged it behaves as short circuit (c) When -capaCitotüisjfully charged it is behaving as open circuit (cp. Both (a) anå (C) C 27. A beam of protons moves at 3x105 m/s 'through uniform magnetic field with fnaghitude 2.0 T, which is directed along the The velocity of each proton slies in the x-z plane at an angle of 300 to the pbSiuve z-axis. Find the force on a proton, (a) + (b) -4.8 Nj (c) 9.6x10 14 Nj (d) -9.6x10 14 •j lake ? (a) 250 cc (c) 237 cc (b) 178 cc (d) 125 cc A capacitor of capacitance is charged to a potential V by using a battery and then the battery is disconnected. Now a thin sheet of mica is inserted between the plates of capacitor, which of the following quantities will increase ? (a) Capacitance, charge, potential difference (b) Energy stored, capacitance, electric field (c) Capacitance, potential difference, electric field (d) None of the above
  4. (c) the wavelength of sound in tbc towards the observer is decreased (d) the amplitude of vibration of the particles For .søven amount' Of gas, PV isotherms are drawn at different temperatures as shown 38. Initially the system shown in figure is at rest. Now a is projected strike the 2 pan of the balance. 'If ball strikes the pan Yith speed u, find the speed of each body, jusc after irnpact of ball with tbe if it sticks to it- afteÖthe collision. Assume the mass of each body {o be equal to •m m, and neglect the rnass of the pulley and the string. (dj u/3 (c) 2u C 39. (A nearly massless rod is pivoted at one end so (d) no relation can be deduced from graph that it can swing freely as a pendulum. Two 35. Find a vector of magnitude 5 along BA where masses,2m and m, are attached to at it distance co-ordinates of points A and B are (0, 1, 3) and (1, 4, 6) respectively : -(9 (b) (c) S[i+ 3j+ 31k] (d) -5[i+ 3j+ 3f
  5. 42, A ball has been dropped from a height of 64m C 46. above the ground lcvel. Find the distance travelled by the ball in 4th second of its flight. Assume ball comes to rest after collision with ground : [Take g = 9.8 m/s2J (a) 34.3 m (c) 44.1 m (b) .19.9 m (d) None of these 43. A star initially has '1040 deuterons. It produces energy via the process In the arrangement shown in the figure masses or the blocks B and A are 2m and m respectively. Surface bet-wreen B and floor is smooth. The block B is connected to the blockC by means of a string as showp in figure. The system is 'released from rest; find the minimum value ofmass of blockC so that block A remains stationary with respect Coefficient of friction between A and Bis and 2 2 1 2 3 3 The masses of the nuclei are as follows : M(H2) = 2.014 amu M(P) = 1.007 emu M(n) = 1.008 amu, M(He4) = 4.001 amu If the avelage, power radiated bHhe star is 10) 6 W, the deuteron supply of the star is exhausted in a time of the order of r: (d) 101% (a) 3m 3m (b) 3m x 44. A particle is moving rectilinearly acceleration a, whose value is given function of distance by the equation a = find displacement as a function of time. [Att = O, particle is at rest at x OJ. with as a 3 4at (a) 2 36 (b) t 144 o c 45. A coil of area A is made to rotate with constant angular velocity d) about its axis in a magnetic field as shown in figure. Att = O, plahe of coil is parallel to B, find 'he induced emf as a function of time. 47. 48. 49. 50. Mark the incorrect one . (a) If electric potential has zero value at certain point then electric field has to be zero at that point (Y) If electric field has zero value at certain point then electric potential has to be zero at that point (c) If E 0 at certain point then V has to be non-zero at that point (d) All of the above A ball of 0.4 kg mass and a speed of 3 m/s has a head on, completely elastic collision with a 0.6 kg mass initially at rest. Find the speeds of 'both bodies after the collision? (a) 0.6 m/s, 2.4 m/s (b) 1.2 am/s, 498 m/s (c) 209 m/s, 11.6 m/s (d) None of the above The ceiling of a long hall is 25 m high. What is the maximum horizontal distance that a ball thrown with a speed of 40 m/s can go without hitüng the ceiling ofwall ? [g = 10 m/s21 (a) 148.6 m (c) 192m (b) 185.4m (d) 105.3m (a) BAO sin (Dt (c) BAO cos ot (b) sin (Dt (D COS Ot Consider the circuit shown in figure. If the current through 60 resistor is 4 A in the direction shown, then find the current in 25 Q and 20 Q resistors.
  6. Consider a hydrogen like atom, if the electron moves from lower energy state to highcr energy state then which of the following statements is correct ? (a) IG and PE both increase (Y) KE increases while PE decreåses (cf KE decreases while PE inch•eå'eS/ (d) KE and PE both decrease If the angular frequency of alteinating source, which is supplying a nigh -potential, difference across the dees of a cyclotron, is different from that of angular frequency of accelerating charge particle, then what will happen with the accelerating charge particle ? (a) Continue the •circular motion with increasing radius (b) Continue the cirCular motion but radius rfmains constant (c) Continue the circular motion inside the dees but radius changes in random manner depending on the relative values of frequency of circular motion and of supply of frequency (d) None ofthe above The drawing show a IS kg ball being whirled in a circular path on the end of string. The motion occurs on a horizontal table. The 56. 25 Q 20 Q (p) 3A, 9.95 A (bf7A, 9.95 A (d) Information is insufficient 51. Two identical point charges are placed at a separation of 2a m. If we place another point charge Q at M, (mid point of AB) then : (a) M is the of stable equilibrium for displacement along the AB ifQ is positive M is the position of unstable equilibrium for displacement along line perpendicular to AB if Q is positive (c) M is the position of stable equilibrium for displacement along the line AB, if Q is negative (d) (a) and (b) both 52. Marlc the correct option : (a) When a slab of dielectric is inserted between the plates of a capacitor a force starts acting on it due to fringing of electric field near the ends (b) If potential is constant and a dielectric slab has been inserted into the plates, then it has been pulled into with a constant force (c) If charge is constant and m dielectric slab has been inserted into the plates, then it •has been attracted wi!h a variable force (d) All of the above Chemistry The number of Welectrons in 3+ 53. 54. 55. (358. angular speed of 'the ball is 0) = 12 rad/s. The suing has a mass of 0.023 How much time does it take for a wave on the string to travel from the of the circle to the ball ? m (a) 6 ms (c) 6.28 ms (a) Fe2+ (c) Rh+ (b) 3.26 ms (d) 6.52 ms (b) zr4+ (d) TL4+ (c)" (df5 Which of the following is the strongest 57. Whichöf the f6Jlowing metal ion is present in Zigg1eßNatta Vatalyst ? reducing agent ? (a) NH3 (c) AsH3 (b) :PH3 (d) sbH3
  7. N/A
  8. (d) c112 CH3CH3 Dji. C) 75. The coconversion CF13 H2S04 OH OH CH3 is called : CH30 (a) Beckmann rearrangement Pinacol-pinacofone rearrangement (cfClaisen rearrangement (d) Fries-rearrangement cl 76. Mark out the correct decreasing order of ease of addition of halogen . (a) CH2 > CFL—CH —CH—CH3 > CH3 —C =CH2 > (CH3)2C (b) (CH3)2C > CH3 —C=CH2 Cl-13 > CFL—CH —CH—CH3 > (c) (CH3)2C > CFL—CH > CE13 —C =CH2 > CH2 =CH2 @ —C =cÄ2 > 77. Which of the-following@oesn't give benzoic acid on treatment with KMn04 ? 'i CHiCH2CH3 78. C 79. 80. Mark out the correct set of increasing order of boiling points : (a) methyl formate propen-l-ol < acetic // acid < actamide (b) propen-l-ol < acetarpide < methyl formate < acetic acid (c) methyl founate IV > 11 > 1 (b) 111 > IV > I > 11 (c) IV > > 11 > 1 (d) IV > 111 > 1 > 11 11 (b) 02N b 810 82. —cha If h is the radius of the first orbit of hydrogen atom, then the radii of second, third and _fourth orbitals in terms of rl are : 234 (b) 8h, 2711, (f)H4n; Oxidation number of A, B and C are + 2, + 5 and 2 respectively. Possible formula of compound is :
  9. When the same amount of zinc is treated separately with excess of sulphuric acid and excess of NaOH, the ratio of the moles of hydrogen evolv.ed is : C 84. What weight of KMnO,1 must be added to 35.0 mLofO.1 (M) RMn04 solution to make it to 0.60 (N) for a leaction in which ICvIn04 changes to mangnous ion (Mn2+) ? Assurnc no change in volume : (a) 0.220 g (b) 0.055 g (c) 0.110 g (d) 0.330 g 85. CSC! has bcc arrangement and its unit cell edge length is 400 Calculate the interionic distance in CsCl : (a) 322.4 pm (Y) 346.6 pm (df 574.7 pm (c) 234.5 pm 86. For coagulation of a positively charged solution, which of thc following electrolyte will have highest coagulation value ? (a) KN03 (c) K2C204 C 87. A viral preparation was inactivated in a chemical bath. The inactivation process was found to be first order in virus concentration and at the beginning of the experiment 2.0% of the virus was found to be inactivated per minute. The value of k for the inactivation 2 d" can't be predicted 91. 92. C 93. 94. 95. When CS2 layer containing both Brz and 12 is shaken with excess of C12 water, the violet colour due to 12 disappears,and orange colour due to Br2 appears. The dispppearance of violet colour is due to the : (bj €110'3 (c) IC12 Consider the following observation : M + white precip_itaté -+ water soluble The metal 'ion Milt "will be : (a) I-lg2€ (c) pi)2+ (Y) Ag+ The rprocess bringing the metal or its ore into solution by thc action of a suitable chemical J •eagent• followed by extraction of the metal either by electrolysis or by a suitable precipitating agent is called (a) electrometallurgy (bp clectrorcfining (cfhydrometallurgy (d) zone-refining Al is more reactive than Fe but Al is less easily corroded than Fe because : (a) it is a 'noble •metal (bp oxygen forms a protective oxide layer (c) iron undergoes reaction easily with water (d) Fe form mono and divalent ions process is : (a) 1.1 x 10-4 s-J (C) 3.3* 10-4 S (b) 1.7x 104 s-1 (d) 1.44* 10 s-1 o Il cH3 —C —CH CH—OTs Nal C 88. A reaction is of first order when : (a) . The amount of product formed increases linearly with time (b) The rate decreases linearly 'With time (c) The rate is linearly related to the concentration of the Écactant (d) The concentration of the reactant decreases linearly with time 89. A mixture containsN204 and NO? in the ratio of 2 : 1 by volume. The vapour density of the mixutre is : (a) 38.3 (b) 25 (c) 42 (d) 46 90. For the following concentration cell, •spontaneoug; ZnJZf12+ (Cl)l Izn2+ zn (-96 to be 80% acetone-Il As the reaction gets completed, mechanism is said to be : (a) elimination-addition mechanism (b) addition-elimination 2 kinetically (d) Both (b) and (c) Reagent can be used g. (a)JåA1114/D20 (c) D2/Pt (b) (d) NaBD4/H20 LiAlH4/H20
  10. L 99. 97. (c) HOOC—CHC12 (9) ctrl —CHOI-I Product is/are . 98. CHO—CHO (a) CH30H (b) HOCJ12—COO- (f) CH30H + HCOOH i(df -OOC—COO- CFL—C08 CFI ----..-.-.-..—--+ product HOCI Predorninant product is : (b) cic = CC] (a) oerÆ—caHC12 102. 103. CH3MgBr + (a) cH3 o D, Dist o NaOBr O + 2NH3 product is : CH29H cH3 cila (d) 2 cH3 CH20H o NH2 (a) o (c) CH2—NHBr cH=cod (b) H2—NH2 2—c000 CH (d) CH2—NH3 104. 105. To 50,0ÄrnL of:azhydrochloric acid solution, 25 mL of O.S N Na2C03 solution were added. The remaining acid required 20 mL of O.S N NaOJl for • complete neutralization. The normality of the acid solution is : (Y) 0.45 N (a) o.9N (df 1.45 N (c) 0.225 N A metal ctystallizes into two cubic phases, face centred cubic (FCC) and body centred cubic (BCC) whose unit cell lengths are 3.5 and 3.0 respectively. Calculate the ratio of the densities of FCC and BCC. 100. Today, lactones are reduced to aldoses by the addition of 'NaBV14 to an aqueous solution of lactones. If however, lactone is added to the NaBH4, another product, not the aldose, is obtained. The product is : (b) alditol (a) aldonic acid (d) kecose (c) aldariC acid 101. Whid of the following is the major pfoduct ? (a) 1.67 (c) 6.23 •1.26 H W (a) hic: KOH product. H CH3 none of these 106. 107. 2NH3 (1) AH x 3H2(g)— 2NH3(g) AH Y Mark out the correct comparison of enthalpy of reactions : (d) can't be predicted Hess's law of constant 'heat suggests that the enthalpy change during a chemical reaction depends on (a) the volume change during the chemical reaction (b) the temperature throughout the process (c), the nature ofinitial reactants and products (d)' the path followed by the process How much ethyl alcohol, C2HsOH, must be added to 1.00 L of water so that the solution will not freeze at- 40 F? CH3 (a) 211 g (c) 85 g (b) 495 g (d) 46 g
  11. 108. 109. A spheHcaJ balloon of 21 cm diameter is to be filled with' hydrogen at STP from a cylinder containing the gas at 20 atm and 270 C. If the cylinder can hold 2.82 L of water, the nurnber balloons that can be filled up is (d) 12 Consider 'the reaction The K a value for the acid HA is 10 value of the K for this reacöon is The (a) 1.0* 10 (c) 1.8*10 3 (b) 1.0*106 (d) 3.3 10 110 7. 8. . Transport number of Cl- is lea9t In 3 2 Ma tics 1. If a, b and care distinct positive numbers, then the expression (b + c— a) (a+ c — b)(a b ,--e c) (a) HCI 1 (a) (d) esfcv/Z 1 abc is : (a) positive (c) non-positive (P) negative (c)/ non-negative 2. Ifx:, as well as yr, yo are in GP with the same common ratio, then the points YD' (x-2, h) and (x3, 3/3) : (a) lie on a straight line (b) lie on an ellipse (c) lie on a circle (d) are vertices of a triangle 100 If A = 0 1 1 = A2 CA + -then (c, d) is : (b) (—11, 6) 11) (d) (6, 11) (c) al, 6) 4. If the normal to the curve y = at the point 24 (3, 4) makes an angle positive x-axis, then f' (3) is equal to 4 5. On the intervåLL0, IJ the function x25(1 - x)? s takes its maximånivalue at the point: 1 If z the line x —1 is the directrix of the parabola y 2 + 8 = O, then one of the value From the top of a light-house 60 m high with its base at the sea-level, the angle of depression of a boat is 150. 'The distance of the boat from the foot of the light-house is : 60 m 60 m 0-1 2 46-1 (d) none of the above A ball oftrnass 3 kg moving with a velocity of 3m/s collides with another ball of mass 1 kg moving with velocity u in the opposite direction. If the first ball comes to rest after the impact and e = 2/7, then u in m/s is 13 19 (c) 17 (b) 23 (d) 10. Chords of an ellipse are drawn through the positive end of the minor axis, Then their mid The area enclosed between the curve; y 2 ax and* = ay2 (a> O)is 1 sq unit. Then the value of 'at is: point lies on t (a) a circle (c) an ellipse (b) a parabola (d) a hyperbola
  12. (c) 4C2 + 41>3 ("none of these any integer n the integral cos3 (Yi + dx has the value : (d) none of these Cl 13. Area of triangle formed by the lines x + y = 3 and angle bisectors of the pair of straight lines 2 (a) 2 sq unit (b) 4 sq unit (c) 6 sq unit (d) 8 sq unit 14. If x = 9 is the chord of the hyperbola x2 —y 2 = 9, then the equation of the corresponding pair of tangents is : (a) 9x2 -832 + 18x- (b) 9x2 -8y2 -18x+ (c) - -18x-9=o (d) 9x2 + d 15. The number of all possible triplets (al *02, aa) such thatq + a2 cos2x+ sin x = : 16. The number of real solutiöns of C Lan-I x(X+ 1) + x2 a is C] Jl. Eight chairs are numbered to S. Two women 18. 2-3 and three Inen wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4 and then the men select the chairs from amongst the remaining. The number Of possible A variable plane distance from origin cuts the co-ordinate axes at A, B and C. Centroid (x, y, z) satisfies the 1 value of k is': arrangements is : 6 3 1 4 4 6 19. G 20. 21. c 22. 1 Two like forces P and 5P act oh a rigid body at a distance x apartv If the forces are interchanged in point of application of 'the resultant will be displÅced through a distance x (c) (b) 3X 4 10 different toys are to be distributed among 10 children. Total number of ways of distributing these toys so that exactly 2 children do not get any toy, is equal to t 1 1 (b) (101)2 1 1 3!71 6! If(l + = co 1-2 c is equal to : q —i. If d is a that a. d c d l, 1 1 n 'c r xn, then 23 + 2 3 -2n+S (b) unit vector such then equals : 3n+2-2n-5 (c) (d) none of these A straight line moves such that the algebraic sum of the perpendicular drawn to it from two fixed points is equal to 2k. Then the straight line always touches a fixed circle of radius (d) none of these
  13. 23. If the base of a triangle and che ratio of the lengths of the other two unequals sides are given, then the vertex lies on a/an : 29. 30. 31. 32. d 33. 34. 35, For the value any vector (a + (a x + (a x is equal to : 2 of (a) straight line (c) ellipse (b) circle (d) parabola 24. The tangent -to the curve x = a (0 — sin 0), Y = a (1 cos 9) the at + k e z are parallel to : points cl 25. If a vertex of a (1, l) tind the mid points of two sides through this vcrtex are 1, 2) and (3, 2), then the 'ccntroid of the triangle is : a and b are two given vectors. On these vectors as adjacent sides of a parallelogram is constructed. The vector which is the altitude of . the parallelogram and which is perpendicular to a is : (a) (b) 2 (d) all of the above The expression polynomial of degree Fifteen coupons arc numbered 1, 2, is a c 26. A parallelopipcd is formed by planes drawn through the points (2, 3, 5) and (5, 9, 7), parallel to the co-ordinate planes. The length of a diagonal of the parallelopipcd is : (cfVi3S (d) -nonc of these 27. The parabolas y 2 = 4x and = 4y divide the square region bounded by the lines + = 4; y = 4 and the co-ordinate, axes. If Sl, S2,S3 are respectively the areas orthese parts numbered from top to bottom, then S] : S2 : SOS : 10 28. If the plane i lax 3ay + 4az + 6=0 passes through Lhe mid point of the line joining the cencress 2 2 or spheres the and x? u/ 2 + —i 10x + 4y 27 = 8, then a equals: 7 respectively seven coupons arc selected at random onc at a timc with replacement. The probability that the largest number appearing on a selected coupon is : (d) none of these 1 cos 2(x 1) is equal to e. lim (a) exists and it equals (b) exists and it equals (c) does not exist because x 1 —Y 0 (d) does not exist because left hand limit is not equal to righl hand limit sin-IG — cos- (x The value of dxiss sin- G + cos-lC-Q none of che above If a > 2b > O, then positive 'Value of m for which y nux—b 1 -ton is a common tangent to x 2 + Y2 = b2 and (x + y 2 is Z
  14. (a) a2 4b2 2b (c) a—2b a2 - 4b2 (b) b a-2b (c) (b) (d) none of these 36. A uniform rod AB of length a hangs with one C end against a smooth vertical wall, being supported by a string of length l, attached to the other end of the rod and to a point of the rod vertically above B. If the rod rests inclined to the wall at an angle 0, then cos20is equal to : 38. G 39. 40. If the ratio of the roots of/ u 2 + v = 0 is equal to the ratio of the roots of x2 + 1 = 0 then v are in : (a) AP (c) I-IP (d) none of these 12 -- a2 (a) 12 — a2 (c) 12 - a2 (b) 2a2 (d) none of these G 37. PQ and RS are two chords of the rectangular hyperbola xy = c2. IfC is the centre of the rectangular hyperbola, Chen the product of the slopes ofCP, CQ) CR and CS is equal to : (dj none of these If ar > 0, reN and q, are in AP, then is equal to : cosß sin x If cosx — 2 tan = is : (a) (c) tan — tan 150 tan 1 50 then the value of (b) tan (d) none of these

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