[Please read the instructions carefully, you are allotted 5 minutes specifically for this purpose] This Paper contains 60 Objective questions.

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1 IIT-JEE 004 Screening Duration: 0 Min Paper Code: ITS/S/04/03 Marks: 80 Topics:- Date: 03/08/03 PHYSICS - Waves, Ray ptics, Newton s Laws, Friction CHEMISTRY PHYSICAL CHEMISTRY - Dilute solution and colligative properties Acids and bases, double Indicators Chemical Kinetics Chemical Equilibrium RGANIC CHEMISTRY - Alkanes, Alkenes, Alkynes [preparation & Properties] MATHS - Diffrential Calculus, Parabola, Circle, Straight lines. [Please read the instructions carefully, you are allotted 5 minutes specifically for this purpose] This Paper contains 60 bjective questions. Attempt All Questions Use of logorithmic table is NT PERMITTED Use of calculator is NT PERMITTED For each question you will be awarded 3 marks if you have darkened correct bubble(s). In case you have not darkened any bubble you will be awarded 0 mark for that question. In all other cases you will be awarded - marks.

2 . The kinetic energy K of a particle moving along a circle of radius R depends on the distance covered s as K = as. The force acting on the particle is (a) as (b) R as m / s + R (c) as (d) a. A uniform rope of length L, resting on a frictionless horizontal surface is pulled at one end by a force F. What is the tension of the rope at a distance l from the end where the force is applied? (a) F ( - l/l) (b) F ( + l/l) (c) F / ( - l/l) (d) F / ( + l/l) 3. A chain consisting of 5 links each of mass 0. kg is lifted vertically with a constant acceleration.5 m/s as shown in figure. The force of interaction between the top link and link immediately below it will be (a) 6.5 N (b) 4.9 N (c) 9.84 N (d).46 N 4. Two blocks of masses M and M are connected to each other through a light spring as shown in figure. If we push the mass M with a force F and cause acceleration a in mass M, what will be the acceleration in M? (a) F/M (b) F/(M + M ) (c) a (d) F M M 5. A solid cube is placed on a horizontal surface. The coefficient of friction between them is µ, where µ </. A variable horizontal force is applied on the cube s upper face, perpendicular to one edge and passing through the mid point of edge, as shown in figure. The maximum acceleration with which it can move without toppling is (a) g ( - µ ) (b) g( + µ ) (c) g/( - µ ) (d) g/( + µ ) 6. An insect crawls up a hemispherical surface very slowly. The coefficient of friction between the insect and the surface is /3. If the line joining the centre of hemispherical surface to the insect makes an angle α with the vertical, the maximum possible values of α is given by (a) cot α = 3 (b) tan α = 3 (c) sec α = 3 (d) cosec α = 3 7. A box is placed on an inclined plane and has to be pushed down. The angle of inclination is (a) equal to angle of friction (b) more than angle of friction (c) equal to angle of repose (d) less than angle of repose 8. The work done in moving a body up a rough inclined plane is given by (a) mg sin θ s (b) mg cosθ s (c) ( mg sin + µ mg cosθ) s mgsinθ a θ (d) ( mgcosθ) s 9. Two waves of intensities I and 4I superimpose. The minimum and maximum intensities will respectively be (a I, 5 I (b) I, 5 I (c) I, 9 I (d) None of the above 0. A sound wave y = a sin ( ω t - kx) is propagating through a medium of density ρ. What is the sound energy per unit volume? (a) ρ a ω (b) ρ a ω (c) ρ a ω (d) 4ρ a ω. The superposition of two harmonic oscillations in the same direction results in the oscillation of a point according to the equation x = a cos. t cos 50 t, where t is in seconds. Find the period in which they beat (a) second (b).497 second (c). second (d).994 second. In a gas two waves of lengths m and.0 m superposed to produce 0 beats in 3 seconds. The velocity of sound in the medium is (a3 m/s (b36.7 m/s (c) 83 m/s (d) 66 m/s 3. y(x, t) = 0.8/[(4x + 5t) + 5] represents a moving pulse, where x and y are in meter and t in second. Then (a) pulse is moving in +x direction (b) in s it will travel a distance of.5 m (c) its maximum displacement is 0.46 m (d) it is a symmetric pulse 4. A cube of side a made of a material of refractive index µ is immersed in a θ A B liquid of refractive index µ. A ray is incident on face AB at angle θ as shown r in fig. Total internal reflection takes place at a point P on face BC. Then. (a) sinθ = [( µ / µ ) ] (b) sinθ = [( µ / µ ) ] (c) sinθ = [ ( µ / µ ) ] (d) sinθ = [ ( µ / µ ) ] F > ITS-03 (IITians Test Series) M µ > D < a a M >P α P C > µ Hyderabad / Trivandrum ITS/S/04/03

3 5. 8 Two media are separated by a plane surface having speeds of light 0 8 m / s and.4 0 m / s respectively. What is the critical angle for a ray going from first medium to second medium? (a) sin - (5/6) (b) sin - (5/) (c) sin - (/) (d) sin - (/ ) 6. A light ray is incident upon a prism in minimum deviation position and suffers a deviation of If the dotted half of the prism is knocked off, the same ray will (a) suffer a deviation of (b) suffer a deviation of 30 0 (c) suffer a deviation of (d) not come out of the prism 7. A diverging beam of light from a point source S having divergence angle α, falls symmetrically on a glass slab as shown. The angles of incidence of the two extreme rays are equal. If the thickness of the glass slab is t and the refractive index n, then the digvergence angle of the emergent beam is (a) zero (b) α (c) sin - (/n) (d) sin - (/n) i Ś α µ i t 8. A convex lens of focal length 0 cm is cut into two equal parts so as to obtain two planoconvex lenses as shown in figure(b). The two parts are then put in contact as shown in fig(c). What is the focal length of combination? (a) Zero (b) 5 cm (c) 0 cm (d) 0 cm (a) (b) (c) 9. A double convex lens of refractive index µ is immersed in a liquid of refractive index µ. This lens will act as (a) diverging lens if µ > µ (b) diverging lens if µ = µ (c) converging lens if µ > µ (d) converging lens if µ < µ 0. We wish to make a plano-convex lens of focal length 6 cm from glass having refractive index.5. It is to be used in air. What should be the radius of curvature of the curved surface? (a) 8 cm (b) cm (c) 6 cm (d) 4 cm. A complex of iron and cyanide ions is 00% ionised at m (molal). If its elevation in b.p. is.08 o. (K b = 0.5 o mol- Kg) then the complex is: (a) K 3 [Fe III (CN] 6 ] (b) K 3 [Fe II (CN] 6 ] (c) K 4 [Fe III (CN) 6 ] (d) K 4 [Fe II (CN) 6 ]. If cost per gram were not a concern which of the following substance would be most efficient per unit molar mass for melting snow from side-walls and roads? (a) glucose,c 6 H 6 (b) LiCl (c) NaCl (d) CaCl o 3. V.P of pure Ap A = 00 mm Hg o V.P of pure Bp B = 50 mm Hg Distillate of vapours of a solution containing moles A and 3 moles B will have total vapour pressure, approximately, on condensation: (a5 mm (b0 mm (c) 40 mm (d) 45 mm 4. Which is/are correct statements? (a) L of N H 3 P 4 solution contains one-third of molecular weight when it is completely neutralised by NaH (b) L of N H 3 P 4 solution contain 0.5 mole of H 3 P 4 when it is reduced to HP 3 (c) both (a) and (b) (d) none of above 5. Which represents first-order reaction out of I,II and III? log(a-x) a log a x T 50 Time I Time II a(conc.) III 6. If (a) I, II and III (b) I and II (c) II and III (d) I and III dx dt =K [H+ ] n and rate becomes 00 times when ph changes from to Hence order is (a) (b) (c (d) 0 Hyderabad / Trivandrum ITS/S/04/03 3

4 7. Following are the values of E a and H for three reactions carried out at the same temperature: I : E a =0 kj mol -, H = -60 kj mol- II: E a =0 kj mol -, H = -0 kj mol- III: E a =40 kj mol -, H= +5 kj mol- If all the three reactions have same frequency factor then fastest and slowest reactions are: Fastest Slowest (a) I II (b) II III (c) I III (d) Can t be predicted 000K 8. Rate constant k varies with temperature as given by equation log k (min - ) = T equation. I: Pre-Exponential Factor is 0 5 II: E a is 9. kcal III: Variation of log k with T. Consider following about this is linear. (a) I, II, III (b) I, II (c) II, III (d) I, III 9. For the following gaseous equilibria X,Y and Z at 300 K X ; S + S 3 Y : PCl 5 PCl 3 + Cl Z : HI H + I ratio of K p and K c in the increasing order is : (a) X = Y = Z (b) X < Y< Z (c) X < Z < Y (d) Z < Y < X 30. Consider the following reactions in equilibrium with equilibrium concentrations 0. M of every species: (I) S + S 3 (II) N + 3H NH 3 (III) N 4 N (IV) 4N+6H 4NH Extent of reaction will be in order : (a) I = II = III = IV (b) I = II = III < IV (c) III < I = IV < II (d) IV < III < I < II 3. If following proceed in forward side HN + HF H F + + N CH 3 CH + HF F - + CH 3 CH + H + CH 3 CH H CH 3 C - then increasing order of acid strength is: (a) H <CH 3 CH<HF<HN (b) HN <HF<CH 3 CH<H (c) HN <HF <H <CH 3 CH (d) HN <CH 3 CH <HF <H 3. Which buffer solution has maximum ph? (a) mixture which is 0. M in CH 3 CH and 0. M is CH 3 CNa [pka (CH 3 CH) =4.74] (b) mixture which is 0. M CH 3 CH and 0. M is CH 3 CNa + (c) mixture which is 0. M in NH 4 Cl and 0. M in NH 4 H[pK a (NH 4 )=9.6] (d) all the solution have equal ph which is Buffer begins to lose its effectiveness when: (a) [ salt] 0. [ weak electrolyte] (b) [ salt] 0 weak electrolyte (c) both (a) and (b) (d) none of these 34. Following are some of the certain facts of stwald s theory of acid-base indicators: A : Ionised and unionised forms have different colours B : Colour change is indicated at the end point when unionised form changes to ionised form due to change in ph C : Benzenoid form changes to quinonoid form and vice-versa due to change in ph, select correct facts: (a) A,B,C (d) A,C (c) A,B (d) B,C 35. H + H 3 P 4 H H P 4,pK =.5 H + H P 4 H 3 + +HP 4, pk = 7.0, hence, ph of 0.0 M NaH P 4 is: (a) 9.35 (b) (c).675 (d) pentyne HgS 4/H S 4 >X BH3.THF/HH - > Y X and Y can be distinguished by: (a) silver-mirror test (b) iodoform test (c) both of these (d) none of these Hyderabad / Trivandrum ITS/S/04/03 4

5 RC CR A, Lindlar / H Na / NH 3 A and B are geometrical isomers (RCH=CHR): 37. B (a) A is cis, B is trans (b) A is trans, B is cis (c) A and B both are cis (d) A and B both are trans 38. (CH 3 CMgCl on reaction with D produces: (a) (CH 3 CD (b) (CH 3 CD (c) (CD 3 CD (d) (CD 3 CD 39. Aq. Solution of potassium acetate is electrolysed. Possible organic products are: (a) CH 3 CH 3 (b) CH 3 CCH 3 (c) CH 3 CH CH CH 3 (d) (a),(b) 40. ctane rating is decided by octane number and is given 00 when centpercent antiknocking property of the petroleum products. Which is given octane number 00: (a) iso-octane (b) n-heptane (c) tetraethyl lead (d) n-octane 4. The circles x + y - 0x + 6 = 0 and x + y = r intersect each other in two distinct points if (a) r < (b) r > 8 (c) < r < 8 (d) < r < 8 4. For a real number x, [x] denotes the integral part of x. The value of is (a) 49 (b) 50 (c) 48 (d) Which one of the following curves cuts the parabola y = 4ax at right angles? (a) x + y = a (b) y = e -x/a (c) y = ax (d) x = 4ay 44. The function f defined by f(x) = (x + ) e -x is (a) decreasing for all x (b) decreasing in (, ) and increasing in (, ) (c) increasing for all x (d) decreasing in (, ) and increasing in (, ) , x < 0 Let f (x) = Then, for all x, which of the following is NT TRUE x x 0 (a) f is differentiable (b) f is differentiable (c) f is continuous (d) f is continuous x sin x Let g(x) = x f(x), where f(x) = x 0 x = 0 (a) g is differentiable but g is not continuous (c) both f and g are differentiable At x = 0 (b) g is differentiable and g is continuous (d) None of these x 47. The function f (x) = [x]cos π, where [.] denotes the greatest integer function, is discontinuous at (a) all x (b) all integer points (c) no x (d) x which is not an integer x 48. Let f(x) be defined for all x > 0 and be continuous. Let f(x) satisfy f = f(x) - f(y) for all x, y and f(e) =. Then y (a) f(x) is bounded (b) f 0 as x 0 x (c) x f (x) as x 0 (d) f(x) = log x 49. n the interval [0, ] the function x 5 (-x) 75 takes its maximum value at the point (a) 0 (b) (c) 4 (d ln ( π + x) 50. The function f (x) = is ln (e + x) (a) increasing on [0, ) (b) decreasing on [0, ) π π (c) increasing on 0, and decreasing on e, e (d) decreasing on π π 0, and increasing on e, e Hyderabad / Trivandrum ITS/S/04/03 5

6 5. Consider a circle with its centre lying on the focus of the parabola y = px such that it touches the directrix of the parabola. Then a point of intersection of the circle and the parabola is p (a), p p (b), p 4 p (c),p p (d), p 5. The function f(x) = max {( - x), ( + x), }, x (, ), is (a) continuous at all points (b) differentiable at all points (c) differentiable at all points except at x = and x = -. (d) continuous at all points except at x = and x = -, where it is discontinuous 53. If sum of the distances of a point from two perpendicular lines in a plane is, then its locus is (a) a square (b) a circle (c) a straight line (d) two intersecting lines. 54. If the lines (sin a + sin b) x - sin (a - b) y = 3 and (cosa + cosb) x + cos (a - b)y = 5 are perpendicular, then sin a + sin b is equal to (a) sin (a - b) - sin (a + b) (b) sin (a - b) - sin (a + b) (c) sin (a - b) - sin (a + b) (d) sin (a - b) - sin (a + b) 55. Locus of the mid-points of the chords of the circle x + y = 4 which subtend a right angle at the centre is (a) x + y = (b) x + y = (c) x + y = (d) x - y = 0 A M (h,k) B 56. If the equation of one tangent to the circle with centre at (, -) from the origin is 3x + y = 0, then the equation of the other tangent through the origin is (ax - y = 0 (b) x + 3y = 0 (c) x - 3y = 0 (d) x + y = A line meets the coordinate axes in A and B. A circle is circumscribed about the triangle AB. If m and n are the distances of the tangent to the circle at the origin from the points A and B respectively, the diameter of the circle is (a) m(m + n) (b) m + n (c) n(m + n) (d) (m + n) Y (0,b) B n M A (a,0) > X 58. The coordinates of an end-point of the latus rectum of the parabola (y - ) = (x + ) are (a) (-, ) (b) (-3/, ) (c) (-3/, 3) (d) (-3/, 0) 59. The set of all points where the function f (x) = e is differentiable is (a) ( 0, ) (b) (, ) (c) (, ) ~ {0} (d) (, ) 60. If f(x) = p sin x + q e x + r x 3 and if f(x) is differentiable at x = 0, then (a) p = q = r = 0 (b) p = 0; q = 0; r is any real number (c) q = 0; r = 0; p is any real number (d) r = 0; p = 0; q is any real number x L m Hyderabad / Trivandrum ITS/S/04/03 6

7 IIT-JEE 004 ANSWER SHEET Q.No A B C D Q.No A B C D Q.No A B C D Name of the Student: Address: ((R) (() Pin Code Date Hyderabad / Trivandrum ITS/S/04/03 7

8 ANSWER KEY IIT-JEE 004. B. A 3. B 4. D 5. C 6. A 7. D 8. C 9. C 0. A. B. B 3. B 4. A 5. A 6. A 7. B 8. D 9. C 0. A. A. D 3. B 4. C 5. A 6. B 7. C 8. A 9. C 30. C 3. A 3. C 33. C 34. C 35. B 36.. C 37. B 38. A 39. D 40. A 4. C 4. B 43. D 44. D 45. A 46. A 47. C 48. D 49. B 50. B 5. A 5. C 53. A 54. B 55. C 56. C 57. B 58. D 59. C 60. B Hyderabad / Trivandrum ITS/S/04/03 8