www.studentguide.co.in Buy Books & Magazines Online Free Email & SMS Solved Question Papers & Video Tutors Mock Exams (CAT, IIT, Gate, etc) Scholarships & Loans Expert Advice & Discussion Board AIEEE -Previous year Papers -MATHEMATICS -2008 1. The point diametrically opposite to the point P(1, 0) on the circle x2 + y2 + 2x + 4y – 3 = 0 is (a) (-3, 4) (b) (3, -4) (c) (-3, -4) (d) (3, 4) 2. Let a, b, c be any real numbers. Suppose that there are real numbers x, y, z not all zero such that x = cy + bz, y = az + cx and z = bx + ay. Then a2 + b2 + c2 + 2abc is equal to (a) 2 (b) 1 (c) –1 (d) 0 3. The area of the plane region bounded by the curves x + 2y2 = 0 and x + 3y2 = 1 is equal to (a) 5/3 (b) 4/3 (c) 1/3 (d) 2/3 4. The vector = α + 2 + β lies in the plane of the vectors = + and = + and bisects the angle between and . Then which one of the following gives possible values of α and β? (a) α = 1, β = 2 (b) α = 2, β = 2 (c) α = 2, β = 1 (d) α = 1, β = 1 5. How many real solutions does the equation x7 + 14x5 + 16x3 + 30x – 560 = 0 have? (a) 3 (b) 5 (c) 7 (d) 1 6. Let R be the real line. Consider the following subsets of the plane R X R: S = {(x, y) : y = x + 1 and 0 < x < 2} T = {(x, y) : x – y is an integer}. Which one of the following is true? (a) S is an equivalence relation on R but T is not (b) Both S and T are equivalence relation on R (c) Neither S nor T is an equivalence relation on R (d) T is an equivalence relation on R but S is not 7. A parabola has the origin as its focus and the line x = 2 as the directrix. Then the vertex of the parabola is at (a) (1, 0) (b) (0, 2) (c) (2, 0) (d) (0, 1) 8. Let A be a 2x2 matrix with real entries. Let I be the 2x2 identity matrix. Denote by tr(A), the sum of diagonal entries of A. Assume that A2 = I. Statement-1 : If A ≠ I and A ≠ -I, then det A = -1. Statement-2 : If A ≠ I and A ≠ -I, then tr(A) ≠ 0. (a) Statement-1 is true, Statement-2 is false (b) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for statement-1 (c) Statement-1 is false, Statement-2 is true (d) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for statement-1www.studentguide.co.in Buy Books & Magazines Online Free Email & SMS Solved Question Papers & Video Tutors Mock Exams (CAT, IIT, Gate, etc) Scholarships & Loans Expert Advice & Discussion Board 9. A dice is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then P(A B) is (a) 3/5 (b) 0 (c) 2/5 (d) 1 10. A focus of an ellipse is at the origin. The directrix is the line x = 4 and the eccentricity is 1/2. Then the length of the semi-major axis is (a) 8/3 (b) 5/3 (c) 2/3 (d) 4/3 11. If the straight lines x – 1/k = y – 2/2 = z – 3/3 and x – 2/3 = y – 3/k = z – 1/2 intersect at a point, then the integer k is equal to (a) 5 (b) – 2 (c) – 5 (d) 2 12. The non-zero vectors , and are related by = 8 and = -7 . Then the angle between and is (a) π/4 (b) 0 (c) π (d) π/2 13. AB is a vertical pole with B at the ground level and A at the top. A man finds that the angle of elevation of the point A from a certain point C on the ground is 60°. He moves away from the pole along the line BC to a point D such that CD = 7 m. From D the angle of elevation of the point A is 45°. Then the height of the pole is (a) 7√3/2 (√3-1) m (b) 7√3/2 (√3+1) m (c) 7√3/2 1/√3+1 m (d) 7√3/2 1/√3-1 m 14. The value of cot [cosec-1 5/3+tan-1 2/3] is (a) 3/17 (b) 4/17 (c) 5/17 (d) 6/17 15. Statement-1 : For every natural number n ≥ 2, 1/√1 + 1/√2+…..+1/√n > √n. Statement-2 : For every natural number n ≥ 2, √n(n+1) < n + 1. (a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for statement-1 (b) Statement-1 is true, Statement-2 is false (c) Statement-1 is false, Statement-2 is true (d) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for statement-1 16. The perpendicular bisector of the line segment joining P(1, 4) and Q(k, 3) hay y-intercept – 4. Then a possible value of k is (a) 1 (b) – 2 (c) – 4 (d) 2 17. Suppose the cubic x3 – px + q has three distinct real roots where p > 0 and q > 0. Then which one of the following holds?www.studentguide.co.in Buy Books & Magazines Online Free Email & SMS Solved Question Papers & Video Tutors Mock Exams (CAT, IIT, Gate, etc) Scholarships & Loans Expert Advice & Discussion Board (a) The cubic has maxima at both √p/3 and -√p/3 (b) The cubic has minima at √p/3 and maxima at -√p/3 (c) The cubic has minima at both √p/3 and -√p/3 (d) The cubic has minima at -√p/3 and maxima at √p/3 18. The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following gives possible values of a and b? (a) a = 5, b = 2 (b) a = 3, b = 4 (c) a = 0, b = 7 (d) a = 1, b = 6 19. The conjugate of a complex numbers is 1/i – 1. Then that complex numbers is (a) 1/i + 1 (b) –1/i – 1 (c) – 1/i + 1 (d) 1/i – 1 20. The quadratic equations x2 – 6x + a = 0 and x2 – cx + 6 = 0 have one root in common. The other roots of the first and second equations are integers in the ration 4 : 3. Then the common root is (a) 4 (b) 3 (c) 2 (d) 1 21. Let f: N → Y be a function defined as f(x) = 4x + 3 where Y = {y N : y = 4x + 3 for some x N}. Show that f is invertible and its inverse is (a) g(y) = 4 + y+3/4 (b) g(y) = y – 3/4 (c) g(y) = 3y + 4/3 (d) g(y) = y+3/4 22. Then which one of the following is true? (a) f is differentiable at x = 0 and at x = 1 (b) f is neither differentiable at x = 0 nor at x = 1 (c) f is differentiable at x = 0 but not at x = 1 (d) f is differentiable at x = 1 but not at x = 0 23. The value of √2 ∫ sin x dx/sin (x – π/4) is (a) x – log|sin (x – π/4)|+c (b) x – log|cos (x – π/4)|+c (c) x + log|cos (x – π/4)|+c (d) x + log|sin (x – π/4)|+c 24. The first two terms of a geometric progression add up to 12. The sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately positive and negative, then the first terms is www.studentguide.co.in Buy Books & Magazines Online Free Email & SMS Solved Question Papers & Video Tutors Mock Exams (CAT, IIT, Gate, etc) Scholarships & Loans Expert Advice & Discussion Board (a) 4 (b) – 12 (c) 12 (d) – 4 25. Let A be a square matrix all of whose entries are integers. Then which one of the following is true? (a) If det A = ± 1, then A-1 exists and all its entries are integers (b) If det A = ± 1, then A-1 need not exist (c) If det A = ± 1, then A-1 exists but all its entries are not necessarily integers (d) If det A ≠ ± 1, then A-1 exists and all its entries are non-integers 26. How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent? (a) 8. 6C4. 7C4 (b) 7. 6C4. 8C4 (c) 6.8. 7C4 (d) 6.7. 8C4 27. The differential equation of the family of circles with fixed radius 5 units and centre on the line y = 2 is (a) (y – 2) y’2 = 25 – (y – 2)2 (b) (x – 2)2 y’2 = 25 – (y – 2)2 (c) (y – 2)2 y’2 = 25 – (y – 2)2 (d) (x – 2) y’2 = 25 – (y – 2)2 28. It is given that the events A and B are such that P(A) = 1/4, P(A | B) = 1/2 and P(B | A) = 2/3. Then P(B) is (a) 1/6 (b) 1/3 (c) 1/2 (d) 2/3 29. The line passing through the points (5, 1, a) and (3, b, 1) crosses the yz-plane at the point (0, 17/2, -13/2). Then (a) a = 4, b = 6 (b) a = 2, b = 8 (c) a = 8, b = 2 (d) a = 6, b = 4 30. Let p be the statement “x is an irrational number”, q be the statement “y is a transcendental number”, and r be the statement “x is a rational number iff y is a transcendental number”. Statement-1 : r is equivalent to either q or p. Statement-2 : r is equivalent to (p ↔ q). (a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for statement-1 (b) Statement-1 is true, Statement-2 is false (c) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for statement-1 (d) Statement-1 is false, Statement-2 is true 31. The statement p → (q → p) is equivalent to (a) p → (p ↔ q) (b) p → (p → q) (c) p → (p ? q) (d) p → (p ? q) 32. The solution of the differential equation dy/dx = x+y/x satisfying the condition y(1) = 1 is (a) y = x ln x + x (b) y = x ln x + x2 (c) y = ln x + x (d) y = x e(x-1)www.studentguide.co.in Buy Books & Magazines Online Free Email & SMS Solved Question Papers & Video Tutors Mock Exams (CAT, IIT, Gate, etc) Scholarships & Loans Expert Advice & Discussion Board 33. Let I = 0∫1 sin x/√x dx and J = 0∫1 cos x/√x dx. Then which one of the following is true? (a) I > 2/3 and J < 2 (b) I < 2/3 and J < 2 (c) I > 2/3 and J > 2 (d) I < 2/3 and J > 2 34. In a shop there are five types of ice-creams available. A child buys six ice-creams. Statement-1 : The number of different ways the child can buy the six ice-creams is 10C5. Statement-2 : The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging 6 A’s and 4 B’s in a row. (a) Statement-1 is true, Statement-2 is false (b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for statement-1 (c) Statement-1 is false, Statement-2 is true (d) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for statement-1 35. Statement-1 : r=0∑n (r+1)nCr = (n+2)2n-1 Statement-2 : r=0∑n (r+1)nCr xr = (1 + x)n + nx (1 + x)n-1 (a) Statement-1 is true, Statement-2 is false (b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for statement-1 (c) Statement-1 is false, Statement-2 is true (d) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for statement-1www.studentguide.co.in Buy Books & Magazines Online Free Email & SMS Solved Question Papers & Video Tutors Mock Exams (CAT, IIT, Gate, etc) Scholarships & Loans Expert Advice & Discussion Board AIEEE -Previous year Papers -PHYSICS-2008 1. A thin spherical shell of radius R has charge Q spread uniformly over its surface. Which of the following graphs most closely represents the electric field E(r) produced by the shell in the range 0 < r < ∞, where r is the distance from the centre of the shell? 2. Consider a uniform square plate of side a and mass m. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is (a) 1/12 ma2 (b) 2/3 ma2 (c) 5/6 ma2 (d) 7/12 ma2 3. A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is 11 km s-1, the escape velocity from the surface of the planet would be (a) 110 km s-1 (b) 1.1 km s-1 (c) 11 km s-1 (d) 0.11 km s-1 4. Statement-1: For a mass M kept at the centre of a cube of side a, the flux of gravitational field passing through its sides is 4πGM. Statement-2: If the direction of a field due to a point source is radial and its dependence on the distance r from the source is given as 1/r2, its flux through a closed surface depends only on the strength of the source enclosed by the surface and not on the size or shape of the surface. (a) Statement-1 is true, stateemtn-2 is true; statement-2 is a correct explanation for statement-1. (b) Statement-1 is true, statement-2 is false. (c) Statement-1 is false, statement-2 is true. (d) Stateemtn-1 is true, statement-2 is true; stateemtn-2 is not a correct explanation for statement-1. 5. In an experiment, electrons are made to pass through a narrow slit of width d comparable to their de Broglie wavelength. They are detected on a screen at a distance D from the slit.www.studentguide.co.in Buy Books & Magazines Online Free Email & SMS Solved Question Papers & Video Tutors Mock Exams (CAT, IIT, Gate, etc) Scholarships & Loans Expert Advice & Discussion Board Which of the following graphs can be expected to represent the number of electrons N detected as a function of the detector position y (y = 0 corresponds to the middle of the slit)? 6. A capillary tube (A) is dipped in water. Another identical tube (B) is dipped in a soap-water solution. Which of the following shown the relative nature of the liquid columns in the two tubes? Directions:-Questions 31, 32 and 33 are based on the following paragraph.www.studentguide.co.in Buy Books & Magazines Online Free Email & SMS Solved Question Papers & Video Tutors Mock Exams (CAT, IIT, Gate, etc) Scholarships & Loans Expert Advice & Discussion Board Wave property of electrons implies that they will show diffraction effects. Davisson and Germer demonstrated this by diffracting electrons from crystals. The law governing the diffraction from a crystal is obtained by requiring that electron waves reflected from the planes of atoms in a crystal interfere constructively (see figure). 7. A body is at rest at x = 0. At t = 0, it starts moving in the positive x-direction with a constant acceleration. At the same instant another body passes through x = 0 moving in the positive x-direction with a constant speed. The position of the first body is given by x1(t) after time t and that of the second body by x2 (t) after the same time interval. Which of the following graphs correctly describes (x1 – x2) as a function of time t? Directions:-Questions 8 and 9 contains statement-1 and statement-2. Of the four choices given, choose the one that best describes the two statements. (a) Statement-1 is true, statement-2 is false. (b) Statement-1 is false, statement-2 is true. (c) Statement-1 is true, stateemtn-2 is true; statement-2 is a correct explanation for statement-1. (d) Stateemtn-1 is true, statement-2 is true; stateemtn-2 is not a correct explanation for statement-1. 8. An athlete in the Olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range (a) 20,000 J – 50,000 J. (b) 2 x 105 J – 3 x 105 J (c) 200 J – 500 J (d) 2,000 J – 5,000 Jwww.studentguide.co.in Buy Books & Magazines Online Free Email & SMS Solved Question Papers & Video Tutors Mock Exams (CAT, IIT, Gate, etc) Scholarships & Loans Expert Advice & Discussion Board 9. A spherical solid ball of volume V is made of a material of density ρ1. It is falling through a liquid of density ρ2(ρ2 < ρ1). Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed v,i.e., Fviscous = -kv2 (k > 0). The terminal speed of the ball is (a) Vgρ1/k (b) Vg(ρ1 – ρ2)/k (c) √Vgρ1/k (d) √Vg(ρ1 – ρ2)/k 10. A jar is filled with two non-mixing liquids 1 and 2 having densities ρ1 and ρ2 respectively. A solid ball, made of a material of density ρ3, is dropped in the jar. It comes to equilibrium in the position shown in the figure. Which of the following is true for ρ1, ρ2 and ρ3? (a) ρ1 < ρ3 < ρ2 (b) ρ3 < ρ1 < ρ2 (c) ρ1 > ρ3 > ρ2 (d) ρ1 < ρ2 < ρ3 11. A body of mass m = 3.513 kg is moving along the x-axis with a speed of 5.00 ms-1. The magnitude of its momentum is recorded as (a) 17.6 kg ms-1 (b) 17.565 kg ms-1 (c) 17.57 kg ms-1 (d) 17.56 kg ms-1. 12. A student measures the focal length of a convex lens by putting an object pin at a distance u from the lens and measuring the distance v of the image pin. The graph between u and v plotted by the student should look like Direction:-Questions 4 and 5 are based on the following paragraph. Consider a block of conducting material of resistivity ρ shown in the figure. Current I enters at A and leaves from D. We apply superposition principle to find voltage ?V developed between B and C. The calculation is done in the following steps: (i) Take current I entering from A and assume it to spread over a hemispherical surface in the block. (ii) Calculate field E(r) at distance r from A by using Ohm’s law E = ρj, where j is the current per unit area at r. (iii) From the r dependence of E(r), obtain the potential V(r) at r. (iv) Repeat (i), (ii) and (iii) for current I leaving D and superpose results for A and D.www.studentguide.co.in Buy Books & Magazines Online Free Email & SMS Solved Question Papers & Video Tutors Mock Exams (CAT, IIT, Gate, etc) Scholarships & Loans Expert Advice & Discussion Board 13. Statement-1 : Energy is released when heavy nuclei undergo fission or light nuclei undergo fusion. Statement-2 : For heavy nuclei, binding energy per nucleon increases with increasing Z while for light nuclei it decreases with increasing Z. (a) Stateemtn-1 is true, statement-2 is true; stateemtn-2 is not a correct explanation for statement-1. (b) Statement-1 is true, statement-2 is false. (c) Statement-1 is false, statement-2 is true. (d) Statement-1 is true, stateemtn-2 is true; statement-2 is a correct explanation for statement-1. 14. The dimension of magnetic field in M, L, T and C (coulomb) is given as (a) MT-2 C-1 (b) MT-1 C-1. (c) MLT-1 C-1 (d) MT2 C-2 15. A wave travelling along the x-axis is described by the equation y(x, t) = 0.005 cos(αx -βt). If the wavelength and the time period of the wave are 0.08 m and 2.0 s, respectively, then α and β in appropriate units are (a) α = 0.08/π, β = 2.0/π (b) α = 12.50π, β = π/2.0 (c) α = 0.04/π, β = 1.0/π (d) α = 25.00π, β = π 16. An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume V1 and contains ideal gas at pressure P1 and temperature T1. The other chamber has volume V2 and contains ideal gas at pressure P2 and temperature T2. If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be (a) P1V1T1 + P2V2T2 /P1V1 + P2V2 (b) T1T2(P1V1 + P2V2) /P1V1T2 + P2V2T1 (c) T1T2(P1V1 + P2V2) /P1V1T1 + P2V2T2 (d) P1V1T2 + P2V2T1 /P1V1 + P2V2 17. Shown in the figure below is a meter-bridge set up with null deflection in the galvanometer. The value of the unknown resistance R iswww.studentguide.co.in Buy Books & Magazines Online Free Email & SMS Solved Question Papers & Video Tutors Mock Exams (CAT, IIT, Gate, etc) Scholarships & Loans Expert Advice & Discussion Board (a) 13.75 Ω (b) 55 Ω (c) 110. Ω (d) 220 Ω 18. The speed of sound in oxygen (O2) at a certain temperature is 460 ms-1. The speed of sound in helium (He) at the same temperature will be (assume both gases to be ideal) (a) 460 ms-1 (b) 330 ms-1 (c) 500 ms-1 (d) 650 ms-1. 19. An experiment is performed to find the refractive index of glass using a travelling microscope. In this experiment distances are measured by (a) a vernier scale provided on the microscope (b) a screw gauge provided on the microscope (c) a meter scale provided on the microscope. (d) a standard laboratory scale 20. Electrons accelerated by potential V are diffracted from a crystal. If d = 1 and i = 30°, V should be about (h = 6.6 x 10-34 Js, me = 9.1 x 10-31 kg, e = 1.6 x 10-19 C) (a) 2000 V (b) 1000 V (c) 50 V (d) 500 V. 21. A parallel plate capacitor with air between the plates has a capacitance of 9 pF. The separation between its plates is d. The space between the plates is now filled with two dielectrics. One of the dielectrics has dielectric constant k1 = 3 and thickness d/3 while the other one has dielectric constant k2 = 6 and thickness 2d/3. Capacitance of the capacitor is now (a) 45 pF (b) 20.25 pF (c) 1.8 pF (d) 40.5 pF. 22. A 5 V battery with internal resistance 2Ω and 2V better with internal resistance 1Ω are connected to a 10Ω resistor as shown in the figure. The current in the 10Ω resistor is (a) 0.27 A P1 to P2 (b) 0.03 A P1 to P2 (c) 0.27 A P2 to P1 (d) 0.03 A P2 to P1.www.studentguide.co.in Buy Books & Magazines Online Free Email & SMS Solved Question Papers & Video Tutors Mock Exams (CAT, IIT, Gate, etc) Scholarships & Loans Expert Advice & Discussion Board 23. Relative permittivity and permeability of a material are εr and μr, respectively. Which of the following values of these quantities are allowed for a diamagnetic material? (a) εr = 1.5, μr = 0.5 (b) εr = 1.5, μr = 1.5 (c) εr = 0.5, μr = 1.5 (d) εr = 0.5, μr = 0.5 24. Suppose an electron is attracted towards the origin by a force k/r where k is a constant and r is the distance of the electron from the origin. By applying Bohr model to this system, the radius of then nth orbital of the electron is found to be rn and the kinetic energy of the electron to be Tn. Then which of the following is true? (a) Tn α 1/n2, rn α n2 (b) Tn α 1/n, rn α n2 (c) Tn α 1/n, rn α n (d) Tn independent of r, rn α n 25. A horizontal overhead powerline is at a height of 4 m from the ground and carries a current of 100 A from east to west. The magnetic field directly below it on the ground is (μ0 = 4π x 10-7 T m A-1) (a) 2.5 x 10-7 T southward (b) 5 x 10-6 T northward (c) 2.5 x 10-7 T northward (d) 5 x 10-6 T southward. 26. While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance condition at a column length of 18 cm during winter. Repeating the same experiment during summer, she measures the column length to be x cm for the second resonance. Then (a) x > 54 (b) 18 > x (c) 36 > x >18 (d) 54 > x >36. 27. A working transistor with its three legs marked P, Q and R is tested using a multimeter. No conduction is found between P and Q. By connecting the common (negative) terminal of the multimeter to R and the other (positive) terminal to P or Q, some resistance is seen on the multimeter. Which of the following is true for the transistor? (a) It is a pnp transistor with R as collector. (b) It is an npn transistor with R as collector. (c) It is an npn transistor with R as base. (d) It is a pnp transistor with R as emitter. 28. For current entering at A, the electric field at a distance r from A is (a) ρI/8πr2 (b) ρI/4πr2 (c)ρI/r2 (d) ρI/2πr2 29. In the circuit below, A and B represent two inputs and C represents the output. The circuit represents www.studentguide.co.in Buy Books & Magazines Online Free Email & SMS Solved Question Papers & Video Tutors Mock Exams (CAT, IIT, Gate, etc) Scholarships & Loans Expert Advice & Discussion Board (a) OR gate (b) NAND gate. (c) AND gate (d) NOR gate 30. Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross-sectional area A = 10 cm3 and length = 20 cm. If one of the solenoids has 300 turns and the other 400 turns, their mutual inductance is (μ0 = 4π x 10-7 T mA-1) (a) 2.4π X 10-4H (b) 4.8π X 10-5H. (c) 4.8π X 10-4H (d) 2.4π X 10-5 H 31. A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is (a) 0.16 J (b) 0.34 J (c) 1.00 J (d) 0.67 J. 32. Two full turns of the circular scale of a screw gauge cover a distance of 1 mm on its main scale. The total number of divisions on the circular scale is 50. Further, it is found that the screw gauge has a zero error of – 0.03 mm. While measuring the diameter of a thin wire, a student notes the main scale reading of 3 mm and the number of circular scale divisions in line with the main scale as 35. The diameter of the wire is (a) 3.38 mm (b) 3.73 mm (c) 3.67 mm. (d) 3.32 mm 33. ΔV measured between B and C is (a) ρI/a – ρI/(a + b) (b) ρI/2πa – ρI/2π(a + b) (c) ρI /2π(a -b) (d) ρI/πa – ρI/π(a + b) 34. If a strong diffraction peak is observed when electrons are incident at an angle i from the normal to the crystal planes with distance d between them (see figure), de Broglie wavelength λdB of electrons can be calculated by the relationship (n is an integer) (a) d cosi = nλdB (b) d sini = nλdB (c) 2d sini = nλdB (d) 2d cosi = nλdB 35. A thin rod of length L is lying along the x-axis with its ends at x = 0 and x = L. Its linear density (mass/length) varies with x as k(x/L)n where n can be zero or any positive number. If the position xCM of the centre of mass of the rod is plotted against n, which of the following graphs best approximates the dependence of xCM on n?www.studentguide.co.in Buy Books & Magazines Online Free Email & SMS Solved Question Papers & Video Tutors Mock Exams (CAT, IIT, Gate, etc) Scholarships & Loans Expert Advice & Discussion Boardwww.studentguide.co.in Buy Books & Magazines Online Free Email & SMS Solved Question Papers & Video Tutors Mock Exams (CAT, IIT, Gate, etc) Scholarships & Loans Expert Advice & Discussion Board AIEEE -Previous year Papers -CHEMISTRY -2008 1. The pKa of a weak acid, HA, is 4.80. The pKb of a weak base, BOH is 4.78. The pH of an aqueous solution of the corresponding salt, BA, will be (a) 4.79 (b) 9.58 (c) 9.22 (d) 7.01 2. Which one of the following constitutes a group of the isoelectronic species? (a) CN-, N2, O22-, C22-(b) C22-, O2-, CO, NO (c) NO+, C22-, CN-, N2 (d) N2, O2-, NO+, CO 3. Larger number of oxidation states are exhibited by the actinoids than those by the lanthanoids, the main reason being (a) More reactive nature of the actinoids than the lanthanoids (b) 4f orbitals more diffused than the 5f orbitals (c) More energy difference between 5f and 6d than between 4f and 5d orbitals (d) Lesser energy difference between 5f and 6d than between 4f and 5d orbitals 4. Standard entropy of X2, Y2 and XY3 are 60, 40 and 50 J K-1 mol-1, respectively. For the reaction, 1/2 X2 + 3/2 Y2 → XY3,ΔH = -30 kJ, to be at equilibrium, the temperature will be (a) 1250 K (b) 1000 K (c) 500 K (d) 750 K 5. Given = -0.72 V, = -0.42 V. The potential for the cell Cr |Cr3+ (0.1 M)| |Fe2+ (0.01 M) | Fe is (a) 0.26 V (b) –0.26 V (c) 0.339 V (d) –0.339 V 6. The treatment of CH3MgX with CH3C ≡ C – H produces (b) CH3C ≡ C – CH3 (c) CH3 – CH = CH2 (d) CH4 7. The absolute configuration of (a) R, R (b) S, R (c) R, S (d) S, Swww.studentguide.co.in Buy Books & Magazines Online Free Email & SMS Solved Question Papers & Video Tutors Mock Exams (CAT, IIT, Gate, etc) Scholarships & Loans Expert Advice & Discussion Board 8. In which of the following octahedral complexes of Co (At. no. 27), will the magnitude of Δoct be the highest? (a) [Co(C2O4)3]3-(b) [Co(NH3)6]3+ (c) [Co(CN)6]3-(d) [CO(H2O)6]3+ 9. The electrophile, E+attacks the benzene ring to generate the intermediate σ-complex. Of the following, which σ-complex is of lowest energy? 10. The ionization enthalpy of hydrogen atom is 1.312 x 106 J mol-1. The energy required to excite the electron in the atom from n = 1 to n = 2 is (a) 9.84 X 105 J mol-1 (b) 8.51 X 105 J mol-1 (c) 6.56 X 105 J mol-1 (d) 7.56 X 105 J mol-1 11. In the following sequence of reactions, the alkene affords the compound B The compound B is (a) CH3CH2CHO (b) CH3COCH3 (c) CH3CHO (d) CH3CH2COCH3 12. They hydrocarbon which can react with sodium in liquid ammonia is (a) CH3CH2CH2C ≡ CCH2CH2CH3 (b) CH3CH = CHCH3 (c) CH3CH2C ≡ CH (d) CH3CH2 C ≡ CCH2CH3 13. The equilibrium constants kp1 and kp2 for the reactions X 2Y and Z P + Q, respectively are in the ratio of 1 : 9. If degree of dissociation of X and Z be equal then the ratio of total pressures at these equilibria is (a) 1 : 9 (b) 1 : 36 (c) 1 : 1 (d) 1 : 3 www.studentguide.co.in Buy Books & Magazines Online Free Email & SMS Solved Question Papers & Video Tutors Mock Exams (CAT, IIT, Gate, etc) Scholarships & Loans Expert Advice & Discussion Board 14. Amount of oxalic acid present in a solution can be determined by its titration with KMnO4 solution in the presence of H2SO4. The titration gives unsatisfactory result when carried out in the presence of HCl, because HCl (a) furnished H+ ions in addition to those from oxalic acid (b) gets oxidised by oxalic acid to chlorine (c) oxidizes oxalic acid to carbon dioxide and water (d) reduces permanganate to Mn2+ 15. Which one of the following is the correct statement? (a) Chlorides of both beryllium and aluminium have bridged chloride structures in solid phase. (b) Boric acid is a protonic acid (c) B2H6. 2NH3 is known as ‘inorganic benzene’. (d) Beryllium exhibits coordination number of six. 16. Toluene is nitrated and the resulting product is reduced with tin and hydrochloric acid. The product so obtained is diazotised and then heated with cuprous bromide. The reaction mixture so formed contains (a) Mixture of o-and p-bromotoluenes (b) Mixture of o-and p-dibromobenzenes (c) Mixture of o-and m-bromotoluenes (d) Mixture of o-and p-bromoanilines 17. Among the following substituted silanes the one which will give rise to cross linked silicone polymer on hydrolysis is (a) RSiCl3 (b) R3SiCl (c) R4Si (d) R2SiCl2 18. In context with the industrial preparation of hydrogen from water gas (CO + H2), which of the following is the correct statement? (a) CO and H2 are fractionally separated using difference in their densities (b) CO is removed by absorption in aqueous Cu2Cl2 solution (c) H2 is removed through occlusion with Pd (d) CO is oxidised to CO2 with steam in the presence of a catalyst followed by absorption of CO2 in alkali 19. Phenol, when it first reacts with concentrated sulphuric acid and then with concentrated nitric acid, gives (a) 2, 4, 6-trinitrobenzene (b) o-nitrophenol (c) nitrobenzene (d) p-nitrophenol 20. Oxidising power of chlorine in aqueous solution can be determined by the parameters indicated below:www.studentguide.co.in Buy Books & Magazines Online Free Email & SMS Solved Question Papers & Video Tutors Mock Exams (CAT, IIT, Gate, etc) Scholarships & Loans Expert Advice & Discussion Board Will be (a) +120 kJ mol-1 (b) –610 kJ mol-1 (c) +152 kJ mol-1 (d) –850 kJ mol-1 21. Which of the following factors is of no significance for roasting sulphide ores to the oxides and not subjecting the sulphide ores to carbon reduction directly? (a) CO2 is more volatile than CS2 (b) Metal sulphides are thermodynamically more stable than CS2 (c) CO2 is thermodynamically more stable than CS2 (d) Metal sulphides are less stable than the corresponding oxides 22. α-D-(+)-glucose and β-D-(+)-glucose are (a) enantiomers (b) anomers (c) epimers (d) conformers 23. In a compound, atoms of element Y for ccp lattice and those of element X occupy 2/3rd of tetrahedral voids. The formula of the compound will be (a) X2Y (b) X2Y3 (c) X4Y3 (d) X3Y4 24. Gold numbers of protective colloids A, B, C and D are 0.50, 0.01, 0.10 and 0.005, respectively. The correct order of their protective power is (a) D < A < C < B (b) B < D < A < C (c) A < C < B < D (d) C < B < D < A 25. The vapour pressure of water at 20°C is 17.5 mm Hg. If 18 g of glucose (C6H12O6) is added to 178.2 g of water at 20°C, the vapour pressure of the resulting solution will be (a) 15.750 mm Hg (b) 16.500 mm Hg (c) 17.675 mm Hg (d) 17.325 mm Hg 26. For species are listed below: (i) HCO3-(ii) H3O+ (iii) HSO4-(iv) HSO3F which one of the following is the correct sequence of their acid strength? (a) ii < iii < i < iv (b) iv < ii < iii < i (c) iii < i < iv < ii (d) i < iii < ii < iv 27. Identify the wrong statement in the following. (a) Acid rain is mostly because of oxides of nitrogen and sulphurwww.studentguide.co.in Buy Books & Magazines Online Free Email & SMS Solved Question Papers & Video Tutors Mock Exams (CAT, IIT, Gate, etc) Scholarships & Loans Expert Advice & Discussion Board (b) Chlorofluorocarbons are responsible for ozone layer depletion (c) Greenhouse effect is responsible for global warming (d) Ozone layer does not permit infrared radiation from the sun to reach the earth 28. At 80°C, the vapour pressure of pure liquid A is 520 mm of Hg and that of pure liquid B is 1000 mm of Hg. If a mixture solution of A and B boils at 80°C and 1 atm pressure, the amount of A in the mixture is (1 atm = 760 mm of Hg) (a) 52 mol percent (b) 50 mol percent (c) 34 mol percent (d) 48 mol percent 29. The organic chloro compound, which shows complete stereochemical inversion during a SN2 reaction, is (a) (C2H5)2CHCl (b) (CH3)2CHCl (c) CH3Cl (d) (CH3)3CCl 30. Which one of the following pairs of species have the same bond order? (a) O2-and CN-(b) CN-and CN+ (c) CN-and NO+ (d) NO+ and CN+ 31. For a reaction 1/2 A → 2B rate of disappearance of A is related to the rate of appearance of B by the expression (a) – d[A]/dt = 1/2d[B]/dt (b) – d[A]/dt = 1/4d[B]/dt (c) – d[A]/dt = d[B]/dt (d) – d[A]/dt = 4d[B]/dt 32. Bakelite is obtained from phenol by reaction with (a) CH3CHO (b) CH3COCH3 (c) (CH2OH)2 (d) HCHO 33. For the following three reactions (i), (ii) and (iii), equilibrium constants are given (i) CO(g) + H2O(g) CO2(g) + H2(g); K1 (ii) CH4(g) + H2O(g) CO(g) + 3H2(g);K2 (iii) CH4(g) + 2H2O(g) CO2(g) + 4H2(g) ; K3 Which of the following relation is correct? (a) K2 K3 = K1 (b) K1 √K2 = K3 (c) K3 .K23 = K12 (d) K3 = K1 K2 34. The correct decreasing order of priority for the functional groups of organic compounds in the IUPAC system of nomenclature is (a) – SO3H, – COOH, – CONH2, – CHO (b) – CONH2, – CHO, – SO3H, – COOH (c) – COOH, – SO3H, – CONH2, – CHO (d) – CHO, – COOH, – SO3H, – CONH2 36. The coordination number and the oxidation state of the element E in the complex [E(en)2 (C2O4)]NO2 (where (en) is ethylene diamine) are, respectively (a) 6 and 2 (b) 6 and 3 (c) 4 and 2 (d) 4 and 3