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1. The constraint A2 = A on any square matrix A is satisfied for

2. The general solution of the different equation d2y/dt2 + dy/dt - 2t = 0 is

3. An aircraft in trimmed condition has zero pitching moment at

4. In an aircraft, constant roll rate can be produced using ailerons by applying

5. For a symmetric airfoil, the lift coefficient for zero degree angle of attack is

2. The line y = x - 1 can be expressed in polar coordinates (r, θ) as

3. The type of pump used in forced water cooling system of a tractor engine is

4. Which one of the following statements is NOT appropriate regarding cone index

5. The draft and total power requirement of a rotary cultivator operating in concurrent mode as compared to a spring tyne cultivator of equal cutting width under the same operating conditions, respectively are

6. The soil erodibility factor needs to be determined for use in the universal soil loss equation. The length, in m and slope, in % of the experimental plot to be used for this purpose, respectively are

1. Consider the following set of linear algebraic equations x1 + 2x2 + 3x3 = 2 x2 + x3 = - 1 2x2 + 2x3 = 0 The system has

2. If a and b are arbitrary constants, then the solution to the ordinary differential equation d2y/dx2 - 4y = 0 is

3. For the function f(t) = e-t/T, the Taylor series approximation for t << T is

4. A box containing 10 identical compartments has 6 red balls and 2 blue balls. If each compartment can hold only one ball, then the number of different possible arrangements are

6. In a throttling process, the pressure of an ideal gas reduces by 50 %. If CP and CV are the heat capacities at constant pressure and constant volume, respectively (r = CP/CV) the specific volume will change by a factor of

1. The estimate of obtained using Simpson’s rule with three-point function evaluation exceeds the exact value by

2. The annual precipitation data of a city is normally distributed with mean and standard deviation as 1000 mm and 200 mm, respectively. The probability that the annual precipitation will be more than 1200 mm is

3. The infinite series 1 + x + x2/2! + x3/3! + x4/4! + ... corresponds to

4. The Poisson’s ratio is defined as

5. The following statements are related to bending of beams: I The slope of the bending moment diagram is equal to the shear force. II The slope of the shear force diagram is equal to the load intensity. III The slope of the curvature is equal to the flexural rotation. IV The second derivative of the deflection is equal to the curvature. The only FALSE statement is

1. Consider the following logical inferences. I1: If it rains then the cricket match will not be played. The cricket match was played. Inference: There was no rain. I2: If it rains then the cricket match will not be played. It did not rain. Inference: The cricket match was played. Which of the following is TRUE?

2. Which of the following is TRUE?

3. Assuming P ≠ NP, which of the following is TRUE?

4. The worst case running time to search for an element in a balanced binary search tree with n2n elements is

6. The decimal value 0.5 in IEEE single precision floating point representation has

3. In a baseband communications link, frequencies upto 3500 Hz are used for signaling. Using a raised cosine pulse with 75% excess bandwidth and for no inter-symbol interference, the maximum possible signaling rate in symbols per second is

4. The electric field of a uniform plane electromagnetic wave in free space, along the positive x direction, is given by . The frequency and polarization of the wave, respectively, are

6. The output Y of a 2-bit comparator is logic 1 whenever the 2-bit input A is greater than the 2-bit input B. The number of combinations for which the output is logic 1, is

9. The average power delivered to an impedance (4 - j3) Ω by a current 5cos(100π t + 100) A is

10. The unilateral Laplace transform of f(t) is 1/(s2 + s + 1). The unilateral Laplace transform of t f (t) is

4. The impulse response of a system is h(t) = t u(t) . For an input u(t -1) , the output is

5. Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system?

6. Two systems with impulse responses h1 (t) and h2 (t) are connected in cascade. Then the overall impulse response of the cascaded system is given by

7. A source vs (t) = V cos 100 πt has an internal impedance of (4 + j3)Ω . If a purely resistive load connected to this source has to extract the maximum power out of the source, its value in Ω should be

8. A single-phase load is supplied by a single-phase voltage source. If the current flowing from the load to the source is 10∠-150oA and if the voltage at the load terminals is 100∠60o V, then the

1. In abrasive jet machining, as the distance between the nozzle tip and the work surface increases, the material removal rate

2. Match the following metal forming processes with their associated stresses in the workpiece. Metal forming process Type of stress 1. Coining P. Tensile 2. Wire Drawing Q. Shear 3. Blanking R. Tensile and compressive 4. Deep Drawing S. Compressive

3. In an interchangeable assembly, shafts of size mate with holes of size The maximum interference (in microns) in the assembly is

4. During normalizing process of steel, the specimen is heated

5. Oil flows through a 200 mm diameter horizontal cast iron pipe (friction factor, f = 0.0225) of length 500 m. The volumetric flow rate is 0.2 m3/s. The head loss (in m) due to friction is (assume g = 9.81 m/s2)

1. ‘Agora’ was provided in Greek towns as a place of

2. The hue at the centre of the Munsell Colour Solid is

3. Which one of the following is NOT a traffic calming measure?

4. ECBC stands for

5. Age-Sex cohort for a state in India is obtained from

1. If x = √-1, then the value of xx is

2. With initial condition x(1) 0.5 , the solution of the differential equation, t dx/dt + x = t is

3. Two independent random variables X and Y are uniformly distributed in the interval [–1, 1]. The probability that max[X, Y] is less than 1/2 is

4. The unilateral Laplace transform of f (t) is 1/(s2 + s + 1). The unilateral Laplace transform of t f (t) is

5. Given f(z) = 1(z + 1) - 2/(z + 3). If C is a counterclockwise path in the z-plane such that |z + 1|, the value of is

1. A is a 2 * 2 matrix with det A = 2. The det (2A) is

3. In a production facility, iron rods are made with a mean diameter of 6 cm and standard deviation of 0.02 cm. If a large number of rods are tested, the approximate percentage of rods whose sizes fall in the range of 5.98 cm to 6.02 cm is

4. Which one of the following methods is NOT used for numerical integration?

6. When a zinc metal rod is immersed in dilute hydrochloric acid, it results in

7. A fluid is flowing with a velocity of 0.5 m/s on a plate moving with a velocity of 0.01 m/s in the same direction. The velocity at the interface of the fluid and plate is

2. For the spherical surface x2 + y2 + z2 = 1, the unit outward normal vector at the point (1/√2, 1/√2, 0) is given by

3. Consider the function f(x) = |x| in the interval -1 ≤ x ≤ 1. At the point x = 0, f(x) is

4. At x = 0, the function f (x) = x3 + 1 has

5. The area enclosed between the straight line y = x and the parabola y = x2 in the x-y plane is

6. For a long slender column of uniform cross section, the ratio of critical buckling load for the case with both ends clamped to the case with both ends hinged is

1. The fibre which has a mineral origin is

2. The chemical that is used to convert soda cellulose to sodium cellulose xanthate in the manufacture of viscose rayon is

3. The fibre that will float on water is

4. The range of spinning speed (m/min) used in the manufacture of partially oriented polyester yarn is

5. Drawing of synthetic filament does not lead to an increase in

1. In the Coward flammability diagram, the respective percentages of methane and oxygen at the nose limit are

2. If the transpose of a matrix is equal to its inverse, then the matrix is

3. In the Moh’s scale of hardness, the minerals in increasing sequence of hardness are

5. For a 25 mm diameter spherical charge, the maximum allowable charge length in cm is

6. Long-hole drilling with crater blasting is used for the construction of

1. The straight lines L1 : x = 0, L2 : y = 0 and L3 : x + y = 1 are mapped by the transformation w = z2 into the curves C1 , C2 and C3 respectively. The angle of intersection between the curves at w = 0 is

2. In a topological space, which of the following statements is NOT always true :

3. Consider the following statements: P: The family of subsets {An = (-1/n, 1/n), n = 1, 2, ...} satisfies the finite intersection property. Q: On an infinite set X , a metric d : X * X --> R is defined as d(x,y) = [0 , x = y and 1, x ≠ y] The metric space (X,d) is compact. R: In a Frechet (T1) topological space, every finite set is closed. S: If f : R --> X is continuous, where R is given the usual topology and (X, t) is a Hausdorff (T2) space, then f is a one-one function. Which of the above statements are correct?

4. A simple random sample of size 10 from 2 N(μ,σ2) gives 98% confidence interval (20.49, 23.51). Then the null hypothesis H0 : μ = 20.5 against HA : μ ≠ 20.5

5. For the linear programming problem Maximize z = x1 + 2x2 + 3x3 - 4x4 Subject to 2x1 + 3x2 - x3 - x4 = 15 6x1 + x2 + x3 - 3x4 = 21 8x1 + 2x2 + 3x3 - 4x4 = 30 x1, x2, x3, x4 ≥ 0, x1 = 4, x2 = 3, x3 = 0, x4 = 2 is

1. f(x) is a symmetric periodic function of x i.e. f(x) = f(-x). Then, in general, the Fourier series of the function f(x) will be of the form

2. In the most general case, which one of the following quantities is NOT a second order tensor?

3. An electron is moving with a velocity of 0.85c in the same direction as that of a moving photon. The relative velocity of the electron with respect to photon is

4. If Planck's constant were zero, then the total energy contained in a box filled with radiation of all frequencies at temperature T would be ( k is the Boltzmann constant and T is nonzero)

5. Across a first order phase transition, the free energy is

1. In mismatch correction repair, the parental DNA strand is distinguished from the daughter strand by

2. The basis for blue-white screening with pUC vectors is

3. Idiotypic determinants of an antibody are associated with the

4. Identification of blood groups involves

5. B-lymphocytes originate from the bone marrow whereas T-lymphocytes originate from

1. I n the proton decoupled 13C NMR spectrum of 7-norbornanone, the number of signals obtained is

4. If Δy and Δpy are the uncertainties in the y-coordinate and the y component of the momentum of a particle respectively, then, according to uncertainty principle ΔyΔpy is (ћ = h/2π and h is Planck’s constant)

5. The average length of a typical α-helix comprised of 10 amino acids is

6. Number of thymine residues in a 5000 kb DNA containing 23% guanine residues is

8. T he ratio of relative intensities of the two molecular ion peaks of methyl bromide (CH3Br) in the mass spectrum is

1. In Mohs’ scale of hardness, how many minerals are of silicate composition?

2. Which one of the following river systems forms the largest fluvio-deltaic system in the world?

3. Which one amongst the following rocks commonly has highest unconfined compressive strength?

4. Eparchean unconformity separates geological units of

5. Point bar deposit is associated with

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