Page 1 ?IN ? GATE 2010 1 Q. No. 1 – 25 Carry One Mark Each 1. The infinite series () 357 xx x f x x ............ 3! 5! 7! = -+- 8 converges to (A) () cos x (B) ( ) sin x (C) ( ) sinh x (D) x e 2. The diameters of 10000 ball bearings were measured. The mean diameter and standard deviation were found to be 10mm and 0.05mm respectively. Assuming Gaussian distribution of measurements, it can be expected that the number of measurements more than 10.15mm will be (A)230 (B) 115 (C) 15 (D)2 3. A person weighing 60 kg receives radiation energy of 0.3J over the entire body. The dose of radiation absorbed (in rad) is (A) 0.005 rad (B) 0.1 rad (C) 0.3 rad (D) 0.5 rad 4. u(t) represents the unit step function. The Laplace transform of () ut- t is (A) 1 s t (B) 1 s - t (C) s e s - t (D) s e -t 5. A measurement system with input x(t) and output y(t) is described by the differential equation dy 35y8x dt += . The static sensitivity of the system is (A)0.60 (B) 1.60 (C) 1.67 (D) 2.67 6. Poisson’s ratio for a metal is 0.35. Neglecting piezo-resistance effect, the gage factor of a strain gage made of this metal is (A) 0.65 (B) 1 (C) 1.35 (D) 1.70 7. Match the Following P. Radiation Pyrometer W. Angular velocity measurement Q. Dall tube X. Vacuum pressure measurement R. Pirani gauge Y. Flow measurement S. Gyroscope Z. Temperature measurement (A) P-Z, Q-W, R-X, S-Y (B) P-Z, Q-Y, R-X, S-W (C) P-W, Q-X, R-Y, S-Z (D) P-Z, Q-X, R-W, S-Y 8. In a pulse code modulated (PCM) signal sampled at f s and encoded into an n-bit code, the minimum bandwidth required for faithful reconstruction is (A) s 2nf (B) s nf (C) s nf 2 (D) s f Page 2 ?IN ? GATE 2010 1 Q. No. 1 – 25 Carry One Mark Each 1. The infinite series () 357 xx x f x x ............ 3! 5! 7! = -+- 8 converges to (A) () cos x (B) ( ) sin x (C) ( ) sinh x (D) x e 2. The diameters of 10000 ball bearings were measured. The mean diameter and standard deviation were found to be 10mm and 0.05mm respectively. Assuming Gaussian distribution of measurements, it can be expected that the number of measurements more than 10.15mm will be (A)230 (B) 115 (C) 15 (D)2 3. A person weighing 60 kg receives radiation energy of 0.3J over the entire body. The dose of radiation absorbed (in rad) is (A) 0.005 rad (B) 0.1 rad (C) 0.3 rad (D) 0.5 rad 4. u(t) represents the unit step function. The Laplace transform of () ut- t is (A) 1 s t (B) 1 s - t (C) s e s - t (D) s e -t 5. A measurement system with input x(t) and output y(t) is described by the differential equation dy 35y8x dt += . The static sensitivity of the system is (A)0.60 (B) 1.60 (C) 1.67 (D) 2.67 6. Poisson’s ratio for a metal is 0.35. Neglecting piezo-resistance effect, the gage factor of a strain gage made of this metal is (A) 0.65 (B) 1 (C) 1.35 (D) 1.70 7. Match the Following P. Radiation Pyrometer W. Angular velocity measurement Q. Dall tube X. Vacuum pressure measurement R. Pirani gauge Y. Flow measurement S. Gyroscope Z. Temperature measurement (A) P-Z, Q-W, R-X, S-Y (B) P-Z, Q-Y, R-X, S-W (C) P-W, Q-X, R-Y, S-Z (D) P-Z, Q-X, R-W, S-Y 8. In a pulse code modulated (PCM) signal sampled at f s and encoded into an n-bit code, the minimum bandwidth required for faithful reconstruction is (A) s 2nf (B) s nf (C) s nf 2 (D) s f ?IN ? GATE 2010 2 9. A beam of unpolarized light is first passed through a linear polarizer and then through a quarter-wave plate. The emergent beam is (A) unpolarized (B) linearly polarized (C) circularly polarized (D) elliptically polarized 10. f(x), shown in the adjoining figure is represented by () ( ) ( ) {} 0n n n1 f x a a cos nx b sin nx 8 = =+ + ? . The value of a 0 is (A) 0 (B) 2 p (C) p (D) 2 p 11. The PMMC ammeter A in the adjoining figure has a range of 0 to 3mA. When switch S1 is opened, the pointer of the ammeter swings to the 1mA mark, returns and settles at 0.9mA. The meter is (A) critically damped and has a coil resistance of 100 O (B) critically damped and has a coil resistance of 200 O (C) under damped and has a coil resistance of 100 O (D) under damped and has a coil resistance of 200 O 12. The open loop transfer function of a unity gain feedback system is given by: () ( ) ()( ) ks 3 Gs s1 s 2 + = ++ . The range of positive values of k for which the closed loop system will remain stable is: (A) 1k 3 << (B) 0<k<10 (C) 5<k< 8 (D) 0<k< 8 13. A real nn × matrix ij Aa ?? = ?? is defined as follows ij a i, if i=j = 0, otherwise = The summation of all n eigen values of A is 2 -p -p 0 p 2 p 3 p x ( ) fx 1.5 1 1.0 - 1.5 - S1 A + - + - 1.8V 1.8k ORead More

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