Page 1 |EC-GATE-2013 PAPER| www.gateforum.com GATEFORUM- India’s No.1 institute for GATE training 1 Q. No. 1 – 25 Carry One Mark Each 1. A bulb in a staircase has two switches, one switch being at the ground floor and the other one at the first floor. The bulb can be turned ON and also can be turned OFF by any one of the switches irrespective of the state of the other switch. The logic of switching of the bulb resembles (A) an AND gate (B) an OR gate (C) an XOR gate (D) a NAND gate Answer: (C) Exp: (C) Let Switches = 1 2 p , p 1 2 p , p Z(o / p) OFF OFF OFF OFF ON ON ON OFF ON ON ON OFF From Truth Table, it can be verified that Ex-OR logic is implemented. 2. Consider a vector field ( ) A r . The closed loop line integral A dl • ? can be expressed as (A) ( ) A ds ?× • ?? over the closed surface bounded by the loop (B) ( ) A dv ?• ??? over the closed volume bounded by the loop (C) ( ) A dv ?• ??? over the open volume bounded by the loop (D) ( ) A ds ?× • ?? over the closed surface bounded by the loop Answer: (D) Exp: (D) Stoke’s Theorem: “ The Line Integral of a vector A around a closed path L is equal to the integral of curl of A over the open surface S enclosed by the closed path L”. ( ) ? = ?× ? ?? A.dl A .ds 3. Two systems with impulse responses ( ) ( ) 1 2 h t and h t are connected in cascade. Then the overall impulse response of the cascaded system is given by (A) Product of ( ) ( ) 1 2 h t and h t (B) Sum of ( ) ( ) 1 2 h t and h t (C) Convolution of ( ) ( ) 1 2 h t and h t (D) Subtraction of ( ) ( ) 2 1 h t from h t Page 2 |EC-GATE-2013 PAPER| www.gateforum.com GATEFORUM- India’s No.1 institute for GATE training 1 Q. No. 1 – 25 Carry One Mark Each 1. A bulb in a staircase has two switches, one switch being at the ground floor and the other one at the first floor. The bulb can be turned ON and also can be turned OFF by any one of the switches irrespective of the state of the other switch. The logic of switching of the bulb resembles (A) an AND gate (B) an OR gate (C) an XOR gate (D) a NAND gate Answer: (C) Exp: (C) Let Switches = 1 2 p , p 1 2 p , p Z(o / p) OFF OFF OFF OFF ON ON ON OFF ON ON ON OFF From Truth Table, it can be verified that Ex-OR logic is implemented. 2. Consider a vector field ( ) A r . The closed loop line integral A dl • ? can be expressed as (A) ( ) A ds ?× • ?? over the closed surface bounded by the loop (B) ( ) A dv ?• ??? over the closed volume bounded by the loop (C) ( ) A dv ?• ??? over the open volume bounded by the loop (D) ( ) A ds ?× • ?? over the closed surface bounded by the loop Answer: (D) Exp: (D) Stoke’s Theorem: “ The Line Integral of a vector A around a closed path L is equal to the integral of curl of A over the open surface S enclosed by the closed path L”. ( ) ? = ?× ? ?? A.dl A .ds 3. Two systems with impulse responses ( ) ( ) 1 2 h t and h t are connected in cascade. Then the overall impulse response of the cascaded system is given by (A) Product of ( ) ( ) 1 2 h t and h t (B) Sum of ( ) ( ) 1 2 h t and h t (C) Convolution of ( ) ( ) 1 2 h t and h t (D) Subtraction of ( ) ( ) 2 1 h t from h t |EC-GATE-2013 PAPER| www.gateforum.com GATEFORUM- India’s No.1 institute for GATE training 2 Answer: (C) Exp: 4. In a forward biased pn junction diode, the sequence of events that best describes the mechanism of current flow is (A) injection, and subsequent diffusion and recombination of minority carriers (B) injection, and subsequent drift and generation of minority carriers (C) extraction, and subsequent diffusion and generation of minority carriers (D) extraction, and subsequent drift and recombination of minority carriers Answer: (A) 5. In IC technology, dry oxidation (using dry oxygen) as compared to wet oxidation (using steam or water vapor) produces (A) superior quality oxide with a higher growth rate (B) inferior quality oxide with a higher growth rate (C) inferior quality oxide with a lower growth rate (D) superior quality oxide with a lower growth rate Answer: (D) 6. The maximum value of ? until which the approximation sin? ˜ ? holds to within 10% error is (A) o 10 (B) o 18 (C) o 50 (D) o 90 Answer: (B) Exp: 3 5 sin ....... 3! 5! ? ? ? = ?- + + 3 sin error Error should 10% of if 0.1 6 ? = ?+ ? ? = ? 3 if 0.1 6 ? = ? Then higher order terms also going to be less than 0.1? So, sin? ˜ ? approximation is valid 3 2 0.1 6 0.6 0.6 ? < ? ? < ? < Consider max 0.6 0.7746 radians ? = = 180 (in degrees) 0.7746 45 ? = × ° p Out of all possible options we need to go for max theta below 45° Hence it is 18° x(t) y(t) 1 2 h(t) *h(t) x(t) y(t) 1 h (t) 2 h (t) Page 3 |EC-GATE-2013 PAPER| www.gateforum.com GATEFORUM- India’s No.1 institute for GATE training 1 Q. No. 1 – 25 Carry One Mark Each 1. A bulb in a staircase has two switches, one switch being at the ground floor and the other one at the first floor. The bulb can be turned ON and also can be turned OFF by any one of the switches irrespective of the state of the other switch. The logic of switching of the bulb resembles (A) an AND gate (B) an OR gate (C) an XOR gate (D) a NAND gate Answer: (C) Exp: (C) Let Switches = 1 2 p , p 1 2 p , p Z(o / p) OFF OFF OFF OFF ON ON ON OFF ON ON ON OFF From Truth Table, it can be verified that Ex-OR logic is implemented. 2. Consider a vector field ( ) A r . The closed loop line integral A dl • ? can be expressed as (A) ( ) A ds ?× • ?? over the closed surface bounded by the loop (B) ( ) A dv ?• ??? over the closed volume bounded by the loop (C) ( ) A dv ?• ??? over the open volume bounded by the loop (D) ( ) A ds ?× • ?? over the closed surface bounded by the loop Answer: (D) Exp: (D) Stoke’s Theorem: “ The Line Integral of a vector A around a closed path L is equal to the integral of curl of A over the open surface S enclosed by the closed path L”. ( ) ? = ?× ? ?? A.dl A .ds 3. Two systems with impulse responses ( ) ( ) 1 2 h t and h t are connected in cascade. Then the overall impulse response of the cascaded system is given by (A) Product of ( ) ( ) 1 2 h t and h t (B) Sum of ( ) ( ) 1 2 h t and h t (C) Convolution of ( ) ( ) 1 2 h t and h t (D) Subtraction of ( ) ( ) 2 1 h t from h t |EC-GATE-2013 PAPER| www.gateforum.com GATEFORUM- India’s No.1 institute for GATE training 2 Answer: (C) Exp: 4. In a forward biased pn junction diode, the sequence of events that best describes the mechanism of current flow is (A) injection, and subsequent diffusion and recombination of minority carriers (B) injection, and subsequent drift and generation of minority carriers (C) extraction, and subsequent diffusion and generation of minority carriers (D) extraction, and subsequent drift and recombination of minority carriers Answer: (A) 5. In IC technology, dry oxidation (using dry oxygen) as compared to wet oxidation (using steam or water vapor) produces (A) superior quality oxide with a higher growth rate (B) inferior quality oxide with a higher growth rate (C) inferior quality oxide with a lower growth rate (D) superior quality oxide with a lower growth rate Answer: (D) 6. The maximum value of ? until which the approximation sin? ˜ ? holds to within 10% error is (A) o 10 (B) o 18 (C) o 50 (D) o 90 Answer: (B) Exp: 3 5 sin ....... 3! 5! ? ? ? = ?- + + 3 sin error Error should 10% of if 0.1 6 ? = ?+ ? ? = ? 3 if 0.1 6 ? = ? Then higher order terms also going to be less than 0.1? So, sin? ˜ ? approximation is valid 3 2 0.1 6 0.6 0.6 ? < ? ? < ? < Consider max 0.6 0.7746 radians ? = = 180 (in degrees) 0.7746 45 ? = × ° p Out of all possible options we need to go for max theta below 45° Hence it is 18° x(t) y(t) 1 2 h(t) *h(t) x(t) y(t) 1 h (t) 2 h (t) |EC-GATE-2013 PAPER| www.gateforum.com GATEFORUM- India’s No.1 institute for GATE training 3 7. The divergence of the vector field x y z ˆ ˆ ˆ A xa ya za = + + is (A) 0 (B) 1/3 (C) 1 (D) 3 Answer: (D) Exp: Given x y z A xa ya za = + + ( ) ( ) ( ) ( ) ( ) ( ) x y z x y z .A A A A x y z A x, A y, A z, x y z x y z 1 1 1 3 ? ? ? ? = + + ? ? ? = = = ? ? ? = + + ? ? ? = + + = 8. The impulse response of a system is ( ) ( ) h t tu t . = For an input ( ) u t 1 - , the output is (A) ( ) 2 t u t 2 (B) ( ) ( ) t t 1 u t 1 2 - - (C) ( ) ( ) 2 t 1 u t 1 2 - - (D) ( ) 2 t 1 u t 1 2 - - Answer: (C) Exp: For LTI system, if input gets delayed by one unit, output will also get delayed by one unit. 2 (t 1) u(t 1) u(t 1) 2 - - ? - 9. The Bode plot of a transfer function G (s) is shown in the figure below The gain ( ) ( ) 20 log G s is 32 dB and –8 dB at 1 rad/s and 10 rad/s respectively. The phase is negative for all ?. The G(s) is (A) 39.8 s (B) 2 39.8 s (C) 32 s (D) 2 32 s 40 32 20 1 0 10 8 - 100 ( ) rad / s ? Gain (dB) U(t) t u (t) 2 t u(t) 2 LTI system Page 4 |EC-GATE-2013 PAPER| www.gateforum.com GATEFORUM- India’s No.1 institute for GATE training 1 Q. No. 1 – 25 Carry One Mark Each 1. A bulb in a staircase has two switches, one switch being at the ground floor and the other one at the first floor. The bulb can be turned ON and also can be turned OFF by any one of the switches irrespective of the state of the other switch. The logic of switching of the bulb resembles (A) an AND gate (B) an OR gate (C) an XOR gate (D) a NAND gate Answer: (C) Exp: (C) Let Switches = 1 2 p , p 1 2 p , p Z(o / p) OFF OFF OFF OFF ON ON ON OFF ON ON ON OFF From Truth Table, it can be verified that Ex-OR logic is implemented. 2. Consider a vector field ( ) A r . The closed loop line integral A dl • ? can be expressed as (A) ( ) A ds ?× • ?? over the closed surface bounded by the loop (B) ( ) A dv ?• ??? over the closed volume bounded by the loop (C) ( ) A dv ?• ??? over the open volume bounded by the loop (D) ( ) A ds ?× • ?? over the closed surface bounded by the loop Answer: (D) Exp: (D) Stoke’s Theorem: “ The Line Integral of a vector A around a closed path L is equal to the integral of curl of A over the open surface S enclosed by the closed path L”. ( ) ? = ?× ? ?? A.dl A .ds 3. Two systems with impulse responses ( ) ( ) 1 2 h t and h t are connected in cascade. Then the overall impulse response of the cascaded system is given by (A) Product of ( ) ( ) 1 2 h t and h t (B) Sum of ( ) ( ) 1 2 h t and h t (C) Convolution of ( ) ( ) 1 2 h t and h t (D) Subtraction of ( ) ( ) 2 1 h t from h t |EC-GATE-2013 PAPER| www.gateforum.com GATEFORUM- India’s No.1 institute for GATE training 2 Answer: (C) Exp: 4. In a forward biased pn junction diode, the sequence of events that best describes the mechanism of current flow is (A) injection, and subsequent diffusion and recombination of minority carriers (B) injection, and subsequent drift and generation of minority carriers (C) extraction, and subsequent diffusion and generation of minority carriers (D) extraction, and subsequent drift and recombination of minority carriers Answer: (A) 5. In IC technology, dry oxidation (using dry oxygen) as compared to wet oxidation (using steam or water vapor) produces (A) superior quality oxide with a higher growth rate (B) inferior quality oxide with a higher growth rate (C) inferior quality oxide with a lower growth rate (D) superior quality oxide with a lower growth rate Answer: (D) 6. The maximum value of ? until which the approximation sin? ˜ ? holds to within 10% error is (A) o 10 (B) o 18 (C) o 50 (D) o 90 Answer: (B) Exp: 3 5 sin ....... 3! 5! ? ? ? = ?- + + 3 sin error Error should 10% of if 0.1 6 ? = ?+ ? ? = ? 3 if 0.1 6 ? = ? Then higher order terms also going to be less than 0.1? So, sin? ˜ ? approximation is valid 3 2 0.1 6 0.6 0.6 ? < ? ? < ? < Consider max 0.6 0.7746 radians ? = = 180 (in degrees) 0.7746 45 ? = × ° p Out of all possible options we need to go for max theta below 45° Hence it is 18° x(t) y(t) 1 2 h(t) *h(t) x(t) y(t) 1 h (t) 2 h (t) |EC-GATE-2013 PAPER| www.gateforum.com GATEFORUM- India’s No.1 institute for GATE training 3 7. The divergence of the vector field x y z ˆ ˆ ˆ A xa ya za = + + is (A) 0 (B) 1/3 (C) 1 (D) 3 Answer: (D) Exp: Given x y z A xa ya za = + + ( ) ( ) ( ) ( ) ( ) ( ) x y z x y z .A A A A x y z A x, A y, A z, x y z x y z 1 1 1 3 ? ? ? ? = + + ? ? ? = = = ? ? ? = + + ? ? ? = + + = 8. The impulse response of a system is ( ) ( ) h t tu t . = For an input ( ) u t 1 - , the output is (A) ( ) 2 t u t 2 (B) ( ) ( ) t t 1 u t 1 2 - - (C) ( ) ( ) 2 t 1 u t 1 2 - - (D) ( ) 2 t 1 u t 1 2 - - Answer: (C) Exp: For LTI system, if input gets delayed by one unit, output will also get delayed by one unit. 2 (t 1) u(t 1) u(t 1) 2 - - ? - 9. The Bode plot of a transfer function G (s) is shown in the figure below The gain ( ) ( ) 20 log G s is 32 dB and –8 dB at 1 rad/s and 10 rad/s respectively. The phase is negative for all ?. The G(s) is (A) 39.8 s (B) 2 39.8 s (C) 32 s (D) 2 32 s 40 32 20 1 0 10 8 - 100 ( ) rad / s ? Gain (dB) U(t) t u (t) 2 t u(t) 2 LTI system |EC-GATE-2013 PAPER| www.gateforum.com GATEFORUM- India’s No.1 institute for GATE training 4 Answer: (B) Exp: Any two paints on same line segment of Bode plot satisfies the equation of straight line. 2 1 2 1 G G i.e, slope of the line segment. log log - = ? - ? For the initial straight line ( ) 2 1 2 1 1 N 1 2 2 G G dB 40 dec log log 0 32 40log 1 6.309 k ;Where N is type of system here initial slope is dB 40 Hence N = 2 dec 6.309 k k 6.309 k 39.8 - ? = - ? - ? ? ? ? ? - = - ? ? ? ? ? ? = = - ? = ? = = Hence ( ) 2 39.8 G s s = 10. In the circuit shown below what is the output voltage ( ) out V if a silicon transistor Q and an ideal op-amp are used? (A) –15V (B) –0.7V (C) +0.7V (D) +15V + - 1 kO 5V 15V + 15V - Q out V + - ( ) 20log G j? 40 32 20 8 - w 10 ( ) w rad 1 Page 5 |EC-GATE-2013 PAPER| www.gateforum.com GATEFORUM- India’s No.1 institute for GATE training 1 Q. No. 1 – 25 Carry One Mark Each 1. A bulb in a staircase has two switches, one switch being at the ground floor and the other one at the first floor. The bulb can be turned ON and also can be turned OFF by any one of the switches irrespective of the state of the other switch. The logic of switching of the bulb resembles (A) an AND gate (B) an OR gate (C) an XOR gate (D) a NAND gate Answer: (C) Exp: (C) Let Switches = 1 2 p , p 1 2 p , p Z(o / p) OFF OFF OFF OFF ON ON ON OFF ON ON ON OFF From Truth Table, it can be verified that Ex-OR logic is implemented. 2. Consider a vector field ( ) A r . The closed loop line integral A dl • ? can be expressed as (A) ( ) A ds ?× • ?? over the closed surface bounded by the loop (B) ( ) A dv ?• ??? over the closed volume bounded by the loop (C) ( ) A dv ?• ??? over the open volume bounded by the loop (D) ( ) A ds ?× • ?? over the closed surface bounded by the loop Answer: (D) Exp: (D) Stoke’s Theorem: “ The Line Integral of a vector A around a closed path L is equal to the integral of curl of A over the open surface S enclosed by the closed path L”. ( ) ? = ?× ? ?? A.dl A .ds 3. Two systems with impulse responses ( ) ( ) 1 2 h t and h t are connected in cascade. Then the overall impulse response of the cascaded system is given by (A) Product of ( ) ( ) 1 2 h t and h t (B) Sum of ( ) ( ) 1 2 h t and h t (C) Convolution of ( ) ( ) 1 2 h t and h t (D) Subtraction of ( ) ( ) 2 1 h t from h t |EC-GATE-2013 PAPER| www.gateforum.com GATEFORUM- India’s No.1 institute for GATE training 2 Answer: (C) Exp: 4. In a forward biased pn junction diode, the sequence of events that best describes the mechanism of current flow is (A) injection, and subsequent diffusion and recombination of minority carriers (B) injection, and subsequent drift and generation of minority carriers (C) extraction, and subsequent diffusion and generation of minority carriers (D) extraction, and subsequent drift and recombination of minority carriers Answer: (A) 5. In IC technology, dry oxidation (using dry oxygen) as compared to wet oxidation (using steam or water vapor) produces (A) superior quality oxide with a higher growth rate (B) inferior quality oxide with a higher growth rate (C) inferior quality oxide with a lower growth rate (D) superior quality oxide with a lower growth rate Answer: (D) 6. The maximum value of ? until which the approximation sin? ˜ ? holds to within 10% error is (A) o 10 (B) o 18 (C) o 50 (D) o 90 Answer: (B) Exp: 3 5 sin ....... 3! 5! ? ? ? = ?- + + 3 sin error Error should 10% of if 0.1 6 ? = ?+ ? ? = ? 3 if 0.1 6 ? = ? Then higher order terms also going to be less than 0.1? So, sin? ˜ ? approximation is valid 3 2 0.1 6 0.6 0.6 ? < ? ? < ? < Consider max 0.6 0.7746 radians ? = = 180 (in degrees) 0.7746 45 ? = × ° p Out of all possible options we need to go for max theta below 45° Hence it is 18° x(t) y(t) 1 2 h(t) *h(t) x(t) y(t) 1 h (t) 2 h (t) |EC-GATE-2013 PAPER| www.gateforum.com GATEFORUM- India’s No.1 institute for GATE training 3 7. The divergence of the vector field x y z ˆ ˆ ˆ A xa ya za = + + is (A) 0 (B) 1/3 (C) 1 (D) 3 Answer: (D) Exp: Given x y z A xa ya za = + + ( ) ( ) ( ) ( ) ( ) ( ) x y z x y z .A A A A x y z A x, A y, A z, x y z x y z 1 1 1 3 ? ? ? ? = + + ? ? ? = = = ? ? ? = + + ? ? ? = + + = 8. The impulse response of a system is ( ) ( ) h t tu t . = For an input ( ) u t 1 - , the output is (A) ( ) 2 t u t 2 (B) ( ) ( ) t t 1 u t 1 2 - - (C) ( ) ( ) 2 t 1 u t 1 2 - - (D) ( ) 2 t 1 u t 1 2 - - Answer: (C) Exp: For LTI system, if input gets delayed by one unit, output will also get delayed by one unit. 2 (t 1) u(t 1) u(t 1) 2 - - ? - 9. The Bode plot of a transfer function G (s) is shown in the figure below The gain ( ) ( ) 20 log G s is 32 dB and –8 dB at 1 rad/s and 10 rad/s respectively. The phase is negative for all ?. The G(s) is (A) 39.8 s (B) 2 39.8 s (C) 32 s (D) 2 32 s 40 32 20 1 0 10 8 - 100 ( ) rad / s ? Gain (dB) U(t) t u (t) 2 t u(t) 2 LTI system |EC-GATE-2013 PAPER| www.gateforum.com GATEFORUM- India’s No.1 institute for GATE training 4 Answer: (B) Exp: Any two paints on same line segment of Bode plot satisfies the equation of straight line. 2 1 2 1 G G i.e, slope of the line segment. log log - = ? - ? For the initial straight line ( ) 2 1 2 1 1 N 1 2 2 G G dB 40 dec log log 0 32 40log 1 6.309 k ;Where N is type of system here initial slope is dB 40 Hence N = 2 dec 6.309 k k 6.309 k 39.8 - ? = - ? - ? ? ? ? ? - = - ? ? ? ? ? ? = = - ? = ? = = Hence ( ) 2 39.8 G s s = 10. In the circuit shown below what is the output voltage ( ) out V if a silicon transistor Q and an ideal op-amp are used? (A) –15V (B) –0.7V (C) +0.7V (D) +15V + - 1 kO 5V 15V + 15V - Q out V + - ( ) 20log G j? 40 32 20 8 - w 10 ( ) w rad 1 |EC-GATE-2013 PAPER| www.gateforum.com GATEFORUM- India’s No.1 institute for GATE training 5 Answer: (B) Exp: 11. Consider a delta connection of resistors and its equivalent star connection as shown below. If all elements of the delta connection are scaled by a factor k, k> 0, the elements of the corresponding star equivalent will be scaled by a factor of (A) 2 k (B) k (C) 1/k (D) k Answer: (B) Exp: a b C a b c R R R R R R = + + = + + = + + a c B a b c b c A a b c R R R R R R R R R R R R Above expression shown that if a b c R , R & R is scaled by k, R A , R B & R C is scaled by k only. 12. For 8085 microprocessor, the following program is executed MVI A, 05H; MVIB, 05H; PTR: ADD B; DCR B; JNZ PTR; ADI 03H; HLT; At the end of program, accumulator contains (A) 17 H (B) 20 H (C) 23 H (D) 05 H b R a R c R C R B R A R a R b R c R C R A R B R out V 1 kO + - Q + - 5V 15V + 15V - 0.7v + - out V 0.7v = -Read More

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