EC GATE 2007 - Online Test

Q1. For the Zener diode shown in the figure, the Zener voltage at knee is 7 V, the knee current is negligible and the Zener dynamic resistance is 10 Ω. If the input voltage (Vi) range is from 10 to 16 V, the output voltage (V0) ranges from

Answer : Option C
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Q2. The following plot shows a function which varies linearly with x . The value of the integral  is

Answer : Option B
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The given plot is straight line whose equation is 


Q3. For |x| << 1, coth (x) can be approximated as
Answer : Option C
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Q4.
Answer : Option A
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Q5. Which one of following functions is strictly bounded?
Answer : Option D
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Q6. For the function ex , the linear approximation around x = 2 is
Answer : Option A
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Neglecting higher powers

Q7. Consider the function f (x) = x − x − . The maximum value of f (x) in the closed interval [− 4, 4] is
Answer : Option A
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We have
                                    f (x) = x − x +


Q8. An examination consists of two papers, Paper 1 and Paper 2. The probability of failing in Paper 1 is 0.3 and that in Paper 2 is 0.2. Given that a student has failed in Paper 2, the probability of failing in Paper 1 is 0.6. The probability of a student failing in both the papers is
Answer : Option C
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Q9. The solution of the differential equation  under the boundary conditions
(i) y = y1 at x = 0 and
(ii) y = y2 at x = , where k, y1 and y2 are constants, is
Answer : Option D
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Q10. The equation x − x + x − = is to be solved using the Newton - Raphson method. If x = is taken as the initial approximation of the solution, then next approximation using this method will be
Answer : Option B
Explaination / Solution: