The gradient of any scalar field always yields __________ . a solenoidal field a

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Question
The gradient of any scalar field always yields __________ .
Options
A. a solenoidal field
B. a conservative field
C. an irrotational field
D. none of these

Correct Answer

a conservative field

Explanation

Dot product is conservative. Gradient is nothing but dot product.

Exam Questions Papers problems

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1. Find 'X' in the circuit below :

f₁(A, B, C, D) = ?(6, 7, 13, 14);
f₂(A, B, C, D) = ?(3, 6, 7);
f₃(A, B, C, D) = ?(5, 6, 7, 14, 15)
Options
A. p(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15)
B. 0
C. ?(14)
D. 1

2. Consider the probability density f(x) = ae^-b|x| where x is a random variable whose allowable values range from x = - ? to x = + ?. P(1 ? x ? 2)
Options
A.
B.
C.
D. (e^-b - e^-2b)

3. A radar receiver has a noise figure of 10 dB at 300 K having a bandwidth of 2.5 MHz. The minimum power it can receive is
Options
A. 3.45 x 10^-15 W
B. 1.38 x 10^-15 W
C. 7.5 x 10^-15 W
D. 93.15 x 10^-15 W

4. For a given voltage, four heating coils will produce maximum heat when connected
Options
A. all in parallel
B. all in series
C. with two parallel pairs in series
D. one pair in parallel with the other two in series

5. The continuous time system with impulse response h(t) = is stable, for n is even, when
Options
A. a = 0
B. a > 0
C. a < 0
D. a ? 0

6. The antenna current of an AM transmitter is 8 A, when only the carrier is sent, but it increases to 8.93 A when the carrier is modulated by a single sine wave. Determine the antenna current when the percent of modulation changes to 0.8
Options
A. 9.19 A
B. 9.91 A
C. 10.56 A
D. 8.61 A

7. Consider the signal flow graph shown in figure below. The gain is :
Options
A.
B.
C.
D.

8. In the following non planar graph number of independent loop equations are
Options
A. 8
B. 12
C. 7
D. 5

9. The amplifier circuit shown below uses a silicon transistor. The capacitors C_c and C_E can be assumed to be short at signal frequency and the effect of output resistance r₀ can be ignored. If C_E is disconnected from the circuit, which one of the following statements is TRUE?
Options
A. The input resistance R_i increases and the magnitude of voltage gain A_v decreases
B. The input resistance R_i decreases and the magnitude of voltage gain A_v decreases
C. Both input resistance R_i and the magnitude of voltage gain A_v decrease
D. Both input resistance R_i and the magnitude of voltage gain A_v increase

10. Consider the amplitude modulated (AM) signal A_c cos ?_ct + 2 cos ?_mt cos ?_ct For demodulating the signal using envelope detector, the minimum value of A_c should be
Options
A. 2
B. 1
C. 0.5
D. 0

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