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Find the divergence of the vector yi + zj + xk.
Answer: b Explanation: Div (yi + zj + xk) = Dx(y) + Dy(z) + Dz(x), which is zero. Here D refers to partial differentiation.
Answer: b
See lessExplanation: Div (yi + zj + xk) = Dx(y) + Dy(z) + Dz(x), which is zero. Here D refers to
partial differentiation.
Compute the divergence of the vector xi + yj + zk.
Answer: d Explanation: The vector given is a position vector. The divergence of any position vector is always 3.
Answer: d
See lessExplanation: The vector given is a position vector. The divergence of any position vector is always 3.
The divergence concept can be illustrated using Pascal’s law. State True/False.
Answer: a Explanation: Consider the illustration of Pascal’s law, wherein a ball is pricked with holes all over its body. After water is filled in it and pressure is applied on it, the water flows out the holes uniformly. This is analogous to the flux flowing outside a closed surface as the volume rRead more
Answer: a
See lessExplanation: Consider the illustration of Pascal’s law, wherein a ball is pricked with holes all over its body. After water is filled in it and pressure is applied on it, the water flows out the holes uniformly. This is analogous to the flux flowing outside a closed surface as the volume reduces.
The divergence of a vector is a scalar. State True/False.
Answer: a Explanation: Divergence can be computed only for a vector. Since it is the measure of outward flow of flux from a small closed surface as the volume shrinks to zero, the result will be directionless (scalar).
Answer: a
See lessExplanation: Divergence can be computed only for a vector. Since it is the measure of
outward flow of flux from a small closed surface as the volume shrinks to zero, the result will be directionless (scalar).
Find the gradient of the function sin x + cos y.
Answer: a Explanation: Grad (sin x + cos y) gives partial differentiation of sin x+ cos y with respect to x and partial differentiation of sin x + cos y with respect to y and similarly with respect to z. This gives cos x i – sin y j + 0 k = cos x i – sin y j.
Answer: a
See lessExplanation: Grad (sin x + cos y) gives partial differentiation of sin x+ cos y with respect to x and partial differentiation of sin x + cos y with respect to y and similarly with respect to z. This gives cos x i – sin y j + 0 k = cos x i – sin y j.
When gradient of a function is zero, the function lies parallel to the x-axis. State True/False.
Answer: a Explanation: Gradient of a function is zero implies slope is zero. When slope is zero, the function will be parallel to x-axis or y value is constant.
Answer: a
See lessExplanation: Gradient of a function is zero implies slope is zero. When slope is zero, the function will be parallel to x-axis or y value is constant.
The gradient can be replaced by which of the following?
Answer: c Explanation: Since gradient is the maximum space rate of change of flux, it can be replaced by differential equations.
Answer: c
See lessExplanation: Since gradient is the maximum space rate of change of flux, it can be
replaced by differential equations.
Find the gradient of the function given by, x2 + y2 + z2 at (1,1,1)
Answer: b Explanation: Grad(x2+y2+z2) = 2xi + 2yj + 2zk. Put x=1, y=1, z=1, the gradient will be 2i +2j + 2k.
Answer: b
See lessExplanation: Grad(x2+y2+z2) = 2xi + 2yj + 2zk. Put x=1, y=1, z=1, the gradient will be 2i +2j + 2k.
Curl of gradient of a vector is
Answer: c Explanation: Gradient of any function leads to a vector. Similarly curl of that vector gives another vector, which is always zero for all constants of the vector. A zero value in vector is always termed as null vector(not simply a zero).
Answer: c
See lessExplanation: Gradient of any function leads to a vector. Similarly curl of that vector gives another vector, which is always zero for all constants of the vector. A zero value in vector is always termed as null vector(not simply a zero).
Find the gradient of t = x2y+ ez at the point p(1,5,-2)
Answer: b Explanation: Grad(t) = 2xy i + x2 j + ez k. On substituting p(1,5,-2), we get 10i + j + 0.135k.
Answer: b
See lessExplanation: Grad(t) = 2xy i + x2 j + ez k. On substituting p(1,5,-2), we get 10i + j +
0.135k.