Bissoy.com
Doctors Medicines MCQs Q&A

The following surface integral is to be evaluated over a sphere for the given steady velocity vector field F = xi + yj + zk defined with respect to a Cartesian coordinate system having i, j and k as unit base vectors.
$$\iint\limits_{\text{S}} {\frac{1}{4}\left( {{\text{F}} \cdot {\text{n}}} \right){\text{dA}}}$$    where S is the sphere, x2 + y2 + z2 = 1 and n is the outward unit normal vector to the sphere.
The value of the surface integral is

The following surface integral is to be evaluated over a sphere for the given steady velocity vector field F = xi + yj + zk defined with respect to a Cartesian coordinate system having i, j and k as unit base vectors.
$$\iint\limits_{\text{S}} {\frac{1}{4}\left( {{\text{F}} \cdot {\text{n}}} \right){\text{dA}}}$$    where S is the sphere, x2 + y2 + z2 = 1 and n is the outward unit normal vector to the sphere.
The value of the surface integral is Correct Answer $$\pi $$

Related Questions

The following Boolean expression $$Y = A \cdot \overline B \cdot \overline C \cdot \overline D + \overline A \cdot B \cdot \overline C \cdot D + \overline A \cdot \overline B \cdot \overline C \cdot D + \overline A \cdot \overline B \cdot \overline C \cdot D + \overline A \cdot B \cdot C \cdot D + A \cdot \overline B \cdot \overline C \cdot D$$                 can be simplified to
W, X and Y are the intermediates in a biochemical pathway as shown below:
$$S \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \to W \to X \to Y \to Z$$
Mutants auxotrophic for Z are found in four different complementation groups, namely Z1, Z2, Z3 and Z4. The growth of these mutants on media supplemented with W, X, Y or Z is shown below (Yes: growth observed: No: growth not observed):
Evaluate the following:
$$\frac{{\cos 2\theta \cdot \cos 3\theta - \cos 2\theta \cdot \cos 7\theta + \cos \theta \cdot \cos 10\theta }}{{\sin 4\theta \cdot \sin 3\theta - \sin 2\theta \cdot \sin 5\theta + \sin 4\theta \cdot \sin 7\theta }}$$
A common convention is: • is evaluated first • and are evaluated next • Quantifiers are evaluated next • is evaluated last.
Statement : It has been reported by one of the TV channels that the answer papers of Board examination of one State are evaluated by students studying in the same standard with the help of model answers as instructed by the examiners.

Courses of Action :
I. All such examiners should be immediately suspended from their official positions.
II. All such papers evaluated by the students should be immediately confiscated and got evaluated by qualified teachers.
III. The Board should explore possibilities even though they are remote, of getting the answer papers of this examination evaluated by computerised machines.
A common convention is:
• is evaluated first
• and are evaluated next
• Quantifiers are evaluated next
• is evaluated last.
Seven people A, B, C, D, E, F and G live on separate floors of a 7-floor building. Ground floor is numbered 1, first floor is numbered. 2 and so on until the topmost floor is numbered 7. Each one of these having a different cars-Cadillac, Ambassador, Fiat, Maruti, Mercedes, Bedford and Fargo but not necessarily in the same order. Only three people live above the floor on which A lives. Only one person lives between A and the one having a car Cadillac. F lives immediately below the one having a car Bedford. The one having a car Bedford lives on an even-numbered floor. Only three people live between the ones having a car Cadillac and Maruti. E lives immediately above C. E is not having a car Maruti. Only two people live between B and the one having a car Fargo. The one having a car Fargo lives below the floor on which B lives. The one having a car Fiat does not live immediately above D or immediately below B. D does not live immediately above or immediately below A. G does not have a car Ambassador. Question : How many people live between the floors on which D and the one having a car Bedford ?
We need to apply vector math sometimes in the calculation of the stability of equilibrium configurations. So the coordinate of the Force vector AB is A (2, 0, 2) and B (-2, 3.46, 3). It has a magnitude of 750N. Which is the best Cartesian representation of the vector AB?
A metal sphere of surface area 0.0225 m2 is in an evacuated enclosure whose walls are held at a very low temperature. Electric current is passed through resistors embedded in the sphere causing electrical energy to be dissipated at the rate of 75 W. If the sphere surfaces temperature is measured to be 560 K, while in steady state, calculate emissivity of the sphere surface
In this question two quantities are given. Find and compare them and choose the appropriate options. A cylinder of radius R and height H has the same volume as that of a sphere of radius r. The surface area of sphere is more than the curved surface area of cylinder. Quantity I: x, where 9x – 2 = 0 Quantity II: R/H; where a cylinder of radius R and height H has the same volume as that of a sphere of radius r. The surface area of sphere is more than the curved surface area of cylinder.