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Considered the following statements about the characteristics of contours - (1) Closed contour lines with higher values inside show a lake, (2) Contour is an imaginary line joining points of equal elevations, (3) Closely spaced contour lines indicate a steep slope. (4) Contour lines of equal height may not converge nor continue as one line but a single contour line may split into two lines Which of the statements given above are correct?
The area of the region enclosed by the curve zz̅+a(z̅+z)+a=0 is 2π. If a2–7a+10=0, find the area of the region enclosed by the curve zz̅+2a(z̅+z)+a=0.
Which of the following statements is/are true? A: If a circle is formed from a wire, which was initially in the shape of a semi-circle, then ratio of radius of circle and that of semi-circle will be 7: 11. B: If in a semi-circle of radius ‘r’, another semi-circle of radius ‘4r/5’ is drawn, then area of the remaining part of larger semi-circle will be ‘3πr2/5’. C: In a circle of radius ‘r’, if ‘O’ is the center of circle and radii OA and OB are at the angle of 45°, then the length of major arc AB will be ‘7πr/8’.
The values of the integral $$\frac{1}{{2\pi {\text{j}}}}\oint\limits_{\text{c}} {\frac{{{{\text{e}}^{\text{z}}}}}{{{\text{z}} - 2}}{\text{dz}}} $$    along a closed contour c in anti-clockwise direction for
i. the point z0 = 2 inside the contour c, and
ii. the point z0 = 2 outside the contour c, respectively, are
With respect to the numerical evaluation of the definite integral $${\text{K}} = \int_{\text{a}}^{\text{b}} {{{\text{x}}^2}{\text{dx,}}} $$   where a and b are given, which of the following statements is/are TRUE?
I. The value of K obtained using the trapezoidal rule is always greater than or equal to the exact value of the definite integral.
II. The value of K obtained using the Simpson's rule is always equal to the exact value of the definite integral.
If the semi-circular contour D of radius 2 is as shown in the figure, then the value of the integral $$\oint\limits_{\text{D}} {\frac{1}{{\left( {{{\text{s}}^2} - 1} \right)}}{\text{ds}}} $$   is
Complex Variable mcq question image
The value of the contour integral in the complex plane $$\oint {\frac{{{{\text{z}}^3} - 2{\text{z}} + 3}}{{{\text{z}} - 2}}{\text{dz}}} $$    along the contour |z| = 3, taken counter-clockwise is
Which of the following statements is/are true? i. Contour lines cross valley line at 90°. ii. Contour lines cross ridge line at 90°. iii. Contour lines are widely spaced where ground has steep slope.  
An air pressure contour line joins locations in a region having the same atmospheric pressure. The following is an air pressure contour plot of a geographical region. Contour lines are shown at 0.05 bar intervals in this plot If the possibility of a thunderstorm is given by how fast air pressure rises or drops over a region, which of the following regions is most likely to have a thunderstorm?
A contour line joins locations having the same height above the mean sea level. The following is a contour plot of a geographical region. Contour lines are shown at 25 m intervals in this plot. If in a flood, the water level rises to 525 m, which of the villages P, Q, R, S, T get submerged?