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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?
Mean Value theorem is applicable to the and continuous in open interval (a, b) b) Functions continuous in closed interval only and having same value at point ‘a’ and ‘b’ c) Functions continuous in closed interval and differentiable in open interval (a, b) d) Functions differentiable in open interval (a, b) only and having same value at point ‘a’ and ‘b’
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.  
AB is a vertical truck of a huge tree with A being the point where the base of the truck touches the ground. Due to a cyclone, the tree has been broken at C which is at a height of 12 meters, broken part is partially attached to the vertical portion of the tree at C. If the end of the broken part B touches the ground at D which is at a distance of 5 metes from A, then the original height of the truck is:
A tree of height 15 m is broken by wind in such a way that its top touches the ground and makes an angle 30° with the ground. What is the height from the ground to the point where tree is broken?
The marks of 30 students in a test is shown as follows: 12, 16, 22, 24, 11, 7, 9, 11, 13, 14, 17, 19, 18, 21, 22, 23, 8, 9, 17, 16, 14, 23, 24, 24, 23, 17, 18, 16, 11, 9  Which Tally table represent the correct data of the marks of the students. (A) Interval of marks Tally marks of students 0-5 0 5-10 ||||  10-15 |||| || 15-20 |||| |||| 20-25 |||| ||||   (B)  Interval of marks Tally marks of students 0-5 0 5-10 |||| | 10-15 |||| ||| 15-20 |||| |||| 20-25 |||| || (C) Interval of marks Tally marks of students 0-5 0 5-10 |||| | 10-15 |||| || 15-20 |||| |||| 20-25 |||| || (D) Interval of marks Tally marks of students 0-5 0 5-10 ||||  10-15 |||| || 15-20 |||| ||| 20-25 |||| ||||
Rolle’s theorem is applicable to the and continuous in open interval (a, b) only and having same value at point ‘a’ and ‘b’ b) Functions continuous in closed interval only and having same value at point ‘a’ and ‘b’ c) Functions continuous in closed interval and differentiable in open interval (a, b) only and having same value at point ‘a’ and ‘b’ d) Monotonically Increasing funtions
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?
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. Which of the following is the steepest path leaving from P?