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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’.
Which of the following statements is/are true? A: In a circle, PQ is a chord and OP and OQ are the radii of the circle. If ∠POQ = 90°, then ratio of the area of triangle POQ and that of circle will be 7: 22. B: Area of a circle is one-fourth of the product of ‘π’ and square of diameter of circle. C: Diameter of a semi-circle is 38(8/9)% of its perimeter.
Which two classes use the Shape class correctly?
A. public class Circle implements Shape { private int radius; }B. public abstract class Circle extends Shape { private int radius; }C. public class Circle extends Shape { private int radius; public void draw(); }D. public abstract class Circle implements Shape { private int radius; public void draw(); }E. public class Circle extends Shape { private int radius; public void draw() { /* code here */ } }F. public abstract class Circle implements Shape { private int radius; public void draw() { /* code here */ } }
Circle A is 4 cm in diameter; circle B is 5 cm in diameter, Circle C has its circumference equal to the sum of the circumferences of both A and B together, What will be the ratio of the area of circle C, with respect to the area of circle A and circle B respectively? 
Consider a circle with centre at C. Let OP, OQ denote respectively the tangents to the circle drawn from a point O outside the circle. Let R be a point on OP and S be a point on OQ such that OR × SQ = OS × RP. Which of the following statement(s) is/are correct? (1) If X is the circle with centre at O and radius OR, and Y is the circle with centre at O and radius OS, then X = Y (2) ∠POC + ∠QCO = 90° Select the correct answer using the code given below.
Given are the steps to draw a tangent to given circle from any point outside the circle. Arrange the steps. i. With OP as diameter, draw arcs on circle at R and R1. ii. Draw the given circle with center O. iii. Join P and R which is one tangent and PR1 is another tangent. iv. Mark the point P outside the circle.
Given below are two quantities named I and II. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose among the possible answers. Quantity I: A circle whose radius is 56 cm and The Rectangle whose length and breadth are in the ratio 7 ∶ 22 respectively. The area of a circle is equal to the area of a rectangle then calculate the perimeter of the rectangle. Quantity II: A cylinder whose radius is (1/7) of the radius of the circle and the height of the cylinder is twice the radius of the circle and the area of the circle is 154 cm2 then, find the volume of the cylinder.
A circle of radius of 10 cm and another circle whose radius is 20% less than that of first circle, intersect at the points P and Q. If length of PQ is 20% more than the radius of first circle. The distance between the centers of the circle is x cm. What is value of x?
Steps are given to draw involute of given circle. Arrange the steps f C is the centre of circle and P be the end of the thread (starting point). i. Draw a line PQ, tangent to the circle and equal to the circumference of the circle. ii. Draw the involute through the points P1, P2, P3 ……..etc. iii. Divide PQ and the circle into 12 equal parts. iv. Draw tangents at points 1, 2, 3 etc. and mark on them points P1, P2, P3 etc. such that 1P1 =P1l, 2P2 = P2l, 3P3= P3l etc.
In the generation of element geometries, if dx dy represents an area element in the real element and dεdη represents the corresponding area element in the master element, then what is the expression for Jacobian je?