Due to heavy storm an electric wire got bent as shown in the figure. It followed a mathematical shape. Answer the following questions below.

i. Name the shape in which the wire is bent

a) Spiral b) ellipse c) linear d) Parabola

ii. How many zeroes are there for the polynomial (shape of the wire)

a) 2 b) 3 d) 1 d) 0

iii. The zeroes of the polynomial are

a) -1, 5 b) -1, 3 c) 3, 5 d) -4, 2

iv. What will be the expression of the polynomial?

a) x²+2x -3 b) x² -2x +3 c) x² - 2x -3 d) x² +2x+3

v. What is the value of the polynomial if x = -1?

a) 6 b) -18 c)) 18 d) 0

Class X students of a secondary school in Krishnagar have been allotted a rectangular plot of a land for gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of 1m from each other. There is a triangular grassy lawn in the plot as shown in the fig. The students are to sow seeds of flowering plants on the remaining area of the plot.

Considering A as origin, answer question (i) to (v)

i. Considering A as the origin, what are the coordinates of A?

a) (0,1) b) (1,0) c) (0,0) d)(-1,-1)

ii. What are the coordinates of P?

a) (4,6) b)( 6,4) c) (4,5) d) (5,4)

iii. What are the coordinates of R?

a) (6,5) b) (5,6) c) ( 6,0) d) (7,4)

iv. What are the coordinates of D?

a) (16,0) b) (0,0) c) (0,16) d) (16,1)

v. What are the coordinate of P if D is taken as the origin?

a) ( 12,2) b ) (-12,6) c) (12,3) d) (6,10)

Rahul is studying in X Standard. He is making a kite to fly it on a Sunday. Few questions came to his mind while making the kite. Give answers to his questions by looking at the figure.

i. Rahul tied the sticks at what angles to each other?

a) 30° b) 60° c) 90° d) 60°

ii. Which is the correct similarity criteria applicable for smaller triangles at the upper part of this kite?

a) RHS b) SAS c) SSA d) AAS

iii. Sides of two similar triangles are in the ratio 4:9. Corresponding medians of these triangles are in the ratio,

a) 2:3 b) 4:9 c) 81:16 d) 16:81

iv. In a triangle, if square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle. This theorem is called as,

a) Pythagoras theorem b) Thales theorem

c) Converse of Thales theorem d) Converse of Pythagoras theorem

v. What is the area of the kite, formed by two perpendicular sticks of length 6 cm and 8 cm?

a) 48 cm² b) 14 cm² c) 24 cm² d) 96 cm²

Find the coordinates of the point which divides the line segment joining the points (4, -3) and (8,5) in the ratio 3:1 internally.

OR

Find a relation between x and y such that the point (x,y) is equidistant from the points (7,1) and (3,5)

In the fig. if LM II CB and LN II CD, prove that