The arch of a bridge has dimensions as shown, where the arch measure 2m at its highest point and its width is 6m. What is the radius of the circle that contains the arch?

In the given figure, ㄥPOQ = 100^o and ㄥPQR = 30^o, then find ㄥRPO

Write down the abscissa and ordinate of the following.
(i) P
(ii) Q
(iii) R
(iv) S

Plot the following points in the coordinate plane and join them. What is your conclusion about the resulting figure?  
(–5, 3) (–1, 3) (0, 3) (5, 3)

Prove that the diagonals of the parallellogram bisect each other. [Hint: Take scale on both axes as 1 cm = a units]

Find the coordinates of a point P on the line segment joining A(1, 2) and B(6, 7) in such a way that AP = \(\frac{2}{5}\)AB

A line segment AB is increased along its length by 25% by producing it to C on the side of B. If A and B have the coordinates (−2,−3) and (2,1) respectively, then find the coordinates of C.

Find the length of median through A of a triangle whose vertices are A(−1, 3), B(1, −1) and C(5, 1).

If  \(\left( \frac { 3 }{ 2 } ,5 \right) ,\left( 7,\frac { -9 }{ 2 } \right) \)and\((\frac{13}{2},\frac{-13}{2})\) are mid-points of the sides of a triangle, then find the centroid of the triangle.

From the given figure, find all the trigonometric ratios of angle \(\theta\)

From the given figure, find the values of 
(i) sin B
(ii) sec B
(iii) cot B  
(iv) cos C
(v) tan C
(vi) cosec C

If 2cos \(\theta\) = \(\sqrt { 3 } \), then find all the trigonometric ratios of angle \(\theta\)

If cos A = \(\frac { 2x }{ 1+{ x }^{ 2 } } \) then find the values of sinA and tan A in terms of x.

If cos \(\theta\) : sin\(\theta\) =1: 2, then find the value of = \(\frac { 8cos\theta -2sin\theta }{ 4cos\theta +2sin\theta } \)

A boy standing at a point O finds his kite flying at a point P with distance OP = 25 m. It is at a height of 5m from the ground. When the thread is extended by 10 m from P, it reaches a point Q. What will be the height QN of the kite from the ground? (use trigonometric ratios) 

Verify the following equalities :
sin²60⁰ + cos²60⁰ = 1

Find the value of the following:
(i) sin65⁰39' + cos24⁰57' + tan10⁰10'
(ii) tan70⁰58' + cos15⁰26' - sin84⁰59'

In the given figure, HT shows the height of a tree standing vertically. From a point P, the angle of elevation of the top of the tree  measures 42° and the distance to the tree is 60 metres. Find the height of the tree.

Find the area of the unshaded region.

The dimensions of a cuboidal box are 6 m × 400 cm × 1.5 m. Find the cost of painting its entire outer surface at the rate of Rs. 22 per cm².

Find the volume of a cuboid whose dimensions are
(i) length = 12 cm, breadth = 8 cm, height = 6 cm
(ii) length = 60 m, breadth = 25 m, height = 1.5 m

The volume of a container is 1440 m³. Th e length and breadth of the container are 15 m and 8 m respectively. Find its height.

What is the probability of drawing a King or a Queen or a Jack from a deck of cards?

Frame two problems in calculating probability, based on the spinner shown here.

1500 families were surveyed and following data was recorded about their maids at homes

Type of maids	Only part time	Only full time	Both
Number of families	860	370	250

A family is selected at random. Find the probability that the family selected has
(i) Both types of maids
(ii) Part time maids
(iii) No maids