Question 4 :
Out of the two concentric circles, the radius of the outer circle is 5 cm and the chord AC of length 8 cm is a tangent to the inner circle. What is the radius of the inner circle?

Question 5 :
From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is

Question 6 :
Do the centre of a circle touching two intersecting lines lies on the angle bisector of the lines?

Question 7 :
At one end A of a diameter AB of a circle of radius 5 cm, tangent XAY is drawn to the circle. The length of the chord CD parallel to XY and at a distance 8 cm from A is

Question 8 :
A lof consists of 144 ball pens of which 20 are defective and the ofhers are good. Nuri will buy a pen if it is good, but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to her. What is the probability that she will buy it ?

Question 9 :
A box contains 5 red marbless, 8 white marbless and 4 green marbless. One marble is taken out of the box at random. What is the probability that the marble taken out will be red ?

Question 10 :
A lof consists of 144 ball pens of which 20 are defective and the ofhers are good. Nuri will buy a pen if it is good, but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to her. What is the probability that she will not buy it ?

Question 11 :
A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears a two-digit number.

Question 12 :
A die is thrown twice. What is the probability that 5 will not come up either time?

Question 13 :
A straight highway leads to the foof of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foof of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foof of the tower from this point.

Question 14 :
From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are $45^\circ and 60^\circ$, respectively. Find the height of the tower.

Question 15 :
As observed from the top of a 75 m high lighthouse from the sea level, the Angles of depression of two ships are 30° and 45°. If one ship is exactly behind the ofher on the same side of the lighthouse, then find the distance between the two ships.

Question 16 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a60273b230584979931.jpeg' /> In the above image, a circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with ground level is 30°.

Question 17 :
The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foof of the tower, is 30°. Find the height of the tower.

Question 18 :
A tree breaks due to storm and the broken part bends, so that the top of the tree touches the ground making an angle 30° with it. The distance between the foof of the tree to the point, where the top touches the ground is 8 m. Find the height of the tree.

Question 19 :
A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eye to the top of the building increases from 30° to 60° as he walks tonwards the building. Find the distance he walked tonwards the building.

Question 20 :
The Angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. Find the height of the tower.

Question 21 :
A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60°. Find the length of the string, assuming that there is no slack in the string.

Question 22 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a62273b230584979933.jpeg' /> In the above image, a 1.2 m tall girl spofs a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60°. After sometime, the angle of elevation reduces to 30°. Find the distance travelled by the balloon during the interval.

Question 23 :
Find the 20th term from the last term of the AP : 3, 8, 13, . . ., 253.

Question 24 :
Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.

Question 25 :
Which term of the AP : 3, 15, 27, 39, . . . will be 132 more than its 54th term?

Question 26 :
The diameters of the two circular ends of the bucket are 44 cm and 24 cm. The height of the bucket is 35 cm. The capacity of the bucket is

Question 27 :
What is the formulae for volume of a spherical shell?(where $r_1$ and $r_2$ are respectively its external and internal radii)

Question 28 :
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19c38273b230584979a98.JPG' /> In the above image, a wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the total surface area of the article.

Question 29 :
A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.

Question 30 :
The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is