Section-1
1) If a cylinder and a cone are of the same radius and height, then how many cones full of milk can fill the cylinder? Answer with reasons.
2) In a △DEF ; A,B and C are the mid-points of EF, FD and DE respectively. If the area of △DEF is 14.4 cm^2, then find the area of △ABC
3) When a die is rolled once unbiased , what is the probability of getting a multiple of 3 out of possible incomes?
4) Show that tan^2𝞱 - 1 = -1
cos^2𝞱
5) How many tangents can be drawn to a circle from a point on the same circle?Justify your answer.
6) How do you find the deviation from the assumed mean for the above data?
7) A person from the top of a building of height 25 m, has observed another building's top and bottom at an angle of elevation 45 deg and at the angle of depression 60 deg respectively.. Draw a diagram for this data.
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Section-2
8) A ladder of 3.9 m length is laid against a wall . The distance between the foot of the wall and the ladder is 1.5m. Find the height at which ladder touches the wall.
9) There are 12 red balls, 18 blue balls, 6 white balls in a box. When a ball is drawn at random from the box, what is the probability of not getting a red ball?
10). Prove that " in two concentric circles , a chord of a bigger circle, that touches the smaller circle is bisected at the point of contact with the smaller circle."
11) Show that (1 + cot^2𝞱) (1 - cos𝞱)(1 + cos𝞱) = 1
12) The radius of a spherical balloon increases from 7 cm to 14 cm as air is pumped into it. Find the ratio of volumes before and after pumping the air.
13) Observes the below diagram and find the values of x and y.
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Section-3
14). In a village, an enumerator has surveyed for 25 households. The size of the family(number of family members) and the number of families is tabulated as follows:-
Find the mode of the data.
OR
(B) There are 100 flash cards labelled from 1 to 100 in a bag.When the card is drawn from the bag at random, what is the probability of getting......
(!) a card with prime number from possible outcomes
(!!) a card without prime number from possible outcomes.
15) (A) Find the value of sec 15 + sin 72 - tan 33
cosec 75 cos 18 cot 57
OR
(B) Observe the figure given below:
In △PQR , if XY//PQ , PX = 5 and QR = 7.2 cm, then find
XR 3
the length of RY.
16). An observer flying in an aeroplane at an altitude of 900 m
observes two ships in front of him, which are in the same direction at an angles of depression of 60 deg and 30 deg respectively. Find the distance between the two ships.
OR
(B) A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. If the length of the cylinder part of the capsule is 14 mm and the diameter of hemisphere is 6 mm, then find the volume of medicine capsule.
17) Draw a circle with radius 3 cm and construct a pair of tangents from a point 8 cm away from the center.
OR
(B) Daily expenditure of 25 householders is given in the following table:
Draw a "less than type" cumulative frequency Ogive curve for this data.
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1) If a cylinder and a cone are of the same radius and height, then how many cones full of milk can fill the cylinder? Answer with reasons.
2) In a △DEF ; A,B and C are the mid-points of EF, FD and DE respectively. If the area of △DEF is 14.4 cm^2, then find the area of △ABC
3) When a die is rolled once unbiased , what is the probability of getting a multiple of 3 out of possible incomes?
4) Show that tan^2𝞱 - 1 = -1
cos^2𝞱
5) How many tangents can be drawn to a circle from a point on the same circle?Justify your answer.
6) How do you find the deviation from the assumed mean for the above data?
7) A person from the top of a building of height 25 m, has observed another building's top and bottom at an angle of elevation 45 deg and at the angle of depression 60 deg respectively.. Draw a diagram for this data.
******************************************************
Section-2
8) A ladder of 3.9 m length is laid against a wall . The distance between the foot of the wall and the ladder is 1.5m. Find the height at which ladder touches the wall.
9) There are 12 red balls, 18 blue balls, 6 white balls in a box. When a ball is drawn at random from the box, what is the probability of not getting a red ball?
10). Prove that " in two concentric circles , a chord of a bigger circle, that touches the smaller circle is bisected at the point of contact with the smaller circle."
11) Show that (1 + cot^2𝞱) (1 - cos𝞱)(1 + cos𝞱) = 1
12) The radius of a spherical balloon increases from 7 cm to 14 cm as air is pumped into it. Find the ratio of volumes before and after pumping the air.
13) Observes the below diagram and find the values of x and y.
******************************************************
Section-3
14). In a village, an enumerator has surveyed for 25 households. The size of the family(number of family members) and the number of families is tabulated as follows:-
Find the mode of the data.
OR
(B) There are 100 flash cards labelled from 1 to 100 in a bag.When the card is drawn from the bag at random, what is the probability of getting......
(!) a card with prime number from possible outcomes
(!!) a card without prime number from possible outcomes.
15) (A) Find the value of sec 15 + sin 72 - tan 33
cosec 75 cos 18 cot 57
OR
(B) Observe the figure given below:
In △PQR , if XY//PQ , PX = 5 and QR = 7.2 cm, then find
XR 3
the length of RY.
16). An observer flying in an aeroplane at an altitude of 900 m
observes two ships in front of him, which are in the same direction at an angles of depression of 60 deg and 30 deg respectively. Find the distance between the two ships.
OR
(B) A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. If the length of the cylinder part of the capsule is 14 mm and the diameter of hemisphere is 6 mm, then find the volume of medicine capsule.
17) Draw a circle with radius 3 cm and construct a pair of tangents from a point 8 cm away from the center.
OR
(B) Daily expenditure of 25 householders is given in the following table:
Draw a "less than type" cumulative frequency Ogive curve for this data.
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