NAVYUG HIGHER SECONDARY SCHOOL
ASSIGNMENT
Class 10 - Mathematics
Time Allowed: Maximum Marks: 20
1. The diagonals of a quadrilateral ABCD intersect each other at the point O such that .
AO CO
=
BO DO
Show that ABCD is a trapezium.
2. Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, -3) and
B is (1, 4).
3. Write all the other trigonometric ratios of ∠A in terms of sec A.
2
4. Prove , where the angles involved are acute angles for which the expressions
1+sec A sin A
=
sec A 1−cos A
are defined.
5. A 1.2 m tall girl spots 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 some time, the angle of elevation reduces to 30°. Find the distance traveled by the
balloon during the interval.
6. Prove that parallelogram circumscribing a circle is a rhombus.
7. A round table cover has six equal designs as shown in figure. If the radius of the cover is 28 cm,
find the cost of making the designs at the rate of ₹ 0.35 per cm 2. (use √3 = 1.7)
–
8. A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm is surmounted
by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that 1 cm3
of iron has approximately 8 g mass. (Use π = 3.14)
9. A gulab jamun, contains sugar syrup up to about 30% of its volume. Find approximately how
much syrup would be found in 45 gulab jamun, each shaped like a cylinder with two
hemispherical ends with length 5 cm and diameter 2.8 cm.
10. A survey was conducted by a group of students as a part of their environmental awareness
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ASSIGNMENT
Class 10 - Mathematics
Time Allowed: Maximum Marks: 20
1. The diagonals of a quadrilateral ABCD intersect each other at the point O such that .
AO CO
=
BO DO
Show that ABCD is a trapezium.
2. Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, -3) and
B is (1, 4).
3. Write all the other trigonometric ratios of ∠A in terms of sec A.
2
4. Prove , where the angles involved are acute angles for which the expressions
1+sec A sin A
=
sec A 1−cos A
are defined.
5. A 1.2 m tall girl spots 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 some time, the angle of elevation reduces to 30°. Find the distance traveled by the
balloon during the interval.
6. Prove that parallelogram circumscribing a circle is a rhombus.
7. A round table cover has six equal designs as shown in figure. If the radius of the cover is 28 cm,
find the cost of making the designs at the rate of ₹ 0.35 per cm 2. (use √3 = 1.7)
–
8. A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm is surmounted
by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that 1 cm3
of iron has approximately 8 g mass. (Use π = 3.14)
9. A gulab jamun, contains sugar syrup up to about 30% of its volume. Find approximately how
much syrup would be found in 45 gulab jamun, each shaped like a cylinder with two
hemispherical ends with length 5 cm and diameter 2.8 cm.
10. A survey was conducted by a group of students as a part of their environmental awareness
1/2
