If each exterior angle of a regular polygon is 18°, then the number of sides of the polygon is

• 10

• 15

• 20

• 30

Two sides of a right triangle measure 15 cm and 17 cm. Which of the following statements can be true of the length of the third side of the triangle ?

A. It is between 4 cm and 7 cm.

B. It is between 20 cm and 23 cm.

C. It is less than 10 cm

• Only B

• A and C

• A and B

• B and C

$$\begin{gathered} \mathrm{In} ∆\mathrm{ABC}, \mathrm{AB} =4\mathrm{cm}, \mathrm{AC} =5 \mathrm{cm} \mathrm{and} \mathrm{BC} = 6 \mathrm{cm}. \\ \mathrm{In} ∆\mathrm{PQR}, \mathrm{PR} = 4 \mathrm{cm}, \mathrm{PQ} = 5 \mathrm{cm} \mathrm{and} \mathrm{RQ} = 6 \mathrm{cm}. ∆\mathrm{ABC} \mathrm{is} \mathrm{congruent} \mathrm{to} \end{gathered}$$

• $∆\mathrm{PQR}$

• $∆\mathrm{RPQ}$

• $∆\mathrm{PRQ}$

• $∆\mathrm{QRP}$

54.

A tank is in the form of a cuboid. It holds a maximum of 540 m³ water. If the tank is 8 m long and 15 m wide, then how many metres,deep must the water be when the tank is full ?

• 2

• 4.5

• 2.5

• 3

The ratio of the areas of two equilateral triangles is 16 : 9. If the perimeter of the smaller triangle is 63 cm, then how much larger is a side of the larger triangle than a side of the smaller triangle ?

• 3cm

• 7cm

• 4cm

• 5cm

The area of a triangle is equal to the area of a circle whose perimeter is 6$\mathrm{\pi }$ cm. If the base of the triangle is 8 cm, then its corresponding height (in cm)

• $\mathrm{\pi }$

• 2.25

• 2

• 2.25$\mathrm{\pi }$

Neeta a Class VII Mathematics teacher, assigns a lot of survey-based projects to Mathematics classrooms. The purpose of such activity is

A. to promote problem-solving skills.
B. to give an opportunity to students to
collect authentic data.
C. to break the monotony of the classroom.
D. to use it as an alternate assessment.
Which of the above purposes are true?

• A and B

• A, B and C

• A and C

• A, B and D

In which one of the following cases, the construction of a quadrilateral ABCD is not possible ?

• BC = 4.5cm, AD = 5.5cm, CD = 5cm, AC = 5.5 cm and BD = 7 cm

• $\mathrm{AB} = 6\mathrm{cm}, \mathrm{BC} = 9.5\mathrm{cm}, \angle A = 75°, \angle \mathrm{B} = 150° \mathrm{and} \angle \mathrm{C} = 140°$

• $\mathrm{AB} = 35\mathrm{cm}, \angle \mathrm{B} = 125°, \angle \mathrm{C} = 80° \mathrm{BC} = 55\mathrm{cm} \mathrm{and} \mathrm{CD} = 5\mathrm{cm}$

• $\mathrm{AB} = 4\mathrm{cm}, \mathrm{BC} = 6\mathrm{cm}, \mathrm{AC} = 8\mathrm{cm}, \mathrm{AD} = 5.5 \mathrm{cm} \mathrm{and} \mathrm{DC} = 5\mathrm{cm}$

Let x be the angle which is equal to its complement and y be the angle which is equal to its supplement. Then, 2x + 3y is equal to

• $135°$

• $270°$

• $360°$

• $180°$

ABCD is a quadrilateral in which BD = 40 cm. The lengths of the perpendiculars drawn from the opposite vertices on BD are 16 cm and 12 cm. The area of the quadrilateral (in cm)

• 560

• 580

• 600

• 500