(English Medium) ICSE Class 9 - CISCE Question Bank Solutions for Mathematics

Observe the given frequency table to answer the following:

a. The true class limits of the fifth class.
b. The size of the second class.
c. The class boundaries of the fourth class.
d. The upper and lower limits of the sixth class.
e. The class mark of the third class.

Construct a rhombus ABCD, given AB = 3.8cm and ∠A = 60°. Measure AC.

Construct a rhombus whose perimeter is 16cm and BD = 6.2cm.

Construct a rhombus whose diagonals AC = 7.4cm and BD = 6cm.

Construct a rhombus whose side AB = 5cm and diagonal AC = 6cm. MEasure DB and AD.

Prove that the diagonals of a parallelogram divide it into four triangles of equal area.

The diagonals AC and BC of a quadrilateral ABCD intersect at O. Prove that if BO = OD, then areas of ΔABC an ΔADC area equal.

PQRS is a parallelogram and O is any point in its interior. Prove that: area(ΔPOQ) + area(ΔROS) - area(ΔQOR) + area(ΔSOP) = `(1)/(2)`area(|| gm PQRS)

In the given figure, AB ∥ SQ ∥ DC and AD ∥ PR ∥ BC. If the area of quadrilateral ABCD is 24 square units, find the area of quadrilateral PQRS.

In the given figure, PQ ∥ SR ∥ MN, PS ∥ QM and SM ∥ PN. Prove that: ar. (SMNT) = ar. (PQRS).

In ΔABC, the mid-points of AB, BC and AC are P, Q and R respectively. Prove that BQRP is a parallelogram and that its area is half of ΔABC.

In ΔPQR, PS is a median. T is the mid-point of SR and M is the mid-point of PT. Prove that: ΔPMR = `(1)/(8)Δ"PQR"`.

In the figure, ABCD is a parallelogram and CP is parallel to DB. Prove that: Area of OBPC = `(3)/(4)"area of ABCD"`

The medians QM and RN of ΔPQR intersect at O. Prove that: area of ΔROQ = area of quadrilateral PMON.

A class room is 7m long, 6m wide and 4m high. It has two doors each of 3m x 1.4m and six windows each of 2m x 1m. The interior walls are to be coloured at the rate of Rs.15per m². Find the cost of colouring the walls.

The cost of papering the four walls of a room at Rs 1 per m² is Rs. 210. The height of the room is 5 m. Find the length and the breadth of the room if they are in the ratio 5:2.

The area of a playground is 4800m². Find the cost of covering it with gravel 2.5cm deep, if the gravel costs Rs.7.25 per m³.

How many cubic meters of earth must be dug out to sink a well 42m deep and 14m in diameter? Find the cost of plastering the inside walls of the well at Rs.15per m².

Simplify : `root(5)(16) xx root(5)(2)`

Simplify : `root(4)(243)/root(4)(3)`