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

In a ABC, ∠A = x°, ∠B = (2x - 30)°, ∠C = y° and also, ∠A + ∠B = one right angle. Find the angles. Also, state the type of this triangle.

A two-digit number is such that the ten's digit exceeds thrice the unit's digit by 3 and the number obtained by interchanging the digits is 2 more than twice the sum of the digits. Find the number.

The ratio of passed and failed students in an examination was 3 : 1. Had 30 less appeared and 10 less failed, the ratio of passes to failures would have been 13 : 4. Find the number of students who appeared for the examination.

Samidha and Shreya have pocket money Rs.x and Rs.y respectively at the beginning of a week. They both spend money throughout the week. At the end of the week, Samidha spends Rs.500 and is left with as much money as Shreya had in the beginning of the week. Shreya spends Rs.500 and is left with `(3)/(5)` of what Samidha had in the beginning of the week. Find their pocket money.

Evaluate the following: `(2^3)^2`

Evaluate the following: `(3^2)^2`

State, true of false:
log 4 x log 1 = 0

Name the greatest and the smallest sides in the following triangles:
ΔABC, ∠ = 56°, ∠B = 64° and ∠C = 60°.

Name the greatest and the smallest sides in the following triangles:
ΔDEF, ∠D = 32°, ∠E = 56° and ∠F = 92°.

Name the greatest and the smallest sides in the following triangles:
ΔXYZ, ∠X = 76°, ∠Y = 84°.

Arrange the sides of the following triangles in an ascending order:
ΔABC, ∠A = 45°, ∠B = 65°.

Arrange the sides of the following triangles in an ascending order:
ΔDEF, ∠D = 38°, ∠E = 58°.

Name the smallest angle in each of these triangles:
In ΔABC, AB = 6.2cm, BC = 5.6cm and AC = 4.2cm

Name the smallest angle in each of these triangles:
In ΔPQR, PQ = 8.3cm, QR = 5.4cm and PR = 7.2cm

Name the smallest angle in each of these triangles:
In ΔXYZ, XY = 6.2cm, XY = 6.8cm and YZ = 5cm

In a triangle ABC, BC = AC and ∠ A = 35°. Which is the smallest side of the triangle?

In ΔABC, the exterior ∠PBC > exterior ∠QCB. Prove that AB > AC.

ΔABC is isosceles with AB = AC. If BC is extended to D, then prove that AD > AB.

Prove that the perimeter of a triangle is greater than the sum of its three medians.

Prove that the hypotenuse is the longest side in a right-angled triangle.