In ΔABC, L and M are two points on the sides AC and BC respectively such that LM || AB and AL are (x - 2) units, AC = 2x + 3 units, BM = (x – 3) units and BC = 2x units. Determine the value of x.

Two triangles are similar if their corresponding sides are ___.

Perimeters of two similar triangles are 27 cm and 16 cm. If the length of a side of the first triangle is 9 cm, then find the length of the corresponding side of the second triangle

In trapezium ABCD, BC ∥ AD and AD = 4 cm. Diagonals AC and BD meet at O such that AO/OC = DO/OB = 1/2. Find the length of BC.

DE ∥ BC of ΔABC where D and E are two points on AB and AC, respectively. If AD = 5 cm, DB = 6 cm, and AE = 7.5 cm, calculate the length of AC.

State True/False: “The equal chords of a circle are at equal distances from the centre of the circle.”

Write a difference between the geometric angle and trigonometrical angle.

Find the value of angle in degree made by the tangent of a circle with the radius of that circle at the point of contact

Mode = 2 × Median – 3 × Mean.

If x be the volume, y be the area of the base and z be the height of a cone then the value of x / yz is 3.

ABCD is a cyclic quadrilateral. If ∠ADB = x° and ∠ABD = y° then ∠BCD is (x + y)°.

If the sum of the square of the roots of the equation 6x² + x + k = 0 is , then the value of k is 12.