Describe the method of construction of a square of the equal area of ​​an equilateral triangle.

Find the value of 2√3 geometrically.

Use graph paper, taking 2 cm = 1 unit along both axes. (a) Plot A(1, 3), B(1, 2) and C(3, 0). (b) Reflect A and B in the x-axis and name their images E and D. Write their coordinates. (c) Reflect A and B through the origin and name their images F and G. (d) Reflect A, B and C in the y-axis and name their images J, I and H. (e) Join A, B, C, D, E, F, G, H, I and J in order and name the closed figure.

Assertion (A): The 9th term of the G.P. 6, −12, 24, −48, … is positive. Reason (R): (−2)⁸ is positive. (a) A is true and R is false. (b) A is false and R is true. (c) Both A and R are true and R is the correct explanation of A. (d) Both A and R are true but R is not the correct explanation of A.

In the given diagram, O is the centre of the circle and the tangent DE touches the circle at B. If ∠ADB = 32°. Find the values of x and y.

The 4th and the 7th terms of an A.P. are 60 and 114 respectively. Find: (a) the first term and the common difference. (b) the sum of the first 10 terms.

In the given figure, ABCD is a cyclic quadrilateral. DE is produced to E and ∠CDE = 65°. If x is the angle subtended by chord AC at the centre, then x is: (a) 32.5° (b) 65° (c) 115° (d) 130°

In the given diagram, O is the centre of the circle. Chord SR produced meets the tangent XTP at P. (a) Prove that △PTR ∼ △PST. (b) Prove that PT² = PR × PS. (c) If PR = 4 cm and PS = 16 cm, find the length of tangent PT.

Refer to the bill below. A customer paid ₹2,000, rounded to the nearest ₹10, to clear it. Note: A 5% discount applies to an article when 10 or more units are purchased. Article Marked price Quantity GST A ₹190 6 12% B ₹50 12 18% Check whether the amount paid is correct. Justify your answer with working.

In the given diagram, chords AC and BC are equal. If ∠ACD = 120°, then ∠AEC is: (a) 30° (b) 60° (c) 90° (d) 120°

If 1701 is the nth term of the Geometric Progression 7, 21, 63, …, find: (a) the value of n. (b) hence, the sum of the n terms of the G.P.

It is given that (x − 2) is a factor of 2x³ − 7x² + kx − 2. (a) Find k. (b) Hence, factorise the resulting polynomial completely.