i) In ∆ABC, AB = 3 cm, BC = 2 cm and AC = 2.5 cm. ∆DEF ~ ∆ABC, EF = 4 cm.What is the perimeter of ∆DEF ?(A) 30 cm (B) 22.5 cm (C) 15 cm (D) 7.5 cm(ii) sin q. cosec q = ______(A) 1 (B) 0 (C) 12 (D) √2(iii) Find the perimeter of a sector of a circle if its measure is 90° and radiusis 7 cm.(A) 44 cm (B) 25 cm (C) 36 cm (D) 56 cm(iv) ______ number of tangents can be drawn to a circle from the point onthe circle.(A) 3 (B) 2 (C) 1 (D) 0Q.1. (B) Solve the following : 41. In trapezium ABCD, A BCDQPside AB || side PQ || side DC,AP = 15, PD = 12, QC = 14, find BQ.2. If sin q = 1161 find the values of cos q using trigonometric identity.3. Find the total surface area of a cylinder if the radius of its base is 5 cmand height is 40 cm.4. Draw seg AB of length 4.5 cm and draw its perpendicular bisector.

Sure, let's solve these problems one by one:

i) In ∆ABC, AB = 3 cm, BC = 2 cm and AC = 2.5 cm. ∆DEF ~ ∆ABC, EF = 4 cm. What is the perimeter of ∆DEF?

Since ∆DEF ~ ∆ABC, the ratio of their corresponding sides is the same. So, DE/AB = EF/BC = DF/AC. We know EF = 4 cm and BC = 2 cm, so the ratio is 4/2 = 2. Therefore, the perimeter of ∆DEF is 2 times the perimeter of ∆ABC, which is 2*(3+2+2.5) = 15 cm. So, the answer is (C) 15 cm.

ii) sin q. cosec q = ______

Since cosec q is the reciprocal of sin q, their product is 1. So, the answer is (A) 1.

iii) Find the perimeter of a sector of a circle if its measure is 90° and radius is 7 cm.

The perimeter of a sector is given by the formula 2πr*(θ/360) + 2r, where r is the radius and θ is the angle of the sector. Substituting the given values, we get 2π7*(90/360) + 2*7 = 11π + 14 ≈ 34.54 cm. None of the given options match this value.

iv) ______ number of tangents can be drawn to a circle from the point on the circle.

From a point on the circle, only one tangent can be drawn. So, the answer is (C) 1.

Q.1. (B) Solve the following :

1. In trapezium ABCD, A BCDQPside AB || side PQ || side DC, AP = 15, PD = 12, QC = 14, find BQ.

This problem seems to be incomplete or incorrectly stated. Please provide the correct problem.

2. If sin q = 1/√61 find the values of cos q using trigonometric identity.

We know that sin²q + cos²q = 1. So, cos²q = 1 - sin²q = 1 - (1/61) = 60/61. Therefore, cos q = √(60/61).

3. Find the total surface area of a cylinder if the radius of its base is 5 cm and height is 40 cm.

The total surface area of a cylinder is given by the formula 2πr(h + r), where r is the radius and h is the height. Substituting the given values, we get 2π5*(40 + 5) = 2π5*45 = 450π cm².

4. Draw seg AB of length 4.5 cm and draw its perpendicular bisector.

I'm sorry, but as a text-based AI, I'm unable to draw figures. However, you can do this by drawing a line segment AB of 4.5 cm, then using a compass to draw arcs from points A and B that intersect at a point above the line. Draw a line from this point to the midpoint of AB to create the perpendicular bisector.