161.A rectangular picture 6cm by 8cm is enclosed by a frame ½cm wide. Calculate the area of the frame
- A. 15sq.cm
- B. 20sq.cm
- C. 13sq.cm
- D. 16sq.cm
162.A regular hexagon is constructed inside a circle of diameter 12cm. The area of the hexagon is
- A. 36πcm²
- B. 36/πcm²
- C. 54√3πcm²
- D. 54/√3πcm²
163.A solid cylinder of radius 3cm has a total surface area of 36πcm². Find its height
164.A square of cardboard is taped at the perimeter by a piece of ribbon 20cm long. What is the area of the board?
- A. 20sq.cm
- B. 25sq.cm
- C. 36sq.cm
- D. 100sq.cm
165.A triangle has angles 30⁰, 15⁰ and 135⁰ , the side opposite to the angle 30⁰ is length 6cm. The side opposite to the angle 135⁰ is equal to
- A. 12cm
- B. 6cm
- C. 6√2cm
- D. 12√2cm
166.An isosceles triangle of sides 13cm, 13cm, 10cm is inscribed in a circle. What is the radius of the circle?
- A. 7 1/24cm
- B. 12cm
- C. 8cm
- D. 7cm
167.Find the area of the curved surface of a cone whose base radius is 6cm and whose height is 8cm (Take π = 22/7).
- A. 188.57cm²
- B. 1320cm²
- C. 188cm²
- D. 188.08cm²
168.Find the total surface area of a solid cone of radius 2√3cm and slanting side 4√3cm.
- A. 8√3πcm³
- B. 24πcm³
- C. 15√3πcm³
- D. 36πcm³
169.If the four interior angles of a quadrilateral are (p+10)⁰,(p-30)⁰,(2p-45)⁰ and (p+15)⁰, then p is
- A. 125
- B. 82⁰
- C. 135⁰
- D. 105
170.If the hypotenuse of a right angled isosceles triangle is 2, what is the length of each of the other sides?
171.If the value of π is taken to be 22/7, the area of a semicircle of diameter 42m is
- A. 5544m²
- B. 1386m²
- C. 132m²
- D. 693m²
172.In a circle of radius 10cm, a cord of length 10cm is xcm from its centre where x is
- A. 10√2
- B. 5√3
- C. 10√3
- D. 5√2
173.PQRS is a cyclic quadrilateral with PQ as diameter of the circle. If angle PQS = 15⁰, find angle QRS
- A. 75⁰
- B. 37 1/2⁰
- C. 127 1/2⁰
- D. 105⁰
174.The difference between the length and width of a rectangle is 6cm and the area is 135cm². What is the length?
- A. 25cm
- B. 18cm
- C. 15cm
- D. 24cm
175.At what value of x does the function y= -3 – 2x +x² attain a minimum value?
176.Evaluate ∫³₂(x²-2x)dx
177.Find the derivative of y=sin(2x²+3x-4)
- A. -cos(2x³+3x-4)
- B. -(6x²+3)cos(2x³+3x-4)
- C. cos(2x³+3x-4)
- D. (6x²+3)cos(2x³+3x-4)
178.If dy/dx =x+cosx, find y
- A. x²/2 - sinx + c
- B. x² -sinx + c
- C. x²/2 + sinx + c
- D. x² + sinx + c
179.If the maximum value of y = 1 + hx - 3x² is 13, find h.
180.If s = (2 + 3t)(5t-4), find ds/dt when t = 4/5 sec
- A. 0 unit per sec.
- B. 15 units per sec.
- C. 22 units per sec.
- D. 26 units per sec.