Q1. ABCD is a square, AC = BD =4√2 cm, AE = DE = 2.5 cm. Find the area of the adjoining figure ABCDE :
(a) 19 cm2
(b) 22 cm2
(c) 17 cm2
(d) None of the above

Q2. A rectangular water reservoir is 15 m by 12 m at the base. Water flows into it through a pipe whose cross-section is 5 cm by 3 cm at the rate of 16 m per second. Find the height to which the water will rise in the reservoir in 25 minutes:
(a) 0.2 m
(b) 2 cm
(c) 0.5 m
(d) None of these

Q3. A large solid sphere of diameter 15 m is melted and recast into several small spheres of diameter 3 m. What is the percentage increase in the surface area of the smaller spheres over that of the large sphere?
(a) 200%
(b) 400%
(c) 500%
(d) Can’t be determined

Q4. A cone is made of a sector with a radius of 14 cm and an angle of 60°. What is total surface area of the cone?
(a) 119.78 cm2
(b) 191.87cm2
(c) 196.5 cm2
(d) None of these

Q5. If a + b + c = 13, what is the maximum value of (a-3)(b-2)(c+1)?
(a) 26
(b) 27
(c) 30
(d) 19

Q6. If x and y are both positive, then the minimum value of (x + y) (1/x+1/y) is:
(a) 0
(b) 1
(c) 2
(d) 4

Q7. If x, y, z are real numbers such that x + y + z = 4 and x^2+y^2+z^2=6, then x, y z lie in:
(a) [3/2 ,2]
(b) [2/3 ,2]
(c) [0 ,2/3]
(d) None of these

Q8. If 1 ≤ x ≤ 3 and 2 ≤ y ≤ 4, what is the maximum value of (x/y)?
(a) 2/3
(b) 4
(c) 3/2
(d) 2
(a) 11/12
(b) 11/96
(c) 29/96
(d) None of these

(a) 3 (x + y + x) = a
(b) 2a = x + y + z
(c) x + y + z = 0
(d) x = y = z =a/3