Practice Test 1: Quant
1.A five digit number is formed using digits 1, 3, 5, 7 and 9 without repeating any one of them. What is the sum of all such possible numbers?
(a) 6666600 (b) 6666660 (c) 6666666 (d) None 35.
2.A box contains 6 red balls, 7 green balls and 5 blue balls. Each ball is of a different size. The probability that the red ball selected is the smallest red ball, is
(a) 1/18 (b) 1/3 (c) 1/6 (d) 2/3
3.ABC forms an equilateral triangle in which B is 2 km from A. A person starts walking from B in a direction parallel to AC and stops when he reaches a point D directly east of C. He, then, reverses direction and walks till he reaches a point E directly south of C. Then D is
(a) 3 km east and 1 km north of A (b) 3 km east and 3 km north of A (c) 3 km east and 1 km south of A (d) 3 km west and 3 km north of A
4. A lead cuboid of 8 inches in length, 11 inches in breadth, and 2 inches thick was melted and resolidified into the form of a rod of 8 inches diameter. The length of such a rod, in inches, is nearest to
(a) 3 (b) 3.5 (c) 4 (d)4.5
5.A quadratic function f(x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1. What is the value of f(x) at x = 10?
(a) -105 (b) –119 (c) –159 (d) –110
6.Neelam rides her bicycle from her house at A to her office at B, taking the shortest path. Then the number of possible shortest paths that she can choose is
(a) 60 (b) 75 (c) 45 (d) 90
7.Two circles with centres P and Q cut each other at two distinct points A and B. The circles have the same radii and neither P nor Q falls within the intersection of the circles. What is the smallest range that includes all possible values of the angle AQP in degrees?
(a) Between 0 and 45
(b) Between 0 and 90
(c) Between 0 and 30
(d) Between 0 and 60
8.Consider four-digit numbers for which the first two digits are equal and the last two digits are also equal. How many such numbers are perfect squares?
(1) 3 (2) 2 (3) 4 (4) 1
9.Two circles with centres P and Q cut each other at two distinct points A and B. The circles have the same radii and neither P nor Q falls within the intersection of the circles. What is the smallest range that includes all possible values of the angle AQP in degrees?
(1) Between 0 and 90 (2) Between 0 and 30 (3) Between 0 and 60 (4) Between 0 and 75
10. A quadratic function ƒ(x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1. What is the value ƒ(x) at x = 10?
(1) –119 (2) –159 (3) –110 (4) –180
9. Ans C
7. When the centers of two circles i.e. P & Q passes through the other circle. APQ forms an equilateral triangle with side = r where r = radius of circle. so max /_APQ = 60`
When two circles just touch each other APQ is a straight line and /_APQ = 0`
So Ans d.
6 . Question seems incomplete. Please complete this question.
2. The probability that the red ball selected is the smallest red ball, is 1/6 (since balls are of different sizes.)
Ans C
4. volume of cuboid = 8 x 11 x 2
Let length of rod = h
Since cuboid is melted and molded into a rod. So 8x 11 x 2 = (22/7) x (4)^2 x h –> h = 3.5
Ans B.