- A box can be completely filled with 2 inch cubes, but when it is filled with three inch cubes
space is left in all three directions (i.e., along the length, width, and height).
How many of the following numbers can possibly be the volume of the box in cubic inches?
i) 1224 ii) 1648 iii) 1872 iv) 2036
A) 1 B) 2 C) 3 D) 4
- The number of ways 5 boys and 3 girls can sit in a row so that no girl sits next to another
is
A) 600 B) 7200 C) 14400 D) 40320
- What is the 49th digit after the decimal point in the decimal expansion of 5/49 ?
A) 4 B) 5 C) 8 D) 9
- What is the 1998th digit after the decimal point in the decimal expansion of 6391/8100 ?
A) 4 B) 5 C) 8 D) 9
- The area of a triangle whose medians are of lengths 7, 8, and 9 is
A) 20Ö3 B) 27Ö7/2 C) 16Ö5 D) 36
- The area of a quadrilateral with sides of lengths a, b, c, d is given by the formula
A) Ö(abcd) sin a a = average of two opposite angles,
B) Ö[(s - a)(s - b)(s - c)(s - d)] where s = (a + b + c + d)/2,
C) ½d1d2sin b d1, d2 = lengths of diagonals, b = angle between them,
- If three points A, B, C move on a plane in such a manner that
i) the sum of squares of their distances from a fixed point O on the plane remains constant = c1 and
ii) the sum of squares of the lengths of the sides of the triangle ABC remains constant = c2
then the centroid of the triangle ABC lies on circle with center at O and with radius
A) Ö(c1 + c2)/2,
B) Ö(3c1 - c2)/3,
C) Ö(9c12 - c22)/3,
D) Ö(c1/3) - Ö(c2)
- Three boys Andy, Bill, and Chris made some statements. Each of them claims that he is
telling the truth and at least one of the other two is lying. Of the following four conclusions
i) All of them are telling the truth,
iii) Only two are lying, and
iv) All of them are lying,
how many can possibly be true?
A) 1 B) 2 C) 3 D) 4
- The curves traced by a point the product of whose distances from two intersecting
straight lines remains constant = 1 are two hyperbolas whose equations in some suitable
coordinate system are
x2/a2 -
y2/b2 = ± 1,
a, b depending on the lines and satisfying the equations
A) 1/a2 + 1/b2 = 1
B) 1/a2 - 1/b2 =
± 1
C) a2 + b2 = ab(a + b)
D) a2 - b2 =
± 1
- A quadrilateral has sides of lengths 4, 5, 7, and 10. Its maximum possible area is
A) 20Ö3 B) 27Ö7/2 C) 16Ö5 D) 36
