Quant Test 64
1. A circle with radius 2 is placed against a right angle. Another smaller circle is also placed as shown in the adjoining figure. What is the radius of the
smaller circle?
3-2SQRT(2)
4-2SQRT(2)
7-4SQRT(2)
6-4SQRT(2)
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2. If the lengths of diagonals DF, AG and CE of the cube shown in the adjoining figure are equal to the three sides of a triangle, then the radius of the
circle circumscribing that triangle will be
equal to the side of the cube
SQRT(3) times the side of the cube
1 /SQRT(3 ) times the side of the cube (4)
impossible to find from the given information
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3. A new flag is to be designed with six vertical stripes using some or all of the colours yellow, green, blue and red. Then, the number of ways this can
be done such that no two adjacent stripes have the same colour is
12 × 81
16 × 192
20 × 125
24 × 216
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4. Let u = (log x)2 – 6 log x + 12 where x is a real number. Then the equation xu = 256, has
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2
2
no solution for x
exactly one solution for x
exactly two distinct solutions for x
exactly three distinct solutions for x
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5. Let C be a circle with centre P0 and AB be a diameter of C. Suppose P1 is the mid point of the line segment P0B, P2 is the mid point of the line
segment P1B and so on. Let C1, C2, C3, ...... be circles with diameters P0P1, P1P2, P2P3 ... respectively. Suppose the circles C1 C2, C3, .... are all
shaded. The ratio of the area of the unshaded portion of C to that of the original circle C is
8 : 9
9:10
10 : 11
11 : 12
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6. In the adjoining figure, the lines represent one-way roads allowing travel only northwards or only westwards. Along how many dist