CSS General Abilities Online Entry Test With Answers

CSS General Abilities Online Entry Test

Sr. # Questions Answers Choice
1 A 5 × 12 rectangle is inscribed in a circle. What is the radius of the circle ? 6.5 7 8.5 13
2 A square of area 2 is inscribed in a circle. What is the area of the circle ? π/4 π/2 π π√2
3 What is the area of a circle that is inscribed in a square of area ? π/4 π/2 π π√2
4 What is the area of a circle whose circumference is π ? π/4 π/2 π 2π
5 What is the circumference of a circle whose area is 100π ? 10 20 10π 20π
6 100 110 120 130
7 If the measures of the angles of a triangle are in the ratio of 1:2:3, and if the length of the smallest side of the triangle is 10, what is the length of the longest side ? 10√2 10√3 15 20
8 5√2 10 11 13
9 Two sides of a right triangle are 12 and 13, which of the following could be the length of the third side ?
i. 5
ii. 11
iii. √313
 1 only 2 only 1 and 2 1 and 3
10 If the difference between the measures of the two smaller angles of a right triangle is 8o , what is the measure, in degrees, of the smallest angle ? 37 41 42 49
11 20 30 40 50
12 Given the following data, which can form two triangles ?
i. ∠C = 30o, c = 8, b = 12
ii. ∠B = 45o, a = 12√2, b = 15√2
iii. ∠C = 60o , b = 12, c = 5√3
 only 1 only 2 only 3 only 1 and 2
13 The area of Δ ABC, = 24√3 , side a = 6, and side b = 16. The value of ∠ C is 30<sup>o</sup> 30<sup>o</sup>&nbsp;or&nbsp;150<sup>o</sup> 60<sup>o</sup> 60<sup>o</sup>&nbsp;or&nbsp;120<sup>o</sup>
14 7 17 9 14
15 a &gt; 4√3 a &gt; 8 a = 4√3 4√3 &lt; a &lt; 8
16 Find the length of the longer diagonal of a parallelogram if the sides are 6 inches and 8 inches and the smaller angle is 60o. 8 11 12 7
17 The sides of a triangle are in a ratio of 4 : 5 : 6. The smallest angle is 82<sup>o</sup> 69<sup>o</sup> 56<sup>o</sup> 41<sup>o</sup>
18 The angles of triangle are in a ratio of 8 : 3 : 1. The ratio of the longest side of the triangle to the next longest side is √6:2 8 : 3 √3:1 8 : 5
19 In Δ ABC, ∠ A = 30o , a = 6, and c = 8. Which of the following must be true ? 0<sup>o</sup>&nbsp;&lt;&nbsp;∠C &lt; 90<sup>o</sup> 90<sup>o</sup>&nbsp;&lt;&nbsp;∠C &lt; 180<sup>o</sup> 45<sup>o</sup>&nbsp;&lt;&nbsp;∠C &lt; 135<sup>o</sup> 0<sup>o</sup>&nbsp;&lt;&nbsp;∠C &lt; 45<sup>o</sup>&nbsp;or 130<sup>o</sup>&nbsp;&lt;&nbsp;∠C &lt; 180<sup>o</sup>
20 In Δ ABC, ∠ A = 30o , b = 8, and a = 4√2 . Angle C could equal 45<sup>o</sup> 135<sup>o</sup> 60<sup>o</sup> 15<sup>o</sup>
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