ECAT Pre Engineering Entry Test With Answers

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ECAT Pre Engineering Entry Test

Sr. # Questions Answers Choice
1 Range of cosecθis W - {y | -1 < y < 1} R - {y | -1 < y < 1} O - {y | -1 < y < 1} R
2 Range of secθis Z - {x | -1 < x < 1} W - {x | -1 < x < 1} R - {x | -1 < x < 1} R
3 Domain of cosecθis
4 Domain of secθis
5 Range of cotθis (+<span style="color: rgb(34, 34, 34); font-family: &quot;Times New Roman&quot;; font-size: 24px; text-align: center; background-color: rgb(255, 255, 248);"><i>∞</i></span>to -<span style="color: rgb(34, 34, 34); font-family: &quot;Times New Roman&quot;; font-size: 24px; text-align: center; background-color: rgb(255, 255, 248);"><i>∞</i></span>) (-1 to +1) (-5 to +5) Set of even numbers only
6 Range of tanθis Set of complex numbers Set of real numbers Set of odd numbers Set of positive integers only
7 Domain of cotθis
8 Range of cosθis
9 Range of sinθis
10 Domain of cosθis Set of odd numbers Set of integers Set of real numbers Set of complex numbers
11 Domain of sinθis Set of real numbers Set of complex numbers Set of natural numbers Set of even numbers
12 Distance between A(3, 8), B(5, 6) is
13 cos (α-β) = cosαcosβ+ sinαsinβis true for all <i style="text-align: center;">α</i>&gt;<i style="text-align: center;">β</i>&gt; 0 <i style="text-align: center;">α</i>&gt;<i style="text-align: center;">β</i> <i style="text-align: center;">β</i>&gt;<i style="text-align: center;">α</i> None of these
14 sin (2π-θ) cos<i style="text-align: center;">θ</i> sin<i style="text-align: center;">θ</i> tan<i style="text-align: center;">θ</i> -sin<i style="text-align: center;">θ</i>
15 Which one is a pair of allied angles (180° -<span style="color: rgb(34, 34, 34); font-family: &quot;Times New Roman&quot;; font-size: 24px; text-align: center; background-color: rgb(255, 255, 224);"><i>θ)</i></span> (180° -<span style="font-family: &quot;Times New Roman&quot;; font-size: 24px; color: rgb(34, 34, 34); text-align: center; background-color: rgb(255, 255, 224);"><i>θ,</i></span>180° +<span style="font-family: &quot;Times New Roman&quot;; font-size: 24px; color: rgb(34, 34, 34); text-align: center; background-color: rgb(255, 255, 224);"><i>θ)</i></span> (180° +<span style="font-family: &quot;Times New Roman&quot;; font-size: 24px; color: rgb(34, 34, 34); text-align: center; background-color: rgb(255, 255, 224);"><i>θ)</i></span> None of these
16 2π+θwill have terminal side in Quad I II III IV
17 cos 315° = ______
18 sec (-360°) = ______ 0 1 2 3
19 tan (-135°) = ______θ 0 1 2 3
20 sin 540° = 0 1 2 3
21 cos (180° -θ)= sin<i style="text-align: center;">θ</i> - cos<i style="text-align: center;">θ</i> - sin<i style="text-align: center;">θ</i> None of above
22 Express as a sum or difference: 2 sin 5θcosθ cos 4<span style="color: rgb(34, 34, 34); font-family: &quot;Times New Roman&quot;; font-size: 24px; text-align: center; background-color: rgb(255, 255, 224);"><i>θ</i></span>- cos 2<span style="color: rgb(34, 34, 34); font-family: &quot;Times New Roman&quot;; font-size: 24px; text-align: center; background-color: rgb(255, 255, 224);"><i>θ</i></span> sin 4<span style="color: rgb(34, 34, 34); font-family: &quot;Times New Roman&quot;; font-size: 24px; text-align: center; background-color: rgb(255, 255, 224);"><i>θ</i></span>+ sin 2<span style="color: rgb(34, 34, 34); font-family: &quot;Times New Roman&quot;; font-size: 24px; text-align: center; background-color: rgb(255, 255, 224);"><i>θ</i></span> cos 4<span style="color: rgb(34, 34, 34); font-family: &quot;Times New Roman&quot;; font-size: 24px; text-align: center; background-color: rgb(255, 255, 224);"><i>θ</i></span>+ cos 2<span style="color: rgb(34, 34, 34); font-family: &quot;Times New Roman&quot;; font-size: 24px; text-align: center; background-color: rgb(255, 255, 224);"><i>θ</i></span> sin 4<span style="color: rgb(34, 34, 34); font-family: &quot;Times New Roman&quot;; font-size: 24px; text-align: center; background-color: rgb(255, 255, 224);"><i>θ</i></span>- sin 2<span style="color: rgb(34, 34, 34); font-family: &quot;Times New Roman&quot;; font-size: 24px; text-align: center; background-color: rgb(255, 255, 224);"><i>θ</i></span>
23 Cos (α+β) - cos (α-β) = -2 sin<span style="font-family: &quot;Times New Roman&quot;; font-size: 24px; color: rgb(34, 34, 34); text-align: center; background-color: rgb(255, 255, 224);"><i>α</i></span> sin<i style="text-align: center;">β</i> 2 sin<span style="font-family: &quot;Times New Roman&quot;; font-size: 24px; color: rgb(34, 34, 34); text-align: center; background-color: rgb(255, 255, 224);"><i>α</i></span>cos<i style="text-align: center;">β</i> -2 sin<span style="font-family: &quot;Times New Roman&quot;; font-size: 24px; color: rgb(34, 34, 34); text-align: center; background-color: rgb(255, 255, 224);"><i>α</i></span>cos<span style="font-family: &quot;Times New Roman&quot;; font-size: 24px; color: rgb(34, 34, 34); text-align: center; background-color: rgb(255, 255, 224);"><i>α</i></span> 4 sin<span style="font-family: &quot;Times New Roman&quot;; font-size: 24px; color: rgb(34, 34, 34); text-align: center; background-color: rgb(255, 255, 224);"><i>α</i></span> cos<i style="text-align: center;">β</i>
24 cos (α+β) + cos (α-β) = 4 cos<i style="text-align: center;">α</i>cos<span style="font-family: &quot;Times New Roman&quot;; font-size: 24px; color: rgb(34, 34, 34); text-align: center; background-color: rgb(255, 255, 224);"><i>β</i></span> 2 cos<i style="text-align: center;">α</i>cos<i style="text-align: center;">β</i> 2 sin<i style="text-align: center;">α</i>sin<i style="text-align: center;">β</i> 2 sin<i style="text-align: center;">α</i>cos<i style="text-align: center;">β</i>
25 cos4θ- sin4θ= cos4<span style="color: rgb(34, 34, 34); font-family: &quot;Times New Roman&quot;; font-size: 24px; text-align: center; background-color: rgb(255, 255, 224);"><i>θ</i></span> cos2<span style="color: rgb(34, 34, 34); font-family: &quot;Times New Roman&quot;; font-size: 24px; text-align: center; background-color: rgb(255, 255, 224);"><i>θ</i></span> -sin<span style="color: rgb(34, 34, 34); font-family: &quot;Times New Roman&quot;; font-size: 24px; text-align: center; background-color: rgb(255, 255, 224);"><i>θ</i></span> sin2<span style="color: rgb(34, 34, 34); font-family: &quot;Times New Roman&quot;; font-size: 24px; text-align: center; background-color: rgb(255, 255, 224);"><i>θ</i></span>
26 sin2αcos2α= -1 0 1 None of these
27 If cosα= 4/5, then cosα/2
28 tanθ/2
29 sin 2 α=
30 cos 2α= 1 - 2 sin<sup>2</sup><i style="text-align: center;">α</i> sin <sup>2</sup><i style="text-align: center;">α</i>+ cos<sup>2</sup><span style="color: rgb(34, 34, 34); font-family: &quot;Times New Roman&quot;; font-size: 24px; text-align: center; background-color: rgb(255, 255, 248);"><i>β</i></span> sin<sup>2</sup><i style="text-align: center;">α</i>- cos<sup>2</sup><span style="font-family: &quot;Times New Roman&quot;; font-size: 24px; color: rgb(34, 34, 34); text-align: center; background-color: rgb(255, 255, 248);"><i>β</i></span> None of these
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