ECAT Pre Engineering Entry Test With Answers

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ECAT Pre Engineering Entry Test

Sr. # Questions Answers Choice
1 1 0 3 -3
2
3 tan-1x > cot-1x holds for x > 1 x < 1 x = 1 All values of x
4 1/3 1 3 None of these
5 Cos 2x = sin 4y Cos 4y = cos 2x Cos 3y = sin 4x None of these
6
7 0 1 -1 None of these
8 1 -1 0 None of these
9 x = 3 x = 1/5 x = 0 None of these
10
11 If cos-1p + cos-1q + cos-1r =πthen p2+ q2+ r2+ 2pqr is equal to 3 1 2 -1
12 1 7 4 None of these
13 <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>π</i></span>/ 4 <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>π</i></span>/ 6 <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>π</i></span>/ 3 <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>2π</i></span>/ 3
14 <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>π</i></span>/ 2 <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>π</i></span>/ 3 <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>π</i></span>/ 4 <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>π</i></span>
15
16 If 2 tan1(cos x) = tan-1(cosec2x), then x is equal 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>π</i></span>/ 3 <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>π</i></span>/ 2 <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>π</i></span>/ 6 <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>π</i></span>
17 1 -1 0 None of these
18 The value of sin [ arc cos (-1/2)] is
19 tan-1(1/4) + tan-1(2/9) is equal to 1/2 cos<sup>-1</sup>(3/5) 1/2 sin<sup>-1</sup>(3/5) 1/2 tan<sup>-1</sup>(3/5) tan<sup>-1</sup>1/2
20 If five triangles are constructed having sides of the lengths indicated below, the triangle that will NOT be a right triangle is 8, 15, 17 3, 4, 5 12, 15, 18 5, 12, 13
21 If Cosθ=0, thenθ= ______ n<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>π</i></span>/2 (2n + 1)<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>π</i></span>/2 (2n - 1)<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>π</i></span>/2 (4n + 1)<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>π</i></span>/2
22 Ifθ= 60° then 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, 248);"><i>θ</i></span>= 1/2 tan<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>θ</i></span>= cot 30° <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>θ</i></span>=<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>π</i></span>/4 sec<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>θ</i></span>= 4
23 If you are looking a high point from the ground, then the angle formed is Angle of elevation Angle of depression Right angle Horizon
24 Area ofΔABC= ab 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>α</i></span> 1/2 ab 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>α</i></span> 1/2 ac 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, 248);"><i>γ</i></span> 1/2 ac 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, 248);"><i>β</i></span>
25 If the angle of a triangle are in the ratio 2 : 3 : 7, the triangle is Obtuse Acute Right angle Isosceles
26 120° degrees are equal to how many radians?
27 PQ is a post of given height a, and AB is a tower at some distance;αandβare the angles of elevation of B, the top of the tower, at P and Q respectively. The height of the tower and its distance from the post are
28 The horizontal distance between the two towers is 60 m. the angular elevation of the top of the taller tower as seen from the top of the shorter one is 30°. If the height of the taller tower is 150 m, the height of the shorter one is 116 m 200 m 216 m None of these
29 The angle of elevation of a tower from a point A due south of it is x and from a point B due east of A is y. If AB = 1, then the height h of the tower is given by
30 The longer side of a parallelogram is 10 cm and the shorter is 6 cm. If the longer diagonal makes an angles 30° with the longer side, the length of the longer diagonal is
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