Mathematics ECAT Pre Engineering Online Test With Answers

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Mathematics ECAT Pre Engineering Online Test

Sr. # Questions Answers Choice
1 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
2 sin (α+β) - sin (α -β) = 4 cos<i style="text-align: center;">α</i>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>β</i></span> 2 cos<i style="text-align: center;">α</i>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>β</i></span> 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> 4 sin <i style="text-align: center;">α</i>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>β</i></span>
3 sin (α+β) + sin (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>cos<i style="text-align: center;">β</i> sin (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, 224);"><i>α</i></span><i style="text-align: center;">β)</i> sin<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>α</i></span> None of these
4 sin (α -β)= 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>- cos<i style="text-align: center;">α</i>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>β</i></span> 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>+ cos<i style="text-align: center;">α</i>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>β</i></span> 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;">α</i>- cos<i style="text-align: center;">β</i>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>β</i></span> 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;">α</i>- cos<i style="text-align: center;">β</i>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>β</i></span>
5 sin (α +β)= 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>cos<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>β</i></span>- cos<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>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>β</i></span> 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>β</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>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>β</i></span> 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;">α</i>- cos<i style="text-align: center;">β</i>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>β</i></span> 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;">α</i>+ cos<i style="text-align: center;">β</i>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>β</i></span>
6 Tan 2θ=
7 cosθ/2=
8 sinα= 2 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>cos<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> 2 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>cos<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>β</i></span> 2 sin<i style="text-align: center;">α</i>/2 cos<i style="text-align: center;">α</i>/2 1+ tan<sup>2</sup><i style="text-align: center;">α</i>/2
9 sin(180° -θ)= cos<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> -cos<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> 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> 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>
10 cos 2α= sin<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, 224);"><i>α</i></span>+ 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, 224);"><i>α</i></span> -cos<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> 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, 224);"><i>θ</i></span> None of these
11 -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> cos<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> -cos<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>
12 Tan(α-β)=
13 Fundamental law is
14 Let P(x1, y1) and Q(x2, y2) be two points in the co-ordinate plane. Let d = distance between P and Q
15 G.P H.P. A.P. No particular sequence
16 Tan 3x tan 2x-tan x is equal to Tan x tan 2x tan 3x -tan x tan 2x tan 3x Tan x tan 2x - tan - tan x tan 3x - tan 2x tan 3x None of these
17 The value of the expression 3 cosθ+ 4 sinθθlie between -7 and 7 -25 and 25 -1 and 1 -5 and 5
18 The value of the expression sinθ+ cosθlies between
19
20
21
22 45° 30° 75° 60°
23 The value of sin 28°cos 17°+cos 28°sin 17°is
24 If sin A = cos A, 0°<A<90° then A is equal to 1 1/2 0 None of these
25 The value of sin220° + sin270° is equal to 1 2 -1 1/2
26 Sin 50°-sin 70°+sin 10° is equal to 1 0 1/2 2
27 Right angled Obtuse angled Isosceles Equilateral
28 The maximum value of sin x + cos x is
29 The maximum value of 12 sinθ-9 sin2θis x 3 4 5 None of these
30 The maximum value of 12 sinθ-9 sin2θis x 3 4 5 None of these
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