Mathematics ECAT Pre Engineering Online Test With Answers

image
image
image

Mathematics ECAT Pre Engineering Online Test

Sr. # Questions Answers Choice
1 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
2 If the elevation of the sun is 30°, then the length of the shadow cast by a tower of 150 ft height is
3 A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is 60° and when he retires 40 meters away from the tree the angle of elevation becomes 30°. The breadth of the river is 40 m 30 m 20 m 60 m
4 The upper 3/4 the portion of a vertical pole subtends an angle tan-13/5 at a point in the horizontal plane through its foot and at a distance 40 m from the foot. A possible height of the vertical pole is 20 m 40 m 60 m 80 m
5 A tower subtends an angleαat a point on the same level as the root of the tower and at a second point, b meters above the first, the angle of depression of the foot of the tower isβ. The height of the tower is b cot<i style="text-align: center;">α</i>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>β</i></span> b tan<i style="text-align: center;">α</i>tan<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> b tan<i style="text-align: center;">α</i>cot<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
6 An observer on the top of a cliff 200 m above the sea level, observes the angles of depression of two ships on opposite sides of the cliff to be 45° and 30°, respectively. The distance between the ships if the line joining them points to the base of cliff is
7 A chimney is such that on walking towards it 50 m in a horizontal line through its base the angular elevation of its top changes from 30° to 45°. The height of the chimney is
8 A person standing on the bank of a river observes that the angle subtended by a tree of the opposite bank is 60°, when he retreats 40 m from the bank, he finds the angle to be 30°. The height of the tree and the breadth of the river are
9 The angle of depression of a point situated at a distance of 70 meters from the base of a tower is 45°. The height of the tower is 70 m 85 m 35 m None of these
10 A person standing on the bank of a river finds that the angle of elevation of the top of a tower on the opposite bank is 45°. then which of the following statements is correct? Breadth of the river is twice the height of the tower Breadth of the river an the height of the tower are the same Breadth of the river is half of the height of the tower None of these
11 At a point 15 meters away from the base of a 15 meters high house, the angle of elevation of the top is 90° 60° 30° 45°
12 A tower subtends an angle of 30° at a point distant d from the foot of the tower and on the same level as the foot of the tower. At a second point, h vertically above the firs, the angle of depression of the foot of the tower, is 60°. The height of the tower is h/3 h/3d 3h 3h / d
13 30° 60° 45° None of these
14 AB is a vertical pole and C is its middle point. The end A is on the level ground and P is any point on the level ground other than A. the portion CB subtends and angleβat P. If AP : AB = 2 : 1 thenβ=
15 The angles of elevation of the top of a tower at the top and the foot of a pole of height 10 m are 30° and 60° respectively. The height of the tower is 10 m 15 m 20 m None of these
16 A man of height 6 ft observes the top of a tower and the foot of the tower at angles of 45° and 30° of elevation and depression respectively. The height of the tower is
17 An airplane flying at height of 300 meters above the ground passes vertically above another plane at an instant when the angle of elevation of the two planes from the same point on the ground are 60° and 45° respectively. Then the height of the lower plane from the ground is (in meters).
18 Sine is a periodic function and its period is ______ <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> s 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>π</i></span> <div style="text-align: start;"><span style="text-align: center; background-color: rgb(255, 255, 255);">4</span><i style="text-align: center;">π</i></div>
19 Tangent is a periodic function and its period is ______ 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>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, 224);"><i>π</i></span> <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> 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, 224);"><i>π</i></span>
20 The period of tan [x/3] is ______ 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>π</i></span> <div style="text-align: start;"><span style="text-align: center; background-color: rgb(255, 255, 255);">4</span><i style="text-align: center;">π</i></div> <div style="text-align: start;"><span style="text-align: center; background-color: rgb(255, 255, 255);">3</span><i style="text-align: center;">π</i></div> 5<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>
21 The period of cosec 10x is _______
22 tan (π-θ) = ______ - 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> - 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> - 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> - cot<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 The Domain of y = sin x is ______ Set of real numbers Rational Irrational no. None of above
24 The range of y = sin x is ______ [1, -1] [-1, 1] [0, -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, 248);"><i>∞</i></span>+<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>∞</i></span>]
25 Domain of y = cot x = ______
26 The range of y = cot x = ______ -<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>&gt; y &gt; +<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> -<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>∞</i></span>&gt; x &gt; +<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>∞</i></span> -<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>∞ &lt;</i></span>y &lt; +<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>∞</i></span> None of above
27 Domain of tangent function is
28 The function sine and Cosine have the closed internal as their range [1, 0] [-1, 1] [0, 1] [-1, 2]
29 Period of Cotangent function is π -π 0 -2π
30 Period of Tangent function is 0° -<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> <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> 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, 248);"><i>π</i></span>
Download This Set
×