Mathematics ECAT Pre Engineering Online Test With Answers

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Mathematics ECAT Pre Engineering Online Test

Sr. # Questions Answers Choice
1 ab > 0 and a > 0 then a > b a < b a = b None
2 r + 3 >5 then which is true r + 2 > 4 r + 2 < 4 r + 2 = 4 None
3 x is a member of the set [-1, 0, 3, 5] y is a member of the set {-2, 1, 2, 4} which is possible? x - y = -6 x - y < -6 x - y > -6 None
4 The total cost of 2 apples and 3 oranges is $1.70, which of the following is true The cost of one apple The cost of one orange Both have equal cost per item Cost of each single item can not be determined
5 p < r p > rr p + r < 0 p - r < 0
6 If -1 < x < 0, which of the following statements must be true? x &lt; x<sup>2</sup>&lt; x<sup>3</sup> x &lt; x<sup>3</sup>&lt; x<sup>2</sup> x<sup>2</sup>&lt; x<sup>3</sup>&lt; x x<sup>2</sup>&lt; x &lt; x<sup>3</sup>
7 For which of the following ordered pairs (s, t) is s + t > 2 and s - t < -3? (3, 2) (2, 3) (1, 8) (0, 3)
8 Which is in the solution set of 4x - 3y < 2 (3, 0) (4, 1) (1, 3) None
9 A farmer possesses 100 hectometers of land and wants to grow corn and wheat. Cultivations of corn requires 3 hours per hectometer while cultivation of wheat requires 2 hours per hectometer. Working hours cannot exceed 240. If he gets a profit of Rs. 20 per hectometer for corn and Rs. 15 per hectometer for wheat. The profit function for the farmer is P(x, y) = 20x + 15y P(x, y) = 2x + 3y P(x, y) = x + y P(x, y) = 3x + 2y
10 A point of a solution region where two of its boundary lines intersect, is called Boundary Inequality Half plane Vertex
11 Which is not a half plane ax + by &lt; c ax + by &gt; c Both A and B None
12 If 4 - x >5, then x &gt; 1 x &gt; -1 x &lt; 1 x &lt; -1
13 If ab > 0 and a < 0, which of the following is negative? b -b -a (a - b)<sup>2</sup>
14 If x < y, 2x = A, and 2y = B, then A = B A &lt; B A &lt; x B &lt; y
15 The equation of the sphere thro' the origin and making intercepts a, b, c on co-ordinate axes is x<sup>2</sup>+ y<sup>2</sup>+ z<sup>2</sup>+ ax + by + cz = 0 x<sup>2</sup>+ y<sup>2</sup>+ z<sup>2</sup>- 2ax - 2 by - 2 cz = 0 x<sup>2</sup>+ y<sup>2</sup>+ z<sup>2</sup>= a + b + c x<sup>2</sup>+ y<sup>2</sup>+ z<sup>2 </sup>- ax - by - cz =0
16 The center of the sphore which passes thro' (a, 0, 0), (0, b, 0), (0, 0, c) and (0, 0, 0) is
17 The equation of the sphere passing thro' (0, 0, 0), (a, 0, 0), (0, b, 0), (9, 0, c) is x<sup>2</sup>+ y<sup>2</sup>+ z<sup>2</sup>+ 2 ax +2 by + 2cz = 0 x<sup>2</sup>+ y<sup>2</sup>+ z<sup>2</sup>- 2ax - 2 by - 2cz = 0 x<sup>2</sup>+ y<sup>2</sup>+ z<sup>2</sup>- ax - by - cz = 0 x<sup>2</sup>+ y<sup>2</sup>+ z<sup>2</sup>+ ax + by + cz = 0
18 x-axis y-axis z-axis None of these
19 The intercepts of the plane 2x - 3y + 4z = 12 on the co-ordinate axes are given by 2, -3, 4 6, -4, -3 6, -4, 3 3, -2, 1.5
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22 64.A point (x, y, z) moves parallel to xy plane. Which of the three variables x, y, z remain fixed? z x y x and y
23 The foot of perpendicular from (α,β,γ) only y-axis 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, 248);"><i>α</i></span>, 0, 0) (0,<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>, 0) (0, 0, <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>γ</i></span>) (0, 0, 0)
24 Parallel to the plane At right angles to the plane Lies in the plane Meet the plane obliquely
25 -10 10/7 -10/7 -7/10
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27 The points (5, -4, 2),(4, -3, 1),(7, -6, 4),(8, -7, 5) are vertices of a Square Parallelogram Rectangle Rhombus
28 The points (5, 0, 2), (2, -6, 0), (4, -9, 6) and (7, -3, 8) are vertices of a Square Rhombus Rectangle Parallelogram
29 The equations of the line thro' the point (2, 3, -5) and equally inclined to the axis are
30 The lines l1and l2intersect. The shortest distance between them is Positive Negative Zero Infinity
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