Mathematics ECAT Pre Engineering Online Test With Answers

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Mathematics ECAT Pre Engineering Online Test

Sr. # Questions Answers Choice
1 The equation of the plane which bisects the line joining (2, 3, 4) and (6, 7, 8) is x + y + z - 15 = 0 x - y + z - 15 = 0 x - y - z - 15 = 0 x + y + z + 15 = 0
2 The distance of the plane 2x - 3y + 6z + 14 = 0 from the origin is 14 2 -2 11
3 The point which divides the line joining the points (2, 4, 5) and (3, 5, -4) in the ratio -2 : 3 lines on ZOX plane XOY plane YOZ plane None of these
4 0 2 4/3 5/3
5 The projections of a line segment on x, y, z axes are 12, 4, 3. The length and the direction cosines of the line segment are
6 The st. lines whose direction cosines satisfy al + bm + cn = 0, fmn + gnl + hlm=0 are perpendicular if
7 (3, 1, -2) (3, -2, 1) (2, -1, 3) (-1, -2, -3)
8 The distance of the points (3, 4, 5) from y-axis is
9 The direction cosines of any normal to the xy-plane are <1, 0, 0> <0, 1, 0> <1, 1, 0> <0, 0, 1>
10 The direction cosines of a line equally inclined with co-ordinate axes are
11 The points (5, 2, 4)(6, -1, 2) and (8, -7, k) are collinear if k is equal to -2 2 3 -1
12 If l, m, n are the d.c.'s of a line, then l2+ m2+ n2= 0 l2+ m2+ n2= 1 l + m + n = 1 l = m = n = 1
13 Which of the following integrals can be evaluated
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15 <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> <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/6</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/2</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, 224);"><i>π</i></span>
16 0 1 2 4
17 Always negative Zero Always positive Infinity
18 If the graph of f is entirely below the x-axis, then the value of definite integral is = 0 &lt; 0 &gt; 0 None
19 If the lower limit of an integral is a constant and the upper limit is a variable, then the integral is a Constant function Variable value Function of upper limit All
20 The arbitrary constants involving in the solution can be determined by the given conditions. Such conditions are called Boundaries Variable separable Initial values None
21 Y = -x log x -x + c Y = x log x + x Y = x log x - x + c None of these
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24 X = 100 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> X = 10 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, 248);"><i>θ</i></span> X = 100 sec<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>θ</i></span> None of these
25 A variable A constant 0 None of these
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28 Which of the following integrals can be evaluated
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