ECAT Pre Engineering Entry Test With Answers

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ECAT Pre Engineering Entry Test

Sr. # Questions Answers Choice
1 y + 1 = Ae<sup>x</sup> y + 1 = Axe<sup>x</sup> xe<sup>x </sup>= C y + xe<sup>x</sup>= C
2
3 The differential equation of all st. lines which are at a constant distance to form the origin is
4 The differential equations of all conis whose axes coincide with the co-ordinate axis is
5 The differential equation representing the family of curves y = A cos (x + B), where A, B are parameters, is
6 1 2 3 4
7 1 2 3 4
8 Te order of the differential equation of all conics whose axes coincide with the axes of co-ordinates is 2 3 4 1
9 2, 3 3, 3 2, 6 2, 4
10 Sand falls from a tube in such a way that it forms a cone whose height is always 4/3 times the radius of its base and radius of the base increases at the rate of 1/8 cm/sec. When this radius is 1 meter, the rate at which the amount of sand increases is
11 Water seeps out of a conical filter at eh constant rate of 5 cm/sec. the height of the cone of water in the filter is 15 cm. the height of the filter is 20 cm and radius of the base is 10 cm. the rate at which the height of the water decreases is
12 If y = sin (ax + b), then fourth derivative of y with respect to x = a<sup>4</sup>cos (ax + b) a<sup>4</sup>sin (ax + b) -a<sup>4</sup>sin (ax + b) a<sup>4</sup>tan (ax + b)
13 Any point, where f is neither increasing nor decreasing and f(x) = 0 at that point, is called a Minimum Maximum Stationary point Constant point
14 Derivative of strictly increasing function is always Zero Positive Negative Both (A) and (B)
15 Second derivative of y = x9+ 10x2+ 2x - 1 at x = 0 is 10 20 12 1
16 -2x cos x<sup>2</sup> -2x<sup>2</sup>sin x<sup>2</sup> -x<sup>2</sup>sin x -2x<sup>2</sup>sin x<sup>2</sup>
17 If c is a constant number and if f is the function defined by the equation f(x) =c for all values of x, then f is differentiable at every x and f is defined by the equation f(x) f 1 C 0
18 The equation of motion of a stone thrown vertically up wards is s = ut - 4.9t2the maximum height attained by it =
19 If s = 2t3- 3t2+ 15t - 8 is the equation of motion of a particle, then its initial velocity is 8 15 -6 None
20 The distance s of a particle in time t is given by s = t3- 6t2- 4t - 8. Its acceleration vanishes at t = 1 2 3 4
21 The velocity of a particle moving along a straight line is given by v = 3t + t2. The acceleration of the particle after 4 seconds from the start is 4 11 26 None
22 If a particle moves according to the law s = t3- t2, then its velocity at time t = 1.5 is 9/2 15/4 5 None
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25
26 xa<sup>x-1</sup> a<sup>x</sup> x in a a<sup>x</sup>In a
27 2x + 2y 4 - x<sup>2</sup> -x/y x/y
28 The parametric equation of a curve are x = t2, y = t3then
29 F(x) = xxdecreases in the interval (0, e) (0, 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, 248);"><i>∞</i></span>,0) None
30 y : x x : y -y : x -x : y
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