ECAT Mathematics Online Test With Answers

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ECAT Mathematics Online Test

Sr. # Questions Answers Choice
1 In following question, a number series is given with one term missing. choose the correct alternative that will same pattern and fill in the blank spaces.1 , 4, 9, 16, 25, x 35 36 48 49
2 0 -1-w<sup>2</sup>
3 The solution of differential equation: dy/dx+y/x = x<sup>2 </sup>is : 4xy = x<sup>4</sup>+ c 4x = x<sup>4</sup>= c 4 y = x<sup>4</sup>+ c 4x=4x<sup>3</sup> + c
4 An equation in which at least one term contains dy/dx, d2 y /dx2etc, is called. Differential equation Initial condition General solution Singular equation
5 The general solution of the differential equation x dy / dx = 1 + y is: 2 1 3 None
6 The area enclosed between the graph y = x2 -4x and the x- axis is: 20/3 41/3 32/3 25/3
7 The area under the curve y = 1/x2 between x = 1 and x =4 is: -25 0.75 -0.35 -10
8 The area between the x-axis the curve y =4x-x2 is : 32/2 15 18 21
9 The area between the x-axis and the curve y = x2 + 1 from x = 1 to 2 is: 15/6 15/4 10/4 10/3
10 ∫x/Sin2 x dx is equal to: x cot x + ln|sin⁡x | -x cot x - ln|sin⁡x | x cot x - ln|sin⁡x | x. tan x- ln|sec⁡x |
11 ∫x sin xdx is equal to: sin x/x + cos x sin x - cos x/x x cos x + sin x - x cos x + sin x
12 ∫ x cos dx is equal to : x cos x + sin x cos x + x sin x x cos x + x sin x x sin x + cos x
13 ∫sin(ax+b) dx is equal to: 1/2a cos (ax + b) -1/a cos (ax +b) 1/a cos (ax +b) 1/a ln (ax + b)
14 ∫Sec2 (ax + b) dx is equal to: tan<sup>2</sup> (ax + b) 1/a tan<sup>2</sup> (ax + b) 1/atan (ax +b) tan (ax + b)
15 The integral of 3x5dx is: 15 x<sup>4</sup> x<sup>6 </sup>/2 1/6x<sup>5</sup> x<sup>5 </sup>/ln3
16 ∫f(x) is known as: Definite itegral Indefinite integral Fixed integral Multiple integral
17 An integral of 1/x dx is: 1/x<sup>2</sup> 1/-x<sup>2</sup> 1/lnx lnx
18 The graph of y> 0 is the upper - half of: y-axis x-axis 1st and 4th quandrant 2nd and 3rd quadrant
19 The corner point of the boundary lines, x- 2x
x+2y=10 is:
 (8,1) (1,8) (6,10) (3,5)
20 The corner point of the boundary lines, x-2y
2x + y = 2 is:
 (2,6) (6,2) (-2,2) (2,-2)
21 A point of a solution regions where two of its boundary lines intersect, is called: Vertex of the solution Feasible point Point of inequality Null point of the solution region
22 For graphing a linear inequality, solid line is drawn if the inequality involves the symbols: &gt; or &lt; <u>&gt;</u> or <u>&lt;</u> = or≠ = or &gt;
23 Which of the following ordered pair is a solution of the inequality x+2y<6? (2,3) (2,2) (6,0) (1,1)
24 The liner equation ax + by = c is called _________ of the inequality ax +by > c. Associated equation Non-associated equation disjoint equation Feasible equation
25 A ________ divides the plane into left and right half planes. Vertical line Horizontal line Non vertical line Inequality
26 The set of ordered pairs (x,y) such that ax+ by < c, and (x,y) such that ax + by>0, are called Half planes Boundary Linear Inequalities Feasible regions
27 The graph of the linear equation of the form ax =by = c is a line which divided the plane into: Two similar regions Two disjoint regions Four equal parts One region
28 Multiplying each side of an inequality by (-1) will: Not effect Change the sign Become zero Not defined
29 Order (or sense) of an inequality is changed by multiplying or dividing its each side by a: Zero one negative constant Non negative constant
30 f(x) = 3x/x2 + 1 is: an even function an odd function an even and implicit function neither even nor a odd
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