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ECAT Pre Engineering Entry 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|sinx | -x cot x - ln|sinx | x cot x - ln|sinx | x. tan x- ln|secx | |
| 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: | > or < <u>></u> or <u><</u> = or≠ = or > |
| 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 |
