ECAT Computer Science Entry Test With Answers

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ECAT Computer Science Entry Test

Sr. # Questions Answers Choice
1 x2+ x - 6 = 0 is a conditional equation and it is true for 2, 3 2, -3 -2, -3 -2, 3
2 (x + 2)2= x2+ 4x + 4 is A linear equation A cubic equation A quadratic equation None
3
4 A = x, B = 1 A = 0, B = 2 A = -1, B = 1 A = x-1, B = x+1
5 Which is the proper rational function
6 2x = 3 is a conditional equation it is true for 2 3 3/2 2/3
7 An open sentence formed by using the sign of equality "=" is called Equation In equation True sentence False sentence
8 If a (p + q)2+ bpq +c = 0 and a (p + r)2+ 2 bpr + c = 0, then qr equals p<sup>2</sup>+ c/a p<sup>2</sup>+ a/c p<sup>2</sup>+ c/a p<sup>2</sup>- c/a
9 If sinαand cosαare the roots of the equation px2+ qx + r =0, then p<sup>2</sup>- q<sup>2</sup>+ 2pr = 0 (p + r)<sup>2</sup>= q<sup>2</sup>- r<sup>2</sup> p<sup>2</sup>+ q<sup>2</sup>- 2pr = 0 (p - r)<sup>2</sup>= q<sup>2</sup>+ r<sup>2</sup>
10 Root of the equation 3x-1+ 31-x= is 2 1 0 -1
11 For the equation |x2| + |x| -6 =0, the roots are One and only one real number Real with sum one Real with sum zero Real with product zero
12 Lies between 4 and 7 Lies between 5 and 9 Has no value between 4 and 7 Has no value between 5 and 9
13
14 15 9 7 8
15 If the roots of ax2+ bx + c = 0 (a > 0) be greater than unity, then a + b + c = 0 a + b + c &gt; 0 a + b + c &lt; 0 None of these
16 Ifα,βare the roots of ax2+ bx + c = 0 andα+ h,β+ h are the roots of px2+ qx + r=0, then h =
17
18 p, q, r and s are integers. If the A.M. of the roots of x2- px + q2= 0 and G.M. of the roots of x2- rx + s2= 0 are equal, then q is an odd integer r is an even integer p is an even integer s is an odd integer
19 If the roots of ax2- bx - c = 0 change by the same quantity, then the expression in a, b, c that does not change is
20 Let the equation ax2- bx + c = 0 have distinct real roots both lying in the open interval (0, 1) where a, b, c are given to be positive integers. Then the value of the ordered triplet (a, b, c) can be (5, 3, 1) (4, 3, 2) (5, 5, 1) (6, 4, 1)
21 Two real roots Two positive roots Two negative roots One positive and one negative root
22 In a quadratic equation with leading co-efficient 1, a student reads the co-obtain the roots as - 15 and -4. The correct roots are 6, 10 -6, -10 8, 8 -8, -8
23 (-1, 2) (-1, 1) (1, 2) {-1}
24 1 2 0 4
25 If the roots of x2+ ax + b = 0 are non-real, then for all real x, x2+ ax + b is Negative Positive Zero Nothing can be said
26 The equation (cos p - 1)x2+ x (cos p) + sin p = 0 in the variable x, has real roots, then p can take any value in the interval (0, 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>) (-<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>, -0) (0,<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>) None of these
27 If 2x1/3+ 2x-1/3= 5, then x is equal to 1 or -1 2 or 1/2 8 or 1/8 4 or 1/4
28 Rational Irrational Non-real Zero
29 Only one real solution Exactly three real solution Exactly one rational solution Non-real roots
30 The value of k (k > 0) for which the equation x2+ kx + 64 = 0 and x2- 8x + k = 0 both will have real roots is 8 -16 -64 16
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