ECAT Mathematics MCQ's Test For Full Book With Answers

ECAT Mathematics MCQ's Test For Full Book

Sr. # Questions Answers Choice
1 Ifα,βare the roots of ax2+ bx + c = 0 andα+ h,β+ h are the roots of px2+ qx + r=0, then h =
2
3 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
4 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
5 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)
6 Two real roots Two positive roots Two negative roots One positive and one negative root
7 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
8 (-1, 2) (-1, 1) (1, 2) {-1}
9 1 2 0 4
10 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
11 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
12 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
13 Rational Irrational Non-real Zero
14 Only one real solution Exactly three real solution Exactly one rational solution Non-real roots
15 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
16 The set of real roots of the equation log(5x + 4)(2x +3)3- log(2x + 3)(10x2+ 23x + 12) = 1 is {-1} {-3/5} Empty set {-1/3}
17 (a - c)<sup>2</sup>= b<sup>2</sup>- c<sup>2</sup> (a - c)<sup>2</sup>= b<sup>2</sup>+ c<sup>2</sup> (a + c)<sup>2</sup>= b<sup>2</sup>- c<sup>2</sup> (a + c)<sup>2</sup>= b<sup>2</sup>+ c<sup>2</sup>
18 If x2 + px + 1 is a factor of ax3+ bx +c, then a<sup>2</sup>+ c<sup>2</sup>= -ab a<sup>2</sup>- c<sup>2</sup>= -ab a<sup>2</sup>- c<sup>2</sup>= ab None of these
19 n if n is even 0 for any natural number n 1 if in odd None of these
20 The roots of the equation 22x- 10.2x+ 16 = 0 are 2, 8 1, 3 1, 8 2, 3
21
22 The value of p for which both the roots of the equation 4x2- 20x + (25p2+ 15 p - 66) = 0 are less than 2, lies in
23 If the roots of ax2+ bx + c =0 are equal in magnitude but opposite in sign, then a = 0 b = 0 c = 0 None of these
24 b = c a = c a = c b = 0
25 The quadratic equation 8 sec2θ- 6 secθ+1 = 0 has Infinitely many roots Exactly two roots Exactly four roots No roots
26 If a > 0, b > 0, c > 0, then the roots of the equation ax2+ bx + c = 0 are Real and negative Non-real with negative real parts Real and positive Nothing can be said
27 If one root of the equation ix2- 2(i + 1) x +(2 - i) = 0 is 2 - i, then the other root is -i 2 + i i 2 - i
28 If the roots of ax2+ b = 0 are real and distinct then ab &gt; 0 a = 0 ab &lt; 0 a &gt; 0, b &gt; 0
29 If ax2+ bx + x = 0 is satisfied by every value of x, then b = 0, c = 0 c = 0 b = 0 a = b = c = 0
30 Both the roots of the equation (x - b) (x - c) + (x - c)(x - a) + (x - a)(x - b) = 0 are always Positive Negative Real None of these
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