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ECAT Pre General Science Mathematics Chapter 6 Quadratic Equations Online Test MCQs With Answers
Question # 1
Choose an answer
15
9
7
8
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Question # 2
The quadratic equation 8 sec
2
θ
- 6 sec
θ
+1 = 0 has
Choose an answer
Infinitely many roots
Exactly two roots
Exactly four roots
No roots
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Question # 3
If 2x
1/3
+ 2x
-1/3
= 5, then x is equal to
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1 or -1
2 or 1/2
8 or 1/8
4 or 1/4
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Question # 4
(x-1) is a factor of
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2x
3
-3x
2
+9
2x
3
-5x-8
48x
2-
46x-9
x
9
-1
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Question # 5
In quadratic equation, if the replacement of y with -y leaves the equation unchanged, then the graph is
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Straight line
Circle
Hyperbola
Symmetric w.r.t.0
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Question # 6
A quadratic equation in x is an equation that can be witten in the form
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ax
2
+ b = 0
ax
3
+b
2
+c=0
ax
2
+bx+c=0
ax
3
+bx
3
+cx=0
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Question # 7
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Question # 8
If w is a cube root of unity then 1 + w + w
2
= ______
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1
2
0
-1
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Question # 9
The equation (cos p - 1)x
2
+ x (cos p) + sin p = 0 in the variable x, has real roots, then p can take any value in the interval
Choose an answer
(0, 2
π
)
(-
π
, -0)
(0,
π
)
None of these
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Question # 10
Roots of the equation x
2
+ 7x + 12 = 0 are
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{3, -4}
{-3, 4}
{3, 4}
{-3, -4}
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Question # 11
If x
3
- x
2
+ 5x
+ 4 is divided by x - 2, then the reminder is
Choose an answer
0
2
18
14
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Question # 12
For the equation |x
2
| + |x| -6 =0, the roots are
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One and only one real number
Real with sum one
Real with sum zero
Real with product zero
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Question # 13
w
28
+ w
38
= ______
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0
1
w
-1
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Question # 14
The roots of px2 - (p-q)x-q=0 are
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equal
Irrational
Rational
Imaginary
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Question # 15
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Lies between 4 and 7
Lies between 5 and 9
Has no value between 4 and 7
Has no value between 5 and 9
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Question # 16
If a,β are the roots of ax2+bx+c=0,the equation whose roots are doubled is
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ay2 +2by+c=0
ay2+2by+4c=0
ay2+2by+c=0
ay2+by+4c=0
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Question # 17
If the equation x2+2x-3=0 and x2+3x-k=0 have a common root then the non - zero value of k is
Choose an answer
1
3
2
4
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Question # 18
The two parts into which 57 should be divided so that their product is 782 are
Choose an answer
43,14
34,23
33,24
44,13
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Question # 19
Only one of the root of ax2 + bx + c =0, a≠ 0 is zero if
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c = 0
c = 0,b≠ 0
b = 0,c = 0
b = 0,c≠ 0
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Question # 20
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(-1, 2)
(-1, 1)
(1, 2)
{-1}
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Question # 21
If one root of the equation ix
2
- 2(i + 1) x +(2 - i) = 0 is 2 - i, then the other root is
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-i
2 + i
i
2 - i
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Question # 22
Two quadratic equation in which xy term is missing and the coefficients of x
2
and y
2
are equal, give a linear equation by ______
Choose an answer
Addition
Subtraction
Multiplication
Division
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Question # 23
If a > 0,b > 0, c > 0 then the roots of the equation ax2+ bx + c =0 are
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Real and negative
Non-real with negative real parts
Real and positive
Nothing can be said
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Question # 24
The value of x for which the polynomials x2 - 1 and x2 -2x + 1 vanish simultaneously is
Choose an answer
2
1
-1
-2
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Question # 25
Find a if 1 is a root of the equation x
2
+ ax + 2 = 0
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3
-3
2
0
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Question # 26
The condition for ax2 + bx c to be expressed as the product of linear polynomials is
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b4 - 4ac =0
b4- 4ac ≥0
b4- 4ac <0
b4= 4ac
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Question # 27
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b = c
a = c
a = c
b = 0
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Question # 28
Ifα,β are non-real roots of ax2 + bx +c =0 (a,b,c∈ Q),then
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α = β
αβ = 1
α = β
α = 1
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Question # 29
The minimum value of the quadratic function f(x) = x2 +6x -2, is
Choose an answer
11
6
-11
13
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Question # 30
The roots of (b-c)x2+(c-a) x+a-b=0 are equal if
Choose an answer
2b = a+c
2a = b+c
2c = a+b
a + b + c =0
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Question # 31
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