Question # 1

If 3x⁴+ 4x³+ x - 5 is divided by x + 1, then the reminder is

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0

7

-7

5

If the roots of ax²+ bx + c = 0 (a > 0) be greater than unity, then

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a + b + c = 0

a + b + c > 0

a + b + c < 0

None of these

The polynomial x - a is a factor of the polynomial f(x) if and only if

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f(a) is positive

f(a) is negative

f(a) = 0

None of these

If b²- 4ac = 0 then the roots of the equation are

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Real and distinct

Real and equal

Imaginary

None of these

If one root of the equation ix²- 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

Roots of the equation x²+ 2x + 3 = 0 are

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Real and equal

Real and distinct

Complex

None of these

If the roots of ax2 + b =0 are real and distinct then

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ab > 0

a = 0

ab < 0

a > 0,b > 0

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

The root of the quadratic equation are

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3

2

1

4

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

(1+w)(1+w2)(1+w4)(1+w8)....50 factors

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0

-1

1

2

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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Only one real solution

Exactly three real solution

Exactly one rational solution

Non-real roots

w²⁸+ w³⁸= ______

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0

1

w

-1

The solution of equation x2 + 2 = 0 in the set of real number is

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Infinite set

Singleton set

Null set

None of these

The two parts into which 57 should be divided so that their product is 782 are

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43,14

34,23

33,24

44,13

The sum of the roots of the equation x2 -6x +2 = 0 is

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-6

2

-2

6

The roots of the equation x2 +6x-7=0,are

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1

2

1 and -7

-7

If sinαand cosαare the roots of the equation px²+ qx + r =0, then

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p²- q²+ 2pr = 0

(p + r)²= q²- r²

p²+ q²- 2pr = 0

(p - r)²= q²+ r²

Roots of the equation 9x²- 12x + 4 = 0 are

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Real and equal

Real and distinct

Complex

None of these

The maximum value of the quadratic function f(x) = -2x2+20x,is

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4

3

50

7

5x³+ 3x - is a ______

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Polynomial of degree 3

Polynomial of degree 2

Polynomial of degree 1

Polynomial of degree 0

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For the equation |x²| + |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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Lies between 4 and 7

Lies between 5 and 9

Has no value between 4 and 7

Has no value between 5 and 9

if one root of the equation ix2 - 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

Consider the equation px2 + qx + r = 0 where p,q,r are real The roots are equal in magnitude but opposite in sign when

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q = 0, r = 0,p ≠ 0

p = 0,qr≠ 0

r = 0,pq≠ 0

q = 0, pq≠ 0

The positive value of k for which the equation x2 + kx + 64 = 0 has one of the roots 0

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4

64

8

All values of k

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

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Which of the following is factor of x11+a11, where n is an odd integer

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x-a

x+a

2x-a

2x+a

If a parabola opens down, then its vertex is at the

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Right of the parabola

Left of parabola

Lowest point on the parabola

Highest point on the parabola

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