Question # 1

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 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

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

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0

-1

1

2

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c/a

-c/a

b/a

-b/a

A polynomial P(x)has a factor (x-a)if P(a) =

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a

x

1

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

Which of the following is factor of p(x) =2x3 +3x2+3x+2 ?

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x+1

2x+1

3x+1

2x-1

(x-1) is a factor of

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2x³-3x²+9

2x³-5x-8

48x^2-46x-9

x⁹-1

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Polynomial of degree 0

Polynomial of degree 2

Quadratic equation

None of these

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n if n is even

0 for any natural number n

1 if in odd

None of these

If a,β are the roots of the equation x2 + kx +12 = 0 such that a - β = 1, the value of k is

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0

±1

±5

±7

The vertex of the graph of the quadratic function f(x) = x2 -10, is

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(0 , -10)

(-10,0)

(10,0)

(0,10)

If f(x) = ax², and a>0, then the lowest point on the parabola is called.

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Vertex of parabola

Co-ordinates of parabola

Roots of the equation

Coefficient of the equation

If ax + bx + c =0 is satisfied by every value of x,then

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b = 0,c = 0

c = 0

b = 0

a = b = c = 0

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

If x³+ 4x³- 2x +5 is divided by x - 1, then the reminder is

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8

6

4

None of these

The expression x2 - x + 1 has

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One proper linear factor

No proper linear factor

Two proper linear factors

None of these

If ax²+ bx + x = 0 is satisfied by every value of x, then

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b = 0, c = 0

c = 0

b = 0

a = b = c = 0

The set of real roots of the equation log_{(5x + 4)}(2x +3)³- log_{(2x + 3)}(10x²+ 23x + 12) = 1 is

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{-1}

{-3/5}

Empty set

{-1/3}

If x²- 7x + a has remainder 1 when divided by x + 1, then a = ______

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-7

7

0

None of these

The roots of the equation 2^2x- 10.2^x+ 16 = 0 are

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2, 8

1, 3

1, 8

2, 3

Roots of the equation x²+ 5x - 1 = 0 are

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Rational

Irrational

Complex

None of these

w^-1= ______

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0

1

w

w²

Roots of the equation x²+ 7x + 12 = 0 are

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{3, -4}

{-3, 4}

{3, 4}

{-3, -4}

If a polynomial P(x) is divided by x - a, then the remainder is

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P(o)

P(-a)

P(a)

None of these

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0

1

2

3

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

w²⁹= ______

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0

1

w

w²

If w is a cube root of unity then 1 + w + w²= ______

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1

2

0

-1

The product of cube roots of unity is

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Zero

1

-1

None of these

The roots of ax2+bx+c=0 are

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Rational ⇔ b2 -4 ac ≥ 0

Irrational ⇔ b2-4 ac > 0

Real ⇔ b2-4 ac ≠ 0

Rational⇔ b2-4 ac = 0

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