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

If x - 1 is a factor of x4 - 5x2 + 4 then other factor is

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(x + 2)2(x - 1)

(x + 2)(x - 1)2

(x+2)(x2- x- 2)

(x + 2)2(x - 1)2

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(-1, 2)

(-1, 1)

(1, 2)

{-1}

The value of x for which the polynomials x2 - 1 and x2 -2x + 1 vanish simultaneously is

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2

1

-1

-2

If x² + px + 1 is a factor of ax³+ bx +c, then

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a²+ c²= -ab

a²- c²= -ab

a²- c²= ab

None of these

The condition for polynomial equation ax2 + bx + c = 0 to be quadratic is

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a > 0

a < 0

a≠ 0

a≠ 0,b ≠ 0

The vertex of the graph of the quadratic function f(x) =-x2+6x+1,is

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(-3,10)

(-3,-10)

(3,10)

(3,-10)

x⁴- 3x³+ 3x + 1 = 0 is called ______

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Reciprocal equation

Exponential equation

Radical equation

None of these

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-1

0

2

1

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(a - c)²= b²- c²

(a - c)²= b²+ c²

(a + c)²= b²- c²

(a + c)²= b²+ c²

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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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

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

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(0, 2π)

(-π, -0)

(0,π)

None of these

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

For any integer k, wⁿ= ______ when n = 3k

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1

2

0

-4

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0

1

2

None of these

Two quadratic equation in which xy term is missing and the coefficients of x²and y²are equal, give a linear equation by ______

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Addition

Subtraction

Multiplication

Division

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

The roots of px2 - (p-q)x-q=0 are

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equal

Irrational

Rational

Imaginary

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The roots of ax2 + bx + c = 0 are always unequal if

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b2 - 4ac = 0

b2- 4ac ≠ 0

b2- 4ac > 0

b2- 4ac ≥ 0

The graph of the quadratic equation is

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Straight line

Circle

Parabola

elipse

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

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(5, 3, 1)

(4, 3, 2)

(5, 5, 1)

(6, 4, 1)

w^-1= ______

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0

1

w

w²

If one root of the equation x²- 3x + a = 0 is 2 then a = ______

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0

1

2

3

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

If w+w2 is a root of (x+1)(x+2)(x+3)(x+4) = k, then

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k=0

k=1

k=w

k=w2

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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

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

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