Which of the following are linear equation in three variables ___________

(a)

2x = z

(b)

2sin x + y cos y + z tan z = 2

(c)

x + 2y² + z = 3

(d)

x - y - z = 7

Graphically an infinite number of solutions represents ___________

(a)

three planes with no point in common

(b)

three planes intersecting at a single point

(c)

three planes intersecting in a line or coinciding with one another

(d)

None

Which of the following is correct
(i) Every polynomial has finite number of multiples
(ii) LCM of two polynomials of degree 2 may be a constant
(iii) HCF of 2 polynomials may be constant
(iv) Degree of HCF of two polynomials is always less then degree of LCM

(a)

(i) and (ii)

(b)

(iii) and (iv)

(c)

(iii) only

(d)

(iv) only

The HCF of two polynomials p(x) and q(x) is 2x(x + 2) and LCM is 24x(x + 2)² (x - 2) if p(x) = 8x³ + 32x² + 32x, then q(x) ___________

(a)

4x³-16x

(b)

6x³-24x

(c)

12x³+24x

(d)

12x³-24x

Consider the following statements:
(i) The HCF of x+y and x⁸-y⁸ is x+y
(ii) The HCF of x+y and x⁸+y⁸ is x+y
(iii) The HCF of x-y nd x⁸+y⁸ is x-y
(iv) The HCF of x-y and x⁸-y⁸ is x-y

(a)

(i) and (ii)

(b)

(ii) and (iii)

(c)

(i) and (iv)

(d)

(ii) and (iv)

For what set of values \(\frac { { x }^{ 2 }+5x+6 }{ { x }^{ 2 }+8x+15 } \) is undefined ___________

(a)

-3, -5

(b)

-5

(c)

-2, -3, -5

(d)

-2, -3

\(\frac { { x }^{ 2 }+7x12 }{ { x }^{ 2 }+8x+15 } \times \frac { { x }^{ 2 }+5x }{ { x }^{ 2 }+6x+8 } =\_ \_ \_ \_ \_ \_ \_ \_ \_ \)

(a)

x+2

(b)

\(\frac { x }{ x+2 } \)

(c)

\(\frac { 35{ x }^{ 2 }+60x }{ { 48x }^{ 2 }+120 } \)

(d)

\(\frac { 1 }{ x+2 } \)

If \(\frac { p }{ q } =a\) then \(\frac { { p }^{ 2 }+{ q }^{ 2 } }{ { p }^{ 2 }-{ q }^{ 2 } } \) ___________

(a)

\(\frac { { a }^{ 2 }+1 }{ { a }^{ 2 }-1 } \)

(b)

\(\frac { 1+{ a }^{ 2 } }{ 1-{ a }^{ 2 } } \)

(c)

\(\frac { 1-{ a }^{ 2 } }{ 1-{ +a }^{ 2 } } \)

(d)

\(\frac { { a }^{ 2 }-1 }{ { a }^{ 2 }+1 } \)

The square root of 4m² - 24m + 36 is ___________

(a)

4(m-3)

(b)

2(m-3)

(c)

(2m-3)²

(d)

(m-3)

The real roots of the quadratic equation x²-x-1 are ___________

(a)

1, 1

(b)

-1, 1

(c)

\(\frac { 1+\sqrt { 5 } }{ 2 } ,\frac { 1-\sqrt { 5 } }{ 2 } \)

(d)

None

The product of the sum and product of roots of equation (a²-b²)x²-(a+b)²x+(a³-b³) = 0 is ___________

(a)

\(\frac { { a }^{ 2 }+ab+{ b }^{ 2 } }{ (a-b) } \)

(b)

\(\frac { a-b }{ a+b } \)

(c)

\(\frac { a-b }{ a+b } \)

(d)

\(\frac { a-b }{ { a }^{ 2 }+ab+{ b }^{ 2 } } \)

A Quadratic polynomial whose one zero is 5 and sum of the zeroes is 0 is given by ___________

(a)

x²-25

(b)

x²-5

(c)

x²-5x

(d)

x²-5x+5

Axis of symmetry in the term of vertical line separates parabola into ___________

(a)

3 equal halves

(b)

5 equal halves

(c)

2 equal halves

(d)

4 equal halves

The parabola y = -3x² is ___________

(a)

Open upward

(b)

Open downward

(c)

Open rightward

(d)

Open leftward

Choose the correct answer
(i) Every scalar matrix is an identity matrix
(ii) Every identity matrix is a scalar matrix
(iii) Every diagonal matrix is an identity matrix
(iv) Every null matrix is a scalar matrix

(a)

(i) and (iii) only

(b)

(iii) only

(c)

(iv) only

(d)

(ii) and (iv) only