A system of three linear equations in three variables is inconsistent if their planes

(a)

intersect only at a point

(b)

intersect in a line

(c)

coincides with each other

(d)

do not intersect

The solution of the system x + y − 3z = −6, −7y + 7z = 7, 3z = 9 is

(a)

x = 1, y = 2, z = 3

(b)

x = −1, y = 2, z = 3

(c)

x = −1, y = −2, z = 3

(d)

x = 1, y = -2, z = 3

If (x - 6) is the HCF of x² - 2x - 24 and x² - kx - 6 then the value of k is

(a)

3

(b)

5

(c)

6

(d)

8

\(\frac { x }{ { x }^{ 2 }-25 } -\frac { 8 }{ { x }^{ 2 }+6x+5 } \) gives

(a)

\(\frac { { x }^{ 2 }-7x+40 }{ \left( x-5 \right) \left( x+5 \right) } \)

(b)

\(\frac { { x }^{ 2 }+7x+40 }{ \left( x-5 \right) \left( x+5 \right) \left( x+1 \right) } \)

(c)

\(\frac { { x }^{ 2 }-7x+40 }{ \left( { x }^{ 2 }-25 \right) \left( x+1 \right) } \)

(d)

\(\frac { { x }^{ 2 }+10 }{ \left( { x }^{ 2 }-25 \right) \left( x+1 \right) } \)

The solution of (2x - 1)² = 9 is equal to

(a)

-1

(b)

2

(c)

-1, 2

(d)

None of these

Graph of a linear equation is a ____________

(a)

straight line

(b)

circle

(c)

parabola

(d)

hyperbola

The father’s age is six times his son’s age. Six years hence the age of father will be four times his son’s age. Find the present ages (in years) of the son and father.

Solve: \(\frac { 1 }{ 2x } +\frac { 1 }{ 4y } -\frac { 1 }{ 3z } =\frac { 1 }{ 4 } \);  \(\frac { 1 }{ x } =\frac { 1 }{ 3y } \); \(\frac { 1 }{ x } -\frac { 1 }{ 5y } +\frac { 4 }{ z } =2\frac { 2 }{ 15 } \)

Solve \(2{ x }^{ 2 }-2\sqrt { 6 } x+3\) = 0

Find the GCD of the polynomials x³ + x² - x + 2 and 2x³ - 5x² + 5x - 3.

Find the square root of the following expressions
16x² + 9y² - 24xy + 24x - 18y + 9

Simplify \(\frac { \frac { 1 }{ p } +\frac { 1 }{ q+r } }{ \frac { 1 }{ p } -\frac { 1 }{ q+r } } \times \left( 1+\frac { { q }^{ 2 }+{ r }^{ 2 }-{ p }^{ 2 } }{ 2qr } \right) \)