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

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

y² + \(\frac {1}{y^{2}}\) is not equal to

(a)

\(\frac {y^{2} + 1}{y^{2}}\)

(b)

\({ \left( y+\frac { 1 }{ y } \right) }^{ 2 }\)

(c)

\({ \left( y-\frac { 1 }{ y } \right) }^{ 2 }+2\)

(d)

\({ \left( y+\frac { 1 }{ y } \right) }^{ 2 }-2\)

The square root of \(\frac { 256{ x }^{ 8 }{ y }^{ 4 }{ z }^{ 10 } }{ 25{ x }^{ 6 }{ y }^{ 6 }{ z }^{ 6 } } \) is equal to

(a)

\(\frac { 16 }{ 5 } \left| \frac { { x }^{ 2 }{ z }^{ 4 } }{ { y }^{ 2 } } \right| \)

(b)

\(16\left| \frac { { y }^{ 2 } }{ { x }^{ 2 }{ z }^{ 4 } } \right| \)

(c)

\(\frac { 16 }{ 5 } \left| \frac { y }{ x{ z }^{ 2 } } \right| \)

(d)

\(\frac { 16 }{ 5 } \left| \frac { x{ z }^{ 2 } }{ y } \right| \)

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

(a)

-1

(b)

2

(c)

-1, 2

(d)

None of these

If the roots of the equation q²x² + p²x + r² = 0 are the squares of the roots of the equation qx² + px + r = 0, then q, p, r are in __________.

(a)

A.P

(b)

G.P

(c)

Both A.P and G.P

(d)

none of these

The number of points of intersection of the quadratic polynomial x² + 4x + 4 with the X axis is

(a)

0

(b)

1

(c)

0 or 1

(d)

2

If A is a 2 x 3 matrix and B is a 3 x 4 matrix, how many columns does AB have

(a)

3

(b)

4

(c)

2

(d)

5

Transpose of a column matrix is

(a)

unit matrix

(b)

diagonal matrix

(c)

column matrix

(d)

row matrix

Which of the following can be calculated from the given matrices A  = \(\left( \begin{matrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{matrix} \right) \), B = \(\left( \begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{matrix} \right) \),
(i) A²
(ii) B²
(iii) AB
(iv) BA

(a)

(i) and (ii) only

(b)

(ii) and (iii) only

(c)

(ii) and (iv) only

(d)

all of these

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

Which of the following is correct
(i) Every polynomial has finite number of multiples
(ii) LCM of two polynimials 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

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

(a)

x+2

(b)

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

(c)

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

(d)

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

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

(a)

4(m-3)

(b)

2(m-3)

(c)

(2m-3)²

(d)

(m-3)

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)

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