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)

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

Which of the following should be added to make x⁴ + 64 a perfect square

(a)

4x²

(b)

16x²

(c)

8x²

(d)

-8x²

Graph of a linear equation is a ____________

(a)

straight line

(b)

circle

(c)

parabola

(d)

hyperbola

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

If A = \(\left( \begin{matrix} 1 & 2 & 3 \\ 3 & 2 & 1 \end{matrix} \right) \), B = \(\left( \begin{matrix} 1 & 0 \\ 2 & -1 \\ 0 & 2 \end{matrix} \right) \) and C = \(\left( \begin{matrix} 0 & 1 \\ -2 & 5 \end{matrix} \right) \), Which of the following statements are correct?
(i) AB + C =  \(\left( \begin{matrix} 5 & 5 \\ 5 & 5 \end{matrix} \right) \)
(ii) BC = \(\left( \begin{matrix} 0 & 1 \\ 2 & -3 \\ -4 & 10 \end{matrix} \right) \)
(iii) BA + C = \(\left( \begin{matrix} 2 & 5 \\ 3 & 0 \end{matrix} \right) \)
(iv) (AB)C = \(\left( \begin{matrix} -8 & 20 \\ -8 & 13 \end{matrix} \right) \) 

(a)

(i) and (ii) only

(b)

(ii) and (iii) only

(c)

(iii) and (iv) only

(d)

all of these

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

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

(a)

x+2

(b)

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

(c)

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

(d)

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

The 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)

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

The parabola y = -3x² is ___________

(a)

Open upward

(b)

Open downward

(c)

Open rightward

(d)

Open leftward

If P and Q are matrices, then which of the following is true?

(a)

PQ ≠ QP

(b)

(P^T)^T ≠ P

(c)

P + Q ≠ Q + P

(d)

All are true