Let A = [a_ij]be a matric of order 2 x 3 and a_ij = \(\frac { i-j }{ i+j } \), write the value of a₂₃

1

(a)

-1/5

Write the order of matrix B if any matrix of order m x n such that AB and BA both are defined

1

(a)

n x m

Find the value of determinant \(\triangle =\left\lfloor \begin{matrix} 1 & 2 & 4 \\ 8 & 16 & 32 \\ 64 & 128 & 256 \end{matrix} \right\rfloor \)

1

(a)

0 (Using properties)

Let A be a diagonal A = (d₁, d₂, …, dn ) write the value of | A |

1

(a)

|A| = d₁,d₂.d₃......d_n

Write thepoints of discontinuity of the function f(x) = \(\frac { { x }^{ 2 }-25 }{ x-5 } \)

1

(a)

\(\text { For continuity, } \lim _{x \rightarrow 5} \frac{x^{2}-25}{x-5}=k \)
\(\Rightarrow \lim _{x \rightarrow 5}(x+5)=k \quad \Rightarrow \quad k=10 \)

Is it true that log (x^sinx+cos^sinx x)=sinxlogx+sin x logcos x?

1

(a)

{No}