Explanation

(a) \(a = \begin{pmatrix} 8 \\ 3 \end{pmatrix} ; b = \begin{pmatrix} 6 \\ -5 \end{pmatrix} ; c = \begin{pmatrix} 2 \\ -3 \end{pmatrix} ; |d| = \sqrt{41}\)

\(p = a + b - 2c\)

= \(\begin{pmatrix} 8 \\ 3 \end{pmatrix} + \begin{pmatrix} 6 \\ -5 \end{pmatrix} + 2\begin{pmatrix} 2 \\ -3 \end{pmatrix}\)

= \(\begin{pmatrix} 8 + 6 + 4 \\ 3 - 5 - 6 \end{pmatrix}\)

= \(\begin{pmatrix} 10 \\ -8 \end{pmatrix}\)

\(|p| = \sqrt{10^{2} + (-8)^{2}} = \sqrt{164}\)

\(|p| = 2\sqrt{41}\)

\(|d| = \frac{1}{2} |p|\)

\(\therefore d = \frac{1}{2} p = \frac{1}{2} \begin{pmatrix} 10 \\ -8 \end{pmatrix}\)

= \(\begin{pmatrix} 5 \\ -4 \end{pmatrix}\)

(b) A(3, 4) ; B(3, n).

\(OA = 3i + 4j ; OB = 3i + nj\)

\(OA \cdot OB = |OA||OB| \cos \theta\)

\((3i + 4j) \cdot (3i + nj) = |3i + 4j||3i + nj| \cos 30\)

\(9 + 4n = 5 (\sqrt{9 + n^{2}}) (\sqrt{3}{2})\)

\(2(9 + 4n) = 5(\sqrt{3(9 + n^{2})})\)

\(18 + 8n = 5\sqrt{27 + 3n^{2}}\)

Squaring both sides,

\(324 + 288n + 64n^{2} = 25(27 + 3n^{2})\)

\(324 + 288n + 64n^{2} = 675 + 75n^{2}\)

\(75n^{2} - 64n^{2} - 288n + 675 - 324 = 0\)

\(11n^{2} - 288n + 351 = 0\)

\(n = \frac{-(-288) \pm \sqrt{(-288)^{2} - 4(11)(351)}}{2(11)}\)

\(n = \frac{288 \pm \sqrt{82944 - 15444}}{22}\)

\(n = \frac{288 \pm \sqrt{67500}}{22}\)

\(n = \frac{288 \pm 259.81}{22}\)

\(n = \frac{288 + 259.81}{22} ; n = \frac{288 - 259.81}{22}\)

\(n = \frac{547.81}{22} ; n = \frac{28.19}{22}\)

\(n = 24.9 ; n = 1.28\)

Correct Answer: A. was arrested

Correct Answer: C. condemnaton of social injustice

Correct Answer: B. interlude

Correct Answer: D. Development of viable alternatives to crude

Correct Answer: D) Trial balance

Correct Answer: A. contesting elections to gain power

Correct Answer: A. developing tourism and other services

Explanation

A government may cause a favourable change in her invisible trade account by developing tourism and other services. Invisible trade account records the movement of services across borders. It includes items such as tourism, transportation, insurance, and royalties.

Explanation

This Surah, which is one of the Meccan Suras, according to some narrations, was revealed after a brief interval that happened in revelation and the holy Prophet (S) was anxiously awaiting its arrival because the enemies had become obnoxious and began to gossip. Then, the verses descended on him, like refreshing rain and gave him a new strength, which ceased his enemies taunts.

This Surah begins with two oaths and then informs the holy Prophet (S) of the good news that Allah has never forsaken him nor left him alone.

It adds that, soon, Allah will provide for him so abundantly that he will become content.

And in the last verses of the Surah, He reminds the Prophet (S) of his past life to illustrate how Allah has always bestowed His loving care on him and in the most difficult moments has supported him in the past and so his future was sure.

That is why, at the end of the Surah. He bids him, (in appreciation of the very great bounties) to be kind with the orphans and the needy, thus:

“Therefore treat not the orphans with harshness,"

"And for the one who asks, repulse not,"

"And as for the bounties of your Lord, do announce (it)”.

Correct Answer: D) decreases both assets and liabilities