If the angles of quadrilateral are (p + 10)°, (2p - 30)°, (3p + 20)° and 4p°, find p.
63
40
36
28
Correct answer is C
The sum of angles in a quadrilateral = 360°
\(\therefore (p + 10) + (2p - 30) + (3p + 20) + 4p = 360\)
\(10p = 360° \implies p = \frac{360}{10} = 36°\)
PPT
pp-1
qp
pp
Correct answer is A
p = \(\begin{vmatrix} 0 & 3 & 0 \\ 2 & 1 & 3\\ 4 & 2 & 2 \end{vmatrix}\)
Q = \(\begin{vmatrix} 0 & 2 & 4 \\ 3 & 1 & 2\\ 0 & 3 & 2 \end{vmatrix}\) = pT
pq = ppT
48
24
-24
-48
Correct answer is B
p = \(\begin{vmatrix} 0 & 3 & 0 \\ 2 & 1 & 3\\ 4 & 2 & 2 \end{vmatrix}\)
PT = \(\begin{vmatrix}0 & 2 & 4 \\ 2 & 1 & 3\\ 0 & 3 & 2 \end{vmatrix}\)
/pT/ = \(\begin{vmatrix}0 & 2 & 4 \\ 3 & 1 & 3\\ 0 & 3 & 2 \end{vmatrix}\)
= 0[2 - 6] - 2[6 - 0] + 4[9 - 0]
= 0 - 12 + 36 = 24
e = 1
e = -1
e = -2
e = 0
Correct answer is D
Identity(e) : a \(\ast\) e = a
m \(\ast\) e = m...(i)
m \(\ast\) e = me + m + e
Because m \(\ast\) e = m
: m = me + m + e
m - m = e(m + 1)
e = \(\frac{0}{m + 1}\)
e = 0
e = 1
e = -1
e = -2
e = 0
Correct answer is B
Identity(e) : a \(\ast\) e = a
m \(\ast\) e = m...(i)
m \(\ast\) e = me + m + e
Because m \(\ast\) e = m
: m = me + m + e
m - m = e(m + 1)
e = \(\frac{0}{m + 1}\)
e = 0