Question : If $x^{3}+2x^{2}-5x+k$ is divisible by $x+1$, then what is the value of $k$?

Option 1:  –6

Option 2:  –1

Option 3: 0

Option 4: 6

Question : If $2x-2(x-2)<5-x>-2x+2$, then the value of $x$ is:

Option 1: 0

Option 2: 2

Option 3: 3

Option 4: –4

Question : If 5x + 3y = 15 and 2xy = 6, then the value of 5x – 3y is:

Option 1: $3\sqrt{3}$

Option 2: $3\sqrt{5}$

Option 3: $3\sqrt{2}$

Option 4: $3\sqrt{4}$

Question : If $ a^{2}+a+1=0$, then the value of $a^{5}+a^{4}+1$ is:

Option 1: $a^2$

Option 2: $1$

Option 3: $0$

Option 4: $a+1$

Question : For the triangle $PQR$, find the equation of altitude $PS$, if the co-ordinates of $P, Q, R$ are (1, 2), (2, –1), and (0, 5), respectively.

Option 1: $x–3y=–7$

Option 2: $x+3y=–5$

Option 3: $x–3y=–5$

Option 4: $x+3y=–7$