Question : The algebraic expression $4x^2-y^2+6y-9$ is equal to______.

Option 1: $(2x + y - 3)(2x - y + 3)$

Option 2: $(2x - y - 3)(2x - y + 3)$

Option 3: $(2x + y - 3)^2$

Option 4: $(2x + y + 3)^2$

Question : If $\small x+y+z=6$ and $xy+yz+zx=10$, then the value of $x^{3}+y^{3}+z^{3}-3xyz$ is:

Option 1: 36

Option 2: 48

Option 3: 42

Option 4: 40

Question : Simplify the expression:
$(2x+13-y)(2x-13-y)$

Option 1: $4x^2-y^2-4xy-169$

Option 2: $4x^2+y^2+4xy-169$

Option 3: $4x^2+y^2-4xy-169$

Option 4: $4x^2+y^2-4xy+169$

Question : If $\sin^4x + \sin^2x = 1$, then what is the value of $\cot^4x+ \cot^2x$?

Option 1: –2

Option 2: 2

Option 3: –1

Option 4: 1

Question : If $2x-3(4-2x)<4x-5<4x+\frac{2x}{3}$, then $x$ can take which of the following values?

Option 1: 2

Option 2: 8

Option 3: 0

Option 4: –8