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: $(2x + y + 3)^2$
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Correct Answer: $(2x + y - 3)(2x - y + 3)$
Solution : $4x^2-y^2+6y-9$ $= 4x^2-(y^2-6y+9)$ $= (2x)^2-(y-3)^2$ $= (2x+y-3)(2x-y+3)$ Hence, the correct answer is $(2x+y-3)(2x-y+3)$.
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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 $4x^2+y^2 = 40$ and $xy=6$, then the value of $2x-y$ is:
Option 1: 1
Option 2: 3
Option 3: 4
Option 4: 2
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
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