Question : If $(x-2)$ is a factor of $x^2+3Qx – 2Q$, then the value of $Q$ is:

Option 1: 2

Option 2: –2

Option 3: 1

Option 4: –1

Question : If $x+\frac{1}{x}=2$, then find the value of $x^{1823}+\frac{1}{x^{1929}}$.

Option 1: 2

Option 2: 1

Option 3: 0

Option 4: –1

Question : If $px + qy = 1$ and $q x+p y=\frac{2 p q}{p^2+q^2}$, then $\left(x^2+y^2\right)\left(p^2+q^2\right)$ is equal to:

Option 1: 2

Option 2: 3

Option 3: 0

Option 4: 1

Question : If $4(x+5)-3>6-4x\geq x-5$, then the value of $x$ is:

Option 1: –2

Option 2: –1

Option 3: 3

Option 4: 4

Question : If $\alpha +\beta =90^{0}$, then value of $\left (1-\sin^{2}\alpha \right)\left (1-\cos^{2}\alpha \right)\times \left (1+\cot^{2}\beta \right)\left (1+\tan^{2}\beta \right)$ is:

Option 1: 1

Option 2:  –1

Option 3: 0

Option 4: 2