10 Question MCQ (including Assertion)

Let \(p(x)=a x+b\) and \(q(x)=c x+d\). The graph of \(p(x)\) passes through the points \((2,3)\) and \((6,11)\). The graph of \(q(x)\) passes through the point \((4,-1)\) and is parallel to the graph of \(p(x)\). What is the polynomial \(q(x)\) ?

If we multiply a number by \(\frac{5}{2}\) and add \(\frac{2}{3}\) to the product, we get \(\frac{-7}{12}\). Find the number.

The value of the polynomial \(5 x-4 x^2+3\), when \(x=-1\) is

If the length of a rectangle is three more than twice its width and its perimeter is 24 cm, what is the length of the rectangle?

Consider the graphs of the three equations \(y=3 x-1, y=3 x\), and \(y=3 x+1\) shown above. What is the fundamental relationship between these lines?

If \(p(x)=x+3\), then \(p(x)+p(-x)\) is equal to

Assertion (A): The degree of the polynomial \(5 x^3+2 x-1\) is 3 .
Reason ( \(\mathbf{R}\) ): The coefficient of \(x^3\) in the given polynomial is 5 .

A mobile phone is bought for ₹10,000. Its value decreases by ₹800 every year. After how many years will the value of the phone be ₹6,000?

The graph of \(y=-2 x\) passes through which quadrants?