Punjab Board Class 9 Mathematics — Important Questions

What is the value of (√5 + √3)(√5 - √3)?

Rationalise the denominator of 1/(√7 - √6). What is the result?

If x = 2 + √3, what is the value of x + 1/x?

If p(x) = x⁴ - x³ - 7x² + x + 6 and (x-3) is a factor, which of the following is the complete factorisation of p(x)?

For what value of k will (x + 2) be a factor of kx³ + 5x² - 2kx - 10?

Using the identity (x+y+z)² = x²+y²+z²+2xy+2yz+2zx, if x²+y²+z²=50 and xy+yz+zx=47, what is (x+y+z)?

The vertices of a triangle are at A(0, 0), B(4, 0) and C(0, 3). A point D is the intersection of the medians of this triangle. In which quadrant does D lie and what are its coordinates?

If the points A(1, 2), B(4, y), C(x, 6) and D(3, 5) are the vertices of a parallelogram taken in order, what are the values of x and y?

A point moves such that it is always equidistant from the x-axis and y-axis, and it lies in the second quadrant. If its distance from each axis is 5 units, what are its coordinates?