Q13 of 45 Page 1

Using properties of determinants, solve the following for x:

Given,

Applying C₂→ C₂ – 2C₁ and C₃→ C₃ – 3C₁

⇒

Applying R₂→ R₂ + R₁ and R₃→ R₃ + 11R₁

⇒

Expanding about the second column-

∴ (-1)

⇒ (-18)(2x – 6) + 2(12x – 30) = 0

⇒ -36x + 24x +108 – 60 = 0

⇒ 12x = 48

∴ x = 48/12 = 4

Let f : R → R be defined as f(x) = 10x + 7. Find the function g : R → R such that
gof = fog =I_R.

A binary operation * on the set {0, 1, 2, 3, 4, 5} is defined as:

Show that zero is the identity for this operation and each element ‘a’ of the set is invertible with 6–a, being the inverse of ‘a’.

Prove that:

Find the relationship between ‘a’ and ’b’ so that the function ‘f’ defined by:

is continuous at x = 3 .

If x^y = e^{x– y}, show that

Prove that is an increasing function in

If the radius of a sphere is measured as 9 cm with an error of 0.03 cm, then find the approximate error in calculating its surface area.