Write the following in roster form. 
{x\(\in \)N : x²<121 and x is a prime}

Write the following in roster form.
The set of all positive roots of the equation (x-1)(x+1)(x²-1) = 0.

By taking suitable sets A, B, C, verify the following results:
A \(\times\) (B\(\cup \)C) = (A\(\times\)B) \(\cup \) (A\(\times\)C)

By taking suitable sets A, B, C, verify the following results:
C-(B-A) = (C\(\cap \) A) \(\cup \) (C\(\cap \)B')

Let f = {(1, 2), (3, 4), (2, 2)} and g = {(2, 1), (3, 1), (4, 2)}. Find g o f and f o g.

Let f = {(1, 4), (2, 5), (3, 5)} and g = {(4, 1), (5, 2), (6, 4)}. Find g o f. Can you find f o g?

Consider N = {1, 2, 3, ..........} set of all natural numbers.

Determine the region in the Plane determined by the inequalities.
\(3x+5y\ge 45,\ x\ge 0,\ y\ge 0\)

If \(\alpha \) and \(\beta \) are the roots of the quadratic equation \({ x }^{ 2 }+\sqrt { 2x } +3=0\) , form a quadratic polynomial with zeros \(\frac { 1 }{ \alpha } ,\frac { 1 }{ \beta } \)

Simplify \(\sqrt{x^2-10x+25}\)

Two vehicles leave the same place P at the same time moving along two different roads. One vehicle moves at an average speed of 60 km/hr and the other vehicle moves at an average speed of 80 km/hr. After half an hour the vehicle reach the destinations A and B. If AB subtends 60^o at the initial point P, then find AB.

Find the value of sin 105^o

If \(\theta +\phi =\alpha\)  and \(tan​​\theta=k\ \tan\ \phi \) then prove that \(\sin { \left( \theta -\phi \right) } =\frac { k-1 }{ k+1 } \sin { \alpha } \).

Find the value of sin 2θ, when sin θ =\(\frac{12}{13}\),θ lies in the first quadrant.

Find the values of cos 15⁰.

Find the principal value of sin^-1\(({\sqrt{3}\over2})\)