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#### Important 2 mark question 2

11th Standard

Reg.No. :
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Maths

Use blue pen Only

Time : 01:00:00 Hrs
Total Marks : 40

Part A

20 x 2 = 40
1. Write the following in roster form.
{x$\in$N:x2<121 and x is a prime}.

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

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

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

5. Let f= {(1, 2), (3,4), (2, 2)} and s = {(2, 1), (3, 1), (4, 2)}. Find gof and fog.

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

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

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

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

10. Simplify $\sqrt{x^2-10x+25}$

11. 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 at the initial point P, then find AB.

12. Find the value of sin 105o

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

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

15. Find the values of cos 150.

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