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#### Important 5mark questions

11th Standard

Reg.No. :
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Maths

Use blue pen Only

Time : 00:50:00 Hrs
Total Marks : 75

Part A

15 x 5 = 75
1. Let A={1,2,3,4} and B = {a,b,c,d}. Give a function from A$\rightarrow$B for each of the following:
neither one- to -one and nor onto.

2. Let A={1,2,3,4} and B = {a,b,c,d}. Give a function from A$\rightarrow$B for each of the following:
not one-to-one but onto.

3. Let A={1,2,3,4} and B = {a,b,c,d}. Give a function from A$\rightarrow$B for each of the following:
one-to-one but not onto.

4. Find the largest possible domain of the real valued function f(x)=$\frac { \sqrt { 4-{ x }^{ 2 } } }{ \sqrt { { x }^{ 2 }-9 } }$

5. Prove that$\frac { sin4x+sin2x }{ cos4x+cos2x } =tan3x$

6. Prove that$1+cos2x+cos4x+cos6x=4cosx\quad cos2x\quad cos3x$

7. Prove that $sin\frac { \theta }{ 2 } sin\frac { 7\theta }{ 2 } +sin\frac { 3\theta }{ 2 } sin\frac { 11\theta }{ 2 } =sin2\theta sin5\theta$

8. find the value of sin $\left( -\frac { 11\pi }{ 3 } \right)$

9. In ABC, prove that (a2 - b2 +c2) tan B = (a2 +b2 -c2) tan C

10. If A + B + C = $\pi$, prove the following
i. cos A + cos B + cos C = 1 + 4 sin $({A\over 2})$ sin $({B\over 2})$ sin $({C\over 2})$
ii. sin $({A\over 2})sin({B\over2})sin({C\over 2})\le{1\over 8}$
iii. 1 < cos A + cos B + cos C $\le\frac{3}{2}$

11. In a triangle  ABC, prove that ${a^2+b^2\over a^2+c^2}={1+cos(A-B)cos C\over 1+cos (A-C)cos B}$

12. Using Heron's formula, show that the equilateral triangle has the maximum area for any fixed perimeter. [Hint: In xyz$\le$  k, maximum occurs when x = y = z]

13. A ray of light coming from the point (1,2)is reflected at a point A on the x-axis and it passes through the point (5,3). Find the co-ordinates of the point A.

14. Find the distance of the line 4x - y = 0 from the point p( 4,1) measured along the line making an angle of 135° with the positive x-axis.