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#### Full Portion Two Marks Question Paper

11th Standard

Reg.No. :
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Maths

Time : 01:00:00 Hrs
Total Marks : 50
25 x 2 = 50
1. State whether the following sets are finite or infinite.
{x $\in$ Z:x is even and less than 10}

2. Discuss the following relations for reflexivity, symmetricity and transitivity :
Let A be the set consisting of all the female members of a family. The relation R defined by "aRb if a is not a sister of b".

3. Discuss the following relations for reflexivity, symmetricity and transitivity :
On the set of natural numbers, the relation R is defined by "xRy if x + 2y = 1".

4. Find the range of the following functions given by f(x) = 1+3cos2x.

5. Simplify $\left( 125 \right) ^{ \frac { 2 }{ 3 } }$

6. Solve $2\left| x+1 \right| -6\le 7$ and graph the solution set in a number line.

7. Solve 23x<100 when (i) x is a natural number (ii) x is an integer.

8. Simplify $\sqrt{x^2-10x+25}$

9. If one of the roots of a quadratic equation is $(1-\sqrt{5})$ find the quadratic equation.

10. Find the principal value of sec-1$\left( -\sqrt { 2 } \right)$

11. Find the value tan ($\frac { 19\pi }{ 3 }$)

12. Find the values of other five trigonometric functions for the following
Sec $\theta$ = $\frac { 13 }{ 5 }$ $\theta$ lies in the IV quadrant

13. Express each of the following as a product.
sin 75o - sin 35o

14. Find the value of cos 135°.

15. Find the value of tan 120°.

16. There are six periods in each working day of a school. In how many ways can one arrange 5 subjects such that each subject is allowed atleast one period?

17. Find the general term in the expansion of ${ \left( \frac { 4x }{ 5 } -\frac { 5 }{ 2x } \right) }^{ 9 }$

18. Evaluate 984 .

19. Find the angle between the lines 3x2 + 10xy + 8y2 + 14x + 22y + 15 = 0.

20. Find the angle between the pair of straight lines given by
(a2 - 3b2)x2 + 8ab xy+(b2 -3a2)y2 =0.

21. If A =$\begin{bmatrix} 4 & 6 & 2 \\ 0 & 1 & 5 \\ 0 & 3 & 2 \end{bmatrix}$ and B= $\begin{bmatrix} 0 & 1 & -1 \\ 3 & -1 & 4 \\ -1 & 2 & 1 \end{bmatrix}$
verify(A-B)T=AT-BT

22. Complete the table using calculator and use the result to estimate the limit.
$lim_{x\rightarrow 2}{x-2\over x^2-x-2}$

 x 1.9 1.99 1.999 2.001 2.01 2.1 f(x)
23. Find the derivation
x2exsinx

24. Integrate the function with respect to x
$a{ sec }^{ 2 }\left( bx+c \right) +\cfrac { q }{ { e }^{ 1-mx } }$

25. If A and B are two events such that $P(A\cup B)=\cfrac { 5 }{ 6 } ,$ $P(A\cap B)=\cfrac { 1 }{ 3 }$ ,$P(\bar { B } )=\cfrac { 1 }{ 2 }$ show that A and B are independent.