#### Term 1 Model Question Paper

11th Standard

Reg.No. :
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Time : 02:00:00 Hrs
Total Marks : 60
5 x 1 = 5
1. The inventor of input-output analysis is

(a)

Sir Francis Galton

(b)

Fisher

(c)

Prof. Wassily W. Leontief

(d)

Arthur Caylay

2. The possible out comes when a coin is tossed five times

(a)

25

(b)

52

(c)

10

(d)

$\frac { 5 }{ 2 }$

3. The slope of the line 7x + 5y - 8 = 0 is

(a)

7/5

(b)

-7/5

(c)

5/7

(d)

-9/7

4. The degree measure of $\frac{\pi}{8}$ is

(a)

20o60'

(b)

22o30'

(c)

20o60'

(d)

20o30'

5. The graph of y = 2x2 is passing through

(a)

(0,0)

(b)

(2,1)

(c)

(2,0)

(d)

(0,2)

6. 7 x 2 = 14
7. Find the minors and cofactors of all the elements of the following determinants
$\begin{vmatrix}5&20\\ 0&-1 \end{vmatrix}$

8. Expand the following by using binomial theorem. (2a - 3b)4

9. Find the rank of the word 'CHAT' in dictionary.

10. Find the center and radius of the circle 5x2 + 5y2 +4x - 8y - 16 = 0

11. Prove that $2\tan^{-1}(x)=\sin^{-1}\left(\frac{2x}{1+x^2}\right)$

12. If $f(x)={ x }^{ 3 }-\frac { 1 }{ { x }^{ 3 } }$ then show that $f(x)+f\left( \frac { 1 }{ x } \right) =0$

13. Evaluate: $\underset { x\rightarrow 2 }{ lim } \frac { { x }^{ 2 }-4x+6 }{ x+2 }$

14. 7 x 3 = 21
15. Solve: $\begin{vmatrix} x & 2 & -1 \\ 2 & 5 & x \\ -1 & 2 & x \end{vmatrix}=0.$

16. Find the 5th term in the expansion of (x - 2y)13.

17. Find the value of 'a' for which the straight lines 3x +4y = 13; 2x -7y = -1  and ax - y -14 = 0 are concurrent

18. Prove that $2\sin^2\frac{3\pi}{4}+2\cos^2\frac{\pi}{4}+2\sec^2\frac{\pi}{4}=10$

19. Prove that: $(cos\alpha -cos\beta )^{ 2 }+(sin\alpha -sin\beta )^{ 2 }=4sin^{ 2 }\left( \frac { \alpha -\beta }{ 2 } \right)$

20. Evaluate the following $\lim _{ x\rightarrow 2 }{ \frac { { x }^{ 3 }+2 }{ x+1 } }$

21. Differentiate $\frac{x^2}{1+x^2}$ with respect to x2

22. 4 x 5 = 20
23. If A = $\begin{bmatrix}3 & -1 & 1 \\ -15 & 6 & -5\\5 & -2 & 2 \end{bmatrix}$ then, find the Inverse of A.

24. By the principle of mathematical induction, prove the following.
13+23+33+.......+n3=$\frac { { n }^{ 2 }(n+1)^{ 2 } }{ 4 }$ for all $n\in N$.

25. How many numbers greater than a million can be formed with the digits 2, 3, 0, 3, 4, 2, 3?

26. Prove that $\tan { \left( \pi +x \right) } \cot { \left( x-\pi \right) } -\left( \cos { \left( 2\pi -x \right) } \cos { \left( 2\pi +x \right) } \right) =\sin ^{ 2 }{ x }$