#### Quarterly Model Question Paper

11th Standard

Reg.No. :
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Time : 02:45:00 Hrs
Total Marks : 90
20 x 1 = 20
1. The value of x, if $\begin{vmatrix} 0 & 1 & 0 \\ x & 2 & x \\ 1 & 3 & x \end{vmatrix}=0$ is

(a)

0, - 1

(b)

0, 1

(c)

- 1, 1

(d)

- 1, - 1

2. The value of the determinant ${\begin{vmatrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & c \end{vmatrix}}^{2}$is

(a)

abc

(b)

0

(c)

a2b2c2

(d)

-abc

3. The number of Hawkins-Simon conditions for the viability of an input - output analysis is

(a)

1

(b)

3

(c)

4

(d)

2

4. If A and B are non-singular matrices then, which of the following is incorrect?

(a)

A2 = Iimplies A-1 = A

(b)

I-1 = I

(c)

If AX = B, then X = B-1 A

(d)

If A is square matrix of order 3 then |adj A|= |A|2

5. If A = $\begin{vmatrix}cos \theta & sin \theta \\ -sin \theta&cons\theta \end{vmatrix}$ then |2A| is equal to

(a)

4 cos 2 $\theta$

(b)

4

(c)

2

(d)

1

6. If nPr = 720 (nCr), then r is equal to

(a)

4

(b)

5

(c)

6

(d)

7

7. The number of parallelograms that can be formed from the set of four parallel lines intersecting another set of three parallel lines is

(a)

18

(b)

12

(c)

9

(d)

6

8. The total number of 9 digit number which have all different digit is

(a)

10!

(b)

9!

(c)

9$\times$9!

(d)

10$\times$10!

9. Number of words with or without meaning that can be formed using letters of the word "EQUATION" , with no repetition of letters is

(a)

7!

(b)

3!

(c)

8!

(d)

5!

10. The angle between the pair of straight lines x2 - 7xy + 4y2 = 0

(a)

$tan^{-1}\left(1\over 3\right)$

(b)

$tan^{-1}\left(1\over 2\right)$

(c)

$tan^{-1}\left(\sqrt{33}\over 5\right)$

(d)

$tan^{-1}\left(5\over\sqrt{33}\right)$

11. The locus of the point P which moves such that P is always at equidistance from the line x + 2y+ 7 = 0 is

(a)

x+2y+2=0

(b)

x - 2y + 1 = 0

(c)

2x - y + 2 = 0

(d)

3x + y + 1=0

12. ax2 + 4xy + 2y2 = 0 represents a pair of parallel lines then 'a' is

(a)

2

(b)

-2

(c)

4

(d)

-4

13. The double ordinate passing through the focus is

(a)

focal chord

(b)

latus rectum

(c)

directrix

(d)

axis

14. The value of $\sin15^o$ is

(a)

$\frac{\sqrt{3}+1}{2\sqrt{2}}$

(b)

$\frac{\sqrt{3}-1}{2\sqrt{2}}$

(c)

$\frac{\sqrt3}{\sqrt2}$

(d)

$\frac{\sqrt3}{2\sqrt2}$

15. If p sec 50o=tan 50o then p is

(a)

cos 50o

(b)

sin 50o

(c)

tan 50o

(d)

sec 50o

16. If f(x) = x2 - x + 1, then f (x + 1) is

(a)

x2

(b)

x

(c)

1

(d)

x2 + x + 1

17. The graph of the line y = 3 is

(a)

Parallel to x-axis

(b)

Parallel to y-axis

(c)

Passing through the origin

(d)

Perpendicular to x-axis

18. The graph of y = ex intersect the y-axis at

(a)

(0,0)

(b)

(1,0)

(c)

(0,1)

(d)

(1,1)

19. $\lim _{ x\rightarrow \infty }{ \frac { \tan { \theta } }{ \theta } } =$

(a)

1

(b)

$\infty$

(c)

$-\infty$

(d)

$\theta$

20. If y = x and z = $\frac{1}{x}$ then $\frac{dy}{dz}=$

(a)

x2

(b)

1

(c)

-x2

(d)

$-\frac{1}{x^2}$

21. 7 x 2 = 14
22. The technology matrix of an economic system of two industries is $\begin{bmatrix} 0.50 & 0.25 \\ 0.40 & 0.67 \end{bmatrix}$. Test whether the system is viable as per Hawkins-Simon conditions.

23. Using the property of determinant, evaluate $\begin{vmatrix} 6 &5 &12 \\ 2 & 4 &4 \\2 & 1 & 4 \end{vmatrix}.$

24. Expand the following by using binomial theorem.$\left( x+\frac { 1 }{ y } \right) ^{ 7 }$

25. Find the angle between the pair of lines represented by the equation 3x2+10xy+8y2+14x+22y+15=0.

26. Find the value of $\cos\left(\frac{5\pi}{12}\right)$

27. Show that the functions f(x) = 5x - $\left| x \right|$ is continuous at x = 0

28. Differentiate ${ x }^{ \frac { 2 }{ 3 } }$ from first principles

29. 7 x 3 = 21
30. Solve: 2x+ 5y = 1 and 3x + 2y = 7 using matrix method.

31. Find the equation of the circle which touches the line x=0, y=0 and x=a.

32. Differentiate the following with respect to x
(ax2+bx+c)n

33. Differentiate the following with respect to x.  $\frac { { e }^{ x } }{ 1+x }$

34. Differentiate the following with respect to x. cos3x

35. If ey (x + 1) = 1, show that $\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } ={ \left( \frac { dy }{ dx } \right) }^{ 2 }$

36. Differentiate: $\sqrt{\frac{(x-3)(x^2+4)}{3x^2+4x+5}}$

37. 7 x 5 = 35
38. Evaluate:$\begin{vmatrix} 1&a&a^2-bc\\1&b&b^2-ca\\1&c&c^2-ab \end{vmatrix}$

39. If $A=\left[ \begin{matrix} 1 & tan\quad x \\ -tan\quad x & \quad \quad \quad 1 \end{matrix} \right]$, then show that ATA-1=$\left[ \begin{matrix} cos\quad 2x & -sin2x \\ sin\quad 2x & cos2x \end{matrix} \right] .$

40. By the principle of mathematical induction, prove the following.
an-bn is divisible by a-b, for all $n\in N$ .

41. If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.

42. Show that the given lines 3x-4y-13=0, 8x-11y=33 and2x-3y-7=0 are concurrent and find the concurrent point.

43. If cosec A + sec A = cosec B + sec B, prove that cot$\left( \frac { A+B }{ 2 } \right)$=tanA tanB

44. Differentiate: $\frac { sinx+cosx }{ sinx-cosx }$with respect to 'x'