#### Term I - Model Question Paper

11th Standard

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Time : 03:00:00 Hrs
Total Marks : 100

Part A

Multiple Choice Question

10 x 1 = 10
1. The co-factor of -7 in the determinant $\begin{vmatrix} 2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7 \end{vmatrix}$ is

(a)

-18

(b)

18

(c)

-7

(d)

7

2. If $\triangle=\begin{vmatrix} 1 & 2 & 3 \\ 3 & 1 & 2 \\ 2 & 3 & 1 \end{vmatrix}$ then $\begin{vmatrix} 3 & 1 & 2 \\ 1 & 2 & 3 \\ 2 & 3 & 1 \end{vmatrix}$ is

(a)

$\triangle$

(b)

-$\triangle$

(c)

3$\triangle$

(d)

-3$\triangle$

3. 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

4. If $\triangle=\begin{vmatrix} {a}_{11} & {a}_{12} & {a}_{13} \\ {a}_{21} & {a}_{22} & {a}_{23} \\ {a}_{31} & {a}_{32} & {a}_{33} \end{vmatrix}$ and Aij is cofactor of aij, then value of $\triangle$ is given by

(a)

a11 A31 + a12 A32 + a13 A33

(b)

a11 A11 + a12 A21 + a13 A31

(c)

a21 A11 + a22 A12 + a23 A13

(d)

a11 A11 + a21 A21 + a31 A31

5. If nC3 = nC2, then the value of nC4 is

(a)

2

(b)

3

(c)

4

(d)

5

6. The value of n, when nP2 = 20 is

(a)

3

(b)

6

(c)

5

(d)

4

7. 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!

8. 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)

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

9. If the lines 2x - 3y - 5 = 0 and 3x - 4y - 7 = 0 are the diameters of a circle, then its centre is

(a)

(-1, 1)

(b)

(1,1)

(c)

(1, -1 )

(d)

(-1, -1)

10. The eccentricity of the parabola is

(a)

3

(b)

2

(c)

0

(d)

1

11. Part B

11 x 2 = 22
12. Evaluate $\begin{vmatrix} 2 &-1 &-2 \\0 & 2 & -1\\3 & -5& 0 \end{vmatrix}.$

13. Find the values of x if $\begin{vmatrix} 2 & 4 \\5 & 1 \end{vmatrix}=\begin{vmatrix} 2x & 4\\6 & x \end{vmatrix}.$

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

15. Verify that 8C4+8C3=9C4

16. How many chords can be drawn through 21 points on a circle?

17. How many triangles can be formed by joining the vertices of a hexagon?

18. Show that 10P3 = 9 P3 + 3. 9P2

19. Find n if 25 Cn+5 = 25 C2n-1.

20. Find the centre and radius of the circle x2 + y2 = 16

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

22. Find the center and radius of the circle (x + 2) ( x - 5) + (y -2 ) ( y -1) = 0

23. Part C

16 x 3 = 48
24. If A = $\begin{bmatrix}1 & 1 & 1 \\ 3 & 4 & 7\\1 & -1 & 1 \end{bmatrix}$ verify that A ( adj A ) = ( adj A ) A = |A| I3.

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

26. Find the adjoint of the matrix $A=\begin{bmatrix}2&3\\1&4 \end{bmatrix}$

27. Using matrix method, solve x+2y+z=7, x+3z = 11 and 2x-3y =1.

28. If A=$\left[ \begin{matrix} -1 & 2 & -2 \\ 4 & -3 & 4 \\ 4 & -4 & 5 \end{matrix} \right]$then, show that the inverse of A is A itself.

29. Using co-factors of elements of  second column evaluate $\left| \begin{matrix} 6 & -1 & 5 \\ 3 & 0 & 4 \\ -2 & 7 & -3 \end{matrix} \right|$

30. Decompose into Partial Fractions:$\frac { 5{ x }^{ 2 }-8x+5 }{ (x-2)({ x }^{ 2 }-x+1) }$

31. Evaluate the following expression.$\frac { 7! }{ 6! }$

32. It the letters of the word are arranged as in dictionary, find the rank of the word "AGAIN".

33. In how many ways can n prizes be given to n boys, when a boy may receive any number of prizes?

34. Find the axis, vertex, focus, equation of directrix length of latus rectum of the parabola (y-2)2=4(x-1).

35. For what value of $\lambda$ are the three lines 2x-5y+3 = 0, 5x-9y+$\lambda$=0 and x-2y+1=0 are concurrent?

36. Find the value of k if the straight line 2x+3y+4+k(6x-y+12) = 0 is perpendicular to the line 7x+5y-4=0

37. Find the locus of a point which moves in such a way that the square of its distance from the point (3, -2) is numerically equal to its distance from the line 5x - 12y = 13

38. Find the locus of a point such that the sum of its distances from the points (0, 2) and (0, -2) is 6.

39. Find the slope of the lines which make an angle of 45° with the line 3x - y + 5 = 0.

40. Part D

4 x 5 = 20
41. Determine the values of x for which the matrix A=$\left[ \begin{matrix} x+1 & -3 & 4 \\ -5 & x+2 & 2 \\ 4 & 1 & x-6 \end{matrix} \right]$is singular.

42. Solve by matrix inversion method: 3x - y + 2z = 13 ; 2x + Y - z = 3 ; x + 3y - 5z = - 8.

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

44. Show that the equation 12x2 -10xy +2y2 +14x -5y +2 = 0 represents a pair of straight lines also find the separate equations of the straight lines