AP Class 11 Model Paper Maths

FOR AP CLASS 11 EXAM PREPARATION

AP Class 11
Model Paper · Maths
EXAM YEAR TYPE SUBJECT

AP Class 11 — Model Paper Maths

Notes · Sample Papers · Previous Year Papers · Mock Tests

.
m .co s e m
e l a

as ag

BOARD OF INTERMEDIATE EDUCATION, ANDHRA PRADESH
TADEPALLI, GUNTUR.

m
Time : 3 hrs. MATHEMATICS - I Max Marks : 100

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SECTION – A

m
ecarries One mark.
I. Answer ALL the questions.
a s
12  1 l= 12
a
Each questions
l 2, 3, 4 }, B = {2, 3, 4}, C = {3, 4, 5, 6} then A  (B  C) = ag[ ]
1. If A = g{1,
a
1) {2, 3, 4} 2) {1, 2, 3, 4} 3) {3, 4, 5, 6} 4) {1, 6}
2. The value of cos 10 cos20 cos30 …. Cos1790 is [ ]
1
1) 2) 0 3) 1 4) -1
2
4

3.   2n  3   [ ]
m
c. o 3) 21
n 1

m
1) 5 2) 12 4) 32

s e
P la
4. The Co-efficient of x8 . y10 in the expansion of (x + y)18 is [ ]
1) C 18
8 2)
a g 18 3) 2
10 4) 0 18

5. The length of the perpendicular drawn from the point P(13, 5, 12) on X axis [ ]
1) 13 2) 2 3 3) 194 4) 313
x2 1
6. Lim  [ ]
x 1 x  1

1) 0 2) 2 3) 2 4) Doesn’t axis
m
m .co
x 2 5 1

.co m
7. If   1, y     ,  . Then find x and y.

s e
3 3  3 3

e m la
s g
8. Express the complex number i9 + i19 in the form of a + ib.

g la a
a
1 1 x
9. If   . Then find x.
6! 7! 8!
10. Find the condition for the points (a, 0), (h, k) and (0, b) where a.b  0 to be collinear…..
11. Find the eccentricity of an equilateral hyperbola.
12. One card is drawn from a well shuffled deck of 52 cards. Then find the probability that the card
is not a red card.

m . c
c. o s e m
s em
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Page 1 of 7

SECTION – B
II. Answer ALL the questions.
Each question carries Two marks. 10 x 2 =20
13. Write down all the subsets of the set {1, 2, 3}.
14. Find the domain and range of f(x) = 9  x2 .
1
15. Find the values of Sin x and Tan x when Cos x = , x lies in third quadrant.
2
1 i 1 i
16. Find the modules of  .
1 i 1 i
17. If 18 Pr 1 : 17 Pr 1  9 : 7 , then find r.

   
4 4
18. Find the value of a  a  1  a  a  1 .
2 2 2 2

19. Find the Co-ordinates of focus and equation of the directrix of the parabola x 2  16 y .
20. Find x if the distance between (5, 1, 7) and (x, 5, 1) in 9 units.
21. Evaluate Lim 1  x  x 2  .......  x10 
x 1

22. Find the mean deviation about the median for the following data... 3, 9, 5, 7, 12,10,18,4,7,19, 21.

SECTION – C
III. Answer ANY SEVEN questions.
Each question carries FOUR marks. 7  4 =28
23. Draw the appropriate venn diagram of A  B .
24. Let f(x) = x2 and g(x) = 2x + 1 be two real functions.
f 
Find (i) (f + g)(x) (ii) ( f – g)(x) (iii) (f .g)(x) (iv)    x 
g

25. Find the conjugate of
 3  2i  2  3i  and simplify..
1  2i  2  i 
3 x  2 52  x
26. Solve the inequation  .
5 3
27. Prove that for 3  r  n,  n3 Cr  3. n3 Cr 1  3. n3 Cr 2   n3 Cr 3  n Cr .
28. Prove that 2.C0 + 5.C1 + 8.C2+…..(3n + 2).Cn = (2n + 4).2n1.

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29. Find the equation of the line passing through the point (2, 2) and cutting of intercepts on the axis
whose sum in 9.
30. Find the equation of the ellipse, with major axis along the X– axis and passing through the points
(4, 3) and (-1, 4).
31. Find the derivative of Sec 3x from the first principle.
32. A and B are two events such that P(A) = 0.54, P(B) = 0.69 and P(A  B) = 0.35. Find
P  A|  B|  (iii) P  A  B|  (iv) P  B  A 
|
(i) P(A  B) (ii)
SECTION – D
IV. Answer ANY FIVE questions.
Each question carries EIGHT marks. 5  8 = 40
33. Determine the quadratic function f defined by f(x) = ax2 + bx + c, if f(0) = 6, f(2) = 1 and
f(-3) = 6.
34. Prove that Sin x + sin 3x + sin 5x + sin 7x = 4 cos x . cos 2x. cos 4x
35. Find the sum of the following series upto n terms. 5 + 55 + 555 +……. up to n terms.
π
36. A straight line passing through Q(3, 2) makes an angle with positive direction of X–axis. If
6
the straight line intersects the line 3 x  4 y  8  0 at P. Then find the distance PQ.
37. Find the equation of the circle passing through the points (3, 4) (3, 2) and (1, 4).
sin  π cos 2 x 
38. (a) compute Lim
x 0 x2
x100 x 99 x2
 ......  x  1 . Then prove that f 1  100.f(0).
1
(b) For the function f(x) = 
100 99 2
39. The diameters of circles (in mms) drawn in a design are given below.
Diameter 33 – 36 37 -40 41 – 44 45 – 48 49 – 52
No of circles 15 17 21 22 25
Calculate the standard deviation and mean deviation of the circles.
40. (a) One card is drawn from a well shuffled deck of 52 cards. If each outcome is equally likely,
calculate the probability that the card will be (a) a diamond (b) not an ace (c) not a diamond
(d) not a black card.
1 1 1
(b) If E and F are events such that P(E) = , P(F) = and P(E and F) = . Find
4 2 8
(i) P(E or F) (ii) P(not E and not F).


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.
m .co s e m
e l a

as ag



m
co
 - I
om .
 : 3    : 100

. c e m
e m  – A
l as
l a s ag
 ag
I. 
   12  1 = 12
1. A = {1, 2, 3, 4 }, B = {2, 3, 4}, C = {3, 4, 5, 6}  A  (B  C) = [ ]

1) {2, 3, 4} 2) {1, 2, 3, 4} 3) {3, 4, 5, 6} 4) {1, 6}

2. cos 10 cos20 cos30 …. Cos1790    [ ]
1

m
1) 2) 0 3) 1 4) -1

.co
2

m
4

  2n  3  
s e
3. [ ]

2) 12 la
n 1

g
4. (x + y)  x . y a
1) 5 3) 21 4) 32
18 8 10
[ ]
1) 18C 2) 18P 3) 218 4) 0
8 10

5. P(13, 5, 12)   X     [ ]

1) 13 2) 2 3 3) 194 4) 313

om
x2 1
6. Lim  [ ]

m . c
x 1 x  1

c. o e m
1) 0 2) 2 3) 2 4) Doesn’t axis

em 7.  x  1, y  2    5 , 1   x  y   las
l as ag
ag
3 3  3 3

8. i9 + i19   a + ib  
1 1 x
9.    x 
6! 7! 8!
10. a.b  0  (a, 0), (h, k)   (0, b)    


m . c
c. o s e m
s em
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11. 
12.   52             
   
 – B
II. 
    10 x 2 =20

13. {1, 2, 3}     

14. f(x) = 9  x2     
1
15. Cos x = , x     Sin x  Tan x  
2
1 i 1 i
16.  
1 i 1 i
17. 18
Pr 1 : 17 Pr 1  9 : 7  r 

      
4 4
18. a2  a2  1  a2  a2 1

19. x 2  16 y        
  
20. (5, 1, 7)  (x, 5, 1)    9   x  

21. Lim 1  x  x 2  .......  x10   
 
x 1

22. 3, 9, 5, 7, 12,10,18,4,7,19, 21      

 – C
III.     
 7  4 = 28
23. A  B     

24. f(x) = x2  g(x) = 2x + 1     
f 
(i) (f + g)(x) (ii) ( f – g)(x) (iii) (f .g)(x) (iv)    x   
g

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25.
 3  2i  2  3i    
1  2i  2  i 
3 x  2 52  x
26.   
5 3
27. 3  r  n   n3 Cr  3. n3 Cr 1  3. n3 Cr 2   n3 Cr 3  n Cr 

28. 2.C0 + 5.C1 + 8.C2+…..(3n + 2).Cn = (2n + 4).2n1  

29. (2, 2)      9 

30. X–   (4, 3) (-1, 4)  

31.    Sec 3x   
32. P(A) = 0.54, P(B) = 0.69  P(A  B) = 0.35  A  B   

P  A|  B|  (iii) P  A  B|  (iv) P  B  A 
|
(i) P(A  B) (ii)


 – D
IV. 
   5  8 = 40
33. f    f(x) = ax2 + bx + c    f(0) = 6, f(2) = 1 
f(-3) = 6  f(x)  

34. Sin x + sin 3x + sin 5x + sin 7x = 4 cos x . cos 2x. cos 4x   

35.    n   
5 + 55 + 555 +……. (n )

π
36. Q(3, 2) X–
   3x  4 y  8  0
6
 P   PQ  

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.
m .co s e m
e l a

as ag

37. (3, 4) (3, 2)  (1, 4)      
sin  π cos 2 x 

m
38. (a) Lim   
co
x 0 x2
x100 x 99
. c
x2
om
 ......  x  1  f 1  100. f(0)  
e m .
s
1
(b) f(x) = 
m
e       l a
100 99 2
 s g
39.
g l a a
a 
 33 – 36 37 -40 41 – 44 45 – 48 49 – 52

  15 17 21 22 25

       
40. (a)  52     

om
 (a)  (b)  (c)  (d)  

. c
e m
1
(b) P(E) = , P(F) =
1
  
l as
P(E    F) =
1
 E  F 
g
4 2 8
(i) P(E  F) (ii) P(E a  F )  



m
m .co
m .co s e m
s e g la
g la a
a

m . c
c. o s e m
s em
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gl a
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