A2S – ACCESS 2 SUCCESS
8750-8750-80
8750-8750-70
2847,Second Floor, Sant Nagar, Rani Bagh
11, Shakti Vihar , Near Saral Diagnostics
SAMPLE PAPER 1
Section A
Q1.
Q2.
Q3.
The number of proper subsets of a set containing n elements is
(a)
(b)
(c)
2n
2n1
2n  1
(d)
None
Find the domain of f ( x)  4  x 2
(a)
 2, 2 
(b)
(c)
 , 2    2,  
(d)
 2, 2
 , 2   2,  
(c)

(c)
4
5
 19 
Find the value of cos ec  

 3 
2
(a)
2
3
(b)
2
3
(d)
 2
(d)
2
5
(d)
 , 5
30
(d)
None
 x y
tan 

 2 
(d)
 x y
 cot 

 2 
4
(d)
2
1  i   x  iy, find the value of x  y.
If
2
Q4.
2i
(a)
Q5.
(b)
(b)
Evaluate :-
sin x  sin y
cos x  cos y
 , 5
(c)
 5,  
 x y
cot 

 2 
(b)
37
(c)
 x y
 tan 
 (c)
 2 
What is the value of r , if P  5, r   P  6, r  1 ?
(a)
Q9.
 5,  
60
(a)
Q8.
4
5
Given n U   60, n  A  37, n  B   30, find maximum n  A  B  .
(a)
Q7.
(b)
Solution set of the inequality 3x  9  5 x  1 for x  R is equal
(a)
Q6.
2
5
9
(b)
5
(c)
The total number of terms in the expansion of  x  a    x  a  after simplification is
10
(a)
4
(b)
5
(c)
6
10
(d)
None
Q10. The range of the function f ( x)  5  x  1
(a)
Q11.
 , 5
(b)
 ,5
x n  2n
 80
x2 x  2
(b)
5
(c)
 0,5
(d)
None
(c)
6
(d)
None
The value of n, if lim
(a)
4
Q12. The image of the point  5,  4,3 in XZ - plane is
(a)
 5,  4,3
(b)
  5, 4,  3
(c)
  5,  4,  3 (d)
 5, 4, 3
Q13. The number of arrangements of the word ‘MOTHER’ in which vowels never come together is
(a)
120
(b)
240
(c)
480
(d)
None
Q14. If y  x 
1
dy
then
at x  1.
x
dx
1
(c)
2
(d)
None
2
Q15. The eccentricity of the ellipse if latus rectum is equal to half of major axis.
(a)
0
(b)
(a)
1
2
(b)
1
2
(c)
(d)
2
None
Q16. The equation of the line passing through 1, 2  and parallel to the line y  3 x  1
(a)
y  2  x 1
(b)
y  2  3  x  1
(c)
y  2  3  x  1
(d)
y  3x  5
Q17. If the third term of G.P is 4, then the product of first 5 terms is
(a)
(b)
44
45
(c)
46
(d)
None
Q18. The value of  if the three lines 2 x  5 y  3  0 , 5 x  9 y    0 and x  2 y  1  0
are concurrent , is
(a)
3
(b)
4
(c)
5
(d)
None
Q19. Two letters are drawn at random from the word ‘HOME’ then the probability that both the
letters are vowels is
(a)
1
6
(b)
5
6
(c)
1
2
(d)
1
3
Q20. Mean deviation of n - observations x1 , x2 , ...... , xn from their mean x is ______ .
n
(a)
 x x
1
i 1
(b)
1 n
 x1  x
n i 1
  x  x
n
(c)
1
i 1
2
(d)

1 n
 x1  x
n i 1

2
Section B
Q21. Find the vertex, focus, latus rectum of x2 = 8y.
Q22.
If U = {1, 2, 3, 4, 5, 6, 7, 8, 9} A = {1, 3, 4, 6} B = {2, 3, 4, 7}. Show that A  B = A  Bc .
Q23.
If A = {1, 2, 3, 4} B = {1, 3, 4, 5, 8},find the relation “is greater than” from B to A.
2
2
2 x y
Q24. Prove that :  cos x  cos y    sin x  sin y   cos 

 2 
Q25.
A solution is to be kept between 40 C and 45 C . What is the range of temperature in degree
9
Fahreheit, If conversion formula is F  C  32?
5
Section C
Q26. Show that the area of the triangle formed by the lines y  m1 x  c1 , y  m2  c2 and x  0 is
 c1  c2  .
2
2 m1  m2
Q27. If the pth, qth and rth terms of a G.P. are a, b and c, respectively. Prove that : aqr brp cpq = 1.
Or
th
If the first and n term of a G.P. are a and b, respectively, and if P is the product of n terms, prove
that P 2   ab  ..
n
sec 8 x  1 tan 8 x
Q28. Prove that : sec 4 x  1  tan 2 x
Or
4 tan x(1  tan 2 x)
tan 4 x 
1  6 tan 2 x  tan 4 x

  x 
1  x  tan 

Q29. Evaluate : lim


x 1
 2 

Or
lim
tan x  sin x
x0
x3
Q30. The mean of 5 observations is 4.4 and their variance is 8.24. If these of the observations are 1,2
and 6, find the other two observations.
Q31. A committee of two persons is selected from two men and two woman What is the probabilirty
that the committee will have (a) no man? (b) one man? (c) two men?
Section D
Q32.
Find the equation of the ellipse that satisfies the conditions Major axis on the y-axis, centre at
the origin and passes through the point (3,2) and (1,6).
Or
An arch is in the form of semi-ellipse. It is 8 m wide and 2 m high at the centre. Find the height
of the arch at a point 1.5 m from one end.
Q33. Differentiate
x
with respect to x ab-intio
sin x
Or
 a  bx, x  1

x  1 and if lim f (x) = f (1). Find the possible values of a and b.
Let f(x) =  4,
x 1
 b  ax, x  1


 3
2
2
2
Q34. Prove that : cos x  cos  x    cos  x    .
3
3 2


Or
Prove that : cos 4

8
 cos 4
3
5
7 3
 cos 4
 cos 4

8
8
8
2
Q35. Calculate the mean and standard deviation for the following distributions :
Marks
20-30 30-40 40-50 50-60 60-70 70-80 80-90
Number of students
3
6
13
15
14
5
4
Section E
Q36. Let A and B be two sets
A : {x : x is a letter in the word KHAZANA}
B : {x : x is a letter in the word MATHEMATICS}
Answer the following :
(i)
How many subsets of A are possible
(ii)
How many improper subsets of B are possible ?
(iii) How many proper subsets of A  B are possible ?
(iv)
How many subsets of A  B are possible ?
Q37. 5 boys and 5 girls were sitting in a music room in a row. Their sitting positions can be anything
Based on the above information, answer the following questions.
(i)
Find the number of ways in which all the girls sit together .
(ii)
Find the number of ways in which all the girls and all the boys sit together .
(iii) Find the number of ways in which all the girls never sit together .
Q38. The cost and revenue functions of a product are given by C  x   20 x  4000 and
R  x   60 x  2000 Respectively , where x is the number of items produced and sold .
Answer the following questions on the basis of information given above :
(i)
How many items must be sold to realise some profit ?
(ii)
What are the values of cost and revenue if number of items are 10 units ?
(iii) Represent the solution on real line for part (a) .
(2)
(1)
(1)
ANSWERS
Q1.
(c)
Q2.
(b)
Q3.
(c)
Q4.
(a)
Q5.
Q8.
(c)
Q9.
(c)
Q10. (b)
Q11.
(b)
Q12. (d)
Q13. (c)
Q16. (d)
Q17. (b)
Q18. (b)
Q19. (a)
Q20. (b)
Q15. (b)
(b)
Q6.
(a)
Q7.
(d)
Q14. (a)
Q21. (0, 0) , (0, 2), 8
Q23.
R   3,1 3,2  4,1 ,  4, 2  ,  4,3 5,1 ,  5, 2  ,  5,3 ,  5, 4  ,  8,1 ,  8, 2  ,  8,3 ,  8, 4 
Q25. The range of temperature in degree Fahrenheit is between 104 F and 113 F
2
or
1
2
Q30. 4 and 9
Q29.

Q32.
y2 x2

 1 or 1.56 m (approx)
40 10
Q31. (a)
Q33.
1
2
1
(b)
(c)
6
3
6
sin x  x cos x
or a  0, b  4.
sin 2 x
KISHORE WADHWA’S MATHS CLASSES (K.W.M.C)
CONTACT 8750-8750-80
Contact no. 8750-8750-80
KISHORE WADHWA’S MATHS CLASSES (K.W.M.C)
CONTACT 8750-8750-80
SAMPLE PAPER 2
Section A
Q1.
A and B are two sets such that n(A B) = 14 + x, n(B A) = 3x and n(A B) = x, If n(A) = n(B)
then find the value of x.
(a)
7
(b)
6
(c)
8
(d)
5
Q2.
If f ( x)  x 2  3x  1 then the value of x such that f (2 x )  f ( x )
(a)
Q3.
If sin   
(a)
Q4.
Q9.
 0,1
(d)
 0,1
1
5
(b)

1
10
1
5
(d)
1
10
(c)

(c)
2
(d)
None
(c)
 4, 2
(d)
 2, 4
(d)
None
1  i   2  i 
0
3 i
(b)
1
 2, 4
(b)
 4, 2
10
11
(b)
21
The values of x for which the numbers
(a)
Q8.
(c)
The number of terms in the expansion of  a 2  2ab  b 2  is
(a)
Q7.
0,1
7
The value of x : 3  4  x  18
2
(a)
Q6.
(b)
4

and  lies in third quadrant then cos is
5
2
The value of
(a)
Q5.
0,1
2
7
(b)
7
2
(c)
31
2
7
are in G.P. is (are)
, x,
7
2
(c)
1
(d)
None
Two finite sets have m and n elements. The number of subsets of the first set is 112 more than
that of the second set. The values of m and n are, respectively
(a)
4, 7
(b)
7, 4
(c)
4, 4
(d)
7, 7
cos 9  sin 9
Value of :cos 9  sin 9
(a)
tan 54
(b)
tan 36
(c)
tan18
(d)
tan 72
Q10. If x is a real number and x  5, then
(a)
(b)
x5
5 x5
(c)
x5
(d)
5 x5
Q11.
The number of arrangement of the word ‘GOLDEN’ in which the vowels occur together, is
(a)
120
(b)
240
(c)
480
(d)
None
Q12.
If lines a1 x  b1 y  c1  0 and a2 x  b2 y  c2  0 are perpendicular then
a1 a2

b1 b2
(a)
(b)
a1a2  b1b2  0
Q13. The range of the function f ( x) 
(a)
R  7
(b)
x7
x7
Z  7
(c) a1a2  b1b2  0
(d)
None
1,1
(d)
 1,1
is
(c)
Q14. The ends of minor axis, if the equation of ellipse is
(a)
Q15.
  a , 0
If 1  i 
(a)
2n
(b)
 0,  a 
(c)
x2 y 2

 1, where a  b.
a2 b2
  b, 0 
(d)
 0,  b 
2n
 1  i  , then the least positive integral value of n is
8
(b)
4
Q16. The value of n, if 2 n C3 : nC3  11:1 is
(a)
4
(b)
5
(c)
2
(d)
16
(c)
6
(d)
None
Q17. The length of the latus rectum of the ellipse 25 x 2  4 y 2  100 is _______ .
(a)
25
2
(b)
16
5
(c)
8
5
(d)
5
8
(c)
4
(d)
None
cot 2 x  3

x  cos ec x  2
Q18. The value of : lim
6
(a)
2
(b)
3
Q19. In a non-leap year, the probability of having 53 tuesday or 53 wednesday is
(a)
1
7
(b)
2
7
(c)
3
7
(d)
Q20. The probability of A but not B is same as _______ .
(a)
P  A  P  B 
(b)
P  B   P  A
(c)
P  A  P  A  B 
(d)
P  B  P  A  B
None of these
Section B
Q21. The foci of an ellipse are (10, 0) and eccentricity is
x5/ 3 1
x 1 x10 / 3  1
Q22. Evaluate : lim
1
. Find the equation of ellipse.
5
3 sin x  sin 3 x
.
x 0
x3
lim
Or
Q23.
A card is drawn from a deck of 52 cards. Find the probability that the card drawn is
neither a spade nor an ace.
Q24.
Find the domain and range of f (x) =
3x  2
.
x2
Q25. Find the equation of line passing through  3,  1  and perpendicular to 2 x  5 y  1
Section C
Q26. A bag contains tickets numbered 1,2,3,.... 50 of which five tickets x1 , x2 ,....... x5 are drawn at
random and arranged in ascending order of magnitude x1  x2  x3  x4  x5 . What is the prob
ability that x3 = 30 ?
Q27.
A boy has 3 library tickets and 8 books of his interest in the library .Of these 8, he does not want
to borrow Mathematics Part II, unless Mathematics Part I also is borrwed . In how many ways
can he choose the 3 books to be borrowed ?
Q28. Prove that : cos10 cos 30 cos 50 cos 70 
3
.
16
Or
2
2
Prove that : cos 4 x  1  8sin x cos x
Q29. If  and  are complex numbers with   1 , then find
 
1  .
Or
Prove that : x4 + 4 = (x + 1 + i) (x + 1  i) (x  1 + i) (x  1  i).
Q30. The hypotenuse of an isosceles right angled triangle has its ends at the points
1,3 and  4,1 . Find the equations of the legs (perpendicular sides) of the triangle.
Q31. Differentiate : x cos x from first principle.
Or
Find the derivative of
2x  3
from first principle.
3x  2
Section D
Q32. The mid-points of the sides of a triangle are  5,7,11 ,  0,8,5  and  2,3  1 . Find its vertices
and hence find its centroid.
Q33. The mean and variance of 7 observations are 8 and 16 respectively. If 5 of the
observations are 2, 4, 10, 12, 14 find the remaining 2 observations.
Or
Calculate mean, variance and standard Deviation for the following distribution
Classes
Frequency
Q34.
30-40
3
40-50
7
50-60
12
60-70
15
70-80
8
80-90
3
90-100
2
If a,b are the roots of x 2  3 x  p  0 and c,d are roots of x 2  12 x  q  0 , where a,b,c,d from a
G.P. Prove that  q  p  :  q  p   17 :15 .
Or
If a,b,c and p are different real numbers such that
 a  b  c  p  2  ab  bc  cd  p   b  c  d   0 , then show that a,b,c and d are in G.P..
2
Q35.
2
2
2
2
2
2
Find the equation of the circle passing through the points (4,1) and (6,5) and whose centre is on the
line 4 x  y  16 .
OR
The equations of the two sides of a triangle are 3 x  2 y  6  0 and 4 x  5 y  20  0 respectively,,
the orthocentre of the triangles is (1,1) find the equation of third side.
Section E
Q36. A state cricket authority has to choose a team of 11 members , to do it so the authority asks 2
coaches of a government academy to select the team members that have experience as well as
the best performers in last 15 matches . They can make up a team of 11 cricketers amongest 15
possible candidates.
Based on the above information , answer the following questions .
(i)
In how many ways can the final eleven be selected from 15 cricket players if there is
no restriction ?
(1)
(ii)
(iii)
In how many ways can the final eleven be selected from 15 cricket players if one of
them must be included ?
(1)
In how many ways can the final eleven be selected from 15 cricket players if one of
them ,who is in bad form , must always be excluded ?
(2)
Q37. In a class of 60 students, 30 opted for NCC, 32 opted for NSS, 24 opted both NCC and NSS.
Based on the above information, answer the following question :
If one of these students is selected at random, find the probability that
(i)
The student opted for NCC or NSS.
(ii)
The student has opted for NSS but not NCC.
(iii) The student opted neither NCC nor NSS.
(1)
(1)
(2)
Q38. Each side of an equilateral triangles is 24 cm . The mid-point of its sides are joined to form
another triangle . This process is going continuously infinite .
Find
(i)
The sum of perimeter of first 6 triangle is (in cm)
(ii)
The side of the 5th triangle is (in cm)
(iii) The perimeter of all the triangle is (in sq cm)
ANSWERS
Q1.
(a)
Q2.
(b)
Q3.
(c)
Q4.
(b)
Q5.
Q8.
(b)
Q9.
(b)
Q10. (b)
Q11.
(b)
Q12. (b)
Q13. (c)
Q16. (c)
Q17. (c)
Q18. (c)
Q19. (b)
Q20. (c)
9
13
R  2 , R  3
Q15. (c)
(b)
Q21.
x2
y2

1
2500 2400
Q22.
Q25.
5 x  2 y  17
Q27. 41
Q30.
7 x  3 y  2 , 3 x  7 y  5 or 3 x  7 y  24, 7 x  3 y  31
Q31.
f '  x   cos x  x sin x or f '  x  
1
or 4
2
x 2  y 2  6 x  8 y  15  0
Q37. (i).
Q24.
(b)
Q7.
(c)
Q14. (a)
Q29. 1
5
 3x  2 
Q32. A  3, 4, 7  , B  7, 2,5  and C  3,12,17 
Q35.
Q23.
Q6.
2
Q33. 6 and 8 or 62, 201, 14.18
Q36. (i). 1365 (ii). 1001 (iii). 364
19
2
11
(ii).
(iii).
30
15
30
KISHORE WADHWA’S MATHS CLASSES (K.W.M.C)
CONTACT 8750-8750-80
Contact no. 8750-8750-80
KISHORE WADHWA’S MATHS CLASSES (K.W.M.C)
CONTACT 8750-8750-80
SAMPLE PAPER 3
Section A
Q1.
If x1 , x2 , x3 , be the observation with mean x and standard deviation  , then the standard
deviation of the observation x1  k , x2  k , x3  k is
(a)
Q2.
(d)
k

k
(b)
1
x
(b)
1
2
(c)
26
51
(d)
27
51
1
1
(c)
0
(d)
Does not exist
x  2y  0
(b)
x  2z  0
(c)
(d)
2x  y  0
(d)
5
3
(d)


(d)
None
2n
(d)
None of these
2x  z  0
For the parabola 3 x 2  5 y, length of the latus rectum is
5
(b)
5
(c)

5
3
an  bn
If n 1 n 1 is the G.M. between a and b then find the value of n .
a b
(a)
Q7.
(c)
The equation of the set of points which equidistant from the points (1,2,3) and  3, 2, 1 .
(a)
Q6.
29
52
x0
(a)
Q5.
k
The value of : lim x sin
(a)
Q4.
(b)
While shuffling a pack of 52 playing cards, 2 are accidentally dropped. The probablity that the
missing cards to be of different colors is
(a)
Q3.

1
(b)
1
2
(c)
1
1
2
sin x
.
x0
x
The value of : Lim
(a)
1
(b)

180
(c)
180
n
Q8.
The value of  2
r 0
(a)
3n
r n
Cr ________
(b)
4n
(c)
Q9.
Derivative of 
(a)

2
with respect to x is
x2
1
x
(b)
4
x3
(c)

2
x4
(d)
1
x
Q10. The number of 6 digit numbers can be formed in which all digits are odd , is
(b)
(c)
(d)
(a)
5!
56
66
46
Q11.
If x  1  5, then
(a)
x   4, 6 
(b)
x   4,6
(c)
x   , 4    6,  
(d)
x   , 4   6,  
Q12. The distance of point  3, 4,5  from x  axis is
(a)
(b)
34
41
(c)
5
(d)
3
Q13.
For what values of k, are the lines x  2 y  9  0 and kx  4 y  5  0 parallel?
(c)
1
(d)
0
(a)
2
(b)
1
Q14.
The value of
25 9 is ______ .
(b)
15i
(c)
15
(d)
15
(c)
50
(d)
51
Q16. The value of tan 36  tan 9  tan 36.tan 9
(a)
0
(b)
1
(c)
2
(d)
None
(a)
15i
Q15. The value of n, if  n  2 !  2550.n !
(a)
48
(b)
49
Q17. The distance between the parallel lines x  3 y  1  0 and 5 x  15 y  1  0 is
(a)
0 units
Q18. The value of x :
(a)
 2,5 
(b)
2 units
(c)
4
units
5
(d)
4
units
5 10
 2,5
(c)
 2,5
(d)
 2,5
 0,  
(d)
None
x 5
0
x2
(b)
Q19. The domain of the function given by f ( x ) 
(a)

(b)
 , 0 
1
x x
(c)
Q20. The range of f ( x)  1  3cos 2x
(a)
 2, 4
(b)
 2,4
(c)
 2, 4
(d)
 2, 4 
Section B
 z .z 
 z .z 
Q21. If z1 and z2 are 1  i and 2 + 4i respectively, find  1 2  and hence Im  1 2  .
 z1 
 z1 
Q22.
A pair of dice is thrown. Find the probability of getting either doublet or sum atleast 10.
Q23.
4
12 3
 A, B  2 , find the value of the following. cos( A  B )
If cos A  , cos B  ,
5
13 2
Q24.
Evaluate lim
Q25.
Find the equation of the line passing through  3,5 and perpendicular to the line through the points
10 x  2 x  5x  1
x 0
x tan x
(2,5) and  3, 6  .
Section C
 x y
 yz
 zx
Q26. Prove that : cos x  cos y  cos z  cos  x  y  z   4 cos 
 cos 
 cos 
.
 2 
 2 
 2 
Or
x
9x
5x
 sin 5 x sin .
Prove that : cos 2 x cos  cos 3 x cos
2
2
2
Q27. If z1 , z2 ,  z3 ....., zn . are complex numbers such that
z1  z2  ...  zn 
1 1
1
  ... 
 1 , find the value of z , z ,  z ....., z .
1 2
3
n
z1 z2
zn
Or
If (x + iy)3 = u + iv, then show that
u v
 = 4(x2  y2).
x y
Q28. If three lines whose equations are y  m1 x  c1 , y  m2 x  c2 and y  m3 x  c3 are concurrent,
then show that m1  c2  c3   m2  c3  c1   m3  c1  c2   0
Or
Find the equation of the line passing through the point of intersection of the lines
4 x  7 y  3  0 and 2 x  3 y  1  0 and having equal intercepts on the axes.
Q29. A fair coin is tossed four times and a person win Re. 1 for each head and lose Rs. 1.50 for
each tail that turns up.From the sample space calculate how many different amounts of money
you can have after four tosses and the probability of having each of these amounts.
Q30. Find the equation of the circle concentric with the circle 2 x 2  2 y 2  8 x  10 y  39  0 and
having its area equal to 16 square units.
Or
Find the equation of the hyperbola whose conjugate axis is 5 and the distance between foci
is 13.
Q31. Evaluate : xlim
 / 4
sin x  cos x
x  / 4
Or
lim
x
2
1  cos 2 x
  2 x 
2
Section D
Calculate the mean and standard deviation for the following table given the age
distribution of a group of people
Age
20 - 30
30 - 40
40 - 50
50 - 60
60 - 70
70 - 80
Number of
3
51
122
141
130
51
persons
Q32.
Q33.
80 - 90
2
If the lines y  3 x  1 and 2 y  x  3 are equally inclined to line y  mx  4. find the value of m.
Q34. Find the derivative of sin x from first principle.
Q35. The sum of two numbers is 6 times their geometric means, show that numbers are in the ratio
(3 + 2 2 ) : (3  2 2 ).
OR
If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers
are A  (A  G)(A  G) .
Section E
Q36. Read the case study given below and attempt .
During the mathematics class , a teacher clears the concept of permutation and combination to
the students . After the class he asks the students some questions , one of the question was in
how many ways number between 99 and 1000 (both excluding) can be formed such that
(i)
Every digit is either 3 or 7
(ii)
No digit is repeated
(iii) The digit at hundred’s place is 7.
(iv)
The digit at the unit’s place is 0 .
Q37. Shweta is doing a designing course . She is working on Cartesian Art now a days . For she
wants to take x-coordinate from the set A  0,1, 2,3,5 and y-coordinate from the
B  3, 2, 1, 0,1, 2,3 . Based on the information answer the following questions .
(i)
How many ordered pairs Shweta can make from A to B ?
(ii)
If a relation from A to B is defined as R   a, b  : a  b, a  A, b  B , then how many
elements are there in R ?
(iii)
Arrow diagram for the Relation R   a, b  : a  b, a  A, b  B is
(a)
(c)
(iv)
A
B
0
1
2
3
4
5
3
2
1
A
B
0
1
2
3
5
3
2
1
A
B
0
1
2
3
5
3
2
1
A
B
0
1
2
3
5
3
2
1
(b)
0
1
2
3
(d)
0
1
2
3
0
1
2
3
0
1
2
3
How many total relation can defined from the set A to the set B?
Q38. Equation of a straight line path is 2 x  y  12  0 . A man is standing at a point  2,3 . He wants
to reach the straight line path in least possible time.
Based on the above information, answer the following question :
(a)
Find the equation of the path followed by man.
(b)
Find the image of the point  2,3 with respect to the given straight line path, assuming
the given path to be a plane mirror.
ANSWERS
Q1.
(a)
Q2.
(c)
Q3.
(c)
Q4.
(b)
Q5.
Q8.
(a)
Q9.
(b )
Q10. (a)
Q11.
(c)
Q12. (b)
Q13. (a)
Q16. (b)
Q17. (d)
Q18. (b)
Q19. (a)
Q20. (a)
5
18
33
65
 log 2  log 5
Q25. 5 x  y  20  0
Q15. (b)
Q21.
4  2i , 2
Q22.
Q23.
Q24.
(d)
(b)
Q6.
Q7.
(b)
Q14. (c)
Q28. 13 x  13 y  6
Q29. Rs 4.00 gain , Rs 1.50 gain, Re 1.00 loss , Rs 3.50 loss , Rs 6.00 loss.
P (Winning Rs 4.00) 
P (Losing Rs 3.50) 
Q30.
1
1
3
, P (Winning Rs 1.50)  , P (Losing Re. 1.00) 
16
4
8
1
1
, P (Losing Rs 6.00)  .
4
16
4 x 2  4 y 2  16 x  20 y  23  0
Q31.
2 or
1
2
Q32. mean x  55.1 and standard deviation   11.8739
Q34.
f ' x 
cos x
2 x
Q33.
Q36. (i). 8 (ii). 648 (iii). 100 (iv). 90
(iii). Option (C) (iv). 2 35
m
1 5 2
7
Q37. (i). 35 (ii). 6
 28 76 
Q38. (i). x  2 y  4  0 (ii).  , 
 5 5 
KISHORE WADHWA’S MATHS CLASSES (K.W.M.C)
CONTACT 8750-8750-80
Contact no. 8750-8750-80
KISHORE WADHWA’S MATHS CLASSES (K.W.M.C)
CONTACT 8750-8750-80
SAMPLE PAPER 4
Section A
Q1.
The centre of circle : 2x2 + 2y2  12x + 8y + 1 = 0.
(a)
Q2.
(b)
 3, 2 
(c)
 3, 2 
(d)
 3, 2 
The value of k if line passing through (2, 5) and (k,9) is perpendicular to 5 x  3 y  1 .
(a)
Q3.
 3, 2
25
3
(b)
8
3
(c)
26
3
(d)
Two events A and B are non mutually exclusive and exhaustive. If P(A) =
17
3
2
1
P(A B) = ,
3
3
find P(B).
(c)
1
2
(d)
5
6
(c)
6
(d)
8
If n (A B) = 75, n (B) = 40, Find n (A) when A and B are disjoint sets.
(a)
25
(b)
30
(c)
35
(d)
40
(a)
Q4.
Q5.
Q6.
2
3
(b)
1
3
If nC2 = nC4 , then the value of n.
(a)
2
(b)
4
The eccentricity of 9x2 + 4y2 = 1.
(a)
1
2
(b)
5
3
5
3
(c)
3
5
(d)
Q7.
The area (in Sq. units) of circle centered at (1, 2) and passing through (4, 6), is
(b)
25
(c)
(d)
(a)
5
10
25
Q8.
The value of : tan
(a)
Q9.
1
3
19
3
(b)

in + in+1 + in+2 + in+3 is equal to
(a)
(b)
i
i
1
3
(c)
 3
(d)
(c)
0
(d)
1
(d)
90
Q10. The value of n (A) given that n(A Bc) = 70 and n(A B)= 20.
(a)
20
(b)
50
(c)
70
3
Q11.
Solution of | x + 2 |  5
(d)
 2,5
Q12. In a quadrilateral ABCD sin (A + B) + sin (C + D) is equal to
(b)
0
(c)
1
(a)
1
(d)
None
Q13. If nC2  nC1  35 , then the value of n.
(a)
3
(b)
7
(d)
10
(a)
Q14.
(b)
 3, 7
(c)
(c)
 7,3
8
sin105  cos105 is equal to
(a)
Q15.
 0,5
1
2
(b)
Solve : 5 
(a)
1
2
(c)
3
2
(d)
1
 34 22 
  3 , 3 
(c)
 17 22 
  3 , 3 
(d)
 34 32 
  3 , 3 
(d)
HDILE
2  3x
 9.
4
 34 52 
 3 , 3 
(b)
Q16. If all the letters of the word DELHI be arranged the 50th word is
(a)
HDEIL
(b)
HDIEL
(c)
HDELI
Q17. If n C3  n C4 11 Cr 1 find n and r
Q18.
(a)
n  11
r4
(b)
n  10
(c)
n  10
r 3
(d)
n  11 r  5
If tan A =
(a)
Q19.
r4
5
1
, tan B = , then the value of tan  A  B 
6
11
0
(b)
1
2
(c)
1
3
(d)
1
1
6
(c)
1
15
(d)
1
9
(c)
15
(d)
20
1  2  3  ....  n
n 
 n  1 3n  1
Evaluate : lim
(a)
1
3
Q20. The latus rectum of
(a)
5
(b)
x2 y2

1
100 25
(b)
10
Section B


2
Q21. Find the multiplicative inverse 2  3i .
Q22. Find the domain and range of f  x   3  2 x  1
Q23. Find dervative of
x 2 log x
w.r.t.x
1  log x
Or
Find the derivative of y  cos 2 x ab-initio
Q24.
If the latus rectum of an ellipse is equal to half of minor axis, then find its eccentricity.
Q25.
The letters of the word ‘CLIFTON’ are placed at random in a row. What is the chance that two
vowels come together ?
Section C
Q26. Find the equation of the circle concentric with circle x2 + y2 2x  4y1 = 0 and which
touches the y-axis.
Q27.
In how many ways can one select a cricket team of eleven from 17 players in which only 5 players
can bowler, if each cricket team of 11 must include exactly 4 bowlers. After selection of team, they
played the match and won the trophy. Identify the value shown by the members of a cricket team?
Or
A box contains 5 different red and 6 different white balls. In how many ways can 6 balls be
selected so that there are atleast two balls of each colur?
Q28. Evaluvate : lim
x  10
7  2x 
 5  2
x 2  10
Or
( x  h) 2 sin( x  h)  x 2 sin x
h 0
h
lim
Q29. Solve the equation z  z  1  2i , where z is a complex number..
Q30.
Find the probility that when a hand of 7 cards is dealt from a well-shuffled deck of 52 cards,It
contains: (i) all 4 kings (ii) exactly 3 kings (iii) at least 3 kings.
Q31.
Calculate the mean and standard deviation for the following data :
Wages upto (Rs.)
15 30 45 60 75 90 105 120
Number of workers 12 30 65 107 157 202 222 230
Section D
Q32. How many litres of water will have to be added to 1125 litres of the 45% solution of acid so
that the resulting mixture will contain more than 25% but less than 30% acid content?
 
3  
5  
7  1

Q33. Prove that : 1  cos 1  cos   1  cos
 1  cos

8 
8 
8 
8  8

Or
If  ,  are the roots of a cos  b sin   c, show that, cos (   ) 
a 2  b2
a 2  b2
Q34. Find the direction in which a straight line must be drawn through the point  1, 2  so that
its point of intersection with the line x  y  4 may be at a distance of 3 units from this point.
Or
A ray of light passing through the point (1, 2) reflects on the x-axis at point A and the reflected
ray passes through the point (5, 3). Find the coordinates of A.
Q35. Let S be the sum, P the product and R the sum of reciprocals of n terms in a G.P. Prove that
S
P  
R
n
2
Section E
Q36. Raveena , a class 12 student invited her friends Bharti , Ravi , Aarush and Ekta for her birthday
party . After cutting cake they all want to take a group photograph sitting in a row.
Based on the given information , answer the following questions .
(i)
Find the number of distinct photographs that can be clicked .
(ii)
In how many of the photographs Raveena be sitting in middle ?
(iii) If Ekta can sit on any place except the middle one , then how many distinct photographs
are possible ?
(iv)
If Raveena wants to be on left corner and Bharti on right corner that the total number
photo graphs.
Q37. Consider the graphs of the functions f  x  , h  x  and g  x 
(a)
Find the range of h  x  .
(b)
Find the domain of f  x  .
(c)
Find the value of f (10).
(d)
Find the range of g  x 
Q38. Read the text carefully and answer the questions :
Four friends Seema , Meena , Rekha and Heena are playing cards Seema , shuffling cards and
told to Rekha choose any four cards .
(i)
(ii)
(iii)
What is the probability that Rekha getting all face card ?
What is the probability that Rekha getting two red cards and two black cards .
What is the probability that Rekha getting one card from each suit ?
OR
What is the probability that Rekha getting two king and two jack cards ?
ANSWERS
Q1.
(b)
Q2.
(c)
Q3.
(a)
Q4.
(c)
Q5.
Q8.
(d)
Q9.
(c)
Q10. (d)
Q11.
(c)
Q12. (b)
Q13. (d)
Q16. (c)
Q17. (c)
Q18. (d)
Q19. (b)
Q20. (a)
Q15. (b)
Q21.
(c)
Q6.
(c)
Q14. (b)
2 x log x  2 x  log x   x
2
1 4 3i

49
49
Q22.
Domain  R , Range =  ,3
or  sin 2x
Q24.
3
2
Q25.
2
7
Q26.
x2  y2  2 x  4 y  4  0
Q28.
x 2 cos x  2 x sin x
Q29.
z
Q27. 3960 ways or 425
Q30. (i).
1
9
46
(ii).
(iii).
7735
1547
7735
(d)
Q7.
Q23.
Q31. 60.65 and 25.88
1  log x 
2
3
 2i
2
Q32. (562.5 , 900)
 13 
Q34. The line is parallel to x-axis or parallel to y-axis or  ,0 
5 
KISHORE WADHWA’S MATHS CLASSES (K.W.M.C)
CONTACT 8750-8750-80
Contact no. 8750-8750-80
KISHORE WADHWA’S MATHS CLASSES (K.W.M.C)
CONTACT 8750-8750-80
SAMPLE PAPER 5
Section A
Q1.
Slope of a line perpendicular to the line 3 x  y  7 , is
(a)
Q2.
3
(b)
3
(c)
7
12
(c)

1
3
(d)
1
3
(d)
5
12
Radian measure of 75 is
(a)
3
4
(b)

5
Q3.
Mean and variance of 100 observations are 50 and 16 , respectively. The sum of the squares of
all the observations is
(a)
25000
(b)
251600
(c)
26000
(d)
256100
Q4.
If a, b, c are in geometric progression, then
(b)
(a)
2b  a  c
b2  a  c
Q5.
Q7.
 7,8
(c)
 6,9 
(d)
Eccentricity of the parabola y 2  12 x
(a)
12
(b)
3
(c)
1
(d)
(b)
 5,5
(b)
 1,1
 1 1
  5 , 5 
(c)
Value (s) of θ,θ   0, 2  for which the complex no .
(a)
Q9.
 6,9
6,9
4
If f  x   3cos x  4sin x , then the range of the function f  x  is
(a)
Q8.
b2  a  c
(d)
Given that A   x : x  R, x  6 and B   x : x  R, x  9 . Then, A  B 
(a)
Q6.
a2  b  c
(c)
 7
4
,
4
(b)
 3
,
2 2
(c)
(d)
 0,5
1  i cos θ
is purely real , is
1  2i cos θ

2
only
(d)
 only
Consider the data : 3, 3, 4, 5, 7, 9, 10, 12, 18, 19, 21 .Let di  xi  M be the respective
deviations from the median . Then  di 
(a)
60
(b)
72
(c)
16
(d)
58
Q10. In the expansion of  x 2  4 x  4  , the coefficient of fifth term is
20
(a)
Q11.
Q12.
Q14.
Q15.
C 4  2  x 36
4
(b)
40
C4  2 
4
(c)
40
C5  2 
5
(d)
40
C4  2  x4
36
Let A be an infinite set and A1 , A 2 , A 3 ,.., A n be the sets such that A1  A 2  A3  ...  A n  A.
Then
(a)
at least one of the sets A i is infinite
(b)
not more than one of the sets A i can be infinite
(c)
at least one of the sets A i is a finite set
(d)
not more than one of the sets A i can be finite
Let y  5  x  2 . Then
(a)
Q13.
40
y   ,5
(b)
y  5,  
(c)
y   ,5
(d)
y   5,  
A committee of two persons is selected from 2 men and 2 women. The probability that the commit
tee will have no man , is
(a)
1
6
If y 
x
a
dy


, then 2 xy
a
x
dx
(a)
x a

a x
(b)
2
3
(c)
5
6
(d)
1
3
(b)
x a

a x
(c)
a x

x a
(d)
0
(b)
16
(c)
3
112
(d)
3
7
x3  8

lim 7
x  2 x  128
(a)
0
Q16. If x, y and z are in the geometric progression, then which of the following is true ?
(a)
2y  x  z
(b)
y 2  xz
(c)
x
yz
2
(d)
y
z
x
Q17. Distance of a point P  x, y, z  from origin is given by
(a)
x2  y2
(b)
x yz
(c)
1
3
(c)
x 2  y 2  z 2 (d)
x2  y 2  z 2
Q18. Value of tan 570 is
(a)
1
3
(b)

 3
(d)
3
Following are Assertion - Reason based questions .
In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R).
Choose the correct answer out of the following choices .
(a)
Both A and R are true and R is the correct explanation of A .
(b)
Both A and R are true and R is not the correct explanation of A .
(c)
A is true but R is false .
(d)
A is false but R is true .
Q19.
Assertion (A) : For the set X   x : x  N, x  5 x  6  0 , n  X   2 .
2
Reason (R) : If Y   p, q, s, t , u, v, w , then n  Y   7 .
Q20.
Assertion (A) : Additive inverse of a complex number 3  4i is  3  4i .
Reason (R) : For a complex number x  iy , Real Part is x and Imaginary Part is iy .
Section B
Q21. Find the values of x for which the functions f ( x)  3 x 2  1 and g ( x )  3  x are equal.
Q22. What are the real numbers ‘x’ and ‘y’ if  x  iy   3  5i  is the conjugate of  1  3i  ?
Q23. The cost and revenue functions of a product are given by C ( x )  20 x  4000 and
R ( x )  60 x  2000, respectively, where x is the number of items produced and sold .How many
items must be sold to realise some profit?
Q24. In how many ways can the word PENCIL be arranged so that N is always next to E?
Q25. A box contains 30 bolts and 40 nuts. Half of the bolts and half of the nuts are rusted. If one
item is drawn at random, what is the probability that either it is rusted or is a bolt ?
Section C
Q26. Find the domain and range of : f (x) =
x 2  16 .
Or
Find the domain and range of : f ( x ) 
3x  1
x5
Q27. In what ratio, is the joining  1,1 and (5, 7) divided by the line x  y  4 ?
cos A  c
A
1 c
B

tan show that cos B =
1  c cos A.
2
1 c
2
Or
If a cos 2  b sin 2  c has  and  as its roots, then prove that
Q28. If tan,
tan   tan  
(i)
2b
ac
(ii)
tan  tan  
ca
ca
tan     
(iii)
b
a
Q29. Find the coordinates of a point on y-axis which is at a distance of 5 2 from the point (3, 2, 5).
Q30.
For the function f ( x) 
x100 x 99
x2

 ....  x  1, prove that f '(1)  100 f '(0).
100 99
2
Or
Find the derivative of the functions w.r.t.x :
Q31.
sin x  cos x
sin x  cos x
Find the number of arrangements of the letters of the word INDEPENDENCE. In how many of
these arrangements do all the vowels always occur together ?
Section D
Q32. Prove that the product of the lengths of perpendiculaars drawn from the points


2
2
and  a  b , 0 to the line
 a  b , 0
2
2
x
y
cos   sin   1 is b 2
a
b
Q33. Clculate mean, variation and standard derviation of the following frequency distribution:
Classes
1  10 11  20
21-30
31-40
41-50
51  60
Frequency
11
29
18
4
5
3
 8x  4 x  2 x  1 
lim
Q34. Evaluate : x0 

x tan x


Or


cos 2 x
lim
: x / 2 

 2  1  sin x 
Q35. Let R be a relation from N to N defined by R   a, b  : a, b  N and a  b  . Are the following
2
true?
(a)
( a, a )  R for all a  N
(b)
 a, b   R implies that  b, a   R
(c)
 a, b   R and  b, c   R implies  a, c   R
Justify your answer in each case.
Section E
Q36. The cable of the uniformly loaded suspension bridge hangs in the form of a parabola. The
roadway which is horizontal and 100 m long is supported by vertical wires attached to the
cable, the longest wire being 30 m and the shortest being 6 m.
(i)
(ii)
Find the length of latus rectum
Find the length of a supporting wire attached to the roadway 18 m from the middle.
Q37. In drilling world’s deepest hole , it was found that the temperature T in degree Celsius , x
below the surface of Earth , was given by : T  30  25  x  3 ,3  x  15 . If the required tem
perature lies between 200 C and 300 C, then
(i)
(a)
(c)
The depth , x will lie between
9 km and 13 km
(b)
9.8 km and 13.8 km
9.5 km and 13.5 km (d)
10 km and 14 km
(ii)
(a)
(c)
Solve for x  9 x  2  18 or 13x  15  4
(b)
x  1913
x  1613
(d)
There
are no solution
1613  x  1913
(iii)
If x  5 then the value of x lies in the interval
(a)
 , 5
(b)
 ,5
(c)
 5,  
(d)
 5,5
Q38. The number of bacteria in a certain culture doubles every hour . Given that the number of
bacteria present at the end of fourth hour was 150000 .
On the basis above information , answer the following questions .
(i)
The number of bacteria present originally was
(ii)
The number of bacteria present at the 7th hour was
(iii) The sum of number of bacteria present at the beginning to the end of 8th hour
(iv)
If the number of bacteria triples every hour , then the number of bacteria present at the
ANSWERS
Q1.
(d)
Q2.
(d)
Q3.
(b)
Q4.
(d)
Q5.
Q8.
(b)
Q9.
(d)
Q10. (b)
Q11.
(a)
Q12. (c)
Q13. (a)
Q16. (b)
Q17. (c)
Q18. (a)
Q19. (d)
Q20. (c)
x  50
Q24.
Q15. (c)
Q21.
x  1, 4 / 3
Q25.
5
7
Q27. 1 : 2
Q22.
x
6
7
,y
17
17
Q23.
(c)
Q6.
(c)
Q7.
(a)
Q14. (b)
5 ! ways
Q26. Domain  , 4    4,   , Range  0,   or Domain R  5 , Range R  {3}
Q29.
 0, 2,0  and  0, 6, 0 
Q33. 21.5 , 161, 12.7
Q34.
2sin 2 x
Q30.
 sin x  cos x 
 log 4  log 2  or 4 2
KISHORE WADHWA’S MATHS CLASSES (K.W.M.C)
2
Q31.
1663200
Q36. (ii) 9.11 m (approx.)
CONTACT 8750-8750-80
Contact no. 8750-8750-80
KISHORE WADHWA’S MATHS CLASSES (K.W.M.C)
CONTACT 8750-8750-80