Summer Vacations
Assignment
Class: - X
Maths
Chapter:
- Polynomials
1. If 
and 
are the zeroes of the quadratic eqn. 
,
Find the value of ‘a’ If 
and are the zeroes of the quadratic eqn. ,
Find the value of ‘a’ If
2. If 
are the zeroes of p(x) = 
,
then find the value of
.
are the zeroes of p(x) = ,
then find the value of.
3. Find the quad.
Polynomial with zeroes
.
.
4. For what value of k, -4 is a zero of p(x) =
.
.
5. Find a quad. Polynomial
whose zeroes are
.
.
6. Form a quad. Poly.
Whose one zero is 8 and the product of zeroes is -56.
7. If the poly.
Is
divided by another poly. 
, the remainder comes out to be ax + b. Find a & b.
Is
divided by another poly. , the remainder comes out to be ax + b. Find a & b.
8. If 
are the two zeroes of poly. 
,
Find a quad. Poly. Whose zeroes are 
.
are the two zeroes of poly. ,
Find a quad. Poly. Whose zeroes are .
9. If 2 & -3 are the zeroes of quad. Poly. 
,
Find the values of a & b.
,
Find the values of a & b.
10. Obtain all the zeroes
of 
.
.
11. On dividing 
by
poly. P(x), the quotient and remainder
are 
resp. Find p(x).
by
poly. P(x), the quotient and remainder
are resp. Find p(x).
12. On dividing 
by the poly.
g(x) the quotient and remainder were
resp. Find
g(x).
by the poly.
g(x) the quotient and remainder were
resp. Find
g(x).
13. Find the value of a & b so that the poly. P(x) =
is
exactly divisible by 
.
is
exactly divisible by .
14. What must be added to
polynomial; 
so
that the resulting polynomial is exactly divisible by 
.
so
that the resulting polynomial is exactly divisible by .
15. If
are the zeroes of the quad. Poly.
f(x) = 
such that 
,
find the value of k .
are the zeroes of the quad. Poly.
f(x) =
such that ,
find the value of k .
16. If one of the zero of a
quad. Poly. f(x) = 
is the –ive of the other, Find the value of k .
is the –ive of the other, Find the value of k .
17. If two zeroes of p(x) =
are
2
,
Find the other zeroes.
are
2 ,
Find the other zeroes.
18.
If the sum of zeroes of a given polynomial f(x) =
-3k
-x+30 is 6. Find the value of K.
-3k -x+30 is 6. Find the value of K.
19.
Form a cubic polynomial with zeroes 3, 2 and -1.
20.
Give an example of polynomials
p(x),g(x),q(x),r(x) which satisfies division algorithm and deg. p(x)= deg. g(x)
21.
Check whether the polynomial 
-3 is a factor of polynomial 2
+ 3
- 2 -9t –12 by applying division algorithm.
-3 is a factor of polynomial 2 + 3 - 2 -9t –12 by applying division algorithm.
22.
If a and b are the zeroes of the polynomial k +4x+4 show that find the value of 
+ 
+4x+4 show that find the value of
+
23.
Obtain all other zeroes of 3
+6
-2 -10x-5 if two of its zeroes are 
and -
+6-2 -10x-5 if two of its zeroes are and -
24.
Find a quadratic polynomial, the sum
and product of whose zeroes are 
and - 
respectively. Also find its zeroes.
and - respectively. Also find its zeroes.
25.
If the remainder on division of + 2 +kt +3 by k-t is 21,find the quotient and the
value of k. hence, find the zeroes of the cubic polynomial + 2 +kt -18
+ 2 +kt +3 by k-t is 21,find the quotient and the
value of k. hence, find the zeroes of the cubic polynomial + 2 +kt -18
26.
If a and b are zeroes of 6 +x-2=0 find
+ 
+x-2=0 find
+
27.
Find the
zeroes of 4 + 8x
+ 8x
Chapter – 3
28. Draw the graph of the
pair of eqns. 2x + y = 4 & 2x – y =
4. Write the vertices of the triangle formed by these lines and the y- axis. Also
find the area of the triangle.
29. For what value of k 2x + 3y =4 & (k + 2) x + 6y = 3k + 2
will have infinitely many soln.
30. For what value of p will
the following system of eqns. Have no soln. (2p
– 1) x + (p – 1) y = 2p + 1 & 3x
+ y = 1.
31. For which value of p
& q will the following pair of linear eqns. Have
infinite no. Of soln. 4x + 5y =
2 & (2p + 7q) x + (p + 8q) y = 2q – p + 1.
32. Find the value of a
& b for which the system of linear eqns. Has
infinite no. Of solution (a + b)x –
2by =
5a + 2b + 1 & 3x – y
= 14.
33. For which values
of p
& q will the following pair of linear eqns. Have infinitely many solutions. (p – 1) x + 3y = 2 & 6x + (2 – q) y = 6.
34. Find the soln. of the pair of eqns. 
& 
. Hence, find 
if
y = λx + 5.
& . Hence, find if
y = λx + 5.
35. Solve x + y = a – b &
ax – by = 
.
.
36. The annual incomes
of A & B are in the ratio of 5: 4 & their monthly expenditure are in
the ratio 7: 5. If each saves Rs. 3000
per month. Find the monthly income of each.
37. If 2x + y =23
& 4x – y = 19. Find the values of
5y – 2x & 
.
.
38. Solve 2(3u – v) = 5uv &
2(u + 3v) = 5uv.
39. It can take 12 hrs to
fill a swimming pool using two pipes. If the pipe of larger diameter is used
for 4 hrs and the pipe of smaller diameter is used for 9 hrs. , only half of
the pool is filled. How long would it take for each pipe to fill the pool separately?
40. 8 men
& 12 boys can finish a piece
of work in 10 days while
6 men &
8 boys can finish in 10 days. Find the time taken by one man alone and
that by one boy alone to finish the work.
41. Solve 
.
.
42.
Find the value of ‘a’ so that the point(3,9) lies
on the line represented by 2x-3y=5
43.
Find the value of k so that the lines 2x – 3y = 9
and kx-9y =18 will be parallel.
44.
Determine the value of ‘a’ if the system of
linear equations 3x+2y -4 =0 and 9x – y – 3 = 0 will represent intersecting
lines
45.
Write any one equation of the line which is
parallel to 2x – 3y =5
46.
Solve the equation:
px + qy = p – q
qx – py = p + q.
47.
Solve the equations by using the method of cross
multiplication:
x + y =7
5x + 12y =7
48.
A man has only 20 paisa coins and 25 paisa coins
in his purse, if he has 50 coins in all totalling Rs. 11.25, how many coins of
each kind does he have.
49.
Draw the graphs of the equations
4x – y = 4
4x + y = 12
Determine the vertices of
the triangle formed by the lines representing these equations and the x-axis. Shade the
triangular region so formed.
50.
Solve Graphically
x – y = -1 and
3x + 2y = 12
Calculate the area bounded
by these lines and the x- axis .
51.
Students of a class are made to stand in rows. If
one student is extra in a row, there would be 2 rows less. If one student is
less in a row there would be 3 rows more. Find the number of the students in
the class.
QUADRATIC EQUATION
52.
find the values of k for which the given
equation has real roots:
a) kx² − 6x –2 = 0 b) 9x² + 3k x
+4 = 0 c) 5x² − kx +1 =
0
53.
Determine the positive values of k for which the equations x² + kx +64 = 0 and
x² − 8x +k = 0 will both have real
roots.
54.
If –5 is a root of quadratic equation 2x² +
px –15 = 0 and the Q.E p(x²+x)+ k = 0 has
equal roots.
55.
A two
digit number is such that the product of its digits is 14. When 45 is added to the
number, then the digits interchange their places. Find the number.
56.
A two digit number is seven times the sum of
its digits is also equal to 12 less than three times the product of its digits.
Find the number.
57.
300
apples are distributed equally among a certain number of students. Had there
been 10 more students, each would have received one apple less. Find the number
of students.
first train travels 5km/hr faster than
the second train. If after two hours they are 50km
apart. Find average speed of each train.
58.
A chess
board contains 64 equal squares and area of each square is 6.25 cm². A border round
the board is 2cm wide. Find the length of the side of chess board.
59.
A person on tour has Rs.360 for his expenses. If
he extends his tour for 4 days, he has to cut down his daily expenses by Rs.3.
Find the original duration of the tour.
60.
Rs.6500
were divided equally among a certain number of persons. Had there been 15 more
persons, each would have got Rs 30 less. Find the original no of persons.
61.
Had Ajita scored 10 more
marks in her mathematics test out of 30 marks, 9 times these marks would have
been the square 11. The denominator of a fraction is one more
than twice the numerator. If the sum of the fraction and its reciprocal is 2
16/21, find the fraction.
62.
. A chess board contains 64 equal
squares and area of each square is 6.25 cm². A border round the board is 2cm
wide. Find the length of the side of chess board.
63.
A person
on tour has Rs.360 for his expenses. If he extends his tour for 4 days, he has
to cut down his daily expenses by Rs.3. Find the original duration of the tour.
64.
Rs.6500
were divided equally among a certain number of persons. Had there been 15 more
persons, each would have got Rs 30 less. Find the original no of persons.
65.
Had Ajita scored 10 more
marks in her mathematics test out of 30 marks, 9 times these marks would
have been the square of her actual
marks. How many marks did she get in the test?
66.
A train travels at a certain average speed for a distance
of 63 km and then travels a distance of 72 km at an average speed of 6 km/h more than its
original speed. If it takes 3 hours to complete the total journey,what is its
original average speed?
67.
Find a natural number
whose square diminished by 84 is equal to thrice of 8 more than the given
number.
68.
A natural number, when
increased by 12, equals 160 times its reciprocal. Find the number.
69.
8. A train, travelling at
a uniform speed for 360 km, would have taken 48 minutes less to travel the same
70.
distance if its speed were 5 km/h more.
Find the original speed of the train.
71.
If Zeba were younger by 5 years than what she
really is, then the square of her age (in years) would have been 11 more than
five times her actual age. What is her age now?
72.
At present Asha’s age (in years) is 2 more
than the square of her daughter Nisha’s age. When Nisha grows to her mother’s
present age, Asha’s age would be one year less than 10 times the present age of
Nisha.Find the present ages of both Asha and Nisha.
PROBABILITY
73. A die is
thrown once. Find ( a) P( a number ≥ 3)
(b) P ( a number < 7)
(c) P(odd
number) (d) P(prime number) (e) P( between 2 and 6)
74. In a single
throw of two dice what is the probability of getting
(a) both odd
numbers (b) a total of 9 or 11 (c) same no. on both the dice( doublet)
(d) the sum
of nos. as whole no. (e) the sum of
nos. as prime nos.
(f) prime as
a whole (g) sum of nos. less than 9 (h) sum more than 9
(i) number
as a whole divisible by 2 and 3 (j)
number as a whole divisible by 2 or 3
75. One card is
drawn from a well shuffled deck of 52 cards . Find the probability of
Drawing:- (a)
an ace (b) a jack (c) red face card
(d) black queen (e) red
card (f) 10 of
black suit
(g) 7 of club (h) a
diamond face card (i) non ace non
face card
(j) a heart (k) non face card (l) a king or a queen
(m) neither king nor a queen (n) a card of spades or
an ace
(o) a face card (p) neither a red face card nor queen
76 The king ,
queen and jack of clubs are removed from a pack of 52 playing cards. The
remaining cards are then well shuffled and one card is selected at random. Find
the probability of getting
(a) a heart (b)
a king (c) a club (d) the 10 of hearts
77. All the three
face cards of spades are removed from a well shuffled pack of 52 cards
A card is
drawn at random from the remaining pack . find the probability of getting
(a) a black
face cards (b) a queen (c) a black card
78. Two unbiased
coins are tossed. Find the probability of getting
(a) exactly
two head (b) exactly one
tail (c) at least
two tails
(d) at most
two tails (e) not less than one
head( or at least one head) (f) no
tail
79. Three coins
are tossed simultaneously. Find the probability of getting
(a) head and
tail alternately (b) at least two
head (c) at most one head
80. In a family,
there are three children. Assuming that chances of a child being a male or
a female are
equal. Find the probability that (a) there is one girl in a family (b) there is no female child
in the family (c) there is at least one male child in the family
81. What is the
probability of having 53 Tuesdays in a (a) non-leap year (b) leap year?
82. If the probability of winning the game is 5/11. What
is the probability of losing?
83. Savita and Hamida are friends . What is the
probability that both will have
(a) different
birthday ? (b) the same
birthday?
84. A box contains cards bearing numbers from 6 to 70. If
one card is drawn at random
from the box,
Find the probability that it bears
(a) one digit numbers
(b) no.
divisible by 5
(c) no. divisible by 3 and 5
(d) no. divisible by 3 or 5
(e) no. which is perfect square
85. A box contains 20 balls bearing numbers
1,2,3,4,…….20, A ball is drawn at random
from the box.
What is the probability that the no. on the ball is
(a) an odd
no. (b) divisible by 2or 3 (c) prime no. (d) not divisible by 10?
86. A bag contains 5 white balls, 7 red balls, 4 black
balls and 2 blue balls. One ball is
Drawn at
random from the bag. What is the probability that the ball drawn is
(a) white or
blue (b) red or black (c) not white (d) neither white nor black
87. Two customers are visiting a particular shop in the
same week( Monday to Saturday)
Each is
equally likely to visit the shop on any one day as on another. What is the
probability
that both will visit the shop on (i) the same day (ii) different days
(iii)
consecutive days
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