Preparation Mathematics 10 for 2014-15
You have four choices for each objective type question as A, B, C and D. The choice which you think is
correct; fill that circle in front of that question number. Use marker or pen to fill the circles. Cutting or filling
more than two circles will result in zero mark in that question.
1
a)
Standard form of Quadratic Equation is
𝒃𝒙 + 𝒄 = 𝟎, 𝒃 ≠ 𝟎
2
1
a) 𝒙 =
5
1
−𝒃±√𝒃𝟐 −𝟒𝒂𝒄
𝟐𝒂
a)
9
a)
11
2
c)
3
d)
4
b)
3
c)
4
d)
5
b) 𝒙 =
𝒃±√𝒃𝟐 −𝟒𝒂𝒄
𝟐𝒂
c) 𝒙 =
−𝒃±√𝒃𝟐 +𝟒𝒂𝒄
𝟐𝒂
d) 𝒙 =
𝒃±√𝒃𝟐 +𝟒𝒂𝒄
𝟐𝒂
b) (𝒙 + 𝟕) and (𝒙 − 𝟖)
c) (𝒙 − 𝟕) and (𝒙 − 𝟖)
d) (𝒙 + 𝟕) and (𝒙 + 𝟖)
𝟏
b) Reciprocal equation
c) Radical equation
d) None of these
An equation of the type 𝟑𝒙 + 𝟑𝟐 − 𝒙 + 𝟔 = 𝟎 is a/an
b) Radical equation
c) Reciprocal equation
d) None of these
The solution set of equation 𝟒𝒙𝟐 − 𝟏𝟔 = 𝟎 is
{± 𝟒}
b)
{𝟒}
c)
{+ 𝟐}
d)
+2
An equation of the form 𝟐𝒙𝟒 − 𝟑𝒙𝟑 + 𝟕𝒙𝟐 − 𝟑𝒙 + 𝟐 = 𝟎 is called a/an
a) Reciprocal equation
10
b)
An equation, which remains unchanged when 𝒙 replaced by is 𝒙 is called
a) Exponential equation
8
𝒂𝒙𝟐 = 𝟎, 𝒂 ≠ 𝟎
Two linear factors of 𝒙𝟐 − 𝟏𝟓𝒙 + 𝟓𝟔 are
a) Exponential equation
7
d)
The Quadratic Formula is
a) (𝒙 − 𝟕) and (𝒙 + 𝟖)
6
𝒂𝒙𝟐 = 𝒃𝒙, 𝒂 ≠ 𝟎
The number of methods to solve quadratic equation is
a)
4
c)
The number of terms in standard quadratic equation 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄 = 𝟎 is
a)
3
b) 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄 = 𝟎,
𝒂≠𝟎
b) Radical equation
c) Exponential equation
d) None of these
If 𝜶, 𝜷 are the rots of 𝟑𝒙𝟐 + 𝟓𝒙 − 𝟐 = 𝟎, then 𝜶 + 𝜷 is
𝟓/𝟑
b)
𝟑/𝟓
c)
If 𝜶, 𝜷 are the rots of 𝟕𝒙𝟐 − 𝒙 + 𝟒 = 𝟎, then 𝜶𝜷 is
−𝟓/𝟑
d)
−𝟐/𝟓
−𝟏/𝟕
a)
12
𝟎
𝟎
𝟏
𝜶
𝟏
+𝜷
𝟏
𝜶
−𝟏
d)
𝟑
c)
−𝟏
d)
𝟑
c) Imaginary
d) None of these
c) Imaginary
d) None of these
𝟏
b)
𝜶
𝟏
−𝜷
c)
𝜶−𝜷
𝜶𝜷
d)
𝜶+𝜷
𝜶𝜷
𝜶𝟐 + 𝜷𝟐 is equal to
b)
𝟏
𝜶𝟐
𝟏
+ 𝜷𝟐
c) (𝜶 + 𝜷)𝟐 − 𝟐𝜶𝜷
d) 𝜶 + 𝜷
c) 𝟏, −𝝎
d) 𝝎, 𝝎𝟐
c) imaginary
d) irrational
Two square roots of unity are
b) 𝟏, 𝝎
Roots of the equation 4𝒙𝟐 − 𝟒𝒙 + 𝟏 = 𝟎 are
b) real, unequal
If 𝜶, 𝜷 are the rots of 𝒙𝟐 − 𝒙 − 𝟏 = 𝟎, then the product of the roots 𝟐𝜶 and 𝟐𝜷 is
b) 𝟐
c) 𝟒
d) −𝟒
The nature of roots of equation 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄 = 𝟎 is determined by
a) sum of the roots
24
c)
is equal to
a) −𝟐
23
𝟏
b) Rational
a) real, equal
22
𝟏
If 𝒃𝟐 − 𝟒𝒂𝒄 > 𝟎, then the roots of 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄 = 𝟎 are
a) 𝟏, −𝟏
21
d) 𝟏, −𝝎, −𝝎𝟐
b) Rational
a) 𝜶𝟐 − 𝜷𝟐
20
c) −𝟏, −𝝎, 𝝎𝟐
If 𝒃𝟐 − 𝟒𝒂𝒄 < 𝟎, then the roots of 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄 = 𝟎 are
a)
19
b) −𝟏, 𝝎, −𝝎𝟐
b)
a) Irrational
18
d) None of these
b)
a) Irrational
17
c) Rational
Product of Cube roots of unity is
a)
16
b) imaginary
Sum of Cube roots of unity is
a)
15
−𝟒/𝟕
d)
Cube roots of −𝟏 are
a) −𝟏, −𝝎, −𝝎𝟐
14
𝟕/𝟒
c)
Roots of the equation 𝒙𝟐 − 𝒙 + 𝟒 = 𝟎 are
a) Irrational
13
𝟒/𝟕
b)
b) Product of the roots
The Discriminant of 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄 = 𝟎 is
c) Synthetic division
d) discriminant
a) 𝒃𝟐 − 𝟒𝒂𝒄
b) 𝒃𝟐 + 𝟒𝒂𝒄
a) relation
b) antecedent
a) relation
d) none of these
b) antecedent
c) consequent
d) none of these
c) fourth proportional
d) none of these
c) fourth proportional
d) none of these
In a proportion 𝒂: 𝒃: : 𝒄: 𝒅, 𝒂 and 𝒅 are called
27
a) means
b) extremes
In a proportion 𝒂: 𝒃: : 𝒄: 𝒅, 𝒃 and 𝒄 are called
28
a) means
b) extremes
In continued proportion 𝒂: 𝒃 = 𝒃: 𝒄, 𝒂𝒄 = 𝒃𝟐 , 𝒃 is said to be ---- proportional between 𝒂 and 𝒄
29
a) third
b) fourth
c) means
d) none of these
In continued proportion 𝒂: 𝒃 = 𝒃: 𝒄, 𝒄, 𝒃 is said to be ---- proportional to 𝒂 and 𝒃
30
a) third
b) fourth
c) means
d) none of these
b) 4/3
c) 3/4
d) 12
b) 𝒖 = 𝒌𝒗𝟐
c) 𝒖𝒗𝟐 = 𝒌
d) 𝒖𝒗𝟐 = 𝟏
b) 𝒚𝟐 = 𝒙𝟑
c) 𝒚𝟐 = 𝒙𝟐
d) 𝒚𝟐 = 𝒌𝒙𝟑
b) 𝒖 = 𝒗𝒌𝟐
c) 𝒖 = 𝒘𝟐 𝒌
d) 𝒖 = 𝒗𝟐 𝒌
Find 𝒙 in proportion 𝟒: 𝒙: : 𝟓: 𝟏𝟓
31
a) 75/4
If 𝒖 ∝ 𝒗𝟐 , then
32
a) 𝒖 = 𝒗𝟐
𝟏
33
If 𝒚𝟐 ∝ 𝒙𝟑 then
𝟏
𝒌
a) 𝒚𝟐 = 𝒙𝟑
𝒖
34
𝒗
If 𝒗 = 𝒘 = 𝒌, then
a) 𝒖 = 𝒘𝒌𝟐
The third proportional of 𝒙𝟐 and 𝒚𝟐 is
35
𝒚𝟐
𝒙𝟐
b) 𝒙𝟐 𝒚𝟐
c)
𝒚𝟒
𝒙𝟐
d)
𝒚𝟐
𝒙𝟒
The fourth proportional 𝒘 of 𝒙: 𝒚: : 𝒗: 𝒘 is
36
37
c) consequent
In the ratio 𝒙: 𝒚, 𝒚 is called
26
a)
d) −𝒃𝟐 − 𝟒𝒂𝒄
In a ratio 𝒂: 𝒃, 𝒂 is called
25
a)
c) −𝒃𝟐 + 𝟒𝒂𝒄
𝒙𝒚
𝒗
b)
𝒗𝒚
𝒙
If 𝒂: 𝒃 = 𝒙: 𝒚 then 𝒂𝒍𝒕𝒆𝒓𝒏𝒂𝒏𝒅𝒐 property is
c) 𝒙𝒚𝒗
d)
𝒙
𝒗𝒚
a)
𝒂
𝒙
𝒂
𝒙
39
a)
40
b)
𝒃
=
If
𝒂
𝒂+𝒃
b)
𝒚
𝒂
𝒃
=
𝒄
𝒄+𝒅
a)
48
𝒙+𝒚
d)
𝒚
𝒂−𝒃
𝒙
=
𝒙−𝒚
𝒚
𝒂−𝒃
=
𝒙
c)
𝒙−𝒚
𝒂+𝒃
𝒃
=
𝒙+𝒚
d)
𝒚
𝒃
𝒂
=
𝒚
𝒙
b)
𝒂
𝒂−𝒃
=
𝒄
c)
𝒄−𝒅
𝒂𝒅
d)
𝒃𝒄
𝒂−𝒃
𝒃
=
𝒄−𝒅
𝒅
b) two values of 𝒙
c) all values of 𝒙
d) none of these
c) a fraction
d) none of these
A fraction in which the degree of the numerator is greater or equal to the degree of denominator is
called
b) an improper fraction
c) an equation
d) algebraic relation
A fraction in which the degree of the numerator is less than degree of denominator is called
b) an improper fraction
c) an identity
d) a proper fraction
b) an equation
c) a proper fraction
d) none of these
b) an equation
c) an identity
d) none of these
b) an improper fraction
c) an identity
d) a constant term
𝟐𝒙+𝟏
is
(𝒙+𝟏)(𝒙−𝟏)
(𝒙 + 𝟑)𝟐 = 𝒙𝟐 + 𝟔𝒙 + 𝟗 is
𝒙𝟑 +𝟏
is
(𝒙−𝟏)(𝒙+𝟐)
a) a proper fraction
47
𝒂
b) an equation
a) a linear equation
46
=
𝑵(𝒙)
a) an improper fraction
45
𝒃
A function of the form 𝒇(𝒙) = 𝑫(𝒙), with 𝑫 ≠ 𝟎, where 𝑵(𝒙) and 𝑫(𝒙) are polynomials in 𝒙 is called
a) an equation
44
𝒂+𝒃
The identity (𝟓𝒙 + 𝟒)𝟐 = 𝟐𝟓𝒙𝟐 + 𝟒𝟎𝒙 + 𝟏𝟔 is true for
a) a proper fraction
43
c)
𝒄
a) an identity
42
𝒙
=𝒚
𝒃
= 𝒅 then Componendo property is
a) One value of 𝒙
41
𝒂
If 𝒂: 𝒃 = 𝒙: 𝒚 then 𝒊𝒏𝒗𝒆𝒓𝒕𝒆𝒏𝒅𝒐 property is
38
a)
𝒃
=𝒚
Partial fraction of
𝑨
𝒙−𝟏
+
𝑩
𝒙+𝟐
𝒙−𝟐
are of the form
(𝒙−𝟏)(𝒙+𝟐)
b)
𝒙−𝟐
𝑨𝒙
𝒙−𝟏
+
𝑩
𝒙+𝟐
Partial fraction of (𝒙+𝟏)(𝒙𝟐 +𝟐) are of the form
c)
𝑨
𝒙−𝟏
+
𝑩𝒙+𝑪
𝒙+𝟐
d)
𝑨𝒙+𝑩
𝒙−𝟏
+
𝑪
𝒙+𝟐
a)
49
𝑨
+ 𝒙𝟐 +𝟐
𝑨
𝒙+𝟏
𝑩
+ 𝒙−𝟏
a)
57
a)
58
a)
59
a)
60
a)
61
+ 𝒙𝟐 +𝟐
𝑨
𝑩
𝑨
d)
𝑩𝒙
𝒙+𝟏
+ 𝒙𝟐 +𝟐
𝑨
𝟏+
𝒙+𝟏
+
𝑩𝒙+𝑪
𝒙−𝟏
c)
𝟏 + 𝒙+𝟏 + 𝒙−𝟏
d)
𝑨𝒙+𝑩
𝒙+𝟏
𝑪
+ 𝒙−𝟏
c) set
d) none of these
b) Natural Numbers
c) Irrational Numbers
d) Rational Numbers
The different number of ways to describe a set are
1
b)
2
c)
3
d)
4
A set with no elements is called
b) empty set
c) singleton set
d) super set
c) Null Set
d) Finite Set
c) Singleton set
d) Subset
The set {𝒙|𝒙 ∈ 𝑾 ˄ 𝒙 ≤ 𝟏𝟎𝟏} is
b) Subset
The set having only one element is called
a) Null set
56
𝑪
𝒙+𝟏
𝒂
a) Infinite Set
50
b)
b) power set
a) subset
55
𝑨𝒙+𝑩
c)
A set 𝑸 = {𝒃 |𝒂, 𝒃 ∈ 𝒁 ˄ 𝒃 ≠ 𝟎} is called a set of
a)
54
𝑩𝒙+𝑪
+ 𝒙𝟐 +𝟐
A collection of well-defined object is called
a)Whole numbers
53
𝑨
𝒙+𝟏
𝒙𝟐 +𝟏
a) subset
52
b)
Partial fractions of (𝒙+𝟏)(𝒙−𝟏) are of the form
a)
51
𝑩
𝒙+𝟏
b) Power set
The power set of an empty set is
∅
b)
{𝒂}
c)
{∅, {𝒂}}
d)
{∅}
6
c)
8
d)
9
B
c)
∅
d)
none of these
B
c)
∅
d)
none of these
B
c)
∅
d)
𝑩−𝑨
The number of elements in power set {𝟏, 𝟐, 𝟑} is
4
b)
If 𝑨 ⊆ 𝑩, then 𝑨𝑼𝑩 is equal to
A
b)
If 𝑨 ⊆ 𝑩, then 𝑨 ∩ 𝑩 is equal to
A
b)
If 𝑨 ⊆ 𝑩, then 𝑨 − 𝑩 is equal to
A
b)
(𝑨 ∪ 𝑩) ∪ 𝑪 is equal to
a)
𝑨 ∩ (𝑩 ∪ 𝑪)
62
𝑨 ∪ (𝑩 ∩ 𝑪) is equal to
a) (𝑨 ∪ 𝑩) ∩ (𝑨 ∪ 𝑪)
63
a)
64
a)
65
a)
66
a)
67
a)
68
a)
69
a)
65
a)
70
a)
b)
b)
(𝑨 ∪ 𝑩) ∩ 𝑪
c)
𝑨 ∩ (𝑩 ∩ 𝑪)
c) (𝑨 ∩ 𝑩) ∪ (𝑨 ∩ 𝑪)
d)
𝑨 ∩ (𝑩 ∩ 𝑪)
d)
𝑨 ∪ (𝑩 ∪ 𝑪)
d)
𝑩∪𝑨
If 𝑨 and 𝑩 are disjoint sets, then 𝑨 ∪ 𝑩 is equal to
A
b)
B
c)
∅
If number of elements in a set 𝑨 is 3 and in set 𝑩 is 4, then number of elements in 𝑨 × 𝑩 is
3
b)
4
c)
12
d)
7
If number of elements in a set 𝑨 is 3 and in set 𝑩 is 2, then number of binary relations in 𝑨 × 𝑩 is
𝟐𝟑
𝟐𝟔
b)
𝟐𝟖
d)
𝟐𝟐
c)
{𝟎, 𝟐, 𝟒}
d)
{𝟐, 𝟑, 𝟒}
c)
{𝟏, 𝟐, 𝟑, 𝟒}
d)
{𝟏, 𝟑, 𝟒}
c)
𝑰𝑰𝑰
d)
𝑰𝑽
c)
not a function
c)
The domain of 𝑹 = {(𝟎, 𝟐), (𝟐, 𝟑), (𝟑, 𝟑), (𝟑, 𝟒)} is
{𝟎, 𝟑, 𝟒}
b)
{𝟎, 𝟐, 𝟑}
The range of 𝑹 = {(𝟏, 𝟑), (𝟐, 𝟐), (𝟑, 𝟏), (𝟒, 𝟒)} is
{𝟏, 𝟐, 𝟒}
b)
{𝟑, 𝟐, 𝟒}
Point (−𝟏, 𝟒) lies in the quadrant
𝑰
𝑰𝑰
b)
The relation {(𝟏, 𝟐), (𝟐, 𝟑), (𝟑, 𝟑), (𝟑, 𝟒)} is
onto function
b)
into function
d) one-one function
The group frequency distribution is also called
data
b)frequency distribution
c) frequency polygon
d)
none of these
c)
circles
d)
triangles
c)
square
d)
triangle
A histogram is a set of adjacent
squares
b)
rectangles
71
A frequency polygon is a many sided
a)
close figure
72
A cumulative frequency distribution is also called
a)frequency distribution
73
𝑨 ∪ (𝑩 ∪ 𝑪)
b)
b)
rectangle
data
c)less than
distribution
A cumulative frequency polygon frequencies are plotted against
frequency d)
none of these
a)
mid points
74
Arithmetic mean is a measure that determines a value of the variable under study by dividing the
sum of all values of the variable by their
a)
75
a)
76
a)
77
a)
78
a)
79
a)
80
a)
81
a)
83
number
a)
85
a)
86
a)
87
b)
group
c)
c)
class limits
denominator
d)
none of these
d)
none of these
sum
d)
none of these
histogram
d)
none of these
A Deviation is defined as a difference of any value of the variable from a
constant
b)
histogram
c)
A data in the form of frequency distribution is called
grouped data
b) ungrouped data
c)
Mean of a variable with similar observations say constant 𝒌 is
negative
b)
𝒌 itself
c)
zero
d)
none of these
ratio
c)
origin
d)
none of these
scale
c)
rate
d)
none of these
d)
none of these
Mean is affected by change in
value
b)
Mean is affected by change in
place
b)
Sum of the deviations of the variable X from its mean is always
zero
b)
one
c)
same
The 𝒏𝒕𝒉 positive root of product of the 𝒙𝟏 , 𝒙𝟐 , 𝒙𝟑 , − − −−, 𝒙𝒏 observations is called
mode
b)
mean
c)
geometric mean
d)
none of these
The value obtained by reciprocating the mean of the reciprocal of 𝒙𝟏 , 𝒙𝟐 , 𝒙𝟑 , − − −−, 𝒙𝒏 observations
is called
a) geometric mean
84
b)upper class boundaries
b)
median
c)
harmonic mean
d)
none of these
The most frequent occurring observation in a data set is called
mode
b)
median
c)
harmonic mean
d)
none of these
The measure which determine the middlemost observation in a data is called
average
b)
dispersion
c) central tendency
d)
none of these
d)
none of these
The observation that divide data into four equal parts are called
Deciles
b)
quartiles
c)
percentiles
The spread or scatterness of observation in a data set is called
a)
88
a)
89
average
dispersion
a)
92
c) central tendency
d)
average
b) central tendency
c)
average
d)
b)
range
c)
quartile
d)
variance
b) standard deviation
c)
range
d)
harmonic mean
b)
range
c) standard deviation
none of these
d)
a radian
The union of two non collinear rays, which have common end point is called
an angle
b)
a degree
c)
a minute
a)
CGS system
94
𝟐𝟎𝒐 =
𝟑𝟔𝟎′
a)
a)
none of these
d)
The system of measurement in which the angle is measured in radians is called
96
none of these
The positive square root of mean of squared deviation of 𝒙𝒊 (𝒊 = 𝟏, 𝟐, 𝟑, − − −, 𝒏) observation from
their arithmetic mean is called
93
a)
none of these
The mean of squared deviations of 𝒙𝒊 (𝒊 = 𝟏, 𝟐, 𝟑, − − −, 𝒏) observation from their arithmetic mean is
called
a)
95
none of these
The extent of variation between two extreme observations of data is measured by
a)
91
dispersion
The measures that are used to determine the degree or extent of variation in a data set are called
measures of
a)
90
b)
𝟑𝝅
𝟒
b) Sexagecimal system
c)
MKS system
d)
circular system
b)
𝟔𝟑𝟎′
c)
𝟏𝟐𝟎𝟎′
d)
𝟑𝟔𝟎𝟎′
b)
𝟏𝟑𝟓𝒐
c)
𝟏𝟓𝟎𝒐
d)
𝟑𝟎𝒐
radians=
𝟏𝟏𝟓𝒐
If 𝒕𝒂𝒏𝜽 = √𝟑, then 𝜽 is equal to
𝟗𝟎𝒐
b)
𝟒𝟓𝒐
c)
𝟔𝟎𝒐
d)
𝟑𝟎𝒐
b)
𝟏 + 𝒕𝒂𝒏𝟐 𝜽
c)
𝟏 + 𝒄𝒐𝒔𝟐 𝜽
d)
𝟏 − 𝒕𝒂𝒏𝟐 𝜽
𝟐𝒄𝒐𝒔𝟐 𝜽
c)
𝒔𝒆𝒄𝟐 𝜽
d)
𝒄𝒐𝒔𝜽
97
𝒔𝒆𝒄𝟐 𝜽 =
a)
𝟏 − 𝒔𝒊𝒏𝟐 𝜽
98
𝟏
𝟏
+
𝟏 + 𝒔𝒊𝒏𝜽 𝟏 − 𝒔𝒊𝒏𝜽
a)
𝟐𝒔𝒆𝒄𝟐 𝜽
99
𝟏
𝒄𝒐𝒔𝒆𝒄 𝟒𝟓𝒐
𝟐
b)
𝟏
a)
100
𝟏
√𝟐
c)
√𝟐
d)
√𝟑
𝟐
𝒔𝒆𝒄𝜽 𝒄𝒐𝒕𝜽 =
𝒔𝒊𝒏 𝜽
a)
101
b)
𝟐√𝟐
b)
𝟏
𝒄𝒐𝒔𝜽
c)
𝟏
𝒔𝒊𝒏𝜽
d)
𝒔𝒊𝒏𝜽
𝒄𝒐𝒔𝜽
𝒄𝒐𝒔𝒆𝒄𝟐 𝜽 − 𝒄𝒐𝒕𝟐 𝜽 =
a)
−𝟏
b)
𝟏
c)
𝟎
Iqbal1st Mock Preparation Mathematics 10 for 2014-15
Section-I
Q.No.1
1
Answers to the following Questions.
Solve 𝒙𝟐 + 𝟐𝒙 − 𝟐 = 𝟎
d)
𝒕𝒂𝒏𝜽
2
Solve by factorization 𝟓𝒙𝟐 = 𝟏𝟓𝒙
3
Write in standard form 𝒙+𝟒 + 𝒙−𝟒 = 𝟑
4
Write the names of the methods for solving a quadratic equation.
5
Solve (𝟐𝒙 − 𝟐) = 𝟒
6
7
8
9
10
Solve √𝟑𝒙 + 𝟏𝟖 = 𝒙
Define quadratic equation.
Define reciprocal equation.
Define exponential equation.
Define radical equation.
Q.No.2
1
2
3
4
𝟏
𝟏 𝟐
𝟏
𝟗
Answers to the following Questions.
Discuss the nature of the roots of the equation
Discuss the nature of the roots of the equation
Discuss the nature of the roots of the equation
Discuss the nature of the roots of the equation
𝒙𝟐 + 𝟑𝒙 + 𝟓 = 𝟎
𝒙𝟐 + 𝟔𝒙 − 𝟏 = 𝟎
𝟐𝒙𝟐 − 𝟕𝒙 + 𝟑 = 𝟎
𝟏𝟔𝒙𝟐 − 𝟖𝒙 + 𝟏 = 𝟎
−𝟏+√−𝟑
6
7
8
9
10
11
12
13
14
Find 𝝎𝟐 , if 𝝎 =
𝟐
Prove that the sum of the all cube roots of unity is zero.
Find the product of complex cube roots of unity.
Show that
𝒙𝟑 + 𝒚𝟑 = (𝒙 + 𝒚) (𝒙 + 𝒘𝒚) (𝒙 + 𝒘𝟐𝒚)
Evaluate
𝒘𝟑𝟕 + 𝒘𝟑𝟖 + 𝟏
Evaluate
(𝟏 − 𝒘 + 𝒘𝟐 )𝟔
If 𝒘 is cube root of unity, form an equation whose roots are 𝟑𝒘 and 𝟑𝒘𝟐 .
Using synthetic division, find the remainder and quotient when (𝒙𝟑 + 𝟑𝒙𝟐 + 𝟐) ′ (𝒙 − 𝟐)
Using synthetic division, show that 𝒙 − 𝟐 is the factor of 𝒙𝟑 + 𝒙𝟐 − 𝟕𝒙 + 𝟐.
Find the sum and product of the roots of the equation 𝟐𝒑𝒙𝟐 + 𝟑𝒒𝒙 − 𝟒𝒓 = 𝟎.
15
Find 𝜶𝟐 + 𝜷𝟐 of the roots of the equation 𝒙𝟐 − 𝟒𝒙 + 𝟑 = 𝟎
16
If 𝒂, 𝒃 are the roots of 𝟒𝒙𝟐 − 𝟑𝒙 + 𝟔 = 𝟎, find 𝒂𝟐 + 𝒃𝟐
17
If 𝒂, 𝒃 are the roots of 𝟒𝒙𝟐 − 𝟑𝒙 + 𝟔 = 𝟎, find
18
19
20
If 𝒂, 𝒃 are the roots of 𝟒𝒙𝟐 − 𝟑𝒙 + 𝟔 = 𝟎, find 𝒂 − 𝒃
If 𝒂, 𝒃 are the roots of 𝒙𝟐 − 𝟓𝒙 + 𝟕 = 𝟎, find an equation whose roots are −𝒂, −𝒃
If 𝒂, 𝒃 are the roots of 𝒙𝟐 − 𝟓𝒙 + 𝟕 = 𝟎, find an equation whose roots are 𝟐𝒂, 𝟐𝒃.
5
Q.No.3
1
2
3
4
5
6
𝟏
𝟏
Answers to the following Questions.
Define ratio and give one example.
Define proportion.
Define direct variation.
Define inverse variation.
State theorem of componendo-dividendo.
Find 𝒙, if 𝟔 ∶ 𝒙 : ∶ 𝟑 ∶ 𝟓.
𝜶
𝜷
+𝜶
𝜷
7
8
9
10
11
If 𝒙 and 𝒚𝟐 varies directly, and 𝒙 = 𝟐𝟕 when 𝒚 = 𝟒. Find the value of 𝒚 when 𝒙 = 𝟑.
If 𝒖 and 𝒗 varies inversely, and 𝒖 = 𝟖, when 𝒗 = 𝟑. Find 𝒗 when 𝒖 = 𝟏𝟐.
Find the fourth proportional to 𝟖, 𝟕, 𝟔.
Find a mean proportional to 𝟏𝟔 and 𝟒9.
Find a third proportional to 𝟐8 and 𝟒.
12
If 𝒚 ∝
13
If 𝒛 ∝ 𝒙𝒚 and 𝒛 = 𝟑𝟔 when 𝒙 = 𝟐, 𝒚 = 𝟑, then find 𝒛.
14
If 𝒘 ∝ 𝒗𝟐 and 𝒘 = 2 when 𝒗 = 𝟑, then find 𝒘
𝒙𝟐
𝒛
𝐚𝐧𝐝 𝒚 = 𝟐𝟖 𝐰𝐡𝐞𝐧 𝒙 = 𝟕, 𝒛 = 𝟐, 𝐭𝐡𝐞𝐧 𝐟𝐢𝐧𝐝 𝒚
𝟏
Q.No.4
1
2
3
4
Answers to the following Questions.
Define a rational fraction.
What is a proper fraction?
What is an improper fraction?
What are partial fractions?
5
How can we make partial fractions of
6
Resolve into partial fraction
7
Find partial fractions of
8
Resolve into partial fraction
9
How we can make the partial fractions of
10
Whether (𝒙 + 𝟑)𝟐 = 𝒙𝟐 + 𝟔𝒙 + 𝟗 is an identity?
𝒙−𝟐
(𝒙+𝟐)(𝒙+𝟑)
𝟏
𝒙𝟐 −𝟏
𝟑
(𝒙+𝟏)(𝒙−𝟏)
𝒙
(𝒙−𝟑)𝟐
Q.No.5
1
2
3
4
5
6
7
8
9
10
Answers to the following Questions.
Define a subset and give one example.
Write all the subsets of the set {𝒂, 𝒃}
Show by Venn diagram 𝑨 ∩ (𝑩 ∪ 𝑪).
Define intersection of two sets.
Define a function.
Define one-one function.
Define an onto function.
Define a bijective function.
Write De Morgan’s laws.
Show 𝑨 ∩ 𝑩 by Venn diagram. When 𝑨 ⊆ 𝑩
Q.No.6
1
2
3
4
5
Answers to the following Questions.
Define class limits
Define class mark
What is cumulative frequency?
Define a frequency distribution
What is histogram?
𝒙
(𝒙+𝒂)(𝒙−𝒂)
6
7
8
9
10
11
12
13
14
Q.No.7
1
2
3
4
5
6
7
8
9
10
Name two measures of central tendency
Define Arithmetic mean.
Write three properties of Arithmetic mean.
Define Median.
Define Mode?
What do you mean by Harmonic mean?
Define Geometric mean.
What is Range?
Define Standard deviation.
Answers to the following Questions.
Define an angle.
What is the sexagesimal system of measurement of angles?
How many minutes are in two right angles?
Define radian measure of an angle.
𝝅
Convert 𝟒 radian to degree measure.
Convert 15o to radians.
What is radian measure of the central angle of an arc 50m long on the circle of radius 25m?
Find r when l = 56 cm and 𝜽 = 𝟒𝟓𝒐
𝟗
Find 𝒕𝒂𝒏𝜽 when 𝒄𝒐𝒔𝜽 = 𝟒𝟏 and terminal side of the angle q is in fourth quadrant
prove that (𝟏 − 𝒔𝒊𝒏𝟐 𝜽)(𝟏 + 𝒄𝒐𝒔𝟐 𝜽)
Fill in the blanks Chapter No: 1
The standard form of the quadratic equation is________.
The number of methods to solve a quadratic equation are ________.
The name of the method to derive a quadratic formula is ________.
The solution of the equation 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄 = 𝟎, 𝒂 ≠ 𝟎 is ________.
The solution set of 𝟐𝟓𝒙𝟐 − 𝟏 = 𝟎 is ________.
An equation of the form 𝟐𝟐𝒙 − 𝟑𝟐𝒙 + 𝟓 = 𝟎 is called a/an ________ equation.
The solution set of the equation 𝒙𝟐 − 𝟗 = 𝟎 is ________.
An equation of the type𝒙𝟒 + 𝒙𝟑 + 𝒙𝟐 + 𝒙 + 𝟏 = 𝟎 called a/an ________ equation.
A root of an equation, which do not satisfy the equation is called ________ root.
An equation involving impression of the variable under ________ is called radical equation.
Fill in the blanks Chapter No: 2
The discriminant of
+ bx + c = 0 is ________.
2
If b - 4ac = 0, then roots of ax2 + bx + c = 0 are ________.
If b2 - 4ac > 0, then the roots of ax2 + bx + c = 0 are ________.
If b2 - 4ac < 0, then the root of ax2 + bx + c = 0 are ________.
If b2 - 4ac > 0 and perfect square, then the roots of ax2 + bx + c = 0 are ________.
If b2 - 4ac > 0 and not a perfect square, then roots of ax2 + bx + c = 0 are ________.
If a, b are the roots of ax2 + bx + c = 0, then sum of the roots is ________.
If a, b are the roots of ax2 + bx + c = 0, then product of the roots is ________.
If a, b are the roots of 7x2 - 5x + 3 = 0, then the sum of the roots is ________.
If a, b are the roots of 5x2 + 3x - 9 = 0, then product of the roots is ________.
ax2
𝟏
For a quadratic equation 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄 = 𝟎, 𝜶𝜷 is equal to ________.
Cube roots of unity are ________.
Under usual notation sum of the cube roots of unity is ________.
If 1, w, w2 are the cube roots of unity, then w-7 is equal to ________.
If a, b are the roots of the quadratic equation, then the quadratic equation is written as ________.
If 2 w and 2 w2 are the roots of an equation, then equation is ________.
Fill in the blanks Chapter No: 3
The simplest form of the ratio
In a ratio 𝒙 ∶ 𝒚; 𝒙 is called ________.
In a ratio 𝒂 ∶ 𝒃; 𝒃 is called ________.
In a proportion 𝒂 ∶ 𝒃 ∶ : 𝒙 ∶ 𝒚; 𝒂 and 𝒚 are called ________.
In a proportion 𝒑 ∶ 𝒒 ∶ : 𝒎 ∶ 𝒏; 𝒒 and 𝒎 are called ________.
In proportion 𝟕 ∶ 𝟒 ∶ : 𝒑 ∶ 𝟖, 𝒑 = ________.
If 𝟔 ∶ 𝒎 ∶ : 𝟗 ∶ 𝟏𝟐, then m = ________.
If 𝒙 and 𝒚 varies directly, then 𝒙 = ________.
If 𝒗 varies directly as 𝒖𝟑 , then 𝒖𝟑 = ________.
If 𝒘 varies inversely as 𝒑𝟐 , then 𝒌 = ________.
A third proportional of 𝟏𝟐 and 𝟒, is ________.
A third proportional of 𝟏𝟐 and 𝟒, is ________.
The mean proportional of 𝟒𝒎𝟐 𝒏𝟒 and 𝒑𝟔 is ________.
Fill in the blanks Chapter No: 5
If 𝑨 ⊆ 𝑩, then 𝑨 ∪ 𝑩 = ________.
If 𝑨 ∩ 𝑩 = 𝝋 then 𝑨 and 𝑩 are ______.
If 𝑨 ⊆ 𝑩 and 𝑩 ⊆ 𝑨 then __________.
𝑨 ∩ (𝑩 ∪ 𝑪) = __________.
𝑨 ∪ (𝑩 ∩ 𝑪) = ________.
The complement of 𝑼 is ___________.
The complement of 𝝋 is ___________.
A∩Ac = ___________.
A∪Ac = ___________.
The set {𝒙|𝒙 ∈ 𝑨 𝒂𝒏𝒅 𝒙 ∉ 𝑩} =__________________.
The point (−𝟓, − 𝟕) lies in ___________ quadrant.
The point (𝟒, − 𝟔) lies in ___________ quadrant.
The y co-ordinate of every point is ___________ on-𝒙 − 𝒂𝒙𝒊𝒔.
The x co-ordinate of every point is ___________ on-𝒚 − 𝒂𝒙𝒊𝒔.
The domain of {(𝒂, 𝒃), (𝒃, 𝒄), (𝒄, 𝒅)} is ___________.
The range of {(𝒂, 𝒂), (𝒃, 𝒃), (𝒄, 𝒄)} is ___________.
Venn-diagram was first used by ___________.
A subset of 𝑨 × 𝑨 is called the ___________ in A.
If 𝒇 : 𝑨 → 𝑩 and 𝒓𝒂𝒏𝒈𝒆 𝒐𝒇 𝒇 = 𝑩, then 𝒇 is an ___________ function.
The relation {(𝒂, 𝒃), (𝒃, 𝒄), (𝒂, 𝒅)} is ___________ a function.
Fill in the blanks Chapter No: 7
𝝅 radians = _________degree.
The terminal side of angle 235o lies in _________quadrant.
Terminal side of the angle -30o lies in _________quadrant.
Area of a circular sector is _________.
If r = 2 cm and q = 3 radian, then area of the circular sector is _________.
The general form of the angle 480o is _________
𝟏
If 𝒔𝒊𝒏𝜽 = 𝟐, then 𝜽 =_________________.
If 𝜽 = 𝟑𝟎𝟎𝒐 , then 𝒔𝒆𝒄(−𝟑𝟎𝟎)𝒐 =_______________
𝟏 + 𝒄𝒐𝒕𝟐 𝜽 =_________________.
𝑺𝒆𝒄𝜽 − 𝒕𝒂𝒏𝜽 =____________