Mathematics 10th Class
SYLLABUS
Qs. 1
Fill in the Blanks (Compulsory) 10 Marks
Section A
Chapter 1 To 9 (50 Marks)
Attempt Any Five Questions Out of Eight
Qs. 2 (A)
Chapter 1
5 Marks
Qs. 2 (B)
Chapter 1
5 Marks
Qs. 3 (A)
Chapter 2
5 Marks
Qs. 3 (B)
Chapter 4
5 Marks
Qs. 4
Chapter 3 & 4
10 Marks
Qs. 5
Chapter 5
10 Marks
Qs. 6 (A)
Chapter 9
5 Marks
Qs. 6 (B)
Chapter 3
5 Marks
Qs. 7 (A)
Chapter 7
5 Marks
Qs. 7 (B)
Chapter 4
5 Marks
Qs. 8 (A)
Chapter 8
5 Marks
Qs. 8 (B)
Chapter 4
5 Marks
Qs. 9
Chapter 5 & 7
8 Marks
Section B
Chapter 10, 11, 12 (30 Marks)
Attempt Any Three Questions Out of Five
Qs. 10
P. Geometry
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10 Marks
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Qs. 11
Theorem
10 Marks
Qs. 12 (A)
Theorem
5 Marks
Qs. 12 (B)
Theorem
5 Marks
Qs. 13 (A)
Theorem
5 Marks
Qs. 13 (B)
Theorem
5 Marks
Qs. 14 (A)
Theorem
5 Marks
Qs. 14 (B)
Theorem
5 Marks
Section C – Chapter 13 & 14
(10 Marks)
Attempt Any One Question Out of Two
Qs. 15 (A)
Chapter 13
5 Marks
Qs. 15 (B)
Chapter 14
5 Marks
Qs. 16 (A)
Chapter 13
5 Marks
Qs. 16 (B)
Chapter 14
5 Marks
IMPORTANT QUESTIONS
Chapter 1
Ex 1.1
Qs. 1, 2, 10, 11
Ex 1.2
Qs. 3, 4, 5
Ex 1.3
Qs. 2, 3, 4, 5
Chapter 2
Ex 2.1 - 2.5
Are Not Important
Ex 2.6
Qs. 13, 14
Ex 2.7
Qs. 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19
Ex 2.8
Qs. 2, 3, 4, 5, 6, 7, 8, 9, 10
Misc. Ex. 2
Qs. 8, 10, 11
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Chapter 3
Ex. 3.1 - 3.4
Are Not Important
Ex 3.5
Qs. 1, 2, 3, 4, 5, 6, 7, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24
Ex 3.6
Qs. 4, 6, 8
Ex 3.7
Qs. 8, 9, 10, 11
Ex 3.8
Qs. 14, 15, 16, 17, 20
Ex 3.9
Qs. 11, 12, 13, 14, 15
Ex 3.10
Qs. 6, 9, 10
Misc. Ex. 3
Qs. 6, 11, 12, 13
Chapter 4
Ex 4.1
Not Important
Ex 4.2
Qs. 1 To 16
Ex 4.3
Qs. 1 To 16
Ex 4.4
Qs. 1 To 21
Ex 4.5
Qs. 1 To 21
Ex 4.6
Qs. 8, 9, 10
Ex 4.7
Qs. 1 To 13
Ex. 4.8 - 4.10 Are Not Important
Ex 4.11
Qs. 8 To 36
Ex 4.12
Qs. 1 To 10
Ex 4.13
Qs. 1 To 7
Misc. Ex. 4
Qs. 6, 7, 8, 9
Chapter 5
Ex 5.1
Qs. 1
Ex 5.2
Qs. 7, 8, 13, 14, 15, 18, 19
Ex 5.3
Qs. 5, 6, 7, 9, 10
Ex 5.4
Qs. 1 To 12
Chapter 6
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Ex 6.1 - 6.3
Are Not Important
Ex 6.4
Qs. 7, 8, 10, 11
Ex 6.5
Qs. 1 To 12
Chapter 7
Ex 7.1
Not Important
Ex 7.2
Qs. 19, 20, 21, 22, 23, 24, 25
Misc. Ex. 7
Qs. 7, 8, 9, 10, 11, 12, 13
Chapter 8
Ex 8
Qs. 9, 10, 11, 12, 13, 14
Misc. Ex. 8
Qs. 5, 6, 7, 8, 9, 10, 11, 12, 13, 14
Chapter 9
Ex. 9.1 - 9.5
Are Not Important
Ex 9.6
Qs. 1 To 12
Misc. Ex. 9
Qs. 9
Chapter 13
Ex. 13.1-13.2 Are Not Important
Ex. 13.3
Qs. 1 To 18
Ex. 13.4
Not Important
Ex. 13.5
Qs. 1 To 11
Misc. Ex. 13
Qs. 4, 5, 6, 7, 8
Trigonometric Ratios of 30, 45, 60 Degrees
Chapter 14
Ex. 14.1
Not Important
Ex. 14.2
Qs. 2, 4, 6, 7, 8, 9, 14
Ex. 14.3
Qs. 4, 7, 8, 9, 10, 11
Egs./ Page
1/310, 2/311, 3/312, 4/313, 3/315, 4/316, 1/322, 2/322, 3/323, 4/325, 5/325
FILL IN THE BLANKS
1.
If A = {2, 3, 5, 10}, B = {5, 2, 10, 3}, then A and B are __________ sets.
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2.
If A = {1, 2, 3}, B = {a, b, c}, then A and B are __________ sets.
3.
If A = {1, 2, 3, 4, 5}, B = {1, 3, 5, 7, 9}, then A and B are __________ sets.
4.
If A = {a, b, c}, B = {b, d, e, f}, then A and B are __________ sets.
5.
If A = {1, 3, 5, 7}, B = {0, 2, 4, 6, 8}, then A and B are __________ sets.
6.
If A = {a, b, c}, B = {e, f, g}, then A and B are __________ sets.
7.
If A = {a, b, c}, B = {l, m, n, p}, then A and B are __________ sets.
8.
If A = {x, y, z}, B = {p, q, r, s}, then A and B are __________ sets.
9.
If A = {x, y, z}, B = {l, m, n, p}, then A and B are __________ sets.
10.
If A = {l, m, n, o}, B = {l, n, q}, then AUB is equal to __________.
11.
If A = {l, m, n, o, p}, B = {l, n, q, s}, then AB is equal to __________.
12.
If A and B are disjoint sets, then AB is __________ set.
13.
If A = {a, b, c, d}, B = {b, d}, then B is a __________ of A.
14.
If A = {p, q, r, s}, B = {p, s}, then A is a __________ of B.
15.
The null set is considered to be the __________ of every set.
16.
The complementary set of a null set is a __________ set.
17.
The power set of a set A is the set of all __________ of A.
18.
A set which contains all possible subsets of A is called __________ set.
19.
If a set has 3 members, the power set of this set will have __________ members.
20.
If A = {1, 2, 3}, then the number of all possible subsets of A is __________.
21.
If A = {1, 2, 3, 4}, then the number of all possible subsets of A is __________.
22.
The power subset of a null set contains __________.
23.
The y-cordinate of all the points on X- axis is __________.
24.
The x-cordinate of all the points on Y- axis is __________.
25.
Any ordered pair of real numbers (x, y) is to be considered a __________.
26.
A cartesian product of A* B __________ B*A.
27.
If R is equal to {(1, 2), (2, 3), (3, 4}, then domain R = __________.
28.
If R is equal to {(1, 2), (2, 3), (3, 4}, then Range R = __________.
29.
N = {1, 2, 3, 4,….} is the set of __________ numbers.
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30.
Z = {0,1, 2, 3, 4,….} is the set of __________ numbers.
31.
I = {…, -3, -2, -1, 0, 1, 2, 3…} is the set of __________.
32.
All those numbers that form complete pair are called __________ numbers.
33.
All those numbers that do not form complete pairs are called __________ numbers.
34.
All those numbers which are divisible by 1 and by themselves are known as __________ numbers.
35.
All those numbers which can be written in the form p/q, where p and q are integers and q is not zero
are called __________ numbers.
36.
37.
1/3 or 0.333 and 1/2 or 0.5 are examples of __________ numbers.
All those numbers, which do not have repeating or terminating decimal representations, are called
__________ numbers.
2
38.
39.
and  are the examples of __________ numbers.
A set is said to be closed for __________ if the sum of every two numbers of the set is also in the
set.
40.
A set is said to be closed for __________ if the product of every two numbers of the set is also in the
set.
41.
A = {1, 3, 5, 7….} is closed for __________.
42.
A = {0, 1} is closed for __________.
43.
5 + 7 = 7 + 5. The property used is __________.
44.
(4 + 3) + 2 = 4 + (3 + 2). The property used is __________.
45.
The identity element of addition of the set of real numbers is __________.
46.
The additive inverse of 7a is __________.
47.
The additive inverse of a-b is __________.
48.
The additive inverse of b-a is __________.
49.
4*7 = 7*4. The property used is __________.
50.
(2*3) 6 = 2*(3*6). The property used is __________.
51.
The identity element for multiplication of the set of real numbers is __________.
52.
The multiplicative inverse of a is __________.
53.
The multiplicative inverse of (a + b) is __________.
54.
The multiplicative inverse of (a - b) is __________.
55.
The multiplicative inverse of 1/(x + y) is __________.
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56.
4*(5 + 7) = 4*5 +4*7. The property used is __________.
57.
If x, y, z are real numbers and x = y, y = z, then x = z (or z = x). The property used is __________.
58.
__________ non collinear points determine a plane.
59.
__________ number of planes pass through a given line.
60.
If two planes intersect, their intersection is a __________.
61.
If a plane meets two parallel planes, then the lines of intersection are __________.
62.
One and only one __________ can be drawn to a plane from a point no on the plane.
63.
If two straight lines are perpendicular to the same plane, they are __________ to each other.
64.
If a line is perpendicular to each of the two planes, then the planes are __________.
65.
An angle is the union of two non-collinear rays having the same end __________.
66.
If the sum of the measures of two angles is 90, then the angles are called complementary angles,
and each one is called the __________ of the other.
67.
The complement of 40 = __________.
68.
The complement of 41 = __________.
69.
If the sum of the measures of two angles is 180, then the angles are called supplementary angles,
and each one is called __________ of the other.
70.
The supplement of 50 = __________.
71.
The supplement of 41 = __________.
72.
If the outer sides of two adjacent angles lie on a line, they are __________ angles.
73.
If two lines intersect, then the vertical angles are __________.
74.
If two sides of a triangle are congruent, then angles opposite to these sides are __________.
75.
If two parallel lines are cut by a transversal, each pair of alternate interior angles are __________.
76.
If two parallel lines are cut by a transversal, each pair of corresponding angles are __________.
77.
If two parallel lines are cut by a transversal, the interior angles on the same side of the transversal
are __________.
78.
In a plane, if a line is perpendicular to one to two parallel lines, it is __________ to the other.
79.
The sum of the measures of three angles of a triangle is equal to __________.
80.
Each angle of an equilateral triangle is __________.
81.
In a right triangle, the acute angles are __________ angles.
82.
The measure of an exterior angle of triangle is __________ to the sum of the opposite interior
angles.
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83.
If two angles and one side of an triangles are congruent to the corresponding angles and side of
another triangle respectively, then the triangles are __________.
84.
If the measure of two angles in a triangle are 80 and 60, then the measure of third angle is
__________.
85.
The sum of the measures of angles of a quadrilateral is __________.
86.
If two angles of a triangle are congruent, then the __________ opposite to them are also congruent.
87.
The opposite sides and angles of a parallelogram are __________.
88.
In a parallelogram, the interior angles of a side are __________.
89.
The measure of one angle of a parallelogram is 75; the measure of the consecutive angle is
__________.
90.
The diagonals of a square bisect each other at __________.
91.
The diagonals of a rhombus bisect each other at __________.
92.
In a triangle, the sum of measure of any two sides is __________ than the measure of the third side.
93.
A set of all points in a plane which are equidistant from a fixed point is called a __________.
94.
If a straight line intersects a circle in two points, then the line is called a __________ of the circle.
95.
If a straight line touches a circle at one point only, then the line is called __________ to the circle.
96.
Two or more circles with the same center are called __________ circles.
97.
Circles having equal radii are called __________ circles.
98.
If a diameter of a circle is perpendicular to one of its chords then it will __________ the chord.
99.
If two chords of a circle are congruent, they are __________ from the center.
100.
If a line is __________ to a radial segment at its point on the circle, it is tangent to the circle.
101.
The sum of the measure of the opposite angles of a cyclic quadrilateral is __________.
102.
The opposite angles of a cyclic quadrilateral are __________.
103.
The measure of an angle subtended in a semicircle is __________.
104.
Sin2 + Cos 2 = __________.
105.
The characteristics of log 0.00753 is __________.
106.
The inscribed angle of a semi-circle is __________.
107.
The additive inverse of a + b is __________.
108.
Sin 20 = Cos __________.
109.
If S = {1, 2, 3, 4}, then the number of elements in P(S) = __________.
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110.
According to the demorgan’s law A’B’ = __________.
111.
The supplement of an angle of 90 is __________.
112.
__________ is the multiplicative inverse of a – b.
113.
A chord which passes through the center of a circle is called __________.
114.
__________ is the multiplicative inverse of 1/X.
115.
The set of all subsets of a set is called __________.
116.
Sin(90 – 40) = Cos __________.
117.
If log8 16 = x, then x =__________.
118.
__________ should be added to 9a2b2 – 12abc to make it a perfect square.
119.
Sin 60 = __________.
120.
X =  fx / f is the formula of __________.
121.
Log5 + log8 – log6 = log __________.
122.
The circle passing through the vertices of a triangle is called __________ circle.
123.
__________ should be added to 4x2 + 12x to make is a perfect square.
124.
X3.X-3 = __________
125.
Sec2 - 1 =__________
126.
Cot 30 = __________
127.
If log4 64 = x, then x = __________.
128.
An angle inscribed in a minor arc is __________ angle.
129.
The set A = {1, 3, 5, 7…..} is closed with respect to __________.
130.
Two circles whose radii are equal are called __________ Circles.
131.
A line segment joining any two points of a circle is called __________ of the circle.
132.
The set A = {0,1} is closed with respect to __________.
133.
The angle inscribed in a major arc is an __________.
134.
The characteristic of log 97.2 is __________.
135.
If all the elements of a matrix are zero, the matrix is called a __________ matrix.
136.
A-1 is called __________.
137.
If A=0, then matrix A is called __________.
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138.
If A0, then the matrix A is called __________.
139.
Measure of radial segment is called __________.
140.
The chord through the centre of the circle is called a __________.
141.
A line segment having both its end points on a circle is called __________.
142.
The distance of any point of a circle from its centre is called __________.
143.
The set of points of a plane, which are equidistant from a given point, is called a __________.
144.
Two circles are congruent if __________.
145.
Sin50 = sin(90 - 40) = cos __________.
146.
Cos 30 = cos(90 - 60) = sin __________.
147.
Tan 60 = tan(- - - 30) = __________.
148.
Cosec 40 = cosec(90 - - -) = __________.
149.
Sec 30 = sec(90 - - -) = __________.
150.
Cot 45 = cot(90 - - -) = __________.
151.
AU(BC) = __________.
152.
A – B = {x __________}.
153.
If A  B then A U B = __________, AB = __________.
154.
The coordinate of every point on x axis is zero.
155.
It __________ necessary that every onto-function should also be a (1-1) function.
156.
Multiplicative Inverse of 0 __________ exist.
157.
Additive inverse of 0 is __________.
158.
x>yy>z __________.
159.
xz=yz  __________ (where z  0).
160.
If z<0 then x>yxz __________yz and x<y  xz __________yz.
161.
The sentence 2x3 – 5x2 – 7x + 9 has been written in the __________ order.
162.
(8x4 – 12x3 + 20x2 – 18x)  2x = __________.
163.
If a – b = 6, a + b = 5, then a2 – b2 = __________.
164.
If x – 1/x = 5, then x2 + 1/x2 = __________.
165.
(a – b + c)2 = a2 + b2 + c2 __________.
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166.
(a – b)(a + b) (a2 + b2) = __________.
167.
(a + b)2 – (a – b)2 = __________.
168.
a3 + b3 + 3ab(a + b) = __________.
169.
(a – b + c)(a2 + b2 + c2 + ab + bc – ca) = __________.
170.
a4b2 – a2b4 = a2b2 (__________).
171.
a3 – 125b3 = (a - 5b) (__________).
172.
a3 – b3 + c3 + 3abc = (a – b + c) (__________).
173.
H.C.F of x2 + x –6 and x2 – 7x + 10 is __________.
174.
L.C.M of x2 + x –6 and x2 – 7x + 10 is __________.
175.
Factorization of a2 + a –2 is __________.
176.
Factorization of a4 – b4 is __________.
177.
H.C.F of a3 – b3 and a2 – b2 is __________.
178.
H.C.F of a2 – 4a + 3 and a2 –5a + 6 is __________.
179.
L.C.M of a2 + 4a + 3, a2 + 3a + 2 and a2 + 5a + 6 is __________.
180.
The solution set of x = -x is __________.
181.
The solution set of x = 4 is __________.
182.
The solution set of x - 2 = 0 is __________.
183.
The solution set of x + y = 6 when x = y is equal to __________.
184.
A linear equation in two variables represents a __________.
185.
Two equations in two variables, which are true for the same ordered pair, are called __________.
186.
The exponent of a variable in the quadratic equation is __________.
187.
ax2 + bx + c = 0 is the __________ form of the quadratic equation in one variable.
188.
The formula with the help of which quadratic equation is solved can be derived from __________.
189.
The solution set of x2 – 5x = 0 is __________.
190.
The solution set of the equation __________ = 0 is
191.
The exponential form of y = logax is __________.
192.
The logarithmic form of ay = x is __________.
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2a
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193.
The integral part of logarithm is called __________.
194.
The fractional part of logarithm is called __________.
195.
Log 5/3 = __________.
196.
Log 729 = __________.
197.
If log 2 = 0.3010, log 3 = 0.4771, log 5 = 0.6990, then log 30 = __________.
198.
The common end point of the rays whose union is an angle is called the __________ of the angle.
199.
If two adjacent angles are supplementary, their outer arms are __________.
200.
__________ can be established between non negative integers and the points of ray.
201.
If A, B and C are three collinear points, then C will between A and B if __________.
202.
The points on a triangle, its interior and exterior are __________ sets.
203.
A triangle whose two sides are congruent is called __________.
204.
A triangle whose three sides are congruent is called __________.
205.
The side opposite to the right angle in a right angled triangle is called __________.
206.
A quadrilateral whose only two sides are parallel is known as __________.
207.
A quadrilateral whose all the four sides are congruent but none of its angles is a right angle is called
__________.
208.
A line segment having both end points on a circle is called __________.
209.
If a line is tangent to a circle, then the point of intersection is called __________.
210.
Angle inscribed in a semicircle is __________ angle.
211.
The line segment joining the centre with any point of the circle is called __________.
212.
If two chords are __________ then they are equidistant from the centre of the circle.
213.
In a semicircle the angle is __________.
214.
Half of diameter is __________.
215.
The intersection of a tangent and a circle is __________.
216.
The line intersecting the circle in two points is __________.
217.
The line segments whose end points are on circle is __________.
218.
The line segment joining the mid-point of a side of a triangle to the opposite vertex is called a
__________.
219.
The line segment, which joins the __________ of a side to the opposite vertex, is called a median.
220.
Two __________ can be drawn to a circle from a point outside the circle.
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221.
222.
The circle drawn inside a triangle touching its sides is called an __________ circle.
If the measure of the angles of a triangle is known, we can construct __________ number of triangles
with the help of them.
223.
Medians __________.
224.
Right bisectors __________.
225.
Tangent __________.
226.
Alternate angles __________.
227.
Four right angles __________.
228.
The reciprocal os sin m<A is __________.
229.
Sin2m<A + cos2m<A = __________.
230.
1  sin 2m  A = __________.
231.
(Sin60)2 + (cos __________)2 = 1
232.
1 + tan2m<A = __________.
233.
In a class interval (121-130) the upper class limit is __________.
234.
In a class interval (25-29), 25 is __________.
235.
The sum of product of mid-point of groups and frequencies is represented by __________.
236.
Arithmetic mean is represented by the symbol __________.
237.
The sum of deviations taken from mean is equal to __________.
238.
When the data are arranged in ascending or descending order the middle item in odd observations is
__________.
239.
In a series 0, 1, 4, 6, 7, 9, 12 the median is __________.
240.
In a series 44, 55, 88, 99, 111, 121, 222, 333 the mode is __________.
241.
In a series 5, 5, 5, 5, 5 the dispersion is __________.
242.
A variable contains the values like 9, 11, 15, 4, 16 18 the range (R) is __________.
243.
Standard deviation is represented by __________.
244.
Variance is __________ of standard deviation.
245.
In (6 – 10) the size of class interval is __________.
246.
In (25 – 29) the mid-point is __________.
247.
In 0, 1, 2 the median is __________.
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248.
In 3, 3, 3, 3, 9 the mode is __________.
249.
In 15, 4, 6, 21, 30 the range R is __________.
250.
Sum of deviation is __________.
251.
The mean frequency distribution is __________.
252.
In –2, -1, 0, 1, 2 the mean is __________.
253.
Sum of frequencies is __________.
IMPORTANT FORMULAE
Operations on Sets; Cartesian Plane; Binary Relations
Power Set
The set of all subsets of a set A is called the power set of A and is written as P(A).It can be proved as:
N(S) = K  n{P(S)} = 2k
That is if a set S has k elements then the number of elements in its power set will be 2 k.
Commutative Property of Union
For any two sets A and B
AUB = BUA
Commutative Property of Intersection
For any two sets A and B
AB = B A
Associative Property of Union
For any three sets A, B and C
AU(BUC) = (AUB)UC
Associative Property of Intersection
For any three sets A, B and C
A(BC) = (AB)C
Distributive Property of Union over Intersection
For any three sets A, B and C
AU(BC) = (AUB)  (AUC)
Distributive Property of Intersection over Union
For any three sets A, B and C
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A(BUC) = (AUB)U(AC)
De Morgan’s Laws
For any two sets A and B which are the subsets of U
(AUB)’ = A’B’
(AB)’ = A’UB’
System of Real Numbers, Exponents and Redicals
Exponent
If n is a negative integer say n=-m where m is a natural number a  0 then
an = a-m = (a-1)m = (1/a)m
an is called nth power of a; a is called the base and n is called exponent or index of a.
Law of Exponents
am x an = am + n
Where a is a real number and m, n are integers.
Law of Power of Product
(a . b)n = an . bn
Where a and b are real numbers and n is an integer.
Law of Power of a Power
(am)n = amxn
Where a is any real number and m, n are any integers.
Law of Quotient of Powers with the Same Base
am
 a m-n
an
Where a is any real number other than O and m, n are integers.
Law of Power of Fraction
For any two real numbers a and b (where b0), n being a natural number
 an 
a
 n 

 
b
b 
n
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This is called the law of power of a fraction.
Algebraic Formulae
Formula 1
(a + b)2 = a2 + 2ab + b2
Formula 2
(a - b)2 = a2 - 2ab + b2
Formula 3
(a + b)2 – (a – b)2 = 4ab
Formula 4
(a + b)2 +(a – b)2= 2(a2 + b2)
Formula 5
(a + b + c)2 = a2 + b2 + c2+2ab + 2bc + 2ac
Formula 6
2
2
 (a - b)   (b - c)   (c - a) 
a  b  c - ab - bc - ca  
 
 

 2   2   2 
2
2
2
2
Formula 7
a2 - b2 = (a + b) (a – b)
Formula 8
(a + b)3 = a3 + 3a2b + 3ab2 + b3
or
(a + b)3= a3 + b3 + 3ab (a + b)
Formula 9
(a - b)3 = a3 - 3a2b + 3ab2 - b3
or
(a - b)3= a3 - b3 - 3ab (a - b)
Formula 10
a3 + b3= (a + b) (a2 – ab + b2)
Formula 11
a3 - b3= (a - b) (a2 + ab + b2)
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Formula 12
a3 + b3 + c3 – 3abc= (a + b + c) (a2 +b2 + c2 – ab –bc –ca)
Logarithms
Laws of Logarithms
First Law
Loga mn = logam + logan
Second Law
m
log a    log a m  log a n
n
Third Law
Loga mn = nlogam
Fourth Law
log a m
 log n m
log a n
MATCH THE FOLLOWING COLUMNS
Exercise 1
Column I
Column II
i.
ii.
iii.
{3, 2, 1}
{}
A ={1, 2, 3}, B =
a.
b.
Set of Prime Numbers
Set of rational numbers
C = {1, 5, 7, 9},
c.
Set of one element
d.
e.
f.
Set of whole numbers
Equal set
Over lapping sets
g.
Empty set
D = {1, 3, 5, 7}
E = {3}
F = {1, 2, 3, 4…}
G = {0, 1, 2, 3,
4…}
vii.
H = {2, 3, 5, 7 …..}
iv.
v.
vi.
Exercise 2
Column I
i.
ii.
iii.
iv.
v.
vi.
vii.
Column II
(x + 3) (x – 2)
1
x2
2
a.
b.
x2 x2 – x – 6
(a + b)3
(x – 3)(x + 2)
(a + b)2 + (a – b)2
c.
d.
e.
a3 + b3
x2 + x –6
4ab
f.
1
x2
1

x 
x

1
1

x  x  
x
x

(a +
b)2
– (a –
b)2
g.
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x2 +
a3
+
3a2b
-2
+ 3ab2 + b3
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viii.
(a + b)(a2 – ab +
h.
2a2 + 2b2
b 2)
Exercise 3
Column I
Column II
i.
a.
{(3, -1)}
b.
{(1, 2)}
c.
{(4, -5)}
d.
{(-1, 2)}
e.
{(3, -2)}
ii.
iii.
iv.
v.
The solution set of
x+y = 1 and x – y = 5
The solution set of
x-y = 4 and 2x + y = 5
The solution set of
x-y =-1 and x + 2y = 5
The solution set of
x+y = 1 and 3x – y + 5 = 0
The solution set of
x= y + 9 and 3x + y = 7
Exercise 4
Column I
Column II
i.
ii.
iii.
iv.
v.
log 1
2 log 5
log 3/2
log 25
log 10
a.
b.
c.
d.
e.
log 3 – log 2
5 log 2
1
0
log 52
Exercise 5
Column I
i.
ii.
iii.
iv.
v.
Column II
0.00325
0.000235
0.0325
2.53
0.253
a.
b.
c.
d.
e.
3.25 x 10-2
2.53 x 10-4
2.53 x 10-1
2.53 x 100
3.25 x 10-3
MULTIPLE CHOICE QUESTIONS
1.
{0, 1, 2, 3,…} is the set of __________.
(Prime Numbers, Irrational Numbers, Whole Numbers, Rational Numbers)
2.
A set containing finite number of elements is called __________.
(Null Set, Super Set, Finite Set, Infinite Set)
3.
If every element of set A is also an element of the set B, then set A is called a __________ of set B.
(Sub Set, Super Set, Null Set, Power Set)
4.
The union of sets A and B is expressed as __________.
(AB, AUB, AxB, A-B)
5.
If the number of elements in a set X is n, the number of elements in P(X) is __________.
(2n, 22n, 2n, n2)
6.
If a relation is given by R = {(0, 1), (1, 2), (3, 4), then the range of R is __________.
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( {0, 1, 3}, {1, 2, 3}, {2, 3, 4}, {1, 2, 4})
7.
If A = {1, 2, 3} and R = {(1, 2), (2, 3), (3, 3)} then R is __________.
(A function from A onto B, not a function, a function from A into A, not a binary relation)
8.
On the y-axis, the x coordinate or abscissa is __________.
(Positive, Negative, Zero, Neither positive nor negative, nor zero)
9.
If b is a real number, the point (0, b) lies __________.
(in the second quadrant, in the third quadrant, on the x-axis, on y-axis)
10.
(2-6)2 = __________.
(2-3, 23, 2-12, 212)
11.
(7 - 2) (7 + 2) = __________.
(47, 51, 9, 5)
12.
If x = 2 – 1 then x2 = __________
(1/2-1, 2 + 1, 1, 3 - 22)
13.
If x = 2 + 3 then x + 1/x = __________.
(2 - 3, 4, 23, 3)
14.
2x2 + 5y + 1/3 is a __________.
(Binomial, Monomial, Trinomial, Not a polynomial)
15.
3x2y + 5 is a polynomial of ___________.
(Degree one, Degree two, Degree three, Degree zero)
16.
2
5 x2 – 5x + 7 is a polynomial on ___________.
(Natural Numbers, Integers, Rational Numbers, Irrational Numbers)
17.
___________ should be added or subtracted from 9x2 + 16y2 so as to make it a perfect square.
(12xy, 7xy, 24xy, 144xy)
18.
(x – 6)(x – 4) = ___________.
(x2 + 10x + 24, x2 - 10x – 24, x2 + 10x – 24, x2 - 10x + 24)
19.
(a + b)2 + (a – b)2 = ___________.
(4ab, a2 + b2, 2a2 + 2b2, 2ab)
20.
If x + y = 8, xy = 15 then x2 + y2 = ___________.
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(94, 34, 49, 38)
21.
If x + y = 5, xy = 6, then x3 + y3 = ___________.
(35, 95, 107, 125)
22.
(a – b – c)(a2 + b2 + c2 + ab – bc + ca) = ___________.
(a3 + b3+ c3 + 3abc, a3 - b3+ c3 + 3abc, a3 - b3+ c3 - 3abc, a3 - b3- c3 - 3abc)
23.
Factors of x2 – 5x + 6 are __________.
{(x + 1)(x – 6), (x – 2) (x – 3), (x + 6)(x – 1), (x + 2)(x + 3)}
24.
The two numbers whose sum is –13 and product –30 are __________.
(2 and 15, 2 and –15, -3 and 10, 3 and –10)
25.
X4 + 64 can be made a perfect square by adding __________.
(8x2, -8x2, 16x2, 4x2)
26.
8x3 + 27y3 = (__________)(__________).
{(2x + 3y)(4x2 +9y2), (2x - 3y)(4x2 -9y2), (2x + 3y)(4x2 – 6xy +9y2), (2x - 3y)(4x2 +6xy +9y2)
27.
H.C.F of a3 + b3 and a2 –ab + b2 is __________.
{(a + b), (a2 –ab + b2), (a – b)2, (a2 – b2)}
28.
L.C.M of (a – b)2 and (a – b)3 is __________.
{(a – b), (a –b)2, ( a – b)3, (a – b)5}
29.
An inequation is a sentence, which is __________.
(True, Open, False, none of these)
30.
The solution set of a first degree equation in two variables has __________.
(One element, Two elements, No element, Infinite number of elements)
31.
a + b __________.
(= a + b,  a + b, > a + b,  a + b)
32.
x  4 means __________.
(x < 4, x = 4, x < 4 or x = 4, x = 4 or x > 4)
33.
The solution set of x = -6 is __________.
({6},{36}, {}, -6)
34.
The ordered pair satisfying x – y = 7 is __________.
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{(7, 7), (0, 7), (7, 0), (-1, -6)}
35.
x2 9
is a __________.
(Linear equation, Quadratic Equation, Radical Equation, Cubic Equation)
36.
The solution set of 5 – 4x = -7, xN is __________.
(({12}, {3}, {1, 2, 3}, {1, 2})
37.
The solution set of 2x< 8 is __________.
({4}, {-4}, {-4<x<4}, {4, -4})
38.
An equation is a sentence, which is __________.
(True, False, Open, None of them)
39.
A quadratic equation in one variable has __________.
(One root, Infinite number of roots, no rott, two roots)
40.
The solution set of x2 –x – 2 = 0 is __________.
({1}, {2}, {2, -1}, {-1})
41.
The solution set of 3x2 – 10x = 0 is __________.
({10}, {0, 10/3}, {10/3}, {0})
42.
Eliminate x from x + b = 0, x + c =0. The result will be __________.
(b = c, b + c = 0, bc = 0, b/c + 1 = 0)
43.
Eliminating t from x = t, y = t2 we get __________.
(x2 = y, x = y2, xy = 1, x2y = 1)
44.
Eliminating t from x – t2 = 0 and y = t3 __________ is obtained.
(x2 = y, x3 = y2, x3 = y3, x = y2)
45.
1
1
Eliminating x from x + x = a and x - x = b, then __________.
(a = b, a2 = b2, a2 – b2 = 1, a2 – b2 = 4)
46.
1
1
2
Eliminating x from x + x = a and x2 + x
= b2, then __________.
( a2 = b2, a2 = b2 + 2, a2 + 2 = b2 a2 + b2 = 2)
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47.
1
1
Eliminating x from x + x = a + b and x - x = a - b, then __________.
(ab = 1, ab = 0, a2 – b2 = 4, a2 + b2 = 4)
48.
If log10 x = 3 then x = __________.
(500, 10/3, 700, 1000)
49.
If log7 x = 2 then x = __________.
(14, 49, 128, 64)
50.
The characteristic of log 19 is __________.
(0, 10, 2, 1)
51.
The characteristic of log 3.216 is __________.
(0, 4, 3, 10)
52.
Common logarithm has the base __________.
(2, e, , 10)
53.
In scientific notation 0.00416 is written as __________.
(0.0416 x 10-1, 0.416 x 10-2, 4.16 x 10-3, 41.6 x 10-4)
54.
In standard form 2.35 x 10-2 is written as __________.
(2.35, 0.0235, 0.00235, 0.000235)
55.
Log5 + log8 – log3 = __________.
(5log 8/3, 3log40, log 40/3, 3log5/8)
56.
Log 50 can be written as __________.
(log2 + 2 log 5, log 2 + log 15, log 2 + 5 log 2, log 2 + log 5)
57.
3 is the characteristic in the logarithm of the number __________.
(879.2, 87.92, 8.792, 8792)
58.
If log2 8 = x, then x = __________.
(28, 64, 32, 3)
59.
54 = 625 is written in the logarithmic form as __________.
(log4 5 = 625, log5 4 = 625, log5 625 = 4, log4 625 = 5)
60.
If log81 x = -3/4, then x = __________.
(27, 1/3, 1/9, 1/27)
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61.
If antilog 3.8716 = 7440 and logx = 0.8716, then x = __________.
(74.40, 7.440, 744.0, 7440)
62.
If log 5 = 0.6990 and log 3 = 0.4771, then log 45 = __________.
(1.6532, 1.1761, 1.8751, 1.2219).
63.
3log2 – 2log5 in the simplified form is __________.
(log 6/10, log 9/32, log 8/25, log 25/8)
64.
A line segment having both end points on a circle and not passing through the centre is called __________.
(Chord, Secant, Diameter, None of these)
65.
The distance of the centre from any point of the circle is called __________.
(Diameter, Secant, Tangent, Radius)
66.
If a point lies in the interior of a circle, then its distance from the centre is __________.
(equal to radius, less than radius, greater than radius, greater than or equal to radius)
67.
A line, which is perpendicular to a radial segment of a circle at its outer end (lying on the circle), is called a
__________.
(Secant, Tangent, Chord, Diameter)
68.
The central angle of a minor arc of circle is 40. The angle subtended by the corresponding major arc
measures __________.
(20, 80, 69, 120)
69.
From a point at a distance of 5cm from the centre of a circle of radius 3cm. Tangents are drawn to the
circle. The length of each tangent will be __________.
(3cm, 5cm, 4cm, 6cm)
70.
The line, which meets the circle in one point, is __________.
(Secant, Diameter, chord, Tangent)
71.
If certain figures are exactly alike, but different in size, they are called __________ figures.
(Similar, Median, Equal, Proportional)
72.
The lines, which bisect the sides of a traingle perpendicularly, are called __________ of the sides.
(Bisectors, Line segments, Altitudes, Right bisectors)
73. In a right angled triangle the sum of squares of the measures of the legs is equal to the square of
__________.
(Hypotenuse, Altitude, Base, None of these)
74. __________ tangents can be drawn from a point.
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(Two, One, More than two, None)
75. The circle passing through the three vertices of a triangle is called __________.
(Inscribed circle. Outer circle, Circumscribed circle, None of these)
76. If the legs of a right-angled triangle are 1, 1 then its hypotenuse is __________.
(1, 2, ½, 2)
77. The value of sin 30 is __________.
(2, ½, -2, d = 1/2)
78. The value of cot 60 is __________.
(3/2, 2/3, -1/3, 3)
79. In a right-angled ABC, m<B = 90 and the measures of its sides a, b, c are 6, 10 and 8 respectively then tan
m <A = __________.
(3/5, 4/5, 3/4, 4/3
TRUE AND FALSE
1.
A chord is a line passing through two points of a circle.
2.
The corresponding arcs of two distinct circles are congruent if their central angles are congruent.
3.
Radius is one half of diameter.
4.
A point will be inside a circle if its distance from the centre is less than or equal to the radius of the circle.
5.
Tangent of a circle is a line meeting the circle at the most in one point.
6.
The set of all points neither inside nor on a circle is called the exterior of the circle.
7.
Radius is a measure, which passes through two points of a circle.
8.
The set of all points on or inside a circle is called the interior of the circle.
9.
A chord is a line segment, which passes through two points of a circle.
10.
An arc of a circle is a subset of the circle.
11.
Tangent of a circle is a line meeting the circle in one and only one point.
12.
Sin 40 = cos 50.
13.
Cos 35 = sin 55.
14.
Tan 70 = cot 70.
15.
Cosec20 = sec 70.
16.
Cot 30 = tan 60.
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17.
Sec 40 = cosec 35.
18.
The set of rational numbers between 4 and 5 is the empty set.
19.
The set {1, 2, 3, ….., 100000000000} is an infinite set.
20.
The intersection of two overlapping sets is non-empty.
21.
For any set A, AA’ = .
22.
If A = {1, 2, 3, 4} and B = {1, 2, 3, 4, 5, 6} then AB.
23.
The set {0, 1} possesses closure property with respect to addition.
24.
A  (b + c) = a  b + a  c.
25.
For every real number x, x = 0, or x < 0 or x > 0.
26.
Multiplication is distributive over subtraction.
27.
If x, y, z are real numbers, then x(yz) = z(xy).
28.
Every algebraic sentence is a polynomial.
1
2
29.
X+
is a polynomial.
30.
X2yz is a polynomial of degree two.
31.
3x + 4y – 7 is a polynomial on natural numbers.
P
Q
32.
If P and Q are polynomials and Q  0, then
33.
a – b – (a + b) = -2b.
34.
(a + b) (a2 + ab + b2) = a3 + b3.
35.
(x3 – 8)  (x – 2) = x2 + 2x + 4.
36.
(a + b)2 + (a – b)2 = 4ab.
37.
The associative property of multiplication has been used in x(a + b) = xa + xb.
38.
(x2 + 5x – 6) = (x + 2)(x – 3).
39.
Ax + by – bx – ay = (a – b)(x – y).
40.
The H.C.F of a3 + b3 and a + b is a + b.
41.
The L.C.M of a3 – b3 and a – b is a3 – b3.
42.
The L.C.M of a4 – b4 and a2 + b2 is a4 – b4.
43.
The solution set of 3x – 2 < 5, x  N is {0, 1, 2}.
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44.
The solution set of x – 4 = 7 is {11}.
45.
The solution set of 5x = 10 is {-2, 2}.
46.
The multiplicative inverse of A is expressed as A-1.
47.
If the greatest degree of the variable in an equation of one variable is two, then the equation is said to be a
quadratic equation in one variable.
48.
The equation ax2 + bx + c = 0 is called Non-standard form of a quadratic equation in one variable.
49.
x2 – 5x –2 = 0 is the standard form of the quadratic equation.
50.
There are two forms of solving a quadratic equation by factorization provided a, b  R, ab = 0. Solution of
Binomial equation by factorization depends upon the factors a, b  R, ab = 0. There can be two possibilities.
51.
Elimination means to eliminate a certain variable.
52.
As a result of elimination the new equation or relation obtained is called eliminant.
53.
The relation obtained as a result of the elimination of a variable will prove the fact that the solution of these
equations is an empty set.
54.
A variable may be eliminated either by comparison or by substitution.
55.
In the log of a number the integral part is called characteristic.
56.
In the log of a number the mantissa is negative.
57.
In 765.0234 the po8int of reference is between 7 and 6.
58.
Because log 2 = 0.3010, log 3 = 0.4771 therefore log 6 = 0.7781.
59.
There are at least four non-collinear points in a plane.
60.
If two points of a line lie on a plane, then the whole line lies on that plane.
61.
A ray has two end points.
62.
The union of two rays with a common end point is called an angle.
63.
If two lines are parallel to a third line, they are parallel to each other.
64.
 is the notation for congruence.
65.
Opposite rays are parallel.
66.
There can be only one right angle in a triangle.
67.
From a point outside a line, one and only one perpendicular can be drawn.
68.
Two circles are congruent if their radii are congruent.
69.
The inscribed angle of a minor arc of a circle is acute.
70.
The circle, its interior and its exterior are three disjoi9nt sets of points.
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71.
The bisectors of one interior and two exterior angles of a triangle are concurrent.
72.
The bisectors of the interior angles of a triangle are concurrent.
73.
The perpendicular bisectors of the sides of a triangle are not concurrent.
74.
The centre of the inscribed circle of a triangle is equidistant from its vertices.
75.
Cosec 50 = sec 40.
76.
Tan 40 = cot 30.
77.
Cos 80 = sin 10.
78.
Numerical facts collected on the first hand and recorded as they stand are known as ungrouped data.
79.
Numerical information when arranged in certain groups or classes, having similar characteristic is known as
classification.
80.
The size of class interval is known as Frequency of that class.
81.
In a class interval (6 – 10) the upper limit is 6.
82.
In class interval (11 – 20) the lower limit is 11.
83.
To find out the mid point of any class we take the difference between the upper and lower limits.
84.
In a data the middle item is the median.
85.
In ungrouped data the arithmetic mean is obtained by the multiplication of the values given.
86.
The number of road accidents is a discrete variable.
87.
The number of rooms in a school is continuous variable.
88.
The group, which contains maximum frequency, is known as modal group.
89.
In a series the difference between the highest and the lowest value is known as Range (R).
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