Preparied By Sir. Imran
SS Teacher at APS & C Zamzama(Nowshera)
CHAPTER NO 1
SETS
1: The objects involved in a set are called its:
a. Operations b. Powers
c. Entries d. Elements
2: The presence of an element in a set is denoted by the symbol:
a. b.
c. U d. ∩
3. Elements which do not belong to a set are denoted by:
a. b. c. U d. ∩
4: How many methods are there to present a set?
a. Four b. Three
c. Two d. None of these
5: If there is no element present in a set it is called a (an):
a. Empty b. Singleton set
c. Even number set d. None of these
6: Null or empty set is denoted by:
a. {Φ} b. { } or Φ
c. {a} d. None of these
7: Set {1, 2, 3…} is called a set of:
a. Whole numbers b. Natural numbers
c. Prime numbers d. Even numbers
8: If the number of elements in a set is finite, it is called:
a. Finite set b. Infinite set
c. Equal set d. None of these
9: If A and B are two sets and every elements of set A is also an element of set B, then A is called:
a. Identity element of B b. Inverse of set B
c. Subset of set B d. Complement of set B
10: If the number of elements in a set is not a finite, it is called:
a. Finite set b. Infinite set
c. Equal set d. None of these
11: If set A is a subset of set B, then it is denoted by:
a. B A b. A A
c. A B d. B < B
12: If set A is not a subset of set B, then it is denoted by:
a. A B b. A < A
c. A A d. A B
13: Empty set is a proper subset of every:
a. Non-empty set b. Empty set
c. Union d. None of these
14: Every set is a subset of itself but not:
a. Proper subset b. Universal set
c. Complement set d. None of these
15: Every set is an improper subset of:
a. Every other set b. Itself
c. Universal set d. None of these
16: There is only one proper subset of a:
a. Singleton set b. Empty set
c. Set having two elements d. None of these
17: There is no proper subset of a:
a. Singleton set b. Empty set
c. Intersection of sets d. None of these
18: If A is any set, then a set consisting of all the subsets of the set A is called:
a. Proper subset of A b. Improper subset of A
c. Power set of A d. None of these
19: power set of A is denoted by:
a. A (P) b. P (A)
c. P (B) d. P (A + B)
20: If a set has 3 elements, then no. of elements in the power set are:
a. 16 b. 8
c. 4 d. 1
21: If a set A has 4 elements, then no. of elements in P(A) is :
a. 16 b. 8
c. 2 d. 1
22: Difference of two sets A and B given by:
a. A ∩B b. A U B
c. (A ∩B)c d. A - B
23: Difference of two sets A and B is a set consisting of those elements which are in set A but not in:
a. Ac b. A
c. Bc d. B
24: If A B, then A – B=
a. A b. B
c. A ∩B d. Φ
25: If A U , then U – A is called:
a. Union of sets b. Intersection of sets
c. Universal set d. None of these
26: If Ac is the complement of set A, then A U Ac :
a. A b. Ac
c U d. None of these
27: A ∩ Ac =
a. A b. Ac
c {Φ} d. { }
28: complement of an empty set is:
a. Empty set b. Universal set
c A d. Ac
29: Set {0, 1, 2, 3…} is called a set of:
a. Whole numbers b. Natural numbers
c. Prime numbers d. Even numbers
30: Set {0, ±1, ±2, ±3…} is called a set of:
a. Whole numbers b. Natural numbers
c. Prime numbers d. Integers
31: Set {2, 3, 5, 7, 11…} is called a set of:
a. Whole numbers b. Natural numbers
c. Prime numbers d. Integers
32: Set {±1, ±3, ±5…} is called a set of:
a. Whole numbers b. Natural numbers
c. Prime numbers d. Odd numbers
33: Set {0, ±2, ±4…} is called a set of:
a. Whole numbers b. Prime numbers
c. Integers d. Even numbers
34: Set of irrational numbers is denoted by:
a. O b. Q
c. Q/ d. R
35: The set of first five natural in set builder notation is written as:
a. {x x N x 5} b. {x x N x 5}
c. {x x W x 5} d. {x x P x 5}
36: The set builder notation of set {2,3,5,7,11} is :
a. {x x P 2 x 11} b. {x x P 2 x 11}
c. {x x O 2 x 11} d. None of these
37: Set of rational numbers in set builder notation is written as:
a. {x x ,q 0, p, q z} b. {x x , q 0, p, q z}
c. {x x , q = 0, p, q z}d. None of these
38: Set of irrational numbers in set builder notation is written as:
a. {x x , q 0, p, q z} b. {x x , q 0, p, q z}
c. {x x , q = 0, p, q z} d. None of these
39: If A and B are the subsets of a universal set U, then (AUB)c =
a. Ac U Bc b. Ac
c. Bc d. Ac ∩ Bc
40: If A and Bare the subsets of a universal set U, then (A∩B)c =
a. Ac U Bc b. Ac
c. Bc d. Ac ∩ Bc
41: (A U B) U C =
a. (A U B) ∩C b. (A ∩ B) UC
c. (A ∩ B) ∩C d. A U (B U C)
42: A∩(B ∩ C) =
a. (A ∩ B) UC b. (A ∩ B) ∩C
c. (A U B) ∩C d. (A U B) U C
43: If A, B and C are disjoint sets then (A∩B)∩C =
a. A b. B
c. C d. Φ
44: In the ordered pair (x, y) are two different numbers, then (x, y) ≠ ( ):
a. x2 , y2 b. y , x
c. y2, x2 d. None of these
45: (1, 2) and (2,1) are two:
a. Same pairs b. Different pairs
c. Sets d. None of these
46: (x, y) and (a, b) are two:
a. Same pairs b. Different pairs
c. Sets d. None of these
47: (a, b) and (a, b) are two:
a. Same pairs b. Different pairs
c. Sets d. None of these
48: Cartesian product of sets A and B is denoted by:
a. A B b. A A
c. B A d. B B
49: Set builder notation of A B is as:
a. {(a, b) a A b B} b. {(a, b) a B b A}
c. {(A, b) a A b B} d. {(a, b) b A b B}
50: If A ≠ B, then A B ≠
a. B A b. A B
c. none of these d. both (a) and (b)
51: If number of elements in set A is 2 and in set B is 3, then no. of elements in set A B is:
a. p q b. p p
c. q q d. None of these
52: If A = {1, -1} and B = {0, 2}, then the number of elements in A B or B A is:
a. 4 b. 6
c. 8 d. 10
53: The point where XX/ and YY/ cut each other perpendicularly is called:
a. Tangent b. Line
c. Origin O(0,0) d. None of these
54: Horizontal line XX/ is called:
a. Vertical line b. x-axis
c. y-axis d. None of these
55: Vertical line YY/ is called:
a. Vertical line b. x-axis
c. y-axis d. None of these
56: In the ordered pair p(a , b) “a” is called:
a. Ordinate b. Abscissa
c. Pain d. None of these
57: In the ordered pair p(a , b) “b” is called:
a. Ordinate b. Abscissa
c. Pain d. None of these
58: Both axes divide the plane into:
a. two parts b. Four parts
c. Six parts d. Eight parts
59: Every part of the plane is called:
a. Half plane b. Quadrant
c. Ordinate d. Abscissa
60: In first quadrant,
a. x >0, y>0 b. x <0,y>0
c. x >0, y<0 d. x <0, y<0
61: In second quadrant,
a. x >0, y>0 b. x <0,y>0
c. x >0, y<0 d. x <0, y<0
62: In third quadrant,
a. x >0, y>0 b. x <0,y>0
c. x >0, y<0 d. x <0, y<0
63: In forth quadrant,
a. x >0, y>0 b. x <0,y>0
c. x >0, y<0 d. x <0, y<0
64: The point (2, 3) lies in quadrant:
a. Ist b. 2nd
c. 3rd d. 4th
65: The point (-2, 3) lies in quadrant:
a. Ist b. 2nd
c. 3rd d. 4th
66: The point (-2, -3) lies in quadrant:
a. Ist b. 2nd
c. 3rd d. 4th
67: The point (2, -3) lies in quadrant:
a. Ist b. 2nd
c. 3rd d. 4th
68: Binary relations of A B and B A are:
a. Same b. Different
c. Not possible d. None of these
69: If A = {1},B = {a , b}then A B=
a. {(1, a), (1, 1)} b. {(1, a), (1, b)}
c. {(a, 1), (b, 1)} d. {(a, 1), (b, a)}
70: If A ={1}, B = {a , b}then no. of binary relations in A B are :
a. 4 b. 8
c. 3 d. 1
71: The point (a, b) lies in quadrant:
a. Ist b. 2nd
c. 3rd d. 4th
72: The point (-a, b) lies in quadrant:
a. Ist b. 2nd
c. 3rd d. 4th
73: The point (-a,-b) lies in quadrant:
a. Ist b. 2nd
c. 3rd d. 4th
74: The point (a,-b) lies in quadrant:
a. Ist b. 2nd
c. 3rd d. 4th
75: Domain of R = {(1, -1), (2, -1), (2, 3)} is:
a. {1, -1} b. {-1, 1}
c. {1, 2} d. {1, -3}
76: Domain of R = {(1, 2),(2, 3),(0, 4)} is:
a. {1, 3, 4} b. {1, 2, 3}
c. {1, 2, 0} d. {2, 3, 4}
77: Range of R = {(1, -1),(2, -1),(2, -3)} is:
a. {1, -1} b. {-1, 1}
c. {1, 2} d. {-1, -3}
78: Range of R = {(1, 2),(2, 3),(0, 4)} is:
a. {1, 3, 4} b. {1, 2, 3}
c. {1, 2, 0} d. {2, 3, 4}
79: If range (f) =B, and f is such a function from set A to set B if:
a. Onto Function b. Into Function
c. Bijective Function d. None of these
80: Binary relation f = {(1, x), (2, 3)}
a. Onto Function b. Into Function
c. One-to-One Function d. None of these
81: f is called one-to-one onto or bijective function if:
a. f is onto function b. f is into function
c. f is one-to-one function d. both (a) and (c)
82: For any two sets A and B, A∩B=
a. BUA b. A∩B
c. B∩A d. AUA
83: For any two sets A and B, AUB=
a. BUA b. A∩B
c. B∩A d. AUA
84: If A U, then A∩Ac =
a. Φ b. U
c. A d. Ac
85: The complement of { } is:
a. Empty set b. Universal set
c. Finite set d. Infinite set
86: If A and B are any two sets with no common element in them, then A∩B is:
a. { } b. Empty set
c. Φ d. All of these
87: (A∩B)c =
a. AcUBc b. Ac∩Bc
c. A∩B d. BcUAc
88: (AUB)c =
a. AcUBc b. Ac∩Bc
c. A∩B d. BcUAc
89: A U (B∩A) =
a. (AUB) ∩ (AUC) b. (A∩B) ∩ (A∩C)
c. (AUB) U (A∩C) d. (AUB) U (AUC)
90: If no. of elements in set A is 3 and in set B is 2, then no. of elements in A B is:
a. 8 b. 4
c. 12 d. 6
91: If A = {x, y} B = {a, b, c} then a binary relation f = {(x, a), (x, b), (x, c)} is……function.
a. Onto b. Into
c. One-to-One d. Not
92: Since A B ≠ B A, so binary relations of A B and B A are………..
a. Equal b. Same
c. Not possible d. Different
93: First three natural numbers set is:
a. {0, 1, 2} b. {±1, ±2, ±3}
c. {1, 2, 3} d. both (b) and (c)
94: If A∩B=Φ, then A and B are called:
a. Joint set b. Equal set
c. Disjoint set d. Unequal set
95: If A = {+, } and B = {-, } So A∩B is:
a. { } b. {+, - , , }
c. Φ d. (a) and (c) both
96: If A ∩ B ≠ Φ, then the set is called_________________:
a. Overlapping set b. Singleton set
c. Disjoint set d. Null set
97: If the number of elements in a set x is n, the number of elements in P(x) is _________:
a. 2n b. 22n
c. 2n d. n2
98: If (2, 6) = (x + 1, y +3) then the value of y is__________________:
a. 1 b. 2
c. 3 d. 9
99: If F:A B such that F = B, then F is called a function from A B
a. Into b. Onto
c. (1- 1) d. None of these
100: A B = B A if and only if_____________:
a. A = B b. A > B
c. A < B d. A ≠ B
CHAPTER NO 2
SYSTEM OF REAL NUMBERS
1: Which of the following sets have closure property w.r.t. addition?
b. A set of odd number b. A set of natural number
c. A set of prime number d. All of these
2: a + b = b + a, shows
a. Commutative property w.r.t. addition
b. Associative property w.r.t. addition
c. Distributive property of multiplication over addition
d. None of these
3: a a-1 = a-1 a = 1, shows
a. Distributive property of multiplication
b. Associative property of multiplication
c. Multiplicative inverse
d.. Multiplicative identity
4: Additive inverse of is
a. b. -
c. d. -
5: “O’’ is called
a. Additive inverse b. Additive identity
c. Multiplicative inverse d. Multiplicative identity
6: is equal to:
a. x2 b.
c. x3 d. x-3
7: a. 4 b.
c. t2 d. t-2
8: The value of is:
a. b. 4
c. - d. -4
9: (-2 4)2 =_____________
a. 64 b. -64
c. -16 d. 16
10: The power of a negative number is positive if its exponent is______________
a. Positive b. Even number
c. Odd number d. None of these
11: =______________
a. 2-3 b. 23
c. 2-12 d. 212
12: (7- ) (7+ ) =_________________
a. 49 b. 47
c. 9 d. 5
13: If x = - 1 then x2 =_______________
a. b. + 1
c. 1 d. 3 - 2
14: In the notation is called______________
a. Radicand b. Index
c. Radical d. None of these
15: If a > b -a__________ -b
a. > b. <
c. d. ≤
16: (-x)2(-x)3(-x)4 =__________
a. (-x)9 b. (x)9
c. (-x)24 d. None of these
17: =_____________
a. b.
c. d. None of these
18. Multiplicative inverse of is___________
a. 2 b. -1
c. d. 1
19: If x = 0 then =_____________
a. 0 b. 1
c. d.
20: 13 (13)0 is equal to
a. 169 b. 1
c. 0 d. 13
21: There exists a closure property w.rt.____________ in {0, 1}
a. Addition b. Subtraction
c. Multiplication d. Division
22: If x = + 2, then x + =_______________________
a. 2 - b. 4
c. -2 d. None of these
23. Multiplicative inverse of “zero” is___________
a. 1 b. Does not exist
c. 0 d. None of these
24: The only even prime number is
a. 0 b. 4
c. 2 d. 6
25: The set {-1, -2, -3…} is closed with respect to
a. Addition b. Subtraction
c. Multiplication d. Division
26: {(2 - )0}2 is equal to
a. 1 b. 0
c. 2 + d. 2 -
27: -3 is a number:
a. Rational b. Irrational
c. Imaginary d. None of these
28: is not a number:
a. Rational b. Irrational
c. Imaginary d. None of these
29: 0.1555……, is a decimal fraction:
a. Recurring b. Terminating
c. Non- recurring d. None of these
30: 0.101001000…. is decimal fraction:
a. Rational b. Terminating
c. Non- terminating d. None of these
31: 2.012 is a decimal fraction:
a. Recurring b. Terminating
c. Non- recurring d. Non- recurring non-terminating
32: The intersection of sets Q and Q/ is:
a. set R b. Empty set
c. set Q d. set Q/
33: The union of sets Q and Q/ is:
a. set R b. Empty set
c. set Q d. set Q/
34: The number is a numbers:
a. Rational b. Irrational
c. Imaginary d. None of these
35: For all a, b R, a + b R this is called:
a. Closure property w.r.t addition
b. Commutative property w.r.t addition
c. Associative property w.r.t addition
d. Additive identity
36: For all a, b R, a + b R this is called:
a. Closure property w.r.t addition
b. Commutative property w.r.t addition
c. Associative property w.r.t addition
d. Additive identity
37: For all a, b, c R: (a + b) + c = a + (b + c), is called:
a. Closure property w.r.t addition
b. Commutative property w.r.t addition
c. Associative property w.r.t addition
d. Additive identity
38: There exists 0 R such that for all x R, x + 0 = 0 + x = x, is called:
a. Closure property w.r.t addition
b. Commutative property w.r.t addition
c. Associative property w.r.t addition
d. Additive identity
39: For all a, b R, ab R this is called:
a. Closure property w.r.t addition
b. Commutative property w.r.t addition
c. Associative property w.r.t addition
d. Multiplicative identity
40: For all a, b, c R: (ab) c = a (bc), is called:
a. Closure property w.r.t multiplication
b. Commutative property w.r.t multiplication
c. Associative property w.r.t multiplication
d. Multiplicative identity
41: For all a R, a 1 = a = 1 a the number “1” is called:
a. Closure property w.r.t multiplication
b. Commutative property w.r.t multiplication
c. Associative property w.r.t multiplication
d. Multiplicative identity
42: For all a, b, c R: (a + b) c = ac + bc , is called:
a. Closure property w.r.t addition
b. Commutative property w.r.t addition
c. Associative property w.r.t addition
d. Distributive property of multiplication over addition
43: x R, x = x this is called:
a. Reflexive property b. Symmetric property
c. Transitive property d. Additive property
44: x, y R, x = y y = x this is called:
a. Reflexive property b. Symmetric property
c. Transitive property d. Additive property
45: x, y, z R, x = y and y = z x = z this is called:
a. Reflexive property b. Symmetric property
c. Transitive property d. Additive property
46: x, y, z R, x = y x +z = y + z this is called:
a. Reflexive property b. Symmetric property
c. Transitive property d. Additive property
47: An expression which involves at least one irrational number is called:
a. Surd b. Polynomial
c. Inequality d. Equality
48: is a:
a. Rational number b. Imaginary number
c. Surd d. None of these
49: 3 + is a:
a. Binomial surd b. Rational number
c. Trinomial d. None of these
50: Simplified form of is:
a. 4 b. 64
c. 125 d. 98
51: If 5 > 3 -10__________ -6
a. > b. <
c. d. ≤
52: Product of (7- ) and (7+ ) is:
a. Irrational number b. Rational number
c. Surd of 7th and 2th order d. None of these
CHAPTER NO 3
LOGRITHMS
1: 3log – 2log3 in simplified is
a. log b. log
c. 2log6 d. log36
2: Characteristic of log 0.00421 is
a. -3 b. -2
c. 3 d. 4
3: The standard form of 2.35 10-2 is
a. 500 b. 0.0235
c. 700 d. 1000
4: x = then x =________________
a. 27 b.
c. d.
5: log5 + log8 –log3 =
a. 5log b. 3log40 c. log d. 3log
6: log 10 =____________________
a. 0 b. 1
c. 10 d. 2
7: Common logarithm has the base_______________________
a. 2 b. e
c. d. 10
8: Find the value of x if log x 216 =3
a. 216 b. 3
c. 6 d. x216
9: Logarithmic form of 54 = 625 is
a. log5625 =4 b. log45 =625
c. log54 =625 d. log4625 =5
10: Natural logarithm has the base_______________________
a. 2 b. e
c. d. 10
11: Characteristic of log 9925.4 is:
a. 1 b. 3
c. 2 d. -1
12: The standard form of 9.3518 102 is :
a. 0.093518 b. 0.0093518
c. 93518 d. 935.18
13: Speed of light is:
a. 3 1010 cm/hour b. 3 1010 cm/sec
c. 3 1010 km/sec d. None of these
14: 30000000000 cm/second in scientific notations:
a. 3 10-8 m/sec b. 3 108 m/sec
c. 10 38 m/sec d. 1 38 m/sec
15: Who is the pioneer of logarithms?
a. Johan Napier b. Briggs
c. Al-khwarizmi d. None of these
16: Value of “e”, the base fixed by Johan Napier was:
a. 2.71828 b. 1.7183
c. 0.7183 d. 0.07183
17: The logarithms to the base “e” are called:
a. Briggs or common logarithms
b. Natural or Naperian logarithms
c. Equivalent statements
d. None of these
18: The logarithms to the base “10” are called:
a. Briggs or common logarithms
b. Natural or Naperian logarithms
c. Equivalent statements
d. None of these
19: The logarithmic value of the number between 10 and 100 is between:
a. 0 and 1 b. 1 and 2
c. 2 and 3 d. 3 and 4
20: The logarithmic value of a number consists of:
a. only one b. two parts
c. three parts d. None of these
21: Characteristic is always:
a. Negative b. Positive
c. both (a) and (b) d. None of these
22: Mantissa is always:
a. Negative b. Positive
c. both (a) and (b) d. None of these
23: The integral part of the logarithm of any number is called:
a. Mantissa b. Characteristic
c. both (a) and (b) d. None of these
24: The fractional part of the logarithm of any number is called:
a. Mantissa b. Characteristic
c. both (a) and (b) d. None of these
25: Reference position is represented by the symbol:
a. “^” b.
c. = d. ≠
26: Mantissa of log x = 0.5019 is:
a. 0.5019 b. 2
c. -2 d. 4
27: If log x = 2 then the value of x is:
a. 10 b. 1
c. 100 d. 0.10
28: If log x = 3.1923, then characteristic of log x is:
a. 1 b. 3
c. 3.1 d. 10.1923
29: Mantissa of log x is_______________ if log x = 2.5321.
a. 0.5321 b. -0.5321
c. 2 d. -2
30: If log x = -2.3781, then, mantissa is:
a. 2 b. -2
c. 0.3781 d. -0.3781
31: Expressing numbers (large or small) as powers of 10 is called:
a. Scientific notation b. Standard notation
c. Logarithmic notation d. None of these
32: Who wrote the first book on Algebra?
a. Johan Napier
b. Briggs
c. Abu-Muhammad Musa Al-Khourarizmi
d. None of these
33: Name of first book on Algebra was:
a. Basic Algebra
b. Aljabar-wal-maqabla
c. Collage Algebra
d. Algebra and Trigonometry
34: Decimal number system is based on:
a. Base 10 b. Base e
c. Both (a) and (b) d. None of these
CHAPTER NO 4
ALGEBRAIC EXPRESSIONS
1: If x + y = 2 and xy = 3, then the value of x2 + y2 =_______________
a. 4 b. -2
c. -4 d. 2
2: ________ will be added to complete the square of x2 + 4xy
a. 4x2 b. 2y2
c. (2y)2 d. 4y
3: (2-4)3 = _________________
a. 2-12 b. 2-4
c 23 d. 212
4: (7 - ) (7 + ) =_________
a. 48 b. 36
c. 25 d. 47
5: 4x3y2 + 3 is a polynomial of degree ______________
a. 2 b. 5
c. 0 d. 3
6: A variable is symbol which represents the elements of:
a. Empty set b. Non-empty set
c. None of these d. All of these
7: In 2x = 3 what is variable?
a. 2 b. 3
c. d. x
8: In 3x2 what is variable?
a. 2 b. 3
c. x d. 6
9: No. of variables in 6x2y3 are:
a. 3 b. 2
c. 1 d. None of these
10: A constant polynomial has degree:
a. 0 b. 1
c. 2 d. 3
11: 2x3 + 5y2 + is:
a. Polynomial of degree 2 b. Not a polynomial
c. Trinomial d. None of these
12: If a polynomial has only one term, it is called:
a. Monomial b. Binomial
c. Trinomial d. None of these
13: If a polynomial has only two terms, it is called:
a. Monomial b. Binomial
c. Trinomial d. None of these
14: If a polynomial has only three terms, it is called:
a. Monomial b. Binomial
c. Trinomial d. None of these
15: x2 + 3x + 2 is a:
a. Monomial b. Binomial
c. Trinomial d. None of these
16: Degree of monomial 5x3yz5 is:
a. 5 b. 3
c. 9 d. 1
17: x2 + 5x + 2 is written in:
a. Descending order b. Ascending order
c. No order d. None of these
18: If P(x) = x3 -7x -6, then find P(-5):
a. -96 b. -166
c. -151 d. -93
19: In division of polynomials, coefficients are to be:
a. Added b. Subtracted
c. Divided d. Multiplied
20: In multiplication of polynomials, coefficients are to be:
a. Added b. Subtracted
c. Divided d. Multiplied
21: (x - 6) (x - 4) = _________________
a. x2 + 10x + 24 b. x2 - 10x – 24
c. x2 + 10x – 24 d. x2 - 10x + 24
22: If a + b = 7, ab = 12, then a2 + b2 =___________
a. 25 b. -25
c. 5 d. 52
23: (a - 1) (a + 1) (a2 + 1) is equal to:
a. a3 – 1 b. (a2 -1)2
c. a4 – 1 d. a4 + 1
24: x2 – 5x + 6 is exactly divisible by:
a. x + 3 b. x + 2
c. x – 2 d. x - 9
25: The number of variables in 5x3 + 3xyz + 5y3 is _______________.
a. 3 b. 1
c. 2 d. 5
26: If a - b = 5, ab = 7, then a2 + b2 =___________
a. 11 b. 21
c. 39 d. 53
27: 2x + 3y + 5 is a polynomial as natural number with:
a. Variables b. Constants
c. Exponent d. None of these
28: a – 2 is a factor of:
a. a – 2 b. a + 4
c. a2 + 4 d. a2 – 4
29: If P(x) = 9x4 – 3x2 + 2x + 11, then P (3) is:
a. 778 b. 680
c. 194 d. 719
30: How many kinds of algebraic expressions are there?
a. Two b. Three
c. Four d. Five
31: A polynomial in one variable “x” is denoted by:
a. P (x, y, z) b. P (x, y)
c. P (x) d. None of these
32: A polynomial in two variables “x and y” is denoted by:
a. P (x, y, z) b. P (x, y)
c. P (x) d. None of these
33: A polynomial in three variables “x, y and z” is denoted by:
a. P (x, y, z) b. P (x, y)
c. P (x) d. None of these
34: 3x + 4 is a:
a. Linear polynomial b. Quadratic polynomial
c. Cubic polynomial d. None of these
35: 5x2 - 3x + 4 is a:
a. Linear polynomial b. Quadratic polynomial
c. Cubic polynomial d. None of these
36: 8x3 + 5x2- 3x + 4 is a:
a. Linear polynomial b. Quadratic polynomial
c. Cubic polynomial d. None of these
37: If a + b = 3, a – b = 2 then a2 – b2______________:
a. 5 b. 2
c. 6 d. 13
38: If a + b = 5, a – b = 3 then 4ab______________:
a. 16 b. 34
c. 17 d. 4
39: If a + b = 5, a – b = 3 then a2 + b2______________:
a. 16 b. 34
c. 17 d. 4
40: If (x – 1) is a factor of (x3 + x2 - 10x + 8) then remainder is _______________:
a. 1 b. 2
c. 0 d. -1
41: If product of two polynomial is x2 – 5x + 6 and one polynomial is x – 2, then other is___________:
a. x + 3 b. x – 3
c. x – 4 d. x + 4
42: If sum of two polynomial is x2 – 5x – 3 and one polynomial is x2 – 6x, then other is___________:
a. x + 3 b. x – 3
c. x – 4 d. x + 4
CHAPTER NO 5
FACTORIZATION, H.C.F, L.C.M,
SIMPLIFICATION AND SQUARE ROOT
1: If P(x) = x3 -7x -6, then find P (-5):
a. -96 b. -166
c. -151 d. -93
2: If a3 + b3 + c3 =3abc then a + b + c =
a. 0 b. 5
c. b d. None of these
3: x2-5x+6 =(x - 2) (…………) =
a. x - 2 b. x - 3
c x + 3 d. x + 2
4: HCF of x2 – 4 and x + 2 is:
a. x +2 b. x - 2
c. x2 - 4 d. x2 + 4
5: LCM of c3a2, c2a5 and 4a4b3c5 =:
a. 4a4b3c5 b. 4a3b3c5
c. 4abc d. 4a5b3c5
6: If P(x) = 9x4 – 3x2 + 2x + 11, then P (3) is:
a. 778 b. 680
c. 194 d. 719
7: Factorization of ac + bc + ad + bd are:
a. (a - b) and (c + d) b. (a + b) and (c + d)
c. (a - b) and (c - d) d. (a + b) and (c - d)
8: Factorization of x2 + x – 6 is:
a. (x - 2) (x - 3) b. (x - 2) (x + 3)
c. (x + 2) (x + 3) d. (x + 2) (x - 3)
9: Factorization of x4 + x2 + 1 is:
a. (x2 – x + 1) (x2 + x + 1) b. (x2 – x + 1)2
c. (x2 + x + 1)2 d. None of these
10: Factorization of 5x2 - 17xy – 12y2 is:
a. (x – 4y) (5x + 3y) b. (x + 4y) (5x - 3y)
c. (x – 4y) (5x - 3y) d. None of these
11: 1 + 2ab – (a2 + b2) =______________.
a. (1 + a - b)(1 – a + b) b. (1 - a - b)(1 + a + b)
c. (1 – a – b )2 d. (1 + a + b )2
12: a3 + b3 =_______________.
a. (a – b) (a2 + ab + b2) b. (a + b) (a2 - ab + b2)
c. (a + b)2 (a + b) d. (a - b)2 (a - b)
13: a3 - b3 =_______________.
a. (a – b) (a2 + ab + b2) b. (a + b) (a2 - ab + b2)
c. (a + b)2 (a + b) d. (a - b)2 (a - b)
14: H.C.F of x2 + 3x + 2, x2 + 4x + 3, x2 + 5x + 4 is:
a. x + 2 b. x + 1
c. x - 1 d. x – 2
15: For what value of m, x2 + 4x + m is a complete square:
a. 8 b. -8
c. 4 d. -4
16: If x3 – 7x – 6 is divided by x + 1, then remainder is:
a. 0 b. 3
c. 7 d. 6
17: Common factor in x2 + 3x + 2, x2 + 4x + 3, x2 + 5x + 4 is:
a. x – 1 b. 2x – 1
c. x + 1 d. x – 2
18: If a + b + c = ……… then a3 + b3 + c3 =3abc:
a. 0 b. 5
c. b d. None of these
19: If a + b + c =0, then a3 + b3 + c3 =_________.
a. -3abc b. 3abc
c. 2abc d. 3a3b3c3
20: One factor of x6 – 81x2 is:
a. x + 3 b. x2 – 3
c. x2 – 9 d. x
21: Square root of a2 – 2a + 1 is:
a. ± (a – 2) b. ± (a + 1)
c. ± (2a – 1) d. ± (a – 1)
22: Factor of x8 – y8 is:
a. x – y b. x2 + y2
c. x + y d. All of these
23: a3 + b3 + c3 – 3abc = ____________________:
a. (a + b + c) (a2 + b2 + c2 – ab – bc + ca)
b. (a + b + c) (a2 + b2 + c2 + ab + bc - ca)
c. (a + b + c) (a2 + b2 + c2 – ab – bc - ca)
d. (a + b + c) (a2 + b2 + c2 + ab + bc + ca)
24: What will be added in 9a2 – 12abc to make it a perfect square?
a. -16b2 b. 16b2
c. 4b2 d. None of these
25: If x2 + 3x + 3 is divided by x + 1, then remainder is:
a. 0 b. 1
c. 3 d. 2
26: H.C.F. of a2 - b2 and a4 – b4 is______________:
a. a2 - b2 b. a2 + b2
c. a4 – b4 d. a4 + b4
27: L.C.M. of a2 - b2 and a4 – b4 is______________:
a. a2 - b2 b. a2 + b2
c. a4 – b4 d. a4 + b4
28: If A = x2 – 1, H = x – 1, L = x2 – 1 then B =______________:
a. x2 – 1 b. x2 + 1
c. x + 1 d. x – 1
CHAPTER NO 6
MATRICES AND DETERMINANTS
1: is a ……………….matrix:
a. Zero b. Identity
c. Rectangular d. Scalar
2: Additives inverse of [-4 8]=
a. [8 -4] b. [4 -8]
c. [4 8] d. [4 -4]
3: If X+ = , then X=
a. b.
c d.
4: If A= and B= then AB=
a. b.
c. d.
5: If A = , then A2=
a. b.
c. d.
6: Who gave the idea of matrices?
a. Arther Kally b. Robert
c. Newton d. None of these
7: A matrices consists of:
a. rows only b. columns only
c. rows and columns d. None of these
8: The number of rows in a matrix is denoted by:
a. m b. n
c. m n d. n m
9: The number of columns in a matrix is denoted by:
a. m b. n
c. m n d. n m
10: Order of a matrix is denoted by:
a. m n b. n m
c. m m d. n n
11: In real numbers, additive identity is:
a. 1 b. -1
c. 0 d. None of these
12: If 0 is added to the real number it:
a. Changes b. Does not change
c. Becomes undefined d. None of these
13: Additive inverse of a matrix A is written as:
a. -A b. At
c. A-1 d. -(-A)
14: PP-1 = P-1P = _____________.
a. I b. -I
c. P-1 d. I-p
15: In general AB_____________ BA.
a. = b. >
c. ≠ d. ≤
16: Elements of A and are:
a. Different b. Equal
c. Same d. None of these
17: Determinant of is:
a. 46 b. 1
c. 24 d. 42
18: If x = , then is equal to:
a. 30 b. -3
c. 6 d. -1
19: If is a singular matrix, then x =_______________.
a. 45 b. -45
c. x + 45 d. 44
20: The product of and is:
a. b.
c. d.
21: is equal to:
a. b.
c. d.
22: Order of matrix [a] is:
a. 1 1 b. 1 2
c. 2 1 d. 2 2
23: Order of matrix [a b] is:
a. 1 1 b. 1 2
c. 2 1 d. 2 2
24: In Cramer’s Rule x =___________.
a. b.
c. d.
25: In Cramer’s Rule y =___________.
a. b.
c. d.
26: is a ………… Matrix:
a. Singular b. Zero
c. Diagonal d. Unit
27: If is singular matrix, then x =_____________.
a. 3 b. 6
c. 4 d. 0
28: The elements of A and are:
a. Different b. Same
c. Only one different d. None of these
29: A square matrix is called a singular matrix if:
a. = 0 b. ≠ 0
c. Both (a) and (b) d. None of these
30: A square matrix is called a non-singular matrix if:
a. = 0 b. ≠ 0
c. Both (a) and (b) d. None of these
31: If A = [3 2], B = , then AB =_____________.
a. [95] b. [-95]
c. [19] d. [-19]
32: The multiplication AB of two matrices A and B is possible only when the no. of columns of matrix A is equal to:
a. no. of rows of B b. no. of rows of B
c. no. of columns of B d. None of these
33: Matrix [2 + 3] is called:
a. Zero matrix b. Row matrix
c. Rectangular matrix d. None of these
34: If A = then matrix A is called:
a. Identity matrix b. Diagonal matrix
b. Zero matrix d. Singular matrix
35: If A = then matrix A is called:
a. Identity matrix b. Diagonal matrix
b. Zero matrix d. Singular matrix
36: If A and B are two matrices the order of A = a b and order of B = c d then order of A B =
a. a a b. a b
c. b a d. b b
37: If A = , B = , show which one is possible:
a. A + B b. A – B
c. BA d. AB
38: If A = [3 2], B = then AB =__________:
a. [13] b. [-17]
c. [17] d. [-13]
39: If = then solution set =_____________:
a. {(2, 3)} b. {(3, 2)}
c. {(2, 2)} d. {(3, 3)}
40: If A = and = 16 then the value of a =______________:
a. 2 b. 14
c. 20 d. -2
41: [2 3] = [10] then the value of x:
a. 2 b. 8
c. -2 d. 5
CHAPTER NO 7
FUNDAMENTAL CONCEPTS OF GEOMETRY
1: If a = b, b = c, then a = c is called:
a. Postulates b. Axiom
c. Given d. Proof
2: A line can not be parallel to two__________ lines.
a. Parallel b. Intersecting
c. Collinear d. Perpendicular
3: Line segment has:
a. One point b. Two points
c. Three points d. Infinite points
4: Two intersecting lines:
a. are parallel b. are not parallel
c. Circle d. Triangle
5: The angle of measure 500 and 1300 are called as:
a. Adjacent angles b. Supplementary angles
c. Complementary angles d. Right angles
6: An angle of 900 is called:
a. Right angle b. Acute angle
c. Obtuse angle d. None of these
7: Two lines can intersect each other at:
a. One point b. Two points
c. Four points d. Many points
8: If un common arms of two adjacent angles are collinear, these are________angles.
a. Supplementary b. Alternate
c. Vertical d. Complementary
9: If m a. Complementary angles b. Supplementary angles
c. Acute angle d. None of these
10: All the points of a line lie on a plane if at least___________points of that lie on the plane.
a. One point b. Two points
c. Three points d. Four points
11: If M lies on AB between A and B, then it belongs to:
a. Half line MB b. HALF Line MA
c. Both half lines d. None of these
12: Each of the two supplementary angles can be:
a. Right angle b. Acute angle
c. Obtuse angle d. None of these
13: One and only one line can pass through:
a. One point b. Two points
c. Three points d. Four points
14: If n1 – n2 = 0, then:
a. n1 < n2 b. n1 > n2
c. n1 = n2 d. None of these
15: Notation of half line is:
a. b.
c. d.
16: If the corresponding ABC DEF, the pair of congruent sides is:
a. AB, DE b. V
c. BC, FE d. AB, FD
17: The measures of two angles of a triangle are 600 and 800. The measure of the
third angle will be:
a. 600 b. 400
c. 800 d. 200
18: A quadrilateral whose diagonals bisect perpendicularly is:
a. Square b. Rectangle
c. Trapezoid d. Parallelogram
19: In ABC, m AB + m BC will be:
a. = m AC b. < m AC
c. > m AC d. None of these
20: The base angles of a parallelogram are:
a. Complementary b. Supplementary
c. Congruent d. Both acute
CHAPTER NO 8
DEMONSTRATIVE GEOMETRY
1: In a triangle ABC, m a. 1000 b. 700
c. 300 d. 800
2: Sum of the measures of the angles of a triangle is:
a. 1800 b. 900
c. 3600 d. 2700
3: In a right triangle:
a. Acute angles are complementary.
b. Acute angles are supplementary.
c. One of the angles is obtuse.
d. One of the angles is of measures 00
4: The measures of two angles of a triangle are 600 and 800. The measure of the
third angle will be:
a. 600 b. 400
c. 800 d. 200
5: To draw a line at least_____________points are required.
a. One b. Two
c. Three d. Four
6: If two lines are cut by a third line, then the number of interior angles is:
a. 2 b. 1
c. 4 d. 8
7: Measure of each of six congruent angles around a point is:
a. 300 b. 600
c. 450 d. 900
8: The no. of different correspondences between two triangles is:
a. 2 b. 3
c. 4 d. 6
9: Measure of one angle of a mombus is 300. An other angle is:
a. 1000 b. 900
c. 1500 d. 1200
10: Measure of every angle of an equilateral triangle is:
a. 300 b. 600
c. 450 d. 900
11: The statement a = b ac = bc for all real numbers a, b, c is:
a. A postulate b. The transitive property of real numbers
c. An axiom d. Commutative Law
12: If more than two points lies on the same line they are said to be________points.
a. Non Collinear b. Equidistant
c. Mid d. Collinear
13: Every plane contains at least:
a. Five collinear points b. More than five collinear points
c. Two collinear points d. Three non collinear points
14: An angle is the union of two rays having common end point and lying on the:
a. Same triangle b. Same plane
c. Same fine d. Same side
15: Any point B is said to be in between of the points A and C if:
a. m
17: The supplement of an angle of measure 600 is angle of measure:
a. 300 b. 600
c. 1800 d. 1200
18: From figure the
b. Non adjacent angles
c. Supplement angles C
d. Obtuse angles
A B
19: If the arms other the common arm of two adjacent angles are opposite rays then
the angles are:
a. Complementary b. Both acute
c. Both obtuse d. Supplementary
20: If two lines intersect each other than the non adjacent angles are called:
a. Corresponding angles b. Reflex angles
c. Vertical angles d. Congruent angles
CHAPTER NO 9
PRACTICAL GEOMETRY
1: Certain figures exactly alike but different in size are called:
a. Similar b. Median
c. Equal d. Proportional
2: Straight lines, which bisect perpendicularly the sides of a triangle, are called
______________of the sides of the triangle.
a. Bisector b. Segment
c. Altitudes d. Right bisector
3: The medians of a triangle are always:
a. Collinear b. Concurrent
c. Congruent d. Perpendicular
4: The right bisectors of the sides of every triangle are:
a. Concurrent b. Parallel
c. Collinear d. Congruent
5: The altitudes of every triangle are always:
a. Concurrent b. Collinear
c. Right bisectors d. Non-concurrent
6: The bisectors of the angles of every triangle are always:
a. Perpendicular b. Concurrent
c. Collinear d. Non-collinear
7: The altitude of an/a_______________angled triangle meets outside:
a. Acute b. Right
c. Obtuse d. None of these
8: Perpendicular dawn form a vertex of a triangle to the opposite side is called:
a. Median b. Altitude
c. Right bisector d. None of these
9: If the medians of a triangle are also the bisectors of the angle the triangle is:
a. Scalene b. Isosceles
c. Equilateral d. None of these
10: With which measures we can construct a triangle?
a. 5cm, 5cm, 10cm b. 11cm, 5cm, 8cm
c. 2cm, 1cm, 3cm d. 6cm, 4cm, 10cm
11: In a right-angled isosceles triangle the other two angles are of measure:
a. 600 , 300 b. 450 , 450
c. 900 , 100 d. 700 , 200
12: Angle bisectors of a triangle are:
a. Perpendicular to each other b. Concurrent
c. Perpendicular to opposite sides d. Bisect the opposite side
13: In circle of a triangle:
a. Passes through its vertices b. Touches its sides
c. Its centre lies out side the circle d. Touches two sides internally
14: Right bisectors of the sides of a triangle:
a. Bisects the sides b. Perpendicular to the sides
c. Passes through the opposite vertex d. Both (a) and (b)
15: Medians of a triangle are:
a. Bisector of the sides through opposite vertex
b. Concurrent
c. Intersects each other in the ratio 2:1
d. All of these above
16: in a right-angled triangle ABC the point of concurrency of three attitudes is:
a. Point A C
b. Point B b. Point C
d. None of these
B A
17: A circle whose radius is 5 cm. A point P is 3.5 cm from its centre.
Then there will be:
a. Only two tangents from P to the circle.
b. Only one tangent to the circle.
c. No tangent can be drawn from P to the circle.
d. None of the above is true
18:
