Hssc i objective workbook

Mathematics
Objective
MathematicsMATHEMATICS
DEPARTMENT
PAKTURK INTERNATIONAL SCHOOLS AND COLLEGES
Intermediate Part I
By Engin Baştürk
PAKTURK

PAKTURK
MATHEMATICS
DEPARTMENT
Copyright PAKTURK MATHS DEPARTMENT, 2015
All rights reserved. No part of this publication may be reproduced,
translated, stored in a retrieval system of transmitted, in any form or by any
means, without the prior permission of PAKTURK MATHS DEPARTMENT.

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CLASS
XI
For any question mail us at info@pakturkmaths.com
Composed by Engin Baştürk FEDERAL BOARD
TYPE Objective Number System No 1
Q1: a bi can be written also as:
A) a bi B)  ,a b
C) a bi D)  ,b a
Q2: a bi can be written also as:
A) a bi B) a bi 
C)  ,a b D)  ,a b
Q3: a bi can be written also as:
A) a bi B) a bi 
C)  ,a b D) a bi
Q4: What is the value of 2
i ?
A) 0 B) -1
C) 1 D) i
Q5: i can be written as:
A)  1,0 B)  0,1
C)  1,0 D)  0, 1
Q6: 2
i can be written as ............
A)  1,0 B)  0,1
C)  1,0 D)  0, 1
Q7: What is the value of 40
i ?
A) 0 B) -1
C) 1 D) i
Q8: The real part of a complex number a bi is .......
A) b B)  0,1
C) a D)  0, 1
Q9: The imaginary part of a complex number a bi is:
A) b B)  0,1
C) a D)  0, 1
Q10: Any real number a can be written as: (as order pair of
complex numbers)
A) ai B)  0,a
C)  ,1a D)  ,0a

Q11:    , , ?a b c d 
A)  ,ac bd ad bc  B)  .ad bc ac bd 
C)  ,bd ac ad bc  D)  ,ac bd ad bc 
Q12:     ?a bi c di   
A)    ac bd ad bc i  
B)    bd ac ad bc i  
C)    ad bc ac bd i  
D)    ac bd ad bc i  
Q13:    , , ?a b c d 
A)  ,a d b c  B)  ,a c b d 
C)  2 ,2a d D)  ,b d a c 
Q14:     ?a bi c di   
A)    a d b c i   B)    a c b d i  
C)    a c b d i   D)    b d a c i  
Q15:  , , ?r R r a b  
A)  ,a b B)  ,ra b
C)  ,a rb D)  ,ra rb
Q16: If 1
, .........z a bi z
   
A) a bi B) a bi
C) 2 2 2 2
a b
i
a b a b

 
D) 2 2 2 2
a b
i
a b a b
 
 
Q17: If   1
, , .........z a b z
  
A)  ,a b B)  ,a b
C) 2 2 2 2
,
a b
a b a b
 
 
  
D) 2 2 2 2
,
a b
a b a b
 
 
  
Q18: If   1
1,2 , .........z z
  
A)
1
1,
2
 
 
 
B)
1 1
,
2 5
 
 
 
C)
1 2
,
5 5
 
 
 
D)
1 2
,
5 5
 
 
 
Q19: If 1
5 3 , .........z i z
   
A)
5 3
34 34
i B)
5 3
34 34
i 
C)
5 3
34 34
i D)
5 3
34 34
i 
Q20: Simplify
4
2 2i
A) 1 i B) 1 i
C) 2i D) i
Answer Key
1 2 3 4 5 6 7 8 9 10
B D A B B C C C A D
11 12 13 14 15 16 17 18 19 20
D A B C D C D D A B

CLASS
XI
Q1: Every real number is also a .............
A) Natural Number B) Complex Number
C) Rational Number D) Whole Number
Q2: If z a bi  then z is:
A) a ib B) a ib 
C) a ib  D) 2 2
a b
Q3: If z a ib  , then z a ib  is called …...... of z
A) Root B) Inverse
C) Conjugate D) Identity
Q4: The complex number "a "i is called purely:
A) Real B) Complex
C) imaginary D) None
Q5: z is same with ……………
A) z B) z
C) z D) z
Q6: If a+ bz i , then z  ________
A) 2 2
a b B) 2 2
a b
C) a b D) None of these
Q7: If z a bi  then z
A) 2 2
a b B) 2 2
a b
C) 2 2
a b D) 2 2
a b
Q8: Find the modulus of 3 4i
A) 5 B) 5
C) 5 D) 5
Q9: If 7 2z i  then z
A) 53 B) 53
C) 53 D) 45
Q10: If 1 5 4z i   and 2 5 2z i  then 1 2 ...........z z 
A) 4i B) 10
C) 10 D) 2i

Q11: Which of the following is equal to
2
z
A) 2
z B) .z z
C)
2
z D) z
Q12: 81 16   is equal to ………
A) 5i B) 5i
C) 13i D) 12i
Q13: 64 100   is equal to ………
A) 2i B) 2i
C) 18i D) 18i
Q14: 12 144  is equal to ………
A) 12 2 3i B) 12 2 3i
C) 12 2 3i  D) 12 4 3i
Q15: The polar form of a complex number is ….
A)  tan cotr i  B)  sin cosr i 
C)  sec cscr i  D)  sec cscr i 
Q16:
1 3
........
2 2
i

 
A) 3 B) 1
C) 2 D) 0
Q17:
2
............
1 i


A) 1 i B) 1 i
C)  2 1 i D)  2 1 i
Q18:
7
5

is ……..
A)
7
5
i
i
B)
7
5
C)
7
5
i D) None of these
Q19: The additive identity in Complex numbers is:
A)  0,0 B)  1,1
C)  1,0 D)  0,1
Q20: In terms of i , 3 ______.
A) 3i B) 3i
C) 3i D) 3i
Answer Key
1 2 3 4 5 6 7 8 9 10
B A C C C B B A A D
11 12 13 14 15 16 17 18 19 20
B A B A B B A C C B

CLASS
XI
Q1: 0 is ................
A) Positive Integer B) Irrational Number
C) Negative Number D) Complex Number
Q2: If z a bi  then z z
A) 2a B) 2a bi 
C) 2 2a bi D) 2bi
Q3: If z a bi  then z
A) a bi  B) a bi 
C) a bi D) a bi
Q4: If 2 3z i  then z
A) 2 3i B) 2 3i 
C) 2 3i  D) 3 2i
Q5: A complex Number is called zero complex number if
............x y 
A) B) 0
C) Non-zero D) Equal
Q6:  
2
2
,z C z z  
A) Imaginary B) Real
C) Zero D) Negative
Q7:  , cos sin ......
n
n Z i    
A) sin cosn i n  B) tan cotn i n 
C) cos sinn i n  D) cos sinn i n 
Q8: The numerical value of 2
i is ________
A) 1 B) 1 C) i D) 1
Q9: The product of two imaginary no is always:
A) Imaginary B) Real
C) Negative D) None of these
Q10: The quotient of two imaginary numbers in simplest
form is always ….
A) Real number B) Imaginary number
C) Positive D) negative

Q11: The value of 56
i is ………..
A) i B) -1 C) 1 D) i
Q12: Simplify
3
2 2i
A) 1 i B) 1 i C) 2i D)
3 3
4
i
Q13: Simplify    4 1 1i i  
A) 8 B) 8i C) 4i D) 8
Q14: Simplify
4 4
1
i
i


A) 8 B) 8i C) 4i D) 4i
Q15: Simplify  
3
1 i
A) 1 i B)  2 1 i 
C) 1 i D)  2 1 i
Q16:  
3
1 ?i 
A) 3 3i  B) 2 2i 
C) 2 2i D) 2 2i 
2
1 i
A) 2 B) 1 C) 2i D) 2i
2
1 i
A) 0 B) 1 C) 2i D) 4i
Q19: Simplify 2
1 2i i 
A) 0 B) 2i C) 4i D) 2i
Q20:  
11
2
?i 
A) 1 B) 0 C) 1 D) 2
Answer Key
1 2 3 4 5 6 7 8 9 10
D A C A B B D B B A
11 12 13 14 15 16 17 18 19 20
B D A C B D D C B C

CLASS
XI
Q1: 7 is ........
A) an irrational number B) a prime number
C) a rational number D) a whole number
Q2: Golden rule of fraction is that for 0, ...........
a
k
b
 
A)
ab
k
B)
k
ab
C)
kb
ka
D)
ka
kb
Q3: Whicf of the following sets has closure property with
respect to addition?
A)  1,1 B)  1
C)  1 D)  0
Q4: Whicf of the following sets has closure property with
respect to multiplication?
A)  1,1 B)  1
C)  1,0 D)  0,2
Q5: For , , , , 0, 0a b c d R b d   then
a c
b d

A)
ac bd
bd

B)
ab cd
bd

C)
ad bc
bd

D) abcd
Q6: Rational Numbers expressed in the form of ……..
A)
a
b
B)
a
b
C)
2
2
a
b
D) ab
Q7: For any two real No’s , 0x y x y   the x and y
are …………. of each other.
A) Identity B) Inverse
C) Reciprocal D) None of these
Q8: For any two real numbers , . 1x y x y  , this property
is called as …………..
A) Multiplicative Identity B) Multiplicative inverse
C) additive inverse D) none of these
Q9: The property used in  11 11 0   is said to be:
A) Additive Inverse B) Additive identity
C) Inverse D) None of These
Q10: For , ,a b c a c b c a b       , this
property is called _________ property w.r.t to addition.
A) Additive B) Multiplicative
C) Cancelation D) None of these

Q11: Which of the following sets has closure property w.r.t
multiplication ________?
A)  0 B)  0,1
C)  1,1 D)  0, 1
Q12: The value of 2 is …………
A) Rational Number B) Irrational number
C) Natural number D) None of these
Q13: Which of the following sets has closure property w.r.t
multiplication ________?
A)  2, 1,0 B)  2,0,1
C)  0, 1,1 D)  0, 1
Q14: The additive identity of real numbers is always ….
A) Two B) Three
C) One D) Zero
Q15: The property used in
 , ,x y z x y z x z y z         is ……… property.
A) Distributive B) Commutative
C) Associative D) None
Q16: The sum of Real and Imaginary numbers is known as
….
A) Real Number B) Complex Number
C) Rational Number D) Irrational Number
Q17: Which of the following is associative property of real
numbers?
A) A B B A  
B)    A B C A B C    
C) A B B A  
D)  A B C A B A C     
Q18: Which of the following is commutative property of real
numbers?
A) A B B A  
B)    3 4 5 3 4 5    
C)  2 2 0  
D) 4 1 4 
Q19: Which of the following is additive property of real
numbers?
A) 4 4a b a b     B) 4 4a b a b    
C)   0a a   D)
1
1a
a
 
Q20: The sum of multiplicative identity and its multiplicative
inverse is:
A) 1 B) 0
C) 1 D) 2
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20

CLASS
XI
Q1: , , 0, 0, .......a b R a b a b     
A) a b B) a b
C)
1 1
a b
 D)
1 1
a b

Q2:
1 1
, , 0, 0, .......a b R a b
a b
     
A) a b B) a b
C)
1 1
a b
 D) a b
Q3: , , 0, 0, .......a b R a b a b     
A) a b B) a b
C) a b   D) a b  
Q4: If 0a  then ..............
A) 0a  B) 0a 
C)
1
0
a
 D)
1
0
a
 
Q5: If 0a  then ..............
A) 0a  B) 0 a 
C)
1
0
a
 D)
1
0
a
 
Q6: If a b b c c d     then .................
A) a d B) a d
C) a d D) c a
Q7: If
1 1
,
a b
   then ………….
A) a b   B) a b
C)
1 1
a b
 D) a b
Q8: If a b   ,then …………..
A) a b B) a b
C)
1 1
a b
 D) a b 
Q9: What is the name of property used in
4 3 1 0     
A) Multiplicative B) Additive
C) Identity D) None
Q10: , ,a b c R  either a b and b c then a c . The
given property is called:
A) Trichotomy B) Transitive
C) Reflexive D) Symmetric

Q11: ,a b R  either a b or a b or a b . The given
property is called:
Q12: What is the property used in 3 2 0 1    
A) Additive property B) Multiplicative property
C) Transitive property D) Multiplicative Identity
Q13: What is the property used in 5 4 20 16    
C) Multiplicative Identity D) Transitive property
Q14: What is the property used in 1 1 3 5     
Q15: What is the property used in 0 0a a   
Q16: What is the property used in
1 1
a b
a b
  
Q17: What is the property used in a b a b    
Q18: What is the property used in 20 40 100 120  
Q19: What is the property used in 1 2 1 2    
Q20: What is the property used in a b b a    
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20

CLASS
XI
Q1: , , 0, 0, .......a b R a b a b     
A) a b B) a b
C)
1 1
a b
 D)
1 1
a b

Q2:
1 1
, , 0, 0, .......a b R a b
a b
     
A) a b B) a b
C)
1 1
a b
 D) a b
Q3: , , 0, 0, .......a b R a b a b     
A) a b B) a b
C) a b   D) a b  
Q4: If 0a  then ..............
A) 0a  B) 0a 
C)
1
0
a
 D)
1
0
a
 
Q5: If 0a  then ..............
A) 0a  B) 0 a 
C)
1
0
a
 D)
1
0
a
 
Q6: If a b b c c d     then .................
A) a d B) a d
C) a d D) c a
Q7: If
1 1
,
a b
   then ………….
A) a b   B) a b
C)
1 1
a b
 D) a b
Q8: If a b   ,then …………..
A) a b B) a b
C)
1 1
a b
 D) a b 
Q9: What is the name of property used in
4 3 1 0     
A) Multiplicative B) Additive
C) Identity D) None
Q10: , ,a b c R  either a b and b c then a c . The
given property is called:

Q11: ,a b R  either a b or a b or a b . The given
property is called:
Q12: What is the property used in 3 2 0 1    
Q13: What is the property used in 5 4 20 16    
Q14: What is the property used in 1 1 3 5    
Q15: What is the property used in 0 0a a  
Q16: What is the property used in
1 1
a b
a b
  
Q17: What is the property used in a b a b    
Q18: What is the property used in 20 40 100 120  
Q19: What is the property used in 1 2 1 2   
Q20: What is the property used in a b b a    
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20

CLASS
XI
TYPE Objective Sets, Functions and Groups No 1
Q1: If A B , then the complement of B is ..........
A) A B B) U B C) A B D) A B
Q2: A set contaning only one element is called ........
A)Null set B) Empty Set
C) Singleton set D) Inverse set
Q3:  0 is ...........
A)Empty Set B) Singleton Set
C) Null Set D) Solution Set
Q4: If  n A k , then   ..........nP A 
A) 2k
B) 2
2 k
C) 2k D) 2
k
Q5: The set of students of PAKTURK is ..............
A) Infinite Set B) Finite Set
C) Empty Set D) Null Set
Q6: The set   1,2,3 is:
A) Infinite Set B) Singleton set
C) Empty Set D) Three point Set
Q7: If A   , then   ...........P A 
A)Empty Set B)  0 C)    D) None
Q8: The number of subsets of a set of 5 elements is ...........
A)32 B) 16 C) 4 D) 25
Q9: The set     1,2,3 , 1,2 has ............
A) Two elements B) Five element
C) Infinite elements D) One element
Q10: The union of two sets A and B is ..............
A) A B B) B A C) A B D) A B

Q11: The intersection of two sets A and B is ..............
A) A B B) B A C) A B D) A B
Q12: If A and B are disjoint sets, then ............
A) A B   B) B A A 
C) A B   D) A B  
Q13: If A and B are overlapping sets, then ...........
A) A B   B) B A A 
C) A B   D) A B  
Q14: ..........A B 
A) B A B) B A C) A B D) B A
Q15: ..........A B 
A) B A B) B A C) A B D) B A
Q16:   ..........A B C  
A)  A B C  B)  A B C 
C)  A B C  D)  B A B 
Q17:   ..........A B C  
A)  A B C  B)  A B C 
C)    A B C A   D)  A B C 
Q18:   ..........A B C  
A)    A B A C   B)    A B A C  
C)    A B A C   D)    A B A C  
Q19:   ..........A B C  
A)    A B A C   B)    A B A C  
C)    A B A C   D)    A B A C  
Q20:   ..........A A B  
A) B B) A B C) A B D) A
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20

CLASS
XI
Q1:   ..........A A B  
A) B B) A B C) A B D) A
Q2: For a set A and the universal set U , C
A A
A) A B) C
A C)   D) U
Q3: For a set A and the universal set U ,  
C
C
A
A) A B) C
A C)   D) U
Q4: For a set A and the universal set U , C
A A
A) A B) C
A C)   D) U
Q5: For any subsets A and B of U ,  
C
A B
A) A B B) C C
A B C) C C
A B D) 
Q6: For any subsets A and B of U ,  
C
A B
A) A B B) C C
A B C) C C
A B D) 
Q7:   ..........
C
C C
A B 
A) A B B) C C
A B C) A B D) C C
A B
Q8:   ..........
C
C C
A B 
A) A B B) C C
A B
Q9: If B A , then the shaded region represents ……
A) A B B) C C
A B
Q10: The number of subsets of a set having three elements is
……………
A)4 B) 6 C) 8 D) 10

Q11: If B A , then the shaded region represents ……
A) A B B) C C
A B
Q12: A subset of A A is called a ……..
A) Relation from A to B B) Relation from B to A
C) Relation in A D) Relation in B
Q13: A subset of B B is called a ……..
Q14: The range of      , ,1 , 0,3f m y n is ……..
A)  ,1,3y B)  , ,m n o
C)  , ,3, ,1,3m n o D)  m
Q15: The domain of    ,1 ,2f a b is ……..
A)  ,a b B)  1,2,3 C)  , ,1,2a b D)  a
Q16: The cancellation laws hold in ………….
A) Sets B) Numbers
C) Group D) Abelian Group
Q17: If p is any proposition its negation is denoted by
………
A) p B) p C) p D) p
Q18: If p is true, then p is ………………….
A) True B) has no information
C) False D) equivalent to p
Q19: If p is true, then p is ………………….
A) True B) has no information
C) False D) equivalent to p
Q20: The conjunction of two statements p and q is denoted
by ………………….
A) p q B) p q C) p q D) p q
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20

CLASS
XI
Q1: p q represents ……………
A) Disjunction B) Conjunction
C) Conditional D) Quantifier
Q2: A conjunction of two statements p and q is true only
if ..
A) p is true B) Both p and q are true
C) q is true D) Both p and q are false
Q3: p: Islamabad is a capital of Pakistan and q: Lohore is
not a city of Pakistan, the conjunction p q is ………..
A) True B) not valid C) False D) unknown
Q4: p: Islamabad is a capital of Pakistan and q: Multan is a
city of Pakistan, the conjunction p q is ………..
Q5: :4 7, :7 11p q  , then the conjunction p q is
………..
Q6: :3 5, :7 4p q  , then the conjunction p q is
………..
Q7: :4 7, :7 11p q  , then the conjunction p q is
……
Q8: p: Islamabad is a capital of Pakistan and q: Lahore is
not a city of Pakistan, the conjunction p q is ………..
Q9: The disjunction of two statements p and q is denoted
by ………………….
A) p q B) p q C) p q D) p q
Q10: A disjunction of two statements p and q is false only
if ……………
A) p is true B) Both p and q are true
C) q is true D) Both p and q are false

Q11: A compound statement of the form “ if p then q ” is
called an ………..
A)Implication B) Hypothesis C) Conclusion D) Unknown
Q12: An implication or conditional “ if p then q ” is
denoted by ……………..
A) p q B) . p q . C) p q D) p q
Q13: An implication or conditional “ if q then p ” is denoted
by ……………..
A) p q B) q p C) q p D) p q
Q14: In a statement “ if q then p ” p is ……………….
A) Implication B) Hypothesis
C) Conclusion D) Unknown
Q15: In a statement “ if q then p ” q is ……………….
A) Implication B) Hypothesis
C) Conclusion D) Unknown
Q16: A conditional is regarded as false only when the
antecedent is true and consequent is …………
A) True B) Known
C) False D) Unknown
Q17: A subset of A B is called a ……..
Q18: A subset of B A is called a ……..
Q19: If  A  then A is called ………………… set.
A) Sub B) Empty C) Singleton D) Null
Q20: The set of real numbers between 1 and 2 is …………..
A) Finite B) Empty
C) Infinite D)Non-Empty
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20

CLASS
XI
Q1: For   , ,a A b B then r a b   is ………
Q2: For   , ,a A b B then r b a   is ………A)
Relation from A to B B) Relation from B to A
Q3: The set of the first elements of the ordered pairs
forming a relation is called its ……………….
A) Relation in A B) Relation in B
C) Range D) Domain
Q4: The set of the second elements of the ordered pairs
forming a relation is called its ……………….
A) Relation in A B) Relation in B
C) Range D) Domain
Q5: The domain of      ,1 ,2 , ,3f a a a is ……..
A)  a B)  1,2,3 C)  ,2,3a D)  2
Q6: The inverse of a relation       ,1 , ,2 , ,3x y z is
…………..
A)       ,1 , ,2 , ,3x y z B)       1, , 2, , 3,x y z
C)       1 1 1
,1 , ,2 , ,3x y z
  
D)       , , , , ,x x y y z z
Q7: The inverse of an identity relation is ……….
A) Not an identity relation B) Not a relation
C) an identity relation D) An empty set
Q8: A subset f of A B is said to be a function from A
to B if domain of f is A and first elements of order pairs of f
………….
A) Do not repeat B) Do not exist
C) The members of B D) Repeat
Q9: Which one is a function from A to B if  , ,A a b c
and  1,2,3B 
A)       ,1 , ,1 , ,2a b c B)       ,1 , ,1 , ,3a b b
C)       ,1 , ,1 , ,2a b a D)       ,1 , ,1 , ,2a b b
Q10: A function in which the second elements of the order
pairs are distinct is called ………..
A) Onto function B) One-one function
C) Identity function D) Inverse function

Q11: A function from A to B is called the onto function if its
range is ………
A) A B) B
C) Neither A nor B D) Both A and B
Q12: A function whose range consists of just one element is
called ………..
A) One-one function B) Constant function
C) Onto function D) Identity function
Q13: If  , ,A a b c ,  1,2,3B  and
     ,1 ,1 , ,1f a b c is ………………
A) One-one function B) Constant function
C) Onto function D) Identity function
Q14: The range of      ,1 ,1 , ,1f a b c is ……..
A)  , ,a b c B)  1
C)  , , ,1a b c D)  a
Q15: The domain of      ,1 ,2 , ,3f a b c is ……..
A)  , ,a b c B)  1,2,3 C)  ,2,3a D)  a
Q16: The function   ,f x y y mx c   is ……..
A) Quadratic function B) Constant function
C) Cubic function D) Linear function
Q17: The graph of a linear function represents ………..
A) Triangle B) Straight Line
C) Circle D) Parabola
Q18: The function   2
,f x y y ax bx c    is ……..
Q19: The function   2
, 3 5f x y y x x    is ……..
Q20: The function   , 11f x y y  is ……..
A) Onto function B) Constant function
C) One-one function D) None of these
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20

CLASS
XI
Q1: If A B then A B  ……………….
A) A B) B C) U D)  
Q2: A bijective function is ……..
A) Onto but not one-one B) One-one but not onto
C) One-one and onto D) Only onto
Q3: A set which has no element is called ……..
A) Power set B) Empty set
C) Non-empty set D) Subset
Q4: Every set is ……………. of itself.
A) an empty B) an improper set
C) proper Subset D) None of these
Q5: If A B and A B , then A is ………….. of B .
A) Proper Subset B) Improper subset
C) Super set D) Power set
Q6: The two sets andA B are said to be …………… if
they have equal number of elements.
A) Equal B) Finite Set
C) Equivalent set D) Singleton set
Q7: A set consisting of only one element is called
………………
A) Equal B) Finite Set
C) Equivalent set D) Singleton set
Q8: Power set is a set which consists of all the possible
…………….. of a given set.
A) Subsets B) Super sets
C) Elements D) None of these
Q9: The power set of an empty set i.e.  P  is ……….
A) Singleton Set B) Empty Set
C) Non-empty Set D) Infinite set
Q10: If A B then A B ……………….
A) A B) B C) U D) c
A

Q11: If A B then A B  …………………
A) A B) B C) U D) c
A
Q12: A set whose last element is known and which is a
containable set is called ………………
A) Singleton set B) Infinite set
C) Finite set D) Non-empty
Q13: If A B then …………………
A) c c
A B B) c c
B A C) c
A B D) c
B A
Q14: If , c
A A    then c
A A  …………..
A) A B)  C) U C) c
A
Q15: If and , thenc c
A A A A   …………..
A) A B) U C) B D) c
A
Q16: If A and B are two sets then A B =………………..
A)  /x x A x B   B)  /x x A x B  
C)  /x x A x B   D)  /x x A x B  
Q17: The two sets A and B are said to be …………. if they
have the same elements.
A) Equivalent B) Equal
C) Empty D) None of these
Q18: The set of all the members under consideration is called
………………
A) Subset B) Power set
C) Universal set D) None of these
Q19: If A U then c
A =…………….
A) A U B) U A
C) U A D) None of these
Q20: If B A , then c
B A  ………………
A) U B) B C) A D) 
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20

CLASS
XI
Q1: The statement " "p q is called ………..
A) Conditional B) Implication
C) Bi-conditional D) Conjunction
Q2:    p q q p   is equal to …………..
A) p q B) q p
C) p q D) p q
Q3:  p q is equal to ………..
A) p q B) p q C) p q D) p q
Q4: For any two sets, A B B A   if ………..
A) A   B) B   C) A B D) A B
Q5: The Cartesian product of A B is defined as …..
A)   ,x y x A y B   B)   ,x y y A x B  
C)   ,x y x A y B   D)   ,x y x B y A  
Q6: For any three sets; A , B andC ,  A B C  
………..
A)  A B C   B)  A B C 
C)  A B C   D) None of these
Q7:  
c c c
A B A B   is called ________ law.
A) Commutative B) Associative
C) De Morgan’s D) Complementation
Q8: A ________.
A) A B) c
A C) U D) 
Q9: The Tabular form of set  2
16 0x x x R   
is__________.
A)  4 B)  4 C)  D) 1
Q10: The presentation of sets through the diagrams is called
________
A) Argand Diagram B) Venn Diagram
C) Circular Diagram D) None of these

Q11: If c
A B A  then A B _______
A) A B B) c
A C)  D) None
Q12: ?c c
A B 
A)  U A B  B)  U A B 
C)  U A B  D) None of these
Q13: The number of elements of a set is …… if it has 31
subsets.
A) 3 B) 4
C) 5 D) All of these
Q14: The set of first co-ordinates of A B is called:
A) Range B) Function
C) Domain D) Binary function
Q15: A function of the type f : x 2x is called:
A) Quadratic B) Linear
B) Trigonometric C) None of these
Q16: If as Set A has m elements and set B has n elements
then A B has _______ elements.
A) 2 2
m n B) 2
m C) 2
n D) n m
Q17: The function which is both one-to-one and onto is
called _______
A) Onto function B) Onto one function
C) Bijective function D) Into function
Q18: The number of subsets of set having 9 elements is:
A) 128 B) 256 C) 420 D) 512
Q19: If " "p is false then p is:
A) True B) False C) Both D) None
Q20: The number of elements of a set having 128 subsets is:
A) 4 B) 5 C) 7 D)8
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20

CLASS
XI
TYPE Objective Matrices and Determinants No 1
Q1: The list of numbers within a square bracket is
called ………..
A) Determinant B) Set
C) Matrix D) Equation
Q2: m n represent ……….. of a Matrix
A) Row B) Columns
C) Order D) None
Q3: A matrix of the form
4
1
4
A
 
   
  
is called ….Matrix
A) Column B) Row
C) Square D) Zero
Q4: A matrix of the form  B a b c is called …
matrix
A) Column B) Row
C) Square D) None
Q5: A matrix is said to be rectangular matrix if its order
is …………
A) m n B) m n
C) 2m  D) 3n 
Q6: What is the additive identity of matrices (2x2)
A)
0 0
0 0
 
 
 
B)
1 0
0 1
 
 
 
C)
1 0
0 0
 
 
 
D) None of these
Q7: A,B and C are three matrices then If AB C what
is A?
A) 1
CB
B) CB
C)
C
A
D) none
Q8: Which of the following is false
A) 1
.A A I
 B) 1
.B B I

C) .A I A D) .0A I
Q9: If
1
3
7
A
 
   
  
then A is
A) 1 2 B) 2 3 C) 3 1 D) 1 3
Q10: If
3 9
1 3
A
 
  
 
then which of the following is true
A) 18A  B) A is a singular matrix
C) A is non singular matrix D) A is a scalar matrix

1 2
3 4
A
 
  
 
is called …….
matrix
A) Rectangular B) Square
C) Identity D) Row
Q12: The order of matrix  aij is ……….. If 1,2i  and
1,2,3j 
A) 2x2 B) 3x2
C) 2x3 D) 3x3
Q13: A matrix “A” will be a square matrix if ………
A) m n B) 2 2
m n
C) m n D) m n
5 0 0
0 7 0
0 0 8
 
 
 
  
is called …….
A) Identity B) Scalar
C) Rectangular D) Diagonal
Q15: If
1 0
0 1
A
 
  
 
then A is not called ………. Matrix
A) Scalar B) Identity
C) Rectangular D) Diagonal
Q16: If
a b
A
c d
 
  
 
and  1 5 4B  then .......
A) A B B) T
A B C) B I D) A B
Q17: The two matrices are said to be conformable for
addition. If ………..
A) Both are square matrices B) Both are row matrices
C) Both are column matrices D) Both are in same order
Q18: A matrix
0 0 0
0 0 0
0 0 0
A
 
   
  
is called ….. matrix
A) Rectangular B) Identity
C) Null D) Rectangular
Q19: The identity matrix in the matrix addition is ……
A) Column matrix B) Square matrix
C) Null matrix D) None of them
Q20: If A nad B are two matrices of the same order such
that 0A B B A    , then ..........B 
A) –B B) Zero matrix
C) –A D) A
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20

CLASS
XI
Q1: The two matrices A and B are said to be additive
inverse of each other if ………
A) A B I  B) 0A B  C) AB I D) 0AB 
Q2: The two matrices A and B are said to be
multiplicative inverse of each other if ………
A) AB BA B) BA A
C) AB BA I  D) 0AB 
Q3: If “A” is a matrix of order mxn and “B” is a matrix
of order pxq, their product AB is defined if ……..
A) m=q B) n=p C) n=q D) m=p
Q4: If
2 5
2 0
A
 
   
and
1 0
1 2
A
 
  
 
then, .....AB 
A)
2 0
2 0
 
  
B)
7 10
2 0
  
 
 
C)
10 0
0 2
 
 
 
D)
7 2
10 0
 
  
Q5:
1 0
0 9
 
 
 
is a …………….
A) Diagonal B) Identity C) Scalar D) Zero
Q6: If
m n
A
k l
 
  
 
then, AdjA is …..
A)
l k
n n
 
  
B)
l k
n m
 
  
C)
l n
k m
 
  
D)
m k
n l
 
 
 
Q7:      3 5 4 9 ... ...  
A)  1 14 B)  1 14 C)  7 14 D)  7 14
Q8: If A and B are the two matrices of the same order
then AB BA if …………
A) A B B) A B C) A B I  D) B A 
Q9: If “B” is diagonal matrix and
11 22 33...... nna a a a k   then “B” is called …… matrix of
order “n” where 0,1k 
A) Identity B) Rectangular
C) Square D) Scalar
Q10: If “B” is diagonal matrix and
11 22 33...... 1nna a a a   then “B” is not called ……
matrix.
A) Scalar B) Rectangular
C) Unit D) Square

Q11: If  A aij then  aji is called …… matrix
A) Symmetric B) Transpose
C) Identity D) Scalar
Q12: If A is any square matrix, then the matrix obtained
by the interchange of rows and columns of A is called
…….. of A
A) Scalar B) Symmetric
C) Transpose D) None of these
Q13: If t
A A then A is known as ……… matrix
A) Transpose B) Scalar
C) Symmetric D) Identity
Q14: If t
A A  , then A is known as ………… matrix
A) Symmetric B) Skew symmetric
C) Transpose D) Zero matrix
Q15: Transpose of identity matrix  t
I is ……
A) Scalar B) Symmetric
C) Identity D) Zero matrix
Q16:
0 0
0 0
0 0
a
a
a
 
 
 
  
is a ………… if 0,1a 
A) Scalar matrix B) Unit Matrix
C) Zero Matrix D) Diagonal matrix
Q17: If A is order of m n , then the order of t
A is
…….
A) m n B) n m C) m m D) n n
Q18:
4 5 6
5 3 2
6 2 8
 
 
 
  
is ………………………………
A) Rectangular Matrix B) Diagonal Matrix
C) Square Matrix D) Scalar Matrix
Q19: If A A , then A is called ………
A) Real Matrix B) Symmetric Matrix
C) Hermitian Matrix D) Skew Hermitian Matrix
Q20: If  
t
A A , then A is called ………
A) Transpose B) Symmetric Matrix
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20

CLASS
XI
Q1: Which of the following is conjugate matrix?
A)
1 5
5 6
 
 
 
B)
2 6
9 4
  
   
C)
3 5
6 7
i i
i i
 
 
 
D)
0 0
0 0
 
 
 
Q2: Transpose of a square matrix is ……………
A) Rectangular Matrix B) Scalar Matrix
C) Square Matrix D) Identity matrix
Q3: If  
t
A A  , then A is called ………
A) Transpose B) Symmetric Matrix
Q4: The additive inverse of
cos sin
tan cot
 
 
 
  
is
………..
A)
sin cos
cot tan
 
 
 
  
B)
cos sin
tan cot
 
 
 
  
C)
cos sin
tan cot
 
 
 
  
D)
sin cos
cot tan
 
 
 
  
Q5: If two rows or two columns of a square matrix A
are identical then ...........A 
A) 1 B) -1
C) 0 D) Non-zero
Q6: Find adjoint matrix of
2 3
3 2
 
  
A)
2 3
3 2
 
 
 
B)
2 3
3 2
  
  
C)
2 3
3 2
 
   
D)
2 3
3 2
 
  
Q7: The determinant of
2 1 3
1 1 0
2 3 4
 
 
 
  
is ………
A) 11 B) 10 C) -10 D) -11
Q8: If ijA a    is any square matrix, then co-factor of
an element ija is ………….
A)  1
i j
ijM

 B)  1
i j
ijM


C)  1
i j
jiM

 D)  1
i j
jiM


Q9: Which of the following is a not scalar matrix?
A)
5 0 0
0 5 0
0 0 5
 
 
 
  
B)
1 0 0
0 1 0
0 0 1
 
 
 
  
C)
4 0 0
0 4 0
0 0 16
 
 
 
 
 
D)
0 0 0
0 0 0
0 0 0
 
 
 
  

Q10: If A and B are of the same order then which one is
always true
A) AB BA B) A B B A  
C) AB BA D) None of these
Q11: What is determinant of zero matrix
A) 1 B) 0
C) -1 D) Not possible
Q12:  
1
...........AB


A) 1 1
A B 
B) AB
C) BA D) 1 1
B A 
Q13:   ...........
t
AB 
A) t t
A B B) AB
C) BA D) t t
B A
Q14: If AB BA then which of the following is correct?
A) A I or B I B) ,A I B I 
C) 2 2
A B D) None of these
Q15: A and B are of the same order and AB BA I 
then ……………
A) A B B) B I
C) A I D) 1
A B

Q16: If A is non-singular matrix then …………….
A) 0A  B) 0A 
C) 1A  D) A is zero matrix
Q17: A is a square matrix then  
11
A

is equal to
………….
A) 1
A
B) A C) t
A D) I
Q18: Determinant of
3 4 2
1 7 3
0 0 0
 
 
 
  
is equal to …………
A) 12 B) 0 C) 15 D) 1
Q19: Determinant of
1 2 9
3 7 8
1 2 9
 
 
 
  
A) 9 B) -3 C) 13 D) 0
Q20: Inverse of a square matrix “A” exists if ………….
A) 0A  B) 0A 
C) 1A  D) A is zero matrix
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20

CLASS
XI
Q1: Determinant of A is possible only when A is
………….
A) Symmetric Matrix B) Rectangular Matrix
C) Square matrix D) None of these
Q2: A is a square matrix, then t
A is equal to ………..
A) t
A B) A C) t
A D) A
Q3: The value of
cos 0 sin
1 1 0
sin 0 cos
   
 
is equal to ….
A) 0 B) 1 C) -1 D) 
Q4: A is a non-singular matrix then  1 t
A
is equal to
….
A) 1
A
B)  
1t
A

C) t
A D) None
Q5: The matrix
0 1 2 4
0 0 1 3
0 0 0 4
0 0 0 0
 
 
 
 
 
 
is ……………..
A) In reduced form B) In echelon form
C) In rank form D) In Identity form
Q6: The number of non-zero rows in the Echelon form
is called …………… of the matrix
A) Transpose B) Determinant
C) Rank D) Adjoint
Q7: The rank of
1 4 2
0 1 3
0 0 0
 
 
 
  
is equal to …….
A)1 B) 2 C) 3 D) 0
Q8: For what value of  the matrix
2 6 5
4 4 6
0 1
A

 
   
  
is
a singular matrix
A) 0 B) 1 C) -2 D) -1
Q9: The order of A is 4 4 then what will be the order
of 1
A
A) 5 5 B) 6 6 C) 4 4 D) None
Q10: If any two rows or columns of a square matrix A
interchanged then determinant will be equal to …………
A) A B) A C)
2
A D) A

Q11: The product of  
a
c d
b
 
 
 
is equal to …..
A)  ab cd B)
ac ad
bc bd
 
 
 
C)  ac bd D) None of these
Q12: The solution set  0,0,0 is called ……….. for
homogeneous system of linear equations
A) Non-trivial B) Trivial
C) Unique D) Infinite
Q13: If a system , 0AX B B  is called ……. If it has
unique or infinite many solutions
A) Trivial B) Non-trivial
C) Consistent D) Inconsistent
Q14: The system of linear equations is said to be ….. if
it has no solution
A) Trivial B) Non-trivial
C) Consistent D) Inconsistent
Q15: Those equations whose solution is common are
called …………..
A) Quadratic Equations B) Linear Equations
C) Simultaneous Equations D) Homogeneous Equations
Q16: A system 0AX  has non-trivial solution if
…………
A) 0A  B) 0A 
C) A A D) A A 
Q17: C and D are two non singular matrices then
 
11 1
C D
 
A) 1 1
D C 
B) CD C) DC D) 1 1
C D 
Q18: The ratio of the adjoint and determinant of non
singular matrix is ……………. of the matrix
A) Inverse B) Transpose
C) Co-factor D) None of these
Q19: Cramer’s Rules is applicable on AX B if ….
A) 0A  B) 0A  C) 0A  D) 0A 
Q20: The value of
1
1
1
y z x
z x y
x y z



is equal to ……
A) 1 B) 0 C) x y z  D) xyz
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20

CLASS
XI
Q1: The square of a scalar matrix is a …………..
A) Identity Matrix B) Rectangular Matrix
C) Scalar Matrix D) Identity Matrix
Q2: A is a unit matrix , then A is equal to …………
A) 0 B) 1 C) -1 D) 2
Q3: Order of  3 5 is ……….
A) 1x1 B) 1x2 C) 2x1 D) 2x2
Q4:
1 0
0 1
 
 
 
is a …………….. matrix
A) Singular B) Zero C) Unit D) None
Q5: If 1
AA I
 , then 1
A
is ……….. of matrix A
A) Adjoint B) Multiplicative inverse
C) Additive inverse D) Transpose of A
Q6: If matrix
4 16
8n
 
 
 
is singular, then ...n 
A) -2 B) 2 C) 4 D) -4
Q7: If A,B and C are three matrices which are
conformable for multiplication, then   ...........A BC 
A)  AC B B)  BC A C)  AB C D)  CA B
Q8:  
3
1 4 .............
5
 
 
 
A)
2 3
4 5
 
 
 
B)
3 12
5 20
 
 
 
C)
2 12
4 25
 
 
 
D)
12 3
16 8
 
 
 
Q9:  
2
...........
3
x y
 
 
 
A)  3x y B)  3x y C)  2 3x y D)  3x y
Q10:
5 0
0 5
 
 
  
is a …………. Matrix
A) Zero B) Identity C) Unit D) Scalar

Q11: If
4 2 92
6 5 12 2 25
m   
   
   
, then ...........m 
A) 3 B) 5 C) 7 D) 9
Q12: The matrix of co-efficient for the equations
3 12x y  and 3 2 8x y  is ………………..
A)
1 3
3 2
 
 
 
B)
1 12
3 8
 
 
 
C)
3 12
2 8
 
 
 
D)
3 1
3 2
 
 
 
Q13: If
2 3
2 1
A
 
    
then A is …….
A) -4 B) 4 C) -5 D) 5
Q14: If
1 0
0 1
A
 
  
 
then, 1
..........A

A)
1 0
0 1
 
  
B)
1 0
0 1
 
  
C)
1 0
0 1
 
 
 
D) None
Q15: If the number of rows and columns in a matrix are
not equal, then the matrix is called....
A) Square matrix B) Zero matrix
C) Unit matrix D) Rectangular matrix
Q16: If
5 3
12 2 5
A
 
  
  
then A is …….
A) -4 B) 4 C) -5 D) 5
Q17: Matrix
0 0
0 0
 
 
 
is a ………. matrix
A) Zero B) Unit
C) Column D) Row
A) 1
AA I
 B) t
I I C)  
t
t
A A D) 1t
A A

Q19: If
1 0
0 1
A
 
  
 
then, which of the following is false
A) A is scalar matrix B) A is unit matrix
C) A is zero matrix D) A is diagonal matrix
Q20: What is the multiplicative identity of matrices
(2x2)?
A)
0 0
0 0
 
 
 
B)
1 0
0 1
 
 
 
C)
1 0
0 0
 
 
 
D) none
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20

CLASS
XI
Q1:
1 0
0 1
 
 
 
is ……………………..
A) not unit matrix B) additive identity
C) zero matrix D) multiplicative identity
Q2:
3
5
A
 
  
 
and
2
7
B
 
  
 
then A+B=?
A)
1
12
 
 
 
B)
5
12
 
 
 
C)
1
2
 
  
D)
1
12
 
 
 
Q3:
10
5
A
 
  
 
and
2
6
B
 
  
 
then A-B=?
A)
8
11
 
 
 
B)
8
11
 
  
C)
12
1
 
  
D)
12
11
 
 
 
Q4: Which of the following is a zero matrix
A)
0 0
0 1
 
 
 
B)
2
1 1 2 4
2 2 0
  
 
 
C)
2 2 0
0 3 1
 
  
D)
0 0
0 11
 
  
Q5: Which of the following is a scalar matrix
A)
2 0
0 2
 
  
B)
7 0
0 17
 
 
  
C)
5 0
0 25
 
 
 
D)
1 0
0 1
 
 
 
Q6: Which of the following is a unit matrix
A)
5 4 0
0 1
 
 
 
B)
0 0
0 0
 
 
 
C)
0 0
0 1
 
 
 
D)
0 1
1 0
 
 
 
Q7: Which of the following is row matrix
A)  3 4 B)
3 0
2 1
 
 
 
C)
0 0
0 1
 
 
 
D) None of these
Q8:  3 9 is a ……….
A) Row matrix B) Column matrix
C) Scalar matrix D) Zero matrix
Q9:
0
0
0
 
 
 
  
is a ………………
A) unit matrix B) zero matrix
C) scalar matrix D) diagonal matrix
Q10:
1 0
0 1
 
 
 
is a …………….
A) unit matrix B) row matrix
C) zero matrix D) None of these

Q11: If
2 4
1 8
A
 
  
 
then ?A 
A) 10 B) -12 C) 12 D) 0
Q12: If
2 4
4 8
A
 
  
 
A) A is a non singular matrix B) A is a singular matrix
C) A is scalar matrix D) A is unit matrix
Q13: If
2 4
1 8
A
 
  
  
then ?A 
A) 2 B) -2 C) 4 D) -4
Q14: Which of the following is diagonal matrix
A)
1 0
0 1
 
 
 
B)
1 9
0 1
 
 
 
C)
1 1.2
0.8 1
 
 
 
D)
1 5
5 1
 
 
 
Q15: If
1 0
0 1
A
 
  
 
then which of the following is false
A) A is a unit matrix B) A is a scalar matrix
C) A is a diagonal matrix D) A is a zero matrix
Q16: If
4
12
x y
x y
 
 
A)
1 1 12
1 1 4
x
y
     
     
     
B)
1 1 12
1 0 4
x
y
     
     
     
C)
1 1 4
1 1 12
x
y
     
     
     
D)
1 1 4
1 1 12
x
y
     
     
     
A) If A is a singular matrix then 0A 
B) If B is a zero matrix then all terms are o
C) If A is unit matrix then 1A 
D) Unit matrix is a zero matrix
Q18: What is the additive inverse of
2 9
5 4
 
  
A)
2 5
9 4
 
  
B)
2 9
5 4
  
  
C)
0 0
0 0
 
 
 
D) None of these
Q19: If
1 2
3 4
A
 
  
 
then ...........t
A 
A)
4 2
3 1
 
  
B)
1 3
2 4
 
 
 
C)
4 3
2 1
 
  
D)
4 3
2 1
 
 
 
Q20: If
4
2 2
x
A
 
   
is a singuler matrix then
.............x 
A) 4 B) -2 C) 2 D) -4
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20

CLASS
XI
Q1: Which of the following matrix is symmetric matrix?
A)
3 4
4 3
 
 
 
B)
1 0
0 1
 
 
 
C)
3 3
0 3
 
 
 
D)
0 4
4 0
 
 
 
Q2: If
2 1 2
0 3 3
1 2 4
 
 
 
 
 
, then what is 23A ?
A) 3 B) 5 C) 3 D) 5
Q3: If
2 1 2
0 2 1
1 3 4
  
 
 
 
 
, then what is 33M ?
A) 3 B) 4 C) 3 D) 4
Q4:
21 22 23
21 22 23
4, 3, 7
?
2, 1, 3
a a a
A
A A A
   

    
A) 18 B) 12 C) 16 D) 21
Q5:
31 32 33
31 32 33
2, 3, 5
?
2, 1, 4
a a a
A
M M M
  

    
A) 13 B) 21 C) 14 D) 19
Q6: Find x if
1 4 7
0 1 8
2 3
0 0
4
x
 
 
 
 
 
 
 
has unique solution.
A)
3
8
B)
3
2
C)
2
3
D)
8
3
Q7: If
1 2
33
4 3
x
x

  , then what is x ?
A) 3 B) 2 C) 3 D) 1
Q8:
5 0 0
3 2 1 ?
1 2 3

A) 15 B) 20 C) 10 D) 15
Q9: If
4
9
4
x
x
 , then what is x ?
A)  5,5 B)  5,5 C)  5,5 D)  5,5
Q10:
5 15 20
7 14 21 ?
4 8 12

A) 140 B) 75 C) 1 D) 0

Q11: Find x and y if
3 1 2 1
3 2 3 2
x    
       
A) 2 B) 3 C) 1 D) 0
Q12: Find .x y if
3 1 7 1
3 3 4 3 11
x
y
   
        
A) 12 B) 9 C) 15 D) 21
Q13: If
1 2 3
1 0 2
A
 
  
 
and
0 3 2
1 1 2
B
 
   
, then find
4 3A B
A)
4 5 6
1 3 2
  
 
 
B)
4 5 6
1 3 2
 
 
 
C)
4 5 6
1 3 2
  
 
 
D)
4 3 6
1 4 2
 
 
 
Q14: Find 2
A if
1 2
3 0
A
 
  
 
A)
7 2
3 6
 
 
 
B)
7 2
0 6
 
 
 
C)
7 2
0 6
 
 
 
D)
7 2
3 6
 
 
 
Q15: If
1 1 2
0 3 1
A
 
  
 
and
2 3 0
1 2 1
B
 
   
, then find
 
t
A B
A)
3 1
3 4
1 0
 
 
 
  
B)
3 1
2 3
2 1
 
 
 
 
 
C)
3 1
2 5
2 0
 
 
 
 
 
D)
4 1
2 3
2 0
 
 
 
 
 
Q16: Find the multiplicative inverse of
2 1
1 1
 
 
 
A)
1 1
1 2
 
 
 
B)
1 1
1 2
 
 
 
C)
1 1
1 2
 
 
 
D)
1 1
1 2
 
 
 
Q17:
2 7
..........
3 5
   
       
A)
2 7
3 5
 
  
B)
5
2
 
  
C)
9
8
 
  
D)
9
8
 
 
 
Q18:
2 2 0 3
....
3 3 1 2
   
        
A)
2 5
2 1
 
  
B)
2 1
2 1
 
  
C)
2 5
2 1
 
  
D)  0
Q19: What is the value of A B if 1
A B

A) 0 B) A C) I D) B
Q20: Determinant of unit matrix is ...............
A) Unit Matrix B) Scalar matrix
C) Diagonal matrix D) Zero matrix
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20

CLASS
XI
TYPE Objective Quadratic Equations No 1
Q1: 2
1 ............   
A) 1 B) 0 C) 1 D) 
Q2: 1 ............ 
A) 1 B)
2
 C) 2
 D) 0
Q3: 2
1 ............ 
A) 1 B)  C)  D) 0
Q4: 50
............ 
A) 1 B)
2
 C)  D) 1
Q5: 3
............ 
A) 1 B)
2
 C) 2
 D) 0
Q6: 1 ............
A) 1  B)
3
 C) 2
 D) 2
 
Q7: Solve 2
5 4 0x x  
A)  1, 4  B)  1,4 C)  1,3 D)  2,4
Q8: Solve 2
36 0x  
A)  6 B)  6 C)  6i D)  
Q9: Solve 2
4 0x  
A)  4 B)  2 C)  4i D)  2i
Q10: Solve   2 3 0x x  
A)  2, 3 B)  3, 2 C)  2 D)  3

Q11: If
2 1 3
2
i

 
 , then what is the value of 
A)
1 3
2
i 
B)
1 3
4
i 
C)
1 3
2
i
D)
1 3
2
i
Q12: If
1 3
2
i

 
 , then what is the value of
2

A)
1 3
2
i 
B)
1 3
2

C)
1 3
2
i
D)
1 3
2
i
Q13: Find the cube root unity of 3
125x 
A)
2
5,5 ,5  B)
2
5, 5 , 5   
C)
2
5, 5 ,5  D)
2 3
5,5 ,5 
Q14: 46 47 48
...........    
A)  B)
3
 C) 2
 D) 0
Q15: Find the product of roots of 2
3 7 12 0x x  
A)
12
3
 B)
12
3
C)
7
3
 D)
7
3
Q16: Find the sum of roots of 2
2 5 3 0x x  
A)
5
2
 B)
5
2
C)
3
2
D)
3
2

Q17: Solve 4
16 0x  
A) 2, 2,2 , 2i i  B) 4, 4,4 , 4i i 
C) 8, 8,8 , 8i i  D) 16, 16,16 16i i 
Q18: What is the sum of roots of 4
81 0m  
A) 12i B) 12i C) 12 D) 0
Q19: What is the product of roots of 4
256 0x  
A) 64 B) 256 C) 16 D) 128
Q20:    
4 4
1 3 1 3 ...............       
A) 16 B) 16 C) 8 D) 8
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20

CLASS
XI
Q1: 1, 1, ,i i    is called.......................
A) The cube roots of unity B) The fourth roots of unity
C) The fifth roots of unity D) None of these
Q2: Which of the following is false?
A) The complex fourth roots of unity are conjugate of each
other
B) The real fourth roots of unity are inverse of each other
C) Sum of all the four fourth roots of unity is zero
D) Product of all the fourth roots of unity is 1
Q3: Product of all the fourth roots of unity is equal to
.............
A) 1 B) i C) 1 D) i
Q4: Find the solution set of 2
1 0x  
A)  1, 1  B)  0, 1 C)  1,0 D)  ,i i 
Q5: Find the solution set of 2
1 0x  
A)  1, 1  B)  0, 1 C)  1,0 D)  ,i i 
Q6: Evaluate  
82
1   
A) 256 B) 128 C) 256 D) 128
Q7: Evaluate 28 29
1  
A) 1 B) 0 C)  D)
2

Q8: Evaluate   2 2
1 1      
A) 4 B) 4 C) 4 D) 4
Q9: Evaluate
7 7
1 3 1 3
2 2
        
      
   
A)  B)  C) 1 D) 1
Q10: Evaluate    
5 5
1 3 1 3      
A) 32 B) 32 C) 32 D) 32

Q11: The highest power of a polynomial function is called
.....
A) Degree B) Power C) Monomial D) Binomial
1 0x  
A) 1 B) 2 2i C) 0 D) 2
1 0x  
A) 1 B) 2 C) 0 D) 2 3
Q14: What is the product of roots of 3
1 0x  
A) 1 B) 2 C) 0 D) 2 3
Q15: What is the sum of real roots of 4
16 0x  
A) 1 B) 1 C) 0 D) 2 3
Q16:
2
.............  
A) 0 B) 1 C) 1 D) 
Q17: Find the remainder when 3 2
2 4 0x x x    is
divided by 1x 
A) 1 B) 2 C) 2 D) 0
Q18: Find the numerical value of k if 3 2
2 6 0x x kx   
has a remainder of12, when divided by 1x 
A) 1 B) 2 C) 4 D) 0
Q19: If 2
0ax bx c   and 2
4 0b ac  then the roots
will be....................
A) real and equal B) complex and equal
C) real and unequal D) complex and unequal
Q20: If 2
0ax bx c   and 2
4 0b ac  and not a perfect
number, then the roots will be....................
A) real and equal B) complex and equal
C) real and unequal D) complex and unequal
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20

CLASS
XI
Q1: Find the solutions set of 2
7 12 0x x  
A)  3,4 B)  4,1
C)  4, 3  D)  4,3
Q2: Find the solutions set of 2
2x x 
A)  1, 2  B)  1,2
C)  3, 4 D)  1,2
Q3: Which of the following is a radical equation?
A) 2
4 0x   B) 3 1x 
C) 2x  D) 2 1 12x  
Q4: Find the solutions set of 2 1 0x  
A) 1x   B)
1
2
x  
C) 2x  D) 2x  
Q5: Find the three cube roots of 8 if
1 3
2

 
 .
A) 2
2, 2 , 2    B) 2
2, , 
C) 2 D) 2
2,2 ,2 
Q6: Find the three cube roots of -8 if
1 3
2

 
 .
A) 2
2, 2 , 2    B) 2
2, , 
C) 2 D) 2
2,2 ,2 
Q7: Find the three cube roots of 27 if
1 3
2

 
 .
A) 2
3,3 ,3  B) 2
3,3 ,3 
C) 3,3 D) 2
1,3 ,6 
Q8: 3 3
...............a b 
A)   2 2
a b a ab b   B)   2 2
a b a ab b  
C)   2 2
2a b a ab b   D)   2 2
a b a ab b  
Q9: 3 3
...............a b 
A)   2 2
a b a ab b   B)   2 2
a b a ab b  
C)   2 2
2a b a ab b   D)   2 2
a b a ab b  
Q10: 2 2
...............a b 
A)   a b a b  B)   a b a b 
C)   a b a b  D) 2 2
a ab b 

Q11: 2
2
1
.............x
x
 
A)
2
1
2x
x
 
  
 
B)
2
1
4x
x
 
  
 
C)
2
1
2x
x
 
  
 
D)
2
1
2x
x
 
  
 
Q12: 2
2
1
.............x
x
 
A)
2
1
2x
x
 
  
 
B)
2
1
4x
x
 
  
 
C)
2
1
4x
x
 
  
 
D)
2
1
2x
x
 
  
 
Q13: 100 200 300
?    
A) 2
 B) 
C) 1 D) 0
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20

CLASS
XI
TYPE Objective Partial Fractions No 1
Q1:
  
3
2 3x x 
can be written in the form of partial
fractions as ...............
A)
2 3
A B
x x

 
B)
 
2
32
A B
xx


C)
 
2
2 3
A B
x x

 
D)
  2 3
A B
x x

 
Q2: If the degree of the polynomial  P x is less than the
degree of the polynomial  Q x in a rational fraction
 
 
P x
Q x
,
then the fraction is called ..................
A) Improper Rational Fraction B) Proper Rational Fraction
C) Improper Rational Equation D) Proper Rational Equation
Q3: If the degree of the polynomial  P x is equal to or
greater than the degree of the polynomial  Q x in a rational
fraction
 
 
P x
Q x
, then the fraction is called ........
A) Improper Rational Fraction B) Proper Rational Fraction
C) Improper Rational Equation D) Proper Rational Equation
Q4: Which of the following is quadratic factor?
A) 2
4x  B) 2
1x 
C) 2
2 1x x  D) 2
5 4x x 
Q5: Which of the following is not quadratic factor?
A) 2
4x  B) 2
1x 
C) 2
1x x  D) 2
2x x 
Q6: Which of the following is a linear factor
A) 2
x ax B) 2
x bx C) ax b D) 3
1x 
Q7: Which of the following is a proper fraction?
A)
 
2
2 3
2 .2
x x
x x
 

B)
3
2 8
9
x x
x
 

C)
   
   
1 1 3
1 1 4
x x x
x x x
  
  
D)
1
x
Q8: Which of the following is an improper fraction?
A)
     
2
2 3
2 . 1 . 1
x x
x x x
 
  
B)
3
4
2 8
9
x x
x
 

C)
   
   
x a x b x c
x a x b x c
  
  
D)
2
3
1
1
x
x


Q9: The partial fraction of 2
1
1x 
is ............
A)
   
1 1
2 1 2 1x x

 
B)
   
1 1
2 1 2 1x x

 
C)
   
1 1
2 1 2 1x x

 
D)
   
1 1
2 1 2 1x x

 
Q10: To resolve a combined fraction into its pars is
called………….
A) Partial Fractions B) Proper Fraction
D) Improper Fraction D) Combined Fraction
Q11: The form of partial fractions of
  2
1
1 4x x 
is:
A) 2
1 4
A B
x x

 
B) 2
1 4
A Bx C
x x


 
C)
1 2 2
A B C
x x x
 
  
D) 2
1
1 4
A
x x

 

  2
4
3 4
x
x x 
is:
A) 2
4
1 4
x
x x

 
B) 2
1 4
A B
x x

 
C)
3 2 2
A B C
x x x
 
  
D) 2
3 4
A Bx C
x x


 
  2 2
1
1 4
x
x x

 
is:
A) 2 2
1 4
A B
x x

 
B) 2 2
1 4
Ax B Cx D
x x
 

 
C)
2
2 2
1 4
Ax B Cx Dx
x x
 

 
D) 2 2
1 4
Ax B Cx D
x x
 

 
   
2
2 2
1
1 3
x
x x

 
is:
A)
 
2 2
1 31
A Bx C Dx E
x xx
 
 
 
B)
 
2 2
1 31
A B C
x xx
 
 
C)
 
2 2
1 31
A B Cx D
x xx

 
 
D)
   
2 2
1 31 3
A B C D
x xx x
  
  
 
1
1
x
x x


is:
A)
1
A B
x x


B)
1
A Bx C
x x



C)
1 1
1x x


D)
1
A B
x x


Q16: Resolve 3
2
1x 
A) 2
2
1 1
x
x x x

  
B) 2
2 2
1 1
x
x x x

  
C) 2
2 2
1 1
x
x x x

  
D) 2
1 2
1 1
x
x x x

  
Q17: Resolve 3
11
1x 
A)
   2
11 11 22
3 1 3 1
x
x x x


  
B)
   2
11 11 22
1 1
x
x x x


  
C)
   2
11 11 22
3 1 3 1
x
x x x


  
D)
   2
11 22 11
3 1 3 1
x
x x x


  
Q18: Partial fractions of 2
1
1x 
are equivalent to:
A)
   
1 1
2 1 2 1x x

 
B)
   
1 1
2 1 2 1x x
 
 
C)
   
1 1
4 1 4 1x x
 
 
D)
   
1 1
2 1 2 1x x

 
1
4x 
are equivalent to:
A)
   
1 1
4 1 4 1x x

 
B)
   
1 1
2 1 2 1x x

 
C)
   
1 1
4 2 4 2x x
 
 
D)
   
1 1
4 2 4 2x x

 
1
9x 
are equivalent to
……………
A)
   
1 1
9 3 9 3x x
 
 
B)
   
1 1
3 3 3 3x x
 
 
C)
   
1 1
6 3 6 3x x
 
 
D)
   
1 1
4 1 4 1x x

 
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20

CLASS
XI
TYPE Objective Sequences and Series No 1
Q1: An arrangement of number formed according to some
definite rule is called:
A) Series B) Polynomial
C) Sequence D) Equation
Q2: A sequence is a function whose domain is the set of:
A) Integers B) Real No.
C) Natural no. D) Even No.
Q3: The sequence whose difference between every two
consecutive terms is a same is called:
A) G.P B) H.P C) Binomial D) A.P
Q4: The general term of .A P is:
A) 1
1
n
na a r 
 B)  1 1na a n d 
C)  1 1na a n d   D)
 1
2
n
n n
a


Q5: The general term of the sequence 1,1, 1,1,.....  is:
A)  1
n
na   B) na n 
C)  
1
1
n
na

  D)  
1
1
n
na

 
Q6: The sequence whose general term is
   1 2
n
n
n
a
n
 
 is:
A)
1 1
1,0, ,
3 2

 B)
1 1
1,0, ,
3 2


C)
1 1
1,0, ,
3 2

D)
1 1
1,0, , ,...
3 2
Q7: The sequence whose general term is
   1 1
n
na n   is:
A) 2,3, 4,5 B) 2,3, 4,5 
C) 2, 3,4,5 D) 2,3,4, 5
Q8: If 1 5a  and 3d  ,then 10 ?a 
A) 30 B) -32 C) 31 D) 32
Q9: If , ,a A b are in A.P , then ?A 
A) Geometric Mean B) Arithmetic Mean
C) Harmonic Mean D) None of these
Q10: The .AM between 4 5 & 2 5 is:
A) 2 5 B)
5
3
C) 3 5 D)
6 5
7

Q11: The10th
term of the sequence
5
2, ,3,....
2
is:
A)
13
2
B)
13
2

C)
11
2
D)
2
13
Q12: The A.M between 2 3x y and8 5x y is:
A) 5x y B) 3x y C) 5x y D) 3x y
Q13: Which term of the .A P
3 13
,2, ,...
4 4
is
98
4
?
A) 21st
B) 19th
C) 20th
D) 18th
Q14: The 8th
term of A.P
3 13
,2, ,...
4 4
is:
A)
39
4
B)
38
4
C)
37
4
D)
43
4
Q15: The A.M between the two numbers 5 4 and
5 4 is:
A) 5 B) 2 5 C) 4 5 D) 5
Q16: How many terms are in A.P if 30,na  25,d 
5a  ?
A) 1 B) 2 C) 3 D) 4
Q17: The A.M between a and b is:
A)
2
a b
B)
2ab
a b
C)
2
a b
D) ab
Q18: The H.M between a and b is:
A)
2
a b
B)
2
a b
C)
2
a b
ab

D)
2ab
a b
Q19: The G.M between a and b is:
A) a b B) ab C) a b D)
2
a b
Q20: The Sum of the terms of a sequence is called:
A) Sequence B) Series C) Function D) Fraction
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20

CLASS
XI
Q1: The sum for 1 2 3 4 ..... n     is:
A)  1 1a n d  B)
 1
2
n n 
C)
 1
2
n n 
D) NONE
Q2:      1 1 1 12 ... 1 ?a a d a d a n d        
A)   1 1
2
n
a n d   
B)   12 1n a n d   
C)   12 1
2
n
a n d   
D)   12 1
2
n
a n d   
Q3: Which formula is used for arithmetic series?
A)   1 1
2
n
n
S a n d    
B)  1
2
n n
n
S a a 
C)  
1
1
1
n
n
r
S a
r



D) NONE
Q4: The sum of 1st
100 positive even integers is:
A) 10000 B) 10111 C) 10101 D) 10100
Q5: The sum of the series 5 9 13 ... 41    is:
A) 220 B) 230 C) 240 D) 280
Q6: The sum of the series 8 6 4 ...   up to 10 terms is:
A) -8 B) 8 C) 10 D) -10
Q7: How many terms of the series
     11 7 3 ...      will sum up 304?
A)
19
2
n

 B) 15n  C) 16n  D) 17n 
Q8: The sequence 1 2 3
1 1 1 1 1, , , ,..., n
a a r a r a r a r is called …
A) A sequence B) H.P
C) G.P D) A.P
Q9: The H.M between 9 and 11is:
A)
9
10
B)
7
10
C)
99
10
D) None of these
Q10: The positive G.M between 4 and 64 is:
A) 4 B) 16 C) 32 D) 64

Q11: In G.P 1
1
n
na a r 
 where r is:
A) Common difference B) Common Ratio
C) Common Factor D) NONE
Q12: If the 1st
three terms of G.P are 1,
3
,
4
9
16
then the 6th
term is:
A)
242
257
B)
241
1024
C)
243
1024
D) None
Q13: The 7th
term of the G.P 5,15,.... is:
A) 3544 B) 3645 C) 3646 D) 3640
Q14: The general term of a G.P is:
A) 1
n
na a r B) 1
1
n
na a r 
 C) 1
1
n
na a r 
 D) 1na a r
Q15: If 1r  then the G.S is called as:
A) Convergent B) Divergent C) Finite D) Constant
Q16: If 1r  then the infinite G.S is called as:
A) Divergent B) Convergent C) Finite D) Constant
Q17: If , ,a G b are in G.P then G is called:
A) Geometric Progression B) Geometric mean
C) A.M D) Harmonic Mean
Q18: If 1 44, 256,a a  then r is:
A) 2 B) 3 C) 4 D)
1
2
Q19: The geometric mean between
1
2
2
and
1
12
2
is:
A)
5 5
3
B)
5
2
C)
5 2
2
D)
5 5
2
Q20: The sum of the series 1 2 3 1
1 1 1 1 1, , , ,..., n
a a r a r a r a r 
if 1r 
is:
A)
 
 
1 1
1
n
a r
r


B)
 
1
1
a
r 
C)
 
 
1 1
1
n
a r
r


D)
 
 
1
1
n
r
r


Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20

CLASS
XI
Q1: If 1r  then, the sum of the finite Geometric Series is:
A)
 
 
1 1
1
n
a r
r


B)
 
 
1 1
1
n
a r
r


C)
 1
2
n n 
D)  1
2
n
n
a a
Q2: For finite geometric series which statement is not true?
A) 1r  B) 1r  C) 2r  D) 1r 
Q3: If 1 3a   , 2r  then 6 .............S 
A) -93 B) -102 C) -190 D) -189
Q4: How many terms are in G.P:
1 1 1
1, , ,...,
2 4 1024
A) 10 B) 11 C) 12 D) None
Q5: Find the last term of 1 3 2 7 3 11 .....     
A)  . 1n n  B)  . 1n n  C)  . 4 1n n D)  . 4 1n n 
Q6: The sum of the 1st
16 terms of the Geometric Series
1 1 1 1 1 1 1....      is:
A) 1 B) -1 C) 0 D) 2
Q7: The sum of the infinite geometric series is:
A) 1
1
a
r
B) 12
1
a
r
C) 1
1
a
r
D)
 1 1
1
n
a r
r


Q8: The sum of the series
1 1 1
1 ....
3 9 27
      is:
A)
2
3
B)
2
3
 C)
3
2
D)
3
2

Q9: Is the series 2 8 32 128 ...    convergent?
A) Yes B) No C) Neither D) None
Q10: The series 1 1 1 1 1 ...     is:
A) Convergent B) Divergent
C) Finite D) Does not converge

Q11: 2.410 in the common fraction is:
A)
410
999
B)
2308
999
C)
2408
999
D) None
Q12: If the first three terms of G.P are 4 3,8 3,16 3,...
then 4a is:
A) 15 3 B) 3 16 C) 16 3 D) 32 3
Q13: The reciprocal of A.P is called:
A) G.P B) G.M C) A.M D) H.P
Q14: If
1 1 1
, , ,...
3 8 13
is H.P, then 12a is:
A)
1
54
B)
1
55
C)
1
59
D)
1
58
Q15: If 1 1 1 1 1 1 1 ...       is a sequence to n terms
then , what is nS if n is even.
A) 1 B) -1 C) 0 D) 2
Q16: If 1
125 2
, , 8,
8 5
a r n   then 8 _____a 
A)
16
625
B)
625
16
C)
17
125
D) NONE
Q17: The series
3 3
6 3 ...
2 4
    is _____
A) Divergent B) Convergent C) G.P. D) Constant
Q18: The series 1 2
1 1 1 .....a a r a r   has a sum 1
1
a
r
if:
A) 1r  B) 1r  C) 1r  D)
2
3
r 
Q19: The sum of    2 1 1 2 1 ....     is____
A) 2 B)
1
2 2
C) Possible D) Impossible
Q20: The common difference fraction of 1.321 is:
A)
44
33
B)
440
333
C)
40
33
D)
441
331
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20

CLASS
XI
Q1: If 2 3
2 3
1 1 1
.....
3 3 3
y x x x    then x is:
A)
2
1
y
y
B)
1
y
y
C)
3
1
y
y
D) NONE
Q2: If
1 1 1
8 16 32
16 16 16 .....y    then y is:
A) 4 B) 2 C) 3 D) 2
Q3: If A,G & H are the . , . .AM G M and H M between a
& b , then which one of the following is true:
A) A G H  B) A G H 
C) H A G  D) G A H 
Q4: The sum of the series 3 3 3 3
1 2 3 ......n   is:
A)
 
22
1
4
n n 
B)
 
22
1
2
n n 
C)
 
23
1
4
n n 
D) NONE
Q5: The general term of the sequence
2 4 6 8
, , ,.....x x x x 
is:
A)   2
1
n n
na x  B)  
1
1
n n
na x

 
C)   3
1
n n
na x  D)  
2n
na x 
Q6: If
1 1 1
, ,
a b c
are in a H.P, then b is:
A)
2ab
a b
B)
2ac
a c
C)
2
a c
D)
2
a b
ac

Q7: If
1 1 1
,
2 1 4 1
and
k k k 
are in H.P, then k is:
A) 1 B) 3 C) 2 D) 5
Q8: The 7th
term of H.P
1 1 1
, , ,.....
3 5 7
is:
A) 15 B)
1
14
C)
1
15
D)
1
10
Q9: If .G G M , .A AM and .H H M then:
A) 2 2 2
.G A H B) .G AH
C) 2
.G A H D) 2
.G A H
Q10: Which one is H.P?
A) 3,6,9,... B)
1 1 1
, , ,...
2 5 11
C)
1 1 1
, , ,...
3 6 9
D) NONE

Q11: If ,2 2,3 3,...y y y  is a G.P, then y is:
A) 1,4 B) 1,4 C) 1, 4  D) 1, 4
Q12: 1 2 3 .............. ?n    
A)  1n n  B)
 1
2
n n 
C)
 1
2
n n 
D)
 2
1
2
n n 
Q13:
2 2 2 2
1 2 3 .............. ?n    
A)
  1 2 1
3
n n n 
B)
  1 2 1
2
n n n 
C)
  1 2
3
n n n 
D)
  1 2 1
6
n n n 
Q14:
3 3 3 3
1 2 3 .............. ?n    
A)
 
2
1
2
n n  
 
 
B)
 
2
1
2
n n  
 
 
C)
 
3
1
2
n n  
 
 
D)
 
2
1
3
n n  
 
 
Q15:
0
1 ?
n
n
k
S

 
A) 1 B) n C) 1n  D) 2
n
Q16:
0
?
n
n
k
S k

 
A)  1n n  B)
 1
2
n n 
C)
 1
2
n n 
D)
 2
1
2
n n 
Q17: 2
0
?
n
n
k
S k

 
A)
  1 2 1
3
n n n 
B)
  1 2 1
6
n n n 
C)
  1 2
3
n n n 
D)
  1 2
6
n n n 
Q18: 3
0
?
n
n
k
S k

 
A)
 
2
1
2
n n  
 
 
B)
 
2
1
2
n n  
 
 
C)
 
3
1
2
n n  
 
 
D)
 
2
1
3
n n  
 
 
Q19: The difference of two consecutive terms of an A.P is
called its:
A) A.M B) G.M
D) Common Difference D) Common Ratio
Q20: 5,15,20,25 ... is:
A) A.M B) G.M D) H.M D) NONE
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20

CLASS
XI
Q1: 2,8,32,...............is ..........................
A) A.M B) G.M D) H.M D) None
Q2: (n-1) th term of an A.P is ..................
A)  1 1a n d  B)  12 1a n d 
C)  1 2a n d  D)  12 2a n d 
Q3: The common difference of the sequence
3,15,27,.............. is ...........
A) 2 B) 12 D) 6 D) None
Q4: Find the common ratio of the sequence 0.5, 0.25,
0,125,............
A) 10 B) 5 D) 0.5 D) 1.5
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20

CLASS
XI
TYPE Objective Permutation, Combination and Probability No 1
Q1: The product of all positive integers equal to or less
than ‘ n ’ is called ……………….. of n.
A) Factor B) Factorial
C) Sequence D) Series
Q2: If ‘ n ’ is a positive integer then !n is:
A)   2 3 ....2.1n n n  B)   4 5n n n 
C)   1 2 ....3.2.1n n n  D) .5.4.3.2.1n
Q3: 0! ?
A) 0 B) 2 C) 1 D) -1
Q4: The arrangement of finite No of objects taken
some or all at a time in certain order is called:
A) Probability B) Factorial
C) Permutation D) Combination
Q5: 5! ?
A) 24 B) 120 C) 720 D) -120
Q6: ?n
rP 
A)
!
!
n
r
B)
 
!
! !
n
r n r
C)
 
 
1 !
! !
n
r n r


D)
 
!
!
n
n r
Q7: ?n
nP 
A) 0 B) 1 C) n D) !n
Q8: 0 ?n
P 
A) 0 B) 1 C) n D) !n
Q9: 10
3 ?P 
A)
10!
3!
B) 5040 C) 720 D)
10!
7!3!
Q10: If 3 4
n n
P P , then n is:
A) 5 B) 0 C) 1 D) 4

Q11: Total number of words formed from the letter
“TRIANGLE” using all the letters is:
A) 41320 B) 4320
C) 40320 D) None of these
Q12: If11
990nP  , then n is:
A) 11 B) 4 C) 19 D) 3
Q13: The numbers of signals that can be given by six
flags of different colors using three flags at a time are:
A) 6 B) 120 C) 24 D) 18
Q14: If 1 30n
P  , then n is:
A) 24 B) 15 C) 30 D) 120
Q15: 16
2 ?P 
A) 250 B) 240 C) 120 D) 230
Q16:
7!
?
2!3!

A) 120 B) 400 C) 420 D) 24
Q17: How many words can be formed from the letter
ARTICLE using all the letters ………………..
A) 5040 B) 5050 C) 5000 D) 720
Q18: If 1
4 3: 9:1n n
P P
 , then n is:
A) 8 B) 9 C) 10 D) 5
Q19: If 4 36n n
P P  then n is:
A) 11 B) 10 C) 9 D) 15
Q20: The number of words can be formed from the letter
“MISSISSIPPI” using all the letters is:
A) 34650 B) 34600 C) 35650 D) None
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20

CLASS
XI
Q1: Total number of words can be formed from the letters
of the word ‘mathematics’ using all letters is:
A) 4889600 B) 4889660
C) 48899600 D) 4899660
Q2: In how many different ways can seven female be seated
at around table?
A) 750 B) 120 C) 24 D) 720
Q3: How many 7-digit numbers can be formed from
2,2,3,3,3,4,4 ?
A) 200 B) 220 C) 210 D) 720
Q4: How many different numbers greater than 3 million can
be formed from the digits 1,1,1,1,2,2,3?
A) 16 B) 15 C) 20 D) 24
Q5: How many different ways are possible of the letter
‘SOME’ ?
A) 2! B) 3! C) 4! D) 5!
Q6: ?n
rC 
A)
 
!
!
n
n r
B)
!
!
n
r
C)
 
!
1 !
n
r 
D)
 
!
! !
n
n r r
Q7: 1 ?n
nC  
A) !n B) 1n  C) n D) !n
Q8: 0 ?n
C 
A) 1 B) 0 C) n D) !n
Q9: 1 ?n
C 
A) 1 B) !n C) 0 D) n
Q10: ?n
nC 
A) 0 B) n C) 1 D) !n

Q11: ?n
n rC  
A) n
nC B)
 
!
! !
n
n r r
C)
 
!
!
n
n r
D)
 
!
1 !
n
r 
Q12: If 5
n
C = 7
n
C than .............n 
A) 7 B) 5
Q13: Which one of the following is true?
A) n
rP = !n
rr C B) n
rC = !n
rP r
C) n
rC = n
rP D) !n n
r rC r P
Q14: 1 1
1 ?n n
r rC C 
 
A) 1n
rC
B) 1
n
rC  C) n
rC D) n
rP
Q15: If 1
3 23 7n n
C C
   then ?n 
A) 5n  B) 4n  C) 6n  D) 10n 
Q16: If 4
n
C = 5
n
C then ...........n 
A) 10n  B) 9n  C) 6n  D) 8n 
Q17: If 6. 4
n
C = 3
n
P , then ?n 
A) 6 B) 7 C) 8 D) 5
Q18: If 220n
rC  and 1320n
rP  , then the values of n
and r are:
A) 12n  , 2r  B) 11, 3n r 
C) 12, 3n r  D) None
Q19: The total No of the diagonals in a ten sided figure is:
A) 40 B) 30 C) 35 D) 20
Q20: 16 16
10 11 ?C C 
A) 16
12C B) 16
10C C) 16
15C D) 17
11C
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20

CLASS
XI
Q1: In how many ways can ‘6’ questions be selected out of
10 questions?
A) 220 B) 120 C) 250 D) 210
Q2: If 2 2
8 4: 7:6n n
C P 
 , then ?n 
A) 50 B) 10
Q3: Number of different committees of 3 men and 4 woman
out of 8 men and 6 woman are:
A) 800 B) 720
C) 840 C) None of these
Q4: The prediction of the chances that an event will occur is
called:
A) Combination B) Permutation
C) Probability D) Event
Q5: The set of all possible outcomes of an experiment is:
A) Sample space B) Permutation
C) Probability D) Event
Q6: Any subset of a sample space “S” called:
A) Event B) Element
C) Probability D) Experiment
Q7: What is the probability of selecting a prime number
from first 10 whole numbers?
A)
2
5
B)
3
10
C)
1
2
D)
3
4
Q8: An event “A”is called sure or absolute certain event if
  ?P A 
A) 200 B) 20 C) 0 D) 1
Q9: If “S” is sample space, then   ?P S 
A) 0 B) 1 C) 2 D) 1/2
Q10: The two events A and B are said to be mutually
exclusive or disjoint if ?A B 
A) A B) A B C) B D) 

Q11: If B S then   ?P B 
A)
 
 
n B
n S
B)
 
 
n S
n B
C)    n B n S D)    n S n B
Q12: If   0P A  , then event “A” is called:
A) absolute impossible event B) favorable event
C) possible event D) sure event
Q13: The two events A and B are said to be mutually
exclusive or disjoint if A B is:
A)  P A B B)    P A P B
C)    .P A P B D) 1
Q14: If for two events A and B,
       P A B P A P B P A B     , then the events A
and B are called:
A) Mutually exclusive B) Disjoint
C) Not mutually exclusive D) Sure
Q15: A dice is rolled, the probability of an event shown even
and odd number is:
A) 0 B) ½ C) 5/6 D) 1
Q16: If “A” is an event that occurs, then  P not A is:
A)  P A B)   1P A 
C)   1P A  D)  1 P A
Q17: Which of the following is true, for an event “A”
A)  0 100P A  B)  0 1P A 
C)  1 2P A   D)  0 0.5P A 
Q18: The probability of selecting a prime number from a list
of natural number  1,2,3,4,.....,33 is:
A) 1/2 B) 1 C) 1/4 D) 1/3
Q19: If there are 6 red balls out of 15 in a box, then the
probability that one ball drawn is red is:
A) 1/2 B) 2/5 C) 3/4 D) 5/2
Q20: If A and B are mutually disjoint events then
  ?P A B 
A)  P A B B)    P A P B
C)    .P A P B D) None of these
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20

CLASS
XI
Q1:  c
P A is equal to:
A)  P A B)   1P A  C)   1P A  D)  1 P A
Q2: If  1,2,3,4,5,6S  then probability of an event A
which denotes numbers less than 4 is:
A)  
1
3
P A  B)  
1
2
P A 
C)  
3
4
P A  D) None of these
Q3: The probability that a three digit number taken at
random is divisible by 5 is:
A) 1/4 B) 11/5 C) 3/4 D) 1/5
Q4: If three coins are tossed, then what is the number of
elements in the sample space?
A) 90 B) 6 C) 8 D) 10
Q5: How many distinct permutations of the letter ENGIN
are possible?
A) 24 B) 120 C) 100 D) 96
Q6: The number of comities of 7 persons formed from a
group of 10 persons is:
A)130 B) 720 C) 120 D) 900
Q7: A dice is thrown, then the probability to get a number
divisible by 2 is:
A) 2/3 B) 1/3 C) 1/2 D) 3/5
Q8: How many distinct words are possible of the letters in
the word “PULLY”?
A) 50 B) 60 C) 120 D) 0 730
Q9:
 
 
3 !
?
2 !
n
n



A)  2 !n  B)  3 !n  C) 3n  D) 1n 
Q10:   2 1 ?n n n  
A) !n B)  2 !n  C)
 
 
1 !
2 !
n
n


D)
 
 
2 !
1 !
n
n



Q11:
 1
?
4.3.2.1
n n 

A) !n B)
 4! 2 !
!
n
n

C)
 
!
4! 2 !
n
n 
D)
 2 !
4! !
n
n

Q12: 10.9.8.7.6 ?
A) 10! 5! B) 10! 5! C)
10!
5!
D)
5!
10!
Q13:
8.7.6
?
3.2.1

A)
8!
3!5!
B)
5!3!
8!
C)
10!
2!8!
D) 10!
Q14:      3 . 2 . 1 ........3.2.1 ?n n n   
A) !n B)  1 !n 
C)  3 !n  D)  3 ! 3!n  
Q15: 5 persons can be seated at a round table in:
A) 25 ways B) 24 ways
C) 20 ways D) 120 ways
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20

CLASS
XI
TYPE Objective Mathematical Induction and Binomial Theorem No 1
Q1: Which of the following is equal to  
4
a b ?
A) 4 3 2 2 3 4
4 6 4a a b a b ab b   
B) 4 3 2 2 3 4
4 6 4a a b a b ab b   
C) 4 3 2 2 3 4
4 12 4a a b a b ab b   
D) 4 3 2 2 3 4
4 12 4a a b a b ab b   
Q2: Which of the following is the binomial coefficients?
A) , , ,....,
1 2 3
n n n n
n
       
       
       
B) , , ,....,
0 1 2
n n n n
n
       
       
       
C)
1 2 3
, , ,....,
n
n n n n
       
       
       
D) , , ,....,
0 1 2
n n n n
n
       
       
       
Q3: The number of terms in the expansion  
7
a b is
equal to:
A) 7 B) 8 C) 6 D) 1n 
Q4: The number of terms in the expansion  
n
a b is
....................... its index
A) one smaller than B) equal to
C) one greater than D) None of these
Q5: The sum of exponents of a and b in each term of the
expansion  
n
a b is equal to its:
A) 1n  B) n C) 1n  D) !n
Q6: The exponent of a in the expansion  
n
a b ............
from index to zero
A) increases B) decreases
C) doubled D) None of these
Q7: ?
n
r
 
 
 
A)
1
n
r
 
 
 
B)
1
n
r
 
 
 
C)
n
n r
 
 
 
D)
n
n r
 
 
 
Q8: ?
n
n r
 
 
 
A)
1
n
r
 
 
 
B)
1
n
r
 
 
 
C)
n
r
 
 
 
D)
n
r n
 
 
 
Q9:
11
?
6
 
 
 
A)
11
5
 
 
 
B)
12
5
 
 
 
C)
10
5
 
 
 
D)
11
10
 
 
 
Q10: 3
n
C exist when n is:
A) 2n  B) 3n  C) 3n  D) 3n 

Q11: 11
rC exist when r is:
A) 11r  B) 12r 
C) 11r  D) Only when 11r 
Q12: 11 11
4 3 ?C C 
A) 11
4C B) 12
3C C) 12
4C D) 11
7C
Q13: The inequality 4 3 4n n
  is valid if:
A) 2n  B) 2n  C) 2n  D) 2n 
Q14: .... ?
0 1 2
n n n n
n
       
           
       
A) !n B) 2n
C)
1
n n
n n
   
   
   
D)  1 !n 
Q15: The inequality  2 2 1n
n  is valid if:
A) 3n  B) 3n  C) 3n  D) 2n 
Q16: If n is any positive integer, then
2 2 2 2
1 2 3 ..... ?n    
A)
  1 2 1
6
n n n 
B)
  1 2 1
2
n n n 
C)
  1 2
6
n n n 
D)
  1 2 1
3
n n n 
1 2 3 .......... ?n    
A)
 1
3
n n 
B)
 1
2
n n 
C)
 2 1
3
n n 
D)
 2 1
2
n n 
3 3 3 3
1 2 3 .......... ?n    
A)
 
2
1
3
n n  
 
 
B)
 
2
1
2
n n  
 
 
C)
 
2
2 1
3
n n  
 
 
D)
 
2
2 1
2
n n  
 
 
4 8 12 .......... 4 ?n    
A)  4 1n n  B)  2 1n n 
C)  2 2 1n n  D)  2 1n n 
Q20: The inequality ! 2 1n
n   is valid if:
A) 3n  B) 3n  C) 4n  D) 4n 
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20

CLASS
XI
TYPE Objective Mathematical Induction and Binomial Theorem No 2
Q1: The inequality
1
! 3n
n 
 is valid if ........
A) 5n  B) 5n  C) 3n  D) 3n 
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20

CLASS
XI
TYPE Objective Fundamentals of Trigonometry No 1
Q1: The union of two non-collinear rays which have a
common endpoint is called:
A)Angle B) Radian
C) Degree D) Minute
Q2: The common end point of two rays is called:
A)Radian B) Degree
C) Vertex D) None of these
Q3: If the circumference of a circle is divided into 360
congruent parts, the angle subtended by one part at the centre of
the circle is called:
A)Angle B) Radian
C) Degree D) Minute
Q4: One degree is denoted by :
A)1 radian B) 1 C) 1 D)
0
1
Q5: The 60th
part of one degree is called one:
A) Second B) Radian C) Degree D) Minute
Q6: One minute is denoted by:
A)1 radian B) 1 C) 1 D)
0
1
Q7:
0
1 is equal to:
A) 60 B) 60 C) 3600 D) 360
Q8: The 60th
part of one minute is called one:
A) Second B) Radian
C) Degree D) Minute
Q9: One second is denoted by:
A) 1 radian B) 1 C) 1 D)
0
1
Q10: 1 is equal to:
A) 60 B) 60 C) 3600 D) 360

Q11: A right angle is the angle of measure:
A) 90 B) 90 C) 0
90 D) 0
360
Q12: The system of measurement in which the angle is
measured in degrees, and its sub units, minutes and seconds is
called:
A) Circular System B) Sexagesimal System
C) M K S System D) CGS System
Q13: Which of the following trigonometric ratio is positive
in third quadrant?
A) Sin B) Cosine C) Tangent D) Secant
A)    sin 23 sin 23   B)  cos 20 cos20  
C) tan0 0 D) cot0 undefined
Q15: 2 2
sin cos ?x x 
A) 1 B) 0
C) 1 D) undefined
Q16: 2
sec 1 ?x  
A) 2
cot x B) 2
tan x
C) 1 D) 2
tan x
A) 2 2
tan 1 secx x  B) 2 2
cot 1 cscx x 
C) 2 2
tan cot 1x x  D) 2 2
sin cos 1x x 
Q18: Which of the following trigonometric ratio is negative
in second quadrant?
A) Sine B) Cosine
C) Cosecant D) Nome of them
Q19: tan45 cot45 ? 
A) 1 B) 2
C) 1 D) undefined
Q20: Which of the following is positive?
A) sin171 B) cos187
C) tan91 D)  sin 30
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20

CLASS
XI
TYPE Objective Fundamentals of Trigonometry No 2
Q1: sin0 ..............
A)   B) 0 C) 1 D) 1
Q2: sin30 ..............
A) 1 B)
3
2
C) 3 D)
1
2
Q3: sin45 ..............
A) 2 B)
1
2
C)
2
2
D)
3
2
Q4: cos60 sin30 ? 
A) 1 B)
2
2
C) 3 D)
1
2
Q5: sin ..............
2


A) 1 B) 0
C) 1 D) Undefined
Q6: cos0 ..............
A) 1 B) 0
Q7: cos30 ..............
A) 1 B)
3
2
C) 3 D)
1
2
Q8: cos45 ..............
A)
2
2
 B)
1
3
C)
2
2
D)
1
2
Q9: cos60 ..............
A) 2 B)
1
2
C)
2
2
D)
3
2
Q10: cos90 ..............
A) 1 B) 0

Q11: tan0 ..............
A) 1 B) 0
Q12: tan30 ..............
A) 2 B) 3 C)
2
2
D)
3
3
Q13: tan45 ..............
A) 1 B) 3 C) 1 D) 2 3
Q14: tan60 ..............
A) 2 B) 3 C)
2
2
D)
3
3
Q15: tan90 ..............
A) 1 B) 0
Q16: cot0 ..............
A) 1 B) 0
Q17: cot30 ..............
A) 2 B) 3 C)
2
2
D)
3
3
Q18: cot 45 ..............
A) 1 B) 3
C) 1 D) 2 3
Q19: cot60 ..............
A) 2 B) 3 C)
2
2
D)
3
3
Q20: cot90 ..............
A) 1 B) 0
Answer Key
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20

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