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INFOMATHS
WORK-SHEET-1(OLD QUESTIONS)
17.
SETS & RELATIONS
1.
The binary relation on the integers defined by R = {(a, b) : |b – a|
 1} is
HCU-2012
(a) Reflexive only
(b) Symmetric only
(c) Reflexive and Symmetric
(d) An equivalence relation
2.
Set of all subsets is a
PUNE-2012
(a) power set
(b) equal sets
(c) equivalent sets
(d) None of these
3.
In a class of 100 students, 55 students have passed in Mathematics
and 67 students have passed in Physics. Then the number of
students who have passed in Physics only is
NIMCET-2012
(a) 22
(b) 33
(c) 10
(d) 45
4.
Let X be the universal set for sets A and B. If n(A) = 200, n(B) =
300 and n(A ∩ B) = 100, then n(A'∩ B') is equal to 300 provided
in n(X) is equal to
NIMCET-2011
(a) 600
(b) 700
(c) 800
(d) 900
5.
In a college of 300 students, every student reads 5 news papers
and every news paper is read by 60 students. The number of news
paper is
NIMCET-2011
(a) atleast 30
(b) atmost 20
(c) exactly 25
(d) exactly 28
6.
If A = {1, 2, 3}, B = {4, 5, 6}, which of the following are relations
from A to B?
BHU-2011
(a) {(1, 5), (2, 6), (3, 4), (3, 6)}
(b) {(1, 6), (3, 4), (5, 2)}
(c) {(4, 2), (4, 3), (5, 1)}
(d) B  A
7.
The number of subsets of an n elementric set is
BHU-2011
(a) 2n
(b) n
(c) 2n
(d)
18.
19.
20.
21.
22.
23.
1 n
2
2
If A = {a, b, d, l}, B = {c, d, f, m} and C = {a, l, m, o}, then C 
(A  B) is given by
BHU-2011
(a) {a, d, l, m}
(b) {b, c, f, o}
(c) {a, l, m}
(d) {a, b, c, d, f, l, m, o}
In question 9 and 10, for sets X and Y, X  Y is defined as X  Y =
(X – Y) (Y – X)
9.
If P = {1,2, 3, 4}, Q = {2, 3, 5, 8}, R = {3, 6, 7, 9} and S = {2, 4,
7, 10} then (P  Q)  (R  S) is
HCU-2011
(a) {4, 7}
(b) {1, 5, 6, 10}
(c) {1, 2, 3, 5, 6 8, 9, 10}
(d) None of the above
10. If X, Y, Z are any three subsets of U, then the subset of U
consisting of elements which belong to exactly two of the sets X,
Y, Z is
HCU-2011
(a) (X  Y)  (Y  Z)  (Z  X)
(b) (X  Y)  (Y  Z)  (Z  X)
(c) ((X  Y)  Z) – ((X  Y)  Z)
(d) None of the above
11. Let A = {1, 2, 3, 4}. The cardinality of the relation R = {(a,b)| a
divides b} over A is :
PU CHD-2011
(A) 10
(B) 9
(C) 8
(D) 4
12. If X={8n –7n–1\nN } and Y= {49(n–1)\nN} then:
PU CHD-2010
(A) X  Y (B) Y X (C) X=Y
(D) XUY=N
13. The relation R={(1,1) (2,2), (3,3), (1,2), (2,3), (1,3) } on the set A
={1,2,3} is :
PU CHD-2010
(A) reflexive but not symmetric
(B) reflexive but not transitive
(C) symmetric and transitive
(D) neither symmetric nor transitive
14. Let R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3,
6)} be a relation on the set A = (3, 6, 9, 12) Then the relation is :
PU CHD-2009
(a) reflexive and transitive only
(b) reflexive only
(c) and equivalence relation
(d) reflexive and symmetric only
8.
15.
16.
For real numbers x and y, we write xRy 
x2  y 2  3
24.
25.
26.
27.
28.
If two sets A and B are having 99 elements in common, then the
number of elements common to each of the sets A  B and B  A
are :
KIITEE-2010
(a) 299
(b) 992
(c) 100
(d) 18
If A, B and C are three sets such that A  B = A  C and A  B
= A  C, then
KIITEE-2010
(a) A = C
(b) B = C
(c) A  B = 
(d) A = B
In a city 60% read news paper A, 40% read news paper B and
30% read C, 20% read A and B, 30% read A and C, 10% read B
and C. Also 15% read paper A, B and C. The percentage of people
who do not read any of these news papers is
(PGCET – 2009)
(a) 65%
(b) 15%
(c) 45%
(d) None of these
The total number of relations that exist from the set A with m
elements into the set A  A is
(NIMCET – 2009)
(a) m2
(b) m3
(c) m
(d) None of these
If P = {(4n – 3n - 1) / n  N} and Q = {(9n - 9) / n  N}, then P 
Q is equal to
(NIMCET – 2009)
(a) N
(b) P
(c) Q
(d) None of these
A1, A2, A3 and A4 are subsets of a set U containing 75 elements
with the following properties : Each subset contains 28 elements;
the intersection of any two of the subsets contains 12 elements;
the intersection of any three of the subsets contains 5 elements;
the intersection of all four subsets contains 1 elements. The
number of elements belongs to none of the four subsets is
(NIMCET – 2009)
(a) 15
(b) 17
(c) 16
(d) 18
From 50 students taking examination in Mathematics, Physics and
Chemistry, 37 passed Mathematics, 24 Physics and 43 Chemistry.
At most 19 passed Mathematics and Physics, at most 29
Mathematics and Chemistry and atmost 20 Physics and
Chemistry. The largest possible number that could have passed all
three examinations is
(NIMCET - 2009)
(a) 10
(b) 12
(c) 9
(d) None of these
Let the sets A = {2, 4, 6, 8 …} and B = {3, 6, 9, 12, …} and n (A)
= 200, n(B) = 250 then
(KIITEE – 2009)
(a) n(A  B) = 67
(b) n(A  B) = 66
(c) n (A  B) = 450
(d) n(A  B) = 380
Let R be relation on the set of positive integers defined as follows:
aRb iff 4a + 5b is divisible by 9 then R is
(Hyderabad Central University – 2009)
(a) Reflexive only
(b) Reflexive and symmetric but not transitive
(c) Reflexive and transitive but not symmetric
(d) An Equivalence relation
The set having only one subset is
(Hyderabad Central University – 2009)
(a) { } (b) {0}
(c) {{}}
(d) None of these
If R and S are equivalence relations on a set A, then
(Hyderabad Central University – 2009)
(a) R  S is an equivalence relation
(b) R  S is an equivalence relation
(c) Both A and B are true
(d) Neither A nor B is true
Identify the wrong statement from the following :
NIMCET-2010
(a) If A and B are two sets, then A- B= A  B
(b) If A,B and C are sets, then (A - B) – C = (A – C)-(B - C)
(C) If A and B are two sets, then
A B= AB
(D) If A, B
and C are sets, then A  B  C  A  B
29. A survey shows that 63% of the Americans like cheese where as
76% like apples. If x% of the Americans lie both cheese and
apples, then we have
NIMCET-2010
(a) x 39
(b) x63
(c) 39x63
(d) N.O.T
30. Suppose P1, P2, … P30 are thirty sets each having 5 elements and
Q1, Q2, …. Qn are n sets with 3 elements each. Let
30
n
i 1
j 1
 Pi   Q j  S
is an
irrational number. Then the relation R is
KIITEE-2010
(a) reflexive
(b) symmetric
(c) transitive
(d) None of these
If X = {4n – 3n – 1: n  N} and Y = {9(n – 1) : n  N}, then X 
Y is equal to
KIITEE-2010
(a) X
(b) Y
(c) N (d) None of these
and each element of S belongs to exactly 10
of the Pi S and exactly 9 of the Qj s. Then, n is equal to
(MCA : NIMCET - 2008)
(a) 15
(b) 3
(c) 45
(d) None
31.
1
If A = {1, 2, 3}, B = {a, b, c, d}. The number of subsets in the
Cartesian product of A & B is
(Pune– 2007)
(a) 212
(b) 27
(c) 12
(d) 7
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
32.
33.
34.
35.
36.
37.
In an election 10 per cent of the voters on the voters’ list did not
cast their votes and 50 voters cast their ballot papers blank. There
were exactly two candidates. The winner was supported by 47 per
cent of all the voters in the list and he got 306 more than his rival.
The number of voters in the list was
(IP University : – 2006)
(a) 6400
(b) 6603
(c) 7263
(d) 8900
(e) N.O.T
Only one of the following statements given below regarding
elements and subsets of the set {2, 3, {1, 2, 3}} is correct. Which
one is it?
(IP University : – 2006)
(a) {2, 3}  {2, 3, {1; 2, 3}}
(b) 1  (2, 3, {1, 2, 3}}
(c) {2, 3}  (2, 3, {1, 2, 3}}
(d) {1, 2, 3,}  {2, 3, {1, 2, 3}}
Which set is the subset of all given sets?
(Karnataka PG-CET : - 2006)
(a) {1, 2, 3, 4, …}
(b) {1}
(c) {0}
(d) { }
A set contains (2n + 1) elements. If the number of subsets which
contain at most n elements is 4096, then the value of n is
(NIMCET – 2009)
(a) 28
(b) 21
(c) 15
(d) 6
If set A has 6 elements, B has 4 elements and C has 8 elements,
the maximum number of elements in (B – C)  (A  B)  C is
(Hyderabad Central University – 2009)
(a) 18
(b) 12
(c) 16
(d) 24
Let A be a set with 10 elements. The total number of relations that
can be defined on A that are both reflexive and asymmetric is
(Hyderabad Central University – 2009)
(a) 245
(b) 255
(c)
10 
 
2
11.
12.
13.
14.
15.
16.
 1  5 1  5 
,


2
2 

 1  5 1  5 
(c) 
,


2
2 

(a)
(d) None of these
17.
THEORY OF EQUATIONS
1.
If the equation x4 – 4x3 + ax2 + bx + 1= 0 has four positive roots
then a =?
BHU-2012
(a) 6, -4
(b) -6, 4
(c) 6, 4
(d) -6, -4
2.
Let P(x) = ax2 + bx + c and Q(x) = - ax2 + bx + c, where ac  0.
Then for the polynomial P(x) Q(x)
HCU-2012
(a) All its roots are real
(b) None of its roots are real
(c) At least two of its roots are real
(d) Exactly two of its roots are real
3.
Let p(x) be the polynomial x3 + ax2 + bx + c, where a, b and c are
real constants. If p(–3) = p(2) = 0 and p'(–3) < 0, which of the
following is a possible value of c ?
PU CHD-2012
(A) – 27
(B) – 18
(C) – 6
(D) – 3
4.
Which of the following CANNOT be a root of a polynomial in x
of the form 9x5 + ax3 + b, where a and b are integers?
PU CHD-2012
(A) – 9
5.
(B) – 5
(C)
1
4
(D)
7.
8.
21.
PU CHD-2012
(C)
3
7
(D)
1 
 2 , 2


 1 
  2 ,1


4
7
(B)
 1, 2
(D)
 1
1, 2 
 
 1 5 1 5 


,


2
2


1  5 1  5 


,
 2

2


and
x 3
 3
4 y
are.
(MP combined – 2008)
22.
23.
If
(c)
24.
25.
26.
27.
28.
11 7
 1
x y
and
9 4
 6
x y
1 1
 2 , 3


1 1
 2 , 3 


then (x, y) =
(b)
(d)
(ICET – 2007)
1 1 
3 , 2


 1 1
 3 , 2 


The maximum value of the expression 5 + 6x – x2 is
(ICET – 2007)
(a) 11
(b) 12
(c) 13
(d) 14
2
If one root of the equation ax + bx + c = 0 is double the other
root, then,
(ICET – 2005)
(a) b2 = 9ac (b) 2b2 = 3ac (c) b = 2a (d) 2b2 = 9ac
2
The maximum value of the expression 2 + 5x – 7x is ICET–2005
(a)
2
(d)
 1 5 1 5 


,


2
2


 1 5 1 5 


,


2
2


(a) x = 9, y = 1
(b) x = 6, y = 1
(c) x = 6, y = 2
(d) x = 3, y = 2
If x2 + x – 2 is a factor of the polynomial x4 + ax3 + bx2 – 12x + 16
then the ordered pair (a, b) =
(ICET – 2007)
(a) (-3, 8)
(b) (3, - 8) (c) (-3, - 8) (d) (3, 8)
(a)
The roots of the equation |x2x6 | x 2 are : PU CHD-2010
(A) – 2, 1, 4 (B) 0, 2, 4 (C) 0, 1, 4 (D) – 2, 2, 4
If one root of the equation ax2 + bx + c = 0 is twice the other then :
(b)
Let ,  be the roots of the equation (x – a) (x – b) = c, c  0, then
the roots of the equation (x + ) (x + ) + c = 0 are
(Hyderabad central university - 2009)
(a) a, - b
(b) – a, b
(c) – a, - b (d) a, b
The number of roots of the equation |x2 – x - 6| = x + 2 is
(NIMCET - 2008)
(a) 2
(b) 3
(c) 4
(d) None
If esin x – e-sin x – 4 = 0 then the number of real values of x is
(KIITEE – 2008)
(a) 0
(b) 1
(c) infinite (d) None
The values of x and y satisfying the equations:
x 2
 1
3 y
If the roots of the equation ax2 + bx + c = 0 are real and of the
form α/ (α -1) and (α + 1) / α then the value of (a + b + c)2 is :
PU CHD-2011
(A) b2 – 4ac (B) b2 – 2ac (C) 2b2 – ac (D) b2 – 3ac
2
2
2
If a + b + c = 1, then ab + bc + ca lies in the interval :
PU CHD-2011
(C)
10.
20.
If a, b, c are real numbers such that a2 + b2 + c2 = 1, then ab + bc +
ca 
PU CHD-2012
(A) 1/2
(B) – 1/2
(C) 2
(D) – 2
(A)
9.
19.
If and are the root of 4x2 + 3x + 7 = 0, then the value of
 1
     is :
  
3
3
(A) 
(B) 
7
4
6.
(c)
18.
1 5 1 5 
,


2 
 2
 1  5 1  5 
(d) 
 2 , 2 


(b)
The roots of the quadratic equation x2 – x – 1 = 0 are
(PGCET – 2009)
(a)
1
3
1


PU CHD-2010
(A) 2a2 = 3c2 (B) 2b2 = 3ac(C) 2b2 = 9ac (D) b2 = ac
2
If both the roots of the quadratic equation x – 2kx + k2 + k – 5 = 0
are less than 5, then k lies in the interval
PU CHD-2009
(a) (5, 6]
(b) (6, )
(c) (-, 4) (d) [4, 5]
The function f(a) and f(b) are of same sign and f(x) = 0 then the
function :
PU CHD-2009
(a)
has either no root or even number of roots between a and b
(b)
must have at least one root between a and B
(c)
has either no root or odd number of roots between a and b
(d)
has complex root
How many real solutions does the equation x7 + 14x5 + 16x3 + 30x
– 560 = 0 have?
KIITEE-2010
(a) 7
(b) 1
(c) 3
(d) 5
If the rots of the quadratic equation x2 + px + q = 0 are tan 30 and
tan 15, respectively, then the value of 2 + q – p is KIITEE-2010
(a) 3
(b) 0
(c) 1
(d)2
The number of real solutions of the equation x2 – 3|x| + 2 = 0 is
KIITEE-2010
(a) 2
(b) 4
(c) 1
(d) 3
2
The roots of the quadratic equation x + x – 1 = 0 are
PGCET-2010
28
81
(b)

28
81
(c)
81
28
(d)

81
28
The solution of the equation x2/3 – 3x1/3 + 2 = 0 is (Pune – 2007)
(a) 1, 2
(b) 1, 8
(c) 2, 6
(d) 1, 4
Which of the following may be true for a quadratic equation ( is
real)?
(Pune – 2007)
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
29.
(a) If  is a root, 1/ is also a root
(b) If  is a root, -  is also a root
(c) If  is a root, i  is also a root
(d) If i  is a root, -i  is also a root
If a + b + c = 0 then one root of the equation ax2 – bx + c = 0 is
(Pune – 2007)
(a)
30.
31.
(c)
33.
34.
36.
37.
(c)
ac
a
(d)
n m 1
 
a b c
n m 1
 
a c b
(b)
48.
   
, 

 2 2
49.
50.
51.
52.
Number of real roots of 3x + 15x – 8 = 0 is
53.
1
log 3 7 is
2
(a)
40.
41.
42.
43.
(b)
If x < - 1 and 2
|x+1|
55.
(d)
(ICET – 2005)
b
a
(b)
c
a

(c)
ac
a
ab
a
(d)
If  and  are the roots of |x2 + x + 5| + 6x + 1 = 0 then  + 
(Pune– 2007)
(a) 7
(b) –7
(c) 5
(d) –5
x  R, The solution set of the inequality
|x – 4| + | x – 6| + |x – 8|  15, is (IP. University : Paper – 2006)
(a) [1, 11] (b) [2, 12] (c) [0, 10] (d) [3, 10]
(e) None of these
x  R. The solution set of the inequality 10[x] 2 – 17[x] – 6  0
(where [x] denotes the greatest integer less than or equal to) is
(IP. University :– 2006)
(b) [-1, 2)
(c) (0, 3]
(d) [-1, 3]
The solution set for real x of the equation
is
(IP. University :– 2006)
(d)
 2
(e) None of these
If a is a positive integer, and the roots of the equation 7x2 – 13x +
2a are rational numbers, then the smallest value of a is
(IP. University : Paper – 2006)
(a) 1
(b) 2
(c) 3
(d) 4
(e) N.O.T
x 2  8x  7  x 2  8x  8  9
(UPMCAT : paper – 2002)
(b) x = - 1
(d) None of these
If
x
1
2


3  1 , then the value of expression 4x3 + 2x2 – 8x
+ 7, is equal to
are
56.
1
,5
3
BHU-2011
(a) 10
(b) 5
(c) 0
(d) – 2
The number of quadratic equations which remain unchanged by
squaring their roots, is
BHU-2011
(a) zero
(b) four
(c) two
(d) infinite
x
- 2x = |2 - 1| + 1, then the value of x is
(NIMCET - 2009)
(a) –2
(b) 2
(c) 0
(d) none
The number of distinct integral values of ‘a’ satisfying the
equation 22a – 3(2a + 2) + 25 = 0 is
(NIMCET - 2009)
(a) 0
(b) 1
(c) 2
(d) 3
The set of real values of x satisfying |x - 1|  3 and |x – 1|  1 is
(KIITEE - 2009)
(a) [2, 4]
(b) [-2, 0]  [2, 4]
(c) (- , 2]  [4, )
(d) None of these
If ,  are non real numbers satisfying x3 – 1 = 0 then the value of
 1 



1

1
 
44.
(c)
2 1
,
5 3

(a) x = - 1, x = 9
(c) x = 9
(NIMCET - 2009)
5
 ,3
2
then x4 + x3 – 4x2 + x + 1 =
(a) x2(y2 + y – 2)
(b) x2(y2 + y – 3)
(c) x2(y2 + y – 4)
(d) x2(y2 + y – 6)
Which of the following may be true for a quadratic equation ( is
real)?
Pune-2007
(a) If  is a root, 1/ is also a root
(b) If  is a root, -  is also a root
(c) If  is a root, i  is also a root
(d) If i  is a root, -i  is also a root
If a + b + c = 0 then one root of the equation ax2 – bx + c = 0 is
Pune-2007
54.
NIMCET-2011
(a) (–2, –1) (b) (–2, 3) (c) (–1, 3) (d) (3, ∞)
If α, β are the roots of the equation x2 − 2x + 4 = 0 then the value
of α6 + β6 is
NIMCET-2011
(a) 64
(b) 128
(c) 256
(d) 132
5
 3,
2
1
x
  (c)  12 
NIMCET-2012
(a) 3
(b) 5
(c) 1
(d) 0
The least integral value of K for which (K–2) x2 + K+ 8x + 4 > 0
for all x  R, is
NIMCET-2011
(a) 5
(b) 4
(c) 3
(d) 6
Solution set of inequality
1
x
yx
8
log x2 4  log x3 2  ,
3
1
 
(a)  
(b)
2 ,4
8 
5
x
If
(a) [0, 3)
(d) (0, π)
If 2x4 + x3 – 11x2 + x + 2 = 0, then the value of
(a) 0
(b) 1
(c) 2
(d) 3
If a, b are the roots of x2 + px + 1 = 0 and c, d are roots of x2 + qx
+ 1 = 0, the value of
E = (a – c) (b – c) (a + d) (b + d) is
(NIMCET - 2008)
(a) p2 – q2 (b) q2 – p2 (c) q2 + p2
(d) None
(a)
(d) None of these
3
39.
47.
n m 1
 
b a c
log3  x  2  x  4   log 1  x  2  
38.
46.
ab
a
Given a  b; The roots of (a – b)x2 – 5(a – b)x + (b – a) = 0 are:
(UPMCAT– 2002)
(a) Real and equal
(b) real and different
(c) complex
(d) None of these
If the real number x when added to its inverse gives the minimum
value of the sum, then the value of is equal to
NIMCET-2012
(a) – 2
(b) 2
(c) 1
(d) – 1
The equation (cos p – 1)x2 + (cos p) x + sin p = 0 where x is a
variable has real roots. Then the interval of p is
NIMCET-2012
(a) (0, 2π)
(b) (-π, 0)
(c)
35.
(b)
c

a
If x2 + ax + 10 = 0 and x2 + bx – 10 = 0, have a common root then
a2 – b2 equal to
(Karnataka PG-CET – 2006)
(a) 10
(b) 20
(c) 30
(d) 40
If
ax2 + bx + c = 0
lx2 + mx + n = 0
have reciprocal roots then:
(UPMCAT– 2002)
(a)
32.
b

a
45.
SEQUENCE & SERIES
1.
1 3 7 15
    ........ upto n-terms is:
2 4 8 16
PU CHD-2012
1
(A) n  1  n
2
1
(C) 2n  n
2
2.
is equal to
The sum of the series
(KIITEE - 2009)
3.
(a) 0
(b) 3 + 1
(c) 3
(d) None of these
The number of positive real roots for the following polynomial
P(x) = x4 + 5x3 + 5x2 – 5x – 6 is
(Hyderabad central university - 2009)
(D)
n 1
1
2n
The harmonic mean of two numbers is 4. The arithmetic mean A
and geometric mean G of these two numbers satisfy the equation
2A + G2 = 27. The two numbers are :
PU CHD-2012
(A) 3, 6
(B) 4, 5
(C) 2, 7
(D) 1, 8
In a geometric progression, (p + q)th term is m and (p - q)th term
is n, then pth term is :
PU CHD-2011
(A) m/n
3
1
(B) n  n
2
(B)
mn (C)
m / n (D)
n/m
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
4.
5.
6.
The arithmetic mean of 9 observations is 100 and that of 6
observations is 80, then the combined mean of all the 15
observations will be :
PU CHD-2011
(A) 100
(B) 80
(C) 90
(D) 92
If in a GP sum of n terms is 255, the last term is 128 and the
common ratio is 2, then the value of n is equal to
BHU-2011
(a) 2
(b) 4
(c) 8
(d) 16
If the ratio of the sum of m terms and n terms of an AP be m2 : n2,
then the ratio of its mth and nth terms will be
BHU-2011
19.
20.
2m  1
2n  1
mn
(d)
mn
mn
mn
2m  1
(c)
2n  1
(a)
7.
(c)
21.
(b)
22.
5  0 is
(a) 2
(d) 8
2
BHU-2011
8.
(b) 4
(c) 6
Arithmetic mean of two positive numbers is
18
23.
3
and their 24.
4
geometric mean is 15. The larger of the two numbers is
9.
10.
11.
HCU-2011
(a) 30
(b) 20
(c) 24
(d) None of the above
Let A (x1, y1), B(x2, y2), C(x3, y3) and D(x4, y4) be four points such
that x1, x2, x3, x4 and y1, y2, y3, y4 are both in arithmetic
progression. Then the area of the quadrilateral ABCD is
HCU-2011
(a) 0
(b) greater than 1
(c) less than 1
(d) Depends on the coordinates of A, B, C, D
If x, 2x+2, 3x+3 are in G.P then the 4 th term is :
PU CHD-2010
(A) 27
(B) –27
(C) 13.5 (D) –13.5
 666.......6
2
  888.......8 is equal to :
n  digits
4
n
(A) 10  1
9
2
4
n
(c) 10  1
9
25.
26.
27.
28.
PU CHD-2010
29.
n  digits
30.
13.
14.
(d)
31.
b a

q p
Which of the following statement is correct?
PU CHD-2009
(a) A.M. < G.M. < H.M.
(b) A.M. > G.M. > H.M.
(c) A.M. > G.M. < H.M.
(d) H.M. < A.M. < G.M.
The sum to infinite terms of the series
2 6 10 14
1   2  3  4  ....... is
3 3 3 3
15.
16.
17.
18.
(d)
02
a2
If K + 2, 4K – 6 and 3K – 2 are three consecutive terms of an
arithmetic progression then, K is
(ICET – 2005)
(a) 4
(b) 3
(c) 1
(d) 4
If a > 1, b > 1 and a + b = ab and if
1
1
1 1
1 1

 .... y  1   2  .... then  
a a2
b b
x y
(ICET – 2005)
(a) 0
(b) 2
(c) 1
(d) 3
th
If tn is the n term of an arithmetic progression with first term ‘a’
n
 t 2k 
k 1
(ICET – 2005)
(a) na + (n – 1)d
(b) n(a + nd)
(c) na + (n + 1)d
(d) na + (2n – 1)d
In a polygon, the smallest angle is 88 and common difference is
10, the number of sides is :
UPMCAT– 2002
(a) 10
(b) 8
(c) 5
(d) N.O.T.
 3  10 
  
 3  1 
 3  10  9
(D)     2
 3  1 
(A) 214
(B)
KIITEE-2010
(C)
2.
 3
10 
   2 
 3
1
In the binomial expansion of (a – b)n, n  5, the sum of 5th and 6th
terms is zero. Then
a
equals:
b
BHU-2012
n5
(a)
6
H H

is
P Q
3.
NIMCET-2012
(a) 2
(c) ab
BINOMIAL THEOREM
1.
The coefficient of x3 in the expansion of (1 + x)3 (2 + x2)10 is :
PU CHD-2012
(a) 3
(b) 4
(c) 6
(d) 2
Sum up to 10 terms of 1 + 3 + 5 + 7 + …. Is
PGCET-2010
(a) 100
(b) 102
(c) 103
(d) 104
Sum of 43 + 83 + 123 + …. + 403 is
(PGCET – 2009)
(a) 193600 (b) 183600 (c) 194600 (d) 183700
In a geometric progression, if the sum of the first four term is
equal to 15 and the sum of the second, third, fourth and fifth terms
is 30, then the sixth term equals to
(KIITEE – 2009)
(a) 16
(b) 32
(c) 48
(d) 64
If H is the Harmonic mean between P and Q, then
(b) a2b2
and common difference “d” then,
is equal to
b a
a c
a c
(b)
(c) 


q p
c a
c a
H1  a H n  b
is equal to

H1  a H n  b
(NIMCET -2008)
(a) n + 1
(b) n – 1
(c) 2n
(d) 2n + 3
If nc4, nc5 and nc6 are in arithmetic progression then n is
(KIITEE – 2008)
(a) 9
(b) 8
(c) 17
(d) 14
If the second term of an arithmetic progression is 20 and its fifth
term is double the first then the sum to 20 terms of the series is
(ICET – 2007)
(a) 64
(b) 108
(c) 1080
(d) 2160
2
1/3
1/9
1/27
If  = b then      , … =
(ICET – 2007)
(a) a
(b) b
(c) 1/a
(d) 1/b
If m is the arithmetic mean of a1, a2, ….. an then the arithmetic
mean of a1 + , a2, +  …. an +  is
(ICET – 2007)
(a) m
(b) m + 
(c) m +  (d) m
The geometric mean between a2 and b2 is
ICET – 2005
x 1
4
2n
(b) 10  1
9
14
(d)
10n  1
9
NIMCET-2010
(a)
If three positive real number a, b, c (c > a) are in H.P., then log (a
+ c) + log (a – 2b + c) is
NIMCET-2011
(a) 2 log (c – b)
(b) 2 log (a + c)
(c) 2 log (c – a)
(d) log a + log b + log c
The sum of 112 + 122 +….+ 302
NIMCET-2011
(a) 8070
(b) 9070
(c)1080
(d) 9700
Suppose a, b, c are in A.P. with common difference d. Then e1/c,
eb/ac, e1/a are
(NIMCET – 2008)
(a) A.P.
(b) GP.
(c) H.P.
(d) None
If H1, H2, …., Hn are n harmonic means between a and b, a  b,
(a) |ab|
12. If a, b, c are in A.P., p, q, r are in H. P. and ap, bq, cr in G.P. , then
p r

r p
(d) None of these
then the value of
The harmonic mean of the roots of the equation
5  2  x   4  5  x  8  2
PQ
PQ
PQ
(b)
Q
4
n4
(b)
5
5
(c)
n4
7
(d)
n5
If nCr-1 = 36, nCr = 84 and nCr+1 = 126, then the value of r is equal
to :
BHU-2012
(a) 1
(b) 2
(c) 3
(d) 4
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
4.

x  2 3
Let

2012
16.
and f = fractional part of x. Then x(1 – f)
In the Binomial expansion of (a – b)n, n  5, the sum of 5th and 6th
HCU-2012
(a) 1
5.
(b) 2
(c)
2  3 (d) 7
(a)
6
n5
23
(a) C12
(b) C12
2n
If for n  N,
  1
K 0
21
(c) 0
(d) C10
2
k
 2 n  
    A, then the value of
 K  
18.
2
  1
K
 2n 
 K  2n    is
 K  
(a) nA
(b) –nA
If the last term in the Binomial expansion of
 1 
 5/3 
3 
NIMCET-2012
then the 5th term from the beginning isKIITEE-2010
(a) 210
(b) 420
(c) 105
(d) None of these
If (1 + x – 2x2)6 = 1 + a1x + a2x2 + … + a12x12, then the value of a2
+ a4 + a6 + … + a12 is
(NIMCET – 2009)
(a) 1024
(b) 64
(c) 32
(d) 31
15
19.
(c) 0
(d) A
 t n is equal to
Let tn = n(n!) then
(a) 15! – 1
 2 1 
If the coefficient of x7 in the expansion of  px 
 is
qx 

 1/3 1 
2 
 is
2

log3 8
NIMCET-2011
11
8.
(d)
n
17.
(a) -216
(b) 216
(c) -110
(d) 300
The sum of 20C8 + 20C9 + 21C10 + 22C11 – 23C11 is
22
7.
n5
6
KIITEE-2010
Coefficient of xyz-2 in (x – 2y + 3z-1)4 is
Pune-2012
6.
a
equals:
b
n4
5
(b)
(c)
5
n4
terms is zero, then
is equal to
(KIITEE – 2009)
n 1
(b) 16! – 1
(c) 15! + 1
(d) None of these
n
20.
11

1 
equal to the coefficient of x in the expansion of  px 
 , 21.
qx 2 

-7
The sum of
(a) n 2
2n – 1
r
2n
r 1
(KIITEE – 2009)
Cr is equal to
n-1
(b) 2
+1
(c) 2
2n – 1
(d) None of these
1
1
1


 ....
1!(n  1)! 3!(n  3)! 5!(n  5)!
then
(KIITEE – 2009)
BHU-2011
(a) pq = 1
9.
10.
(b)
p
1
q
(a)
(c) p + q = 1
(d) p – q = 1
The coefficient of x15 the product
(x – 1) (2x – 1) (22x – 1) (23x – 1) …. (215 x – 1) is equal to
BHU-2011
(a) 2120 – 2108
(b) 2105 – 2121
(c) 2120 – 2105
(d) 2120 – 2104
The nth term of the series
(b)
(c)
1
7
1 20
2 1 1 
 ... is
2 13 9 23
22.
BHU-2011
20
(a)
5n  3
2
(b)
5n  3
20
(d)
5n 2  3
(c) 20(5n + 3)
11.
The remainder when 599 is divided by 13 is :
(A) 6
(B) 8
(C) 9
(D) 10
23.
If the co–efficient of x7 in the expansion of
(a)
(c)
15.
nn 1
 n  1!
(b)
(d)
49 + 16n – 1 is divisible by
(a) 3
(b) 19
(c) 64
(e) None of these
(b) - 15C6
(d) 1
Value of
27.
integer) depends on
Hyderabad Central Univ. – 2009
(a) Value of A
(b) Value of n
(c) neither A nor n
(d) Both A and n
In the expression
(x + 1) (x + 4) (x + 9) (x + 16) … (x + 400) the coefficient of x19
is
(NIMCET – 2008)
(a) 2870
(b) 210
(c) 4001
(d) 1900
The sum of the numerical co-efficients in the expansion of
n
29.
KIITEE-2010
30.
(d) 29
31.
5
is
n n
n i
i
(for n, a positive
   sin A1  sin A
i  0 i 
X 2Y 

1  

3
3 

n!
 1
n
1   (1  x)
x

26.
28.
n
n
(c) 0
25.
n!
 n  1
the constant term is
(KIITEE – 2009)
(a) 2nCn
(b) –2nCn
(c) –2nCn-1
(d) None of these
What is the value of the ten’s digit in the sum
1! + 2! + 3! + … + 2008!
Hyderabad Central Univ. – 2009
(a) 0
(b) 1
(c) 9
(d) 4
PU CHD-2009


an 
a1   a2  a3 
1   1  1   ....... 1 
 NIMCET-2010
a1  a2 
 a0  
 an 1 
 n  1
15
The middle term in the expansion of
PU CHD-2010
nn
n!
 3 1 
x  2 
x 

24.
11
1 

expansion of  ax 
are equal then ab is equal to :
2 
bx


14.
In the expansion of
n
PU CHD-2011
the coefficient of x-7 in the
13.
(d) None of these
The coefficient of a8 b10 in the expansion of (a + b)18 is
(KIITEE – 2009)
(a) 18C8
(b) 18C10
(c) 218
(d) None of these
(KIITEE – 2009)
 2 1 
 ax   and
bx 

(A) 1
(B) 2
(C) 3
(D) 4
What is the value of factorial zero (0!)?
(a) 10 (b) 0
(c) 1
(d) – 1
If (1+x)n = ao + a1x + a2 x2 +….an xn ,then
2 n1
for even values of n only
n!
2 n1  1
 1 for odd values of n only
n!
2 n1
for all n  N
n!
(a) 15C6
11
12.
is equal to
12
is
KIITEE – 2008
(a) 212
(b) 1
(c) 2
(d) None
The co-efficients of x3 in the expansion of (1 – x + x2)5 is
KIITEE – 2008
(a) 10
(b) – 20
(c) – 30
(d) – 50
In the expansion of (1 + x + x2)-3 the coefficient of x6 will be :
(MP combined – 2008)
(a) 9
(b) 3
(c) 1
(d) – 3
If (1 + x)n = C0 + C1x + C2x2 + … + Cnxn then C0C1 + C1C2 + C2C3
+ … + Cn-1 Cn will be equal to:
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
(MP combined – 2008)
(a)
n
(c)
(b)
| (n 2  1)
2n
(d)
 n  1  n  1
2n
 1
2
3
x2
1 x 
8
128
3 2
x
(c) 1 
128
(a)
2| n
2n
(n  1)(n  1)
45.
46.
3n
32.
1 

In the expansion of  x 
 , the term independent of x
x2 

| 3n
(a)
33.
3| n
| n| 2n
(b)
| n| 2n
(c)
2  n
2
(d)
34.
35.
(a)
36.
45
256
(b)
If the 5th term of
C0 
(a)
(c)
38.
39.
40.
(d) None
 2 3
 2x  
x

log e 5 
3.
Pune– 2007
(a)
Pune– 2007
4.
(a)
(b)
2n 1
n 1
(c)
IP Univ.– 2006
(d)
225
24!
(e) N.O.T
5.
4 10
44.
(b) fifth
 3
10 
   2 
3
 
1
2n 1  1
n 1
1
4  x
1/ 2

(c) sixth
1
4  x
1/ 2
2

log e (625 )
42
 ...
is
(b) loge 5
log e 5
(c)
(d) (log e 5)(log e 2)
log e 2
(d)
(b)
1
60
(1  4 x  x 2 )
ex
(c)
1

120
is :
1
1
1
1



 ...
2
3
2 22
3 2
4  24
MP COMBINED - 2008
(b)
1  x  
log e
1
2
(d) 1 – loge2
Find the sum of the infinite series
If
to
MP COMBINED - 2008
1  log e 2
(a) e
7.
1
60
(c) e2 (d) e
The value of the series :
(c)
2n
n 1

(log e 2) 2 (log e 2) 2 (log e 2) 4


 ...
|2
|3
|4
(a) loge2
6.
(d)
Value of the series:
to infinity is :
 2 1
The term independent of x in  3x   is MP Paper – 2004
x

(a) third
log e (125 )
3
infinity is :
(a) 2
(b) 1
6
43.

MP COMBINED - 2008
1
120
log e 2 
C0 C1 C2
  ....... is equal to : MP Paper – 2004
1
2
3
2n
n 1
2
2
MP COMBINED - 2008
The coefficient of x in the expansion of (1 + x ) (2 + x ) is
IP Univ. Paper – 2006
(a) 214
(b) 31
The sum
(d) None
Coefficient of x5 in the expansion of
(e) None of these
42.
C r a  r  is equal to
(c) a
log e (25)
(a) loge 2
2 n1  1
n 1
n
2 1
n 1
226
25!
(d)
r 1
KIITEE – 2008
ICET – 2005
2 3
 3  10 
  
 3  1 
(d) None
r 1 n
infinity is :
6
(c)
  1
The sum of the series
ICET – 2005
1
The sum 
equals
k
!
25
 k !

0  k 12
KIITEE – 2008
is equal to
C r 1
EXPONENTIAL AND LOGARITHMIC SERIES
1.
If log103 = 0.477, the number of digits in 340 is : PU CHD-2011
(A) 18
(B) 19
(C) 20
(D) 21
2.
The sum of the series
The remainder in the divisor of 3 by 23 is
(a) 13
(b) 12
(c) 14
(d) 15
(12! + 1) is divisible by
(a) 11
(b) 13
(c) 14
(d) 7
(c)
Cr
(a) n.2n-1 + a (b) 0
(d)  8
(d)
(b)
49.
64
256
is 10, then, x =
(b)
225
25!
r 1
n
n
5
C
C1 C 2

 ...  n =
2
3
n 1
224
25!
n
r
The value of
UPMCAT– 2005
(d) None of these
(c) 10C6
(a) 9 (n – 4) (b) 5 (2n – 9) (c) 10n
ICET – 2005
(d)
(c)  9
2 n 1
n 1
2 n1  1
n 1
(b) 10C3
10
is
(d) 1/3
 3 1 
 x  2  , the term independent of x is
x 

10
48.
40
(a)
41.
45
64
(b) – 6
(a) 6
37.
2 
x
  2
2
x 

68
(c)
45
In the expression
equal to :
(a) 10C5
If the 21st and 22nd terms in the expression (1 + 6a)24 are equal
then a =
ICET - 2007
(a) 7/8
(b) 8/7
(c) 5/8
(d) 8/5
The coefficient of x4 in
(c) 1/2
10
47.
ICET - 2007
(c)
(b) 1/4
2| 2n
9
1
2
2
is equal to :
UPMCAT– 2005
(a) 1
The coefficient of the term independent of x in the expansion of
3 2 1 
 2 x  3x  is


1
1
(a) 1
(b)  1
2
2
Coefficient of x4 in log (1 + x + x2) is : UPMCAT paper – 2005
(a) 5/12
(b) 13/12
(c) -5/12
(d) N.O.T
If b is taken to be positive, then the following series
2
3| n
3n
3 2
x
128
(d) None of these
1  b 
1
1 b


 .........
2
1  b 1  b  1  b 3
(MP combined – 2008)
will be
1
(b)
(b) e-2
1  x 
2 4 6 8
    .... .
1! 3! 5! 7!
(c) 1/e
MP Paper – 2004
(d) None of these
2
2!
 ..........  inf. coeff. of xn is
UPMCAT Paper - 2002
2e
(a)
n!
(d) seventh
UPMCAT paper – 2005
6
(b)
2n e
n!
(c)
2n e
2n !
(d)
e
n!
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
ANSWERS
WORK-SHEET-1 (OLD QUESTIONS)
1
C
11
D
21
C
31
A
1
A
11
C
21
C
31
A
41
CD
51
A
2
A
12
A
22
C
32
A
2
12
A
22
B
32
B
42
B
52
D
1
A
11
B
21
B
31
A
3
A
13
B
23
A
33
C
43
C
53
C
2
A
12
B
22
C
3
D
13
A
23
D
33
C
SETS & RELATIONS
4
5
6
7
B
C
A
C
14
15
16
17
A
AC
B
B
24
25
26
27
B
D
A
B
34
35
36
37
D
D
B
D
8
C
18
B
28
B
9
C
19
D
29
C
THEORY OF EQUATIONS
4
5
6
7
8
C
B
B
A
C
14
15
16
17
18
A
B
A
C
C
24
25
26
27
28
D
D
C
B
ABCD
34
35
36
37
38
D
C
B
B
C
44
45
46
47
48
B
B
D
ABCD
B
54
55
56
D
A
B
3
B
13
B
23
C
SEQUENCE & SERIES
4
5
6
7
D
C
B
B
14
15
16
17
A
A
A
B
24
25
26
27
C
B
C
A
8
A
18
A
28
B
9
A
19
C
29
C
10
C
20
D
30
C
9
D
19
B
29
B
39
A
49
B
1
A
11
B
21
C
31
A
41
A
10
C
20
D
30
D
40
BC
50
A
2
B
12
A
22
B
32
A
42
C
3
C
13
C
23
B
33
D
43
B
4
A
14
B
24
A
34
A
44
B
BINOMIAL
5
6
A
C
15
16
C
B
25
26
B
C
35
36
A
C
45
46
D
C
7
B
17
A
27
A
37
B
47
C
8
A
18
D
28
A
38
A
48
B
9
B
19
B
29
C
39
B
49
C
10
A
20
A
30
B
40
A
EXPONENTIAL & LOGARITHMIC SERIES
1
2
3
4
5
6
7
C
D
C
B
A
A
D
10
D
20
B
30
B
7
INFOMATHS/MCA/MATHS/OLD QUESTIONS