Download quintessence

INFOMATHS
OLD QUESTIONS-CW1
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
7.
(c)
19.
The harmonic mean of the roots of the equation
5  2  x   4  5  x  8  2
(a) 2
5  0 is
20.
(b) 4
(c) 6
(d) 8
Arithmetic mean of two positive numbers is
18
3
21.
and their
4
geometric mean is 15. The larger of the two numbers is
10.
11.
If H is the Harmonic mean between P and Q, then
22.
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
10n  1
9
2
4
n
(c) 10  1
9
23.
24.
25.
PU CHD-2010
26.
4
102n  1
9
14
(d)
10n  1
9
(b)
27.
28.
is equal to
29.
NIMCET-2010
(a)
13.
14.
16.
(d)
b a

q p
2 6 10 14
    ....... is
3 32 33 34
30.
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
If  = b2 then 1/3  1/9  1/27, … =
(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
(b) a2b2
(c) ab
(d)
31.
(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
a2
1
1
1 1
1 1
 2  .... y  1   2  .... then  
a a
b b
x y
(ICET – 2005)
(a) 0
(b) 2
(c) 1
(d) 3
If tn is the nth term of an arithmetic progression with first term ‘a’
n
 t 2k 
and common difference “d” then,
KIITEE-2010
02
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
x 1
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
1
15.
b a
a c
a c
(b)
(c) 


q p
c a
c a
(d) None of these
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
PQ
PQ
then the value of
n  digits
(A)
H H
is

P Q
PQ
(b)
Q
(a) 2
BHU-2011
9.
18.
(b)
2
8.
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
NIMCET-2012
2m  1
2n  1
mn
(d)
mn
mn
mn
2m  1
(c)
2n  1
(a)
17.
(ICET – 2005)
k 1
(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.
ANSWERS (OLD QUESTIONS-CW1)
SETS & RELATIONS
1
4
2
3
4
5
6
7
8
9
10
INFOMATHS/MCA/MATHS/OLD QUESTIONS
INFOMATHS
C
11
D
21
C
31
A
1
A
11
C
21
C
31
A
41
A
12
A
22
C
32
A
2
12
A
22
B
32
B
42
3
A
13
B
23
A
33
C
43
D
13
A
23
D
33
C
B
14
A
24
B
34
D
C
15
AC
25
D
35
D
A
16
B
26
A
36
B
C
17
B
27
B
37
D
C
18
B
28
B
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
C
19
D
29
C
C
20
D
30
C
9
D
19
B
29
B
39
A
49
CD
51
A
10
C
20
D
30
D
40
BC
50
5
B
52
D
C
53
C
1
A
11
B
21
B
31
A
2
A
12
B
22
C
B
54
D
3
B
13
B
23
C
B
55
A
D
56
B
ABCD
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
B
8
A
18
A
28
B
B
9
A
19
C
29
C
A
10
D
20
B
30
B
INFOMATHS/MCA/MATHS/OLD QUESTIONS