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Mathematics

Question 1Single Answer

The elements of the set {x : x is an integer, x² : 4} can be represent as .....Z..... . Here, Z refers to

A
{–2, 2}
B
{–1, 0, 1}
C
{–2, –1, 0, 1, 2}
D
{0, 1, 2}

Question 2Single Answer

A
B
C
D
None of these

Question 3Single Answer

If Y = {x : x is a positive factor of the number 2p – 1(2p – 1), where 2p – 1 is a prime number}, then Y can be represent in roster form as

A
{2}
B
{1, 2}
C
{1, 2, 22, ....., 2p – 1}
D
{1, 2, 22, 23,.... 2p – 1, (2p – 1)}

Question 4Single Answer

The set {x : x is a positive integer less than 6 and 3x – 1 is an even number} in roster form is

A
{1, 2, 3, 4, 5}
B
{1, 2, 3, 4, 5, 6}
C
{2, 4, 6}
D
{1, 3, 5}

Question 5Single Answer

If A

B and A

B, then

A
A is called a proper subset of B
B
A is called a super set of B
C
A is not a subset of B
D
B is a subset of A

Question 6Single Answer

The number of non-empty subsets of the set{1, 2, 3, 4} is

A
15
B
14
C
16
D
17

Question 7Single Answer

The number of elements of the power set of a set containing m elements is

A
2^m – 1
B
m
C
m²
D
2^m

Question 8Single Answer

If A = {x : x = n², n = 1, 2, 3}, then number of proper subsets is

A
3
B
8
C
7
D
None of these

Question 9Single Answer

If A = {x : x = 4n + 1, 2 £ n £ 5},then number of subsets of A is

A
16
B
15
C
4
D
None of these

Question 10Single Answer

Let A and B be two non-empty subsets of a set X such that A is not a subset of B, then

A
A is always a subset of the complement of B
B
B is always a subset of A
C
A and B are always disjoint
D
A and the complement of B are always non-disjoint

Question 11Single Answer

Which of the following is/are empty set?
A = {x : x2 + x + 1 = 0 and x Î Z} B = {x : x is a prime number and 19 < x < 23}

A
A
B
B
C
Both A and B
D
None of the above

Question 12Single Answer

The set {x : x⁴ = 1 and x

R} is .....X.... set. Here, X refers to

A
empty
B
finite
C
infinite
D
singleton

Question 13Single Answer

The universal set for the sets
A = {x : x² – 5x + 6 = 0} and
B = {x : x² – 3x + 2 = 0} having least number of elements is

A
{1, 2}
B
{1, 3}
C
{1, 2, 3}
D
{0, 1, 2, 3}

Question 14Single Answer

If A = {1, 2, 3}, B = {x € R : x2 – 2x + 1 = 0},

C = {1, 2, 2, 3} and

D = {x € R : x3 – 6x2 + 11x – 6 = 0}, then the equal sets are

A
A and B
B
A and C
C
A, B and C
D
A, C and D

Question 15Single Answer

If A = (–3, 5) and B = [–7, 9], then

A
A = B
B
A B
C
B A
D
None of these

Question 16Single Answer

Two finite sets have m and n elements, respectively. The total number of subsets of first set is 56 more than the total number of subsets of the second set. The value of m and n respectively are

A
7, 6
B
5, 1
C
6, 3
D
8, 7

Question 17Single Answer

Combine terms: 12a + 26b - 4b – 16a .

A
4a + 22b
B
-28a + 30b
C
-4a + 22b
D
28a + 30b

Question 18Single Answer

The average of first 50 natural numbers is ………… .

A
25.30
B
25.5
C
25.00
D
12.25

Question 19Single Answer

60 Times of 8 Equals to

A
480
B
300
C
250
D
400

Question 20Single Answer

Consider the sets

A = {x : x is a real number and x² + 1 = 0}

B = {x : x is a real number and x² – 16 = 0}

C = {x : x is a real number and x² = x + 2}

Which of the following is are null set ?

A
A
B
A and B
C
A and C
D
A, B and C

Question 21Single Answer

If X = {4n – 3n – 1: n Î N} and Y = {9(n – 1): n Î N}; where N is the set of natural numbers, then X È Y is equal to

A
N
B
Y – X
C
X
D
Y

Question 22Single Answer

Which of the following is / are correct?

I. {2, 3, 4} {1, 2, 3, 4, 5}

II. {a, b, c} {b, c, d}

III. {x : x is an equilateral triangle in a plane} Ì {x : x is a triangle in the same plane}

IV. {x : x is an even natural number} {x : x is an integer}

A
I and III are correct
B
II and III are correct
C
Only IV is correct
D
All above are correct

Question 23Single Answer

Question 24Single Answer

Consider the following statements :
1. The set of all irrational numbers between √2 and √5 is an infinite set .
2. The set of all odd integers less than 100 is a finite set .
Which of the statements given above is/are correct ?

A
1 only
B
2 only
C
Both 1 and 2
D
Neither 1 nor 2

Question 25Single Answer

What is the Next Prime Number after 7 ?

A
13
B
12
C
14
D
11

Question 26Single Answer

If A and B are two given sets, then A

B)^C is equal to

Question 27Single Answer

121 Divided by 11 is

A
11
B
10
C
19
D
18

Question 28Single Answer

Let X be the universal set for sets A and B, if n(A) = 200, n(B) = 300 and n

= 100, then n

is equal to 300 provided n(X) is equal to

A
600
B
700
C
800
D
900

Question 29Single Answer

A
{3, 4, 10}
B
{2, 8, 10}
C
{4, 5, 6}
D
{3, 5, 14}

Question 30Single Answer

Let A = {x : x is a prime factor of 240} B = {x : x is the sum of any two prime factors of 240}, then

Question 31Single Answer

If A = {x : x is a multiple of 4 and x

N} and B = {x : x is a multiple of 6 and x

N}, then A

B consists of all multiples of

A
16
B
12
C
8
D
4

Question 32Single Answer

A
A = B
B
B = C
C
A = C
D
None of these

Question 33Single Answer

A
equal
B
disjoint
C
either equal or disjoint
D
none of the above

Question 34Single Answer

A
{–i, i}
B
{–1, 1}
C
{–1, 1, i, –i}
D
None of these

Question 35Single Answer

If A = {x : f(x)= 0} and
B = {x : g(x) = 0}, then A

B will be

A
[f(x)]2 + [g(x)]2 = 0
B
C
D
None of the above

Question 36Single Answer

In a group of 400 people, 250 can speak Hindi and 200 can speak English. Then, people who can speak both Hindi and English are

A
60
B
80
C
50
D
45

Question 37Single Answer

20 teachers of a school either teach Mathematics or Physics. 12 of them teach Mathematics while 4 teach both the subjects. The number of teacher teaching Physics only, is

A
12
B
8
C
16
D
20

Question 38Single Answer

In a class of 100 students, 70 have taken Science, 60 have taken Mathematics, 40 have taken both Science and Mathematics. The number of students who have not taken Science or Mathematics or both Science and Mathematics, is equal to

A
90
B
10
C
30
D
20

Question 39Single Answer

A market research group conducted a survey of 1000 consumers and reported that 720 consumers like product A and 450 consumers like the product B, then least number that must have like both products, is

A
730
B
170
C
180
D
1270

Question 40Single Answer

If there are three athletic teams in a school, 21 are in the basketball team, 26 in hockey team and 29 in the football team. 14 play hockey and basketball, 15 play hockey and football, 12 play football and basketball and 8 play all the games. The total number of members is

A
42
B
43
C
45
D
None of these

Question 41Single Answer

A college awarded 38 medals in football, 15 in basketball and 20 in cricket. If these medals went to a total of 58 men and only three men got medals in all the three sports, then number of men who received meal in exactly two of the three sports is

A
18
B
15
C
9
D
24

Question 42Single Answer

In the class of 175 students, the following data shows the number of students opting one or more subjects. Mathematics 100; Physics 70; Chemistry 40; Mathematics and Physics 30; Mathematics and Chemistry 28; Physics and Chemistry 23; Mathematics, Physics and Chemistry 18. Then, number of students opted Mathematics alone is

A
35
B
48
C
60
D
20

Question 43Single Answer

In a town of 10000 families it was found that 40% family buy newspaper A, 20% family buy newspaper B and 10% family buy newspaper C, 5% families buy and B, 3% families buy B and C and 4% families buy A and C. If 2% families buy all the three newspapers. Then, number of families which by A only is

A
3100
B
3300
C
2900
D
1400

Question 44Single Answer

In a city, 20% of the population travles by car, 50% travles by bus and 10% travles by both car and bus. Then, person travelling by car or bus, is

A
80%
B
40%
C
60%
D
70%

Question 45Single Answer

Universal set,
U = {x | x⁵ – 6x⁴ + 11x³– 6 x 2 = 0}
A = {x | x² – 5x + 6 = 0}
B = {x | x²– 3x + 2 = 0}
What is the value of (A

B)?

A
{1, 3}
B
{1, 2, 3}
C
{0, 1, 3}
D
{0, 1, 2, 3}

Question 46Single Answer

Question 47Single Answer

If P(A) denotes the power set of A and A is the void set, then what is the number of elements in P{P{P{P(A)}}}?

A
Zero
B
1
C
4
D
16

Question 48Single Answer

If A = {1, 2, 3, 4, 5}, b = {x : x2 – 5x + 6 = 0} and C = {x : x2 = 4 or x = 1}, then

A
B
C
Both (a) and (b)
D
None of the above

Question 49Single Answer

In a group of 50 people, 35 speak Hindi, 25 speak both English and Hindi and all the people speak atleast one of two languages. The number of people who speak 'English', 'English but not Hindi' are respectively

A
40, 15
B
15, 40
C
35, 15
D
25, 15

Question 50Single Answer

If P = {1, 2}, then P × P × P = {(1, 1, 1), (1, 1, 2), (1, 2, 1), (2, 1, 2), (2, 2, 1), (2, 2, 2)}. The ordered triplet missing in P × P × P are

A
(1, 2), (2, 1)
B
(1, 2, 1), (2, 1, 1)
C
(1, 2, 2), (2, 1, 2)
D
(1, 2, 2), (2, 1, 1)

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Mathematics

Question 51Single Answer

If A = {1, 2, 3, 4} and B = {5, 7, 9} then

A
A × B = B × A
B
n(A × B) =n(B × A)
C
Both (a) and (b)
D
None of the above

Question 52Single Answer

Let A and B are two sets having 3 elements in common. If n(A) = 5 and n(B) = 4, then n[(A × B)

(B × A)] is equal to

A
20
B
25
C
16
D
9

Question 53Single Answer

If n(A) = 3, n(B) = 4 then, n(A × A × B) is equal to

A
36
B
12
C
108
D
None of these

Question 54Single Answer

If A = {1, 2, 3}, B = {3, 8}, then (A

B) × (A

B) is equal to

A
{(8, 3), (8, 2), (8, 1), (8, 8)}
B
{(1, 2), (2, 2), (3, 3), (8, 8)}
C
{(3, 1), (3, 2), (3, 3), (3, 8)}
D
{(1, 3), (2, 3), (3, 3), (8, 3)}

Question 55Single Answer

The Cartesian product A × A has 9 elements among which are found (–1, 0) and (0, 1). Then, the remaining elements of A × A are

A
(0, 0), (0, 1), (0, –1), (–1, 1), (–1, 0), (1, 0), (1, –1)
B
(–1, 1), (–1, 0), (0, 0), (0, –1), (0, 1), (1, 0), (1, –1)
C
(0, –1), (1, 0), (1, –1)
D
None of the above

Question 56Single Answer

Let A = {1, 2, 3}. The total number of distinct relations that can be defined over A, is

A
2⁹
B
6
C
8
D
None of these

Question 57Single Answer

Let A = {x, y, z} and B = {1, 2}. Then, the number of relations from A to B is

A
32
B
64
C
128
D
8

Question 58Single Answer

Let A = {x, y, z} and B = {a, b, c, d}. Then, which one of the following is not a relation from A to B?

A
{(x, a), (x, c)}
B
{(y, c), (y, b)}
C
{(z, a), (z, d)}
D
{(z, b), (y, b), (a, d)}

Question 59Single Answer

The relation R defined on the set of natural numbers as {(a, b): a differs from b by 3} is given by

A
{(4, 1), (5, 2), (6, 3),....}
B
{(1, 3), (2, 6), (3, 9),....}
C
{(1, 4), (2, 5), (3, 6),....}
D
None of the above

Question 60Single Answer

If R is a relation on a finite set A having (n – 1) elements, then the number of relations on A is

A
2^n-1
B
C
(n-1)²
D
(n-1)^n-1

Question 61Single Answer

A
{ 0, 1, 2, }
B
{ 0, -1 , -2 }
C
{ -2 , -1 ,0 , 1 , 2 , }
D
None of the above

Question 62Single Answer

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}
The relation is

A
an equivalence reation
B
reflexive symmetric
C
reflexive and trasitive
D
Only reflexive

Question 63Single Answer

A
reflexive and transitive
B
symmetric only
C
reflexive and symmetric
D
equivalence relation

Question 64Single Answer

A
reflexive and transitive
B
an equivalence relation
C
symmetric but neither reflexive nor transitive
D
neither reflexive nor symmetic but transitive

Question 65Single Answer

The relation ' has the same father as ' over the set of children is

A
Only reflexive
B
Only symmetric
C
Only transitive
D
an equivalence relation

Question 66Single Answer

If N be the set of natural numbers and define the relation R on N by R = {(1, 2)(2, 5), (3, 10)(4, 17)(5, 26)}. Then, the set builder form of R is

A
{(x, x²+ 1) | N and x < 6}
B
{(x, x² – 1) | N and x < 6}
C
{(x, 2x + 1) | N and x < 6}
D
None of the above

Question 67Single Answer

Let R be a relation in the set {1, 2, 3, 4} given by

R = {(1, 1), (1, 2), (2, 2), (4, 4), (1, 3), (3, 3), (3, 2)}.

Choose the correct option

A
R is reflexive
B
R is transitive
C
R is symmetric
D
R is reflexive and transitive but not symmetric

Question 68Single Answer

Which of the following functions is inverse of itself?

A
B
C
D
None of the above

Question 69Single Answer

If f(x) = e^x and g(x) = logex, then which of the following is true?

A
f{g(x)} g{f(x)}
B
f{g(x)} = g{f(x)}
C
f{g(x)} + g{f(x)} = 0
D
f{g(x)} – g{f(x)} = 1

Question 70Single Answer

The value of parameter a, for which the function f : R → R given by f(x) = 1 + ax, a

0 is the inverse of itself, is

A
–2
B
–1
C
1
D
2

Question 71Single Answer

Let f: (2, 3) → (0, 1) be defined by f(x) = x – [x]. Then, f–1(x) equals to

A
x – 2
B
x + 1
C
x – 1
D
x + 2

Question 72Single Answer

The greatest integer function f: R → R, given by f(x) = [x] is

A
one-one
B
onto
C
both one-one and onto
D
neither one-one nor onto

Question 73Single Answer

The number of all one-one functions from set

A = {1, 2, 3} to itself is

Question 74Single Answer

Question 75Single Answer

Question 76Single Answer

The number of 3-digit numbers divisible by 6, is ………….. .

A
149
B
166
C
50
D
151

Question 77Single Answer

A
-1
B
-2
C
D
None of these

Question 78Single Answer

Let N be the set of natural numbers and the relation R be defined such that R = {(x, y): y = 2x, x,

N}. Then,

A
R is a function
B
R is not a function
C
domain range and codomain is N
D
None of the above

Question 79Single Answer

If G represents the name of the function in below graph, then G is a/an

A
identity function
B
constant function
C
modulus function
D
None of the above

Question 80Single Answer

Let X = {–1, 0, 1}, Y = {0, 2} and a function f: X → Y defined by y = 2x4, is

A
one-one onto
B
one-one into
C
many-one onto
D
many-one into

Question 81Single Answer

Let f : R→ R be a function defined by

A
one-one onto
B
one-one but not onto
C
onto but not one-one
D
None of the above

Question 82Single Answer

The mapping f: N→ N given by f(n) = 1 n², n € N where, N is the set of natural numbers is

A
one-one and onto
B
onto but not one-one
C
one-one but not onto
D
neither one-one nor onto

Question 83Single Answer

A
B
C
[ 0 , 1 ]
D
None of the above

Question 84Single Answer

A relation R in a set A is called _______, if (a₁, a₂) ∈ R implies (a₂, a₁) ∈ R, for all a₁, a₂ ∈ A .

A
symmetric
B
transitive
C
equivalence
D
non-symmetric

Question 85Single Answer

A
f is one-one onto
B
f is one-one into
C
f is many-one onto
D
f is many-one into

Question 86Single Answer

Domain of f(x) = sin–1[2 – 4x2] ([.] denotes the greatest integer function) is

A
[–1, 1]
B
(–2, 2)
C
D
None of the above

Question 87Single Answer

Question 88Single Answer

If f(x) = [x²] – [x]², where [.] denotes the greatest integer function and x € [0, 2] then the set of values of f(x) is

A
{–1, 0}
B
{–1, 0, 1}
C
{0}
D
{0, 1, 2}

Question 89Single Answer

A
B
C
D
None of these

Question 90Single Answer

If f: A → B and g: B → C be two functions, then the composition of functions f and g is given by

A
gof(x) = g(f(x))
B
gof(x) = g(x)f(x)
C
fog(x) = g(f(x))
D
None of the above

Question 91Single Answer

If the function gof is defined an onto, then

A
neither f nor g is onto
B
f and g both are necessarily onto
C
f must be onto
D
None of the above

Question 92Single Answer

If f(x) = 2x + 7 and g (x) = x2 + 7, x

R, then which value of x will satisfy fog (x) = 25?

A
–1, 1
B
–2, 2
C
D
None of these

Question 93Single Answer

A
3
B
1
C
D
None of these

Question 94Single Answer

Question 95Single Answer

Question 96Single Answer

A
Zero
B
1
C
-1
D

Question 97Single Answer

a + ib > c + id can be explained only when

A
b = 0, c = 0
B
b = 0, d = 0
C
a = 0, c = 0
D
a = 0, d = 0

Question 98Single Answer

If 3x² + 4x + 2 = 0, then equation has

A
real roots
B
imaginary roots
C
one real and one imaginary root
D
distinct real roots

Question 99Single Answer

Question 100Single Answer

Question 101Single Answer

Question 102Single Answer

If square root of –7 + 24i is x + iy, then x is equal to

A
±1
B
±2
C
±3
D
±4

Question 103Single Answer

Question 104Single Answer

Question 105Single Answer

Question 106Single Answer

Question 107Single Answer

A
i
B
C
1
D
Zero

Question 108Single Answer

A
B
1/2
C
n
D
Zero

Question 109Single Answer

A
B
C
-12 - 9i
D
-12 + 9i

Question 110Single Answer

The locus of the poins z which satisfy the condition

A
a straight line
B
a circle
C
a parabola
D
none of these

Question 111Single Answer

A
x = 1
B
x = –1
C
x = ±1
D
No real roots

Question 112Single Answer

If z is a complex number such that Re(z) = Im(z), then

A
Re(z²) = 0
B
Im(z²) =0
C
Re(z²) = Im(z²)
D
Re(z²) = –Im(z²)

Question 113Single Answer

If 2a = –1 – i and 2b = –1 + i then
5a4 + 5b4 + 7a–1b–1 is equal to

A
–1
B
–2
C
Zero
D
2

Question 114Single Answer

The real value of a for which the expression

is purely real is, when n € N

A
B
C
D
None of these

Question 115Single Answer

Question 116Single Answer

A
1
B
–1
C
2
D
–2

Question 117Single Answer

What is the conjugate of

Question 118Single Answer

be the conjugate of the complex number z,then which of the following relations is false?

Question 119Single Answer

If z₁, z₂ and z₃ be the three complex numbers such that |z₁ + 1| < 1, |z₂ + 2| < 2 and |z₃ + 4| < 4, then the maximum value of |z₁| + |z₂| + |z₃| is

A
7
B
10
C
12
D
14

Question 120Single Answer

Question 121Single Answer

A
Zero
B
C
D

Question 122Single Answer

Question 123Single Answer

Question 124Single Answer

Re(z²) = 1 is represented by

A
the circle x² + y² = 1
B
the hyperbola x² – y² = 1
C
parabola or a circle
D
all of the above

Question 125Single Answer

If the complex numbers iz, z and z + iz represent the three vertices of a triangle, then the area of the triangle is

Question 126Single Answer

If Z₁, Z_2, Z₃ and z₄are the affixes of four points in the argand plane and z is the affix of a point, such that |z – z₁| = |z – z₂| = |z – z₃| = |z – z₄|, then z₁, z₂, z₃ and z₄ are

A
concyclic
B
vertices of parallelogram
C
vertices of a rhombus
D
in a straight line

Question 127Single Answer

Let z₁ and z₂ be the non-real roots of the equation + 3z² + b = 0. If the origin together with the points represented by z₁ and z₂ form an equilateral triangle, then the value of b is

A
1
B
2
C
3
D
None of these

Question 128Single Answer

If the sum of a certain n number of terms of the AP, 25, 22, 19,....... is 116, then the last term is

A
4
B
3
C
2
D
–4

Question 129Single Answer

If a, 4, b are in Arithmetic Progression; a, 2, b are in Geometric Progression; then a, 1, b are in

A
A.P
B
G.P
C
H.P
D
None of these

Question 130Single Answer

What is the value of n sot that

geometric mean between a and b ? where

A
B
C
n = 2
D
–2

Question 131Single Answer

If logax, logbx, logex be in HP, then a, b, c are in

A
AP
B
HP
C
GP
D
None of these

Question 132Single Answer

If A is the arithmetic mean and G1, G2 be two geometric means between any two numbers, then

is equal to

A
2A
B
A
C
3A
D
None of these

Question 133Single Answer

Question 134Single Answer

Question 135Single Answer

A
B
log_e2
C
D
log_e2 + 1

Question 136Single Answer

Question 137Single Answer

The domain of a sequence can be subset of natural numbers of the type

A
{3, 4, 5,.....k}
B
{1, 2, 3, 4, 5,......k}
C
{0, 1, 2, 3, 4.,....k}
D
None of the above

Question 138Single Answer

A
4
B
6
C
8
D
10

Question 139Single Answer

The number which should be added to the numbers 2, 14, 62, so that the resulting numbers may be in GP, is

Question 140Single Answer

The sum of the geometric progression 0.15, 0.015, 0.0015, ..... 20 terms is

A
B
C
D
None of these

Question 141Single Answer

The value of 0.234 is

Question 142Single Answer

If log 2, log (2ⁿ– 1) and log (2ⁿ + 3) are in AP, then n is is equal to

A
B
log₂5
C
log₃5
D

Question 143Single Answer

In a cricket tournament 16 school terms participated. A sum of Rs,8000 is to be awarded among themselves as prize money. If the last placed team is awarded `Rs 275 in prize money and the award increases by the same amount for successive finishing places, amount will be first place team received is

A
Rs 720
B
Rs 725
C
Rs 735
D
Rs 780

Question 144Single Answer

A
909
B
75
C
750
D
900

Question 145Single Answer

The sum of integers from 1 to 100 that are divisible by 2 or 5 is

A
3000
B
3050
C
4050
D
None of these

Question 146Single Answer

If a², b², c² are in AP, then which of the following is also in AP?

A
sinA, sinB, sinC
B
tanA, tanB, tanC
C
cotA, cotB, cotC
D
None of the above

Question 147Single Answer

A
20
B
30
C
40
D
None of the above

Question 148Single Answer

If a, b, c are in GP and loga – log 2b, log 2b – log 3c and log 3c – log a are in AP, then a, b, c are the length of the sides of a triangle which is

A
acute angled
B
obtuse angled
C
right angled
D
equilateral

Question 149Single Answer

A
AP
B
HP
C
GP
D
None of these

Question 150Single Answer

If x, 1, z are in AP and x, 2, z are in GP, then x, 4, z will be in

A
AP
B
GP
C
HP
D
None of these

Question 151Single Answer

A
AP
B
GP
C
HP
D
None of these

Question 152Single Answer

Question 153Single Answer

Let n > 1 be a positive integer, then the largest integer m such that (n^m + 1) divides (1 + n + n² + ..... n¹²⁷), is

A
32
B
63
C
64
D
127

Question 154Single Answer

If b², a², c² are in AP, then a + b, b + c, c + a, will be in

A
AP
B
GP
C
HP
D
None of these

Question 155Single Answer

A
(n – 1)(a₁ – a_n)
B
na₁a_n
C
(n – 1)a₁a_n
D
n(a₁ – a_n)

Question 156Single Answer

A
AP
B
GP
C
HP
D
None of these

Question 157Single Answer

Question 158Single Answer

Sum of n terms of the following series 13 + 33 + 53 + 73 + ..... is

A
n²(2n² – 1)
B
n³(n – 1)
C
n³ + 8n + 3
D
2n⁴ + 3n²

Question 159Single Answer

A
e + 1
B
C
e – 1
D
None of these

Question 160Single Answer

A
2log_e2 – 2
B
2 – log_e2
C
2log_e4
D
log_e4

Question 161Single Answer

In how many ways can the number 7056 be resolved into two factors ?

A
20
B
21
C
23
D
22

Question 162Single Answer

The sum of the cubes of three consecutive intergers is divisible by

A
36
B
18
C
12
D
9

Question 163Single Answer

The number of integers less than 720 and prime to it

A
144
B
192
C
216
D
36

Question 164Single Answer

The number of ways in which N = 2,778,300 can be resolved into the two factors prime to each other

A
10
B
9
C
8
D
7

Question 165Single Answer

The sum of the divisors of 630 is

A
809
B
1439
C
1872
D
1579

Question 166Single Answer

The number of zeroes at the end, if 100! is fully expanded and written out is

A
23
B
26
C
25
D
24

Question 167Single Answer

What is the highest power of 3 contained in 100!?

A
49
B
48
C
47
D
46

Question 168Single Answer

The least positive integer having remainders 2, 3, 2 when divided by 3, 5, 7 respectively
is

A
27
B
25
C
24
D
23

Question 169Single Answer

If n is positive odd integer, then n3 – n is divisible by

A
32
B
24
C
18
D
15

Question 170Single Answer

n⁷ – n is divisible by

A
50
B
45
C
40
D
42
E
42

Question 171Single Answer

3²ⁿ – 8n – 1 is divisible by

A
65
B
67
C
71
D
64

Question 172Single Answer

If n > 2, then n5 – 5n3 + 4n is divisible by

A
120
B
110
C
100
D
90

Question 173Single Answer

n(n + 1)(n + 5) is a multiple of

A
5
B
6
C
7
D
None of these

Question 174Single Answer

Question 175Single Answer

What is the largest number that divides 245 and 1029, leaving remainder 5 in each case?

A
15
B
16
C
9
D
5

Question 176Single Answer

What is the largest number that divides each one of 1152 and 1664 exactly?

A
32
B
64
C
128
D
256

Question 177Single Answer

Question 178Single Answer

The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is

A
1651
B
2032
C
127
D
None of these

Question 179Single Answer

If p is a prime, then 2(p – 3)! + 1 is a multiple of

A
p – 1
B
p
C
p + 1
D
None of the above

Question 180Single Answer

If (n, 7) = 1 i.e. if n is prime to 7, then n¹² – 1 is divisible by

Question 181Single Answer

16! + 86 is divisible by

A
320
B
323
C
232
D
None of these

Question 182Single Answer

18! +1 is divisible by

A
19
B
23
C
both (a) and (b)
D
None of the above

Question 183Single Answer

The remainder when 2¹⁰⁰⁰is divisible by 17 is

Question 184Single Answer

Remainder when 1! + 2! + 3! +..... + 50! is divided by

Question 185Single Answer

The remainder obtained by dividiing
1! + 2! + 3! + 4! + ...... + 100! by 12 is

A
7
B
8
C
9
D
10

Question 186Single Answer

2²ⁿ,+ 1 where n is a positive integer greater than one, ends in

A
5
B
7
C
9
D
any number

Question 187Single Answer

If 2^{n – 1} is a prime, then sum of all the divisiors including 1 and itself of 2ⁿ – 1(2ⁿ – 1) is

A
2ⁿ(2ⁿ – 1)2
B
2^{n + 1}(2ⁿ – 1)
C
2ⁿ(2ⁿ – 1)
D
2^{n – 1}(2ⁿ – 1)

Question 188Single Answer

When 2ⁿ – 1 is a prime number, then the sum of the reciprocals of all the divisors of the number 2ⁿ(2ⁿ – 1) is

Question 189Single Answer

If m, n are primes, then mⁿ – 1 + n^m – 1 – 1 is a multiple of

A
m + n
B
m – n
C
D
mn

Question 190Single Answer

Let P(n) : n² + n + 1(n € N) is an even integer. Therefore, P (n) is true.

A
for n > 1
B
for all n
C
for n > 2
D
None of these

Question 191Single Answer

A
1904
B
2000
C
2002
D
2006

Question 192Single Answer

A
an irrational number
B
a non-integer rational number
C
an odd number
D
an even number

Question 193Single Answer

Question 194Single Answer

If P(n) = 2 + 4 + 6 + ..... + 2n, n € N, then P(k) = k(k + 1) + 2 Þ P(k + 1) = (k + 1)(k + 2) + 2 for all k € N. Then, we can conclude that P(n) = n(n + 1) + 2 for