## Discrete Mathematics MCQ Set 1

1. Let the sequence be 2, 8, 32, 128,……… then this sequence is

a) An airthmetic sequence

b) A geometic progression

c) A harmonic sequence

d) None of the mentioned

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2. In the given Geometric progression find the number of terms

32, 256, 2048, 16384,………,2^{50}.

a) 11

b) 13

c) 15

d) None of the mentioned

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^{th}term = first term(ratio

^{n – 1})., 2

^{50}= 2

^{5}(2

^{3(n-1)}), n=15. This implies 16

^{th}term.

3. In the given Geometric progression the term at position 11 would be

32, 256, 2048, 16384,………,2^{50}.

a) 2^{35}

b) 2^{45}

c) 35

d) None of the mentioned.

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^{th}term = first term(ratio

^{n – 1})., g

_{n}= 2

^{5}(2

^{3(n-1)}), n=11. This implies 2

^{35}.

4. For the given Geometric progression find the position of first fractional term?

2^{50}, 2^{47}, 2^{44},………

a) 17

b) 20

c) 18

4) None of the mentioned.

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^{th}term=1 ,the next term would be first fractional term. G

_{n}= 1 = 2

^{50}(2

^{3(-n+1)}), n=17.66.. therfore at n = 18 the first fractional term would occur.

5. For the given geometric progression find the first fractional term?

2^{50}, 2^{47}, 2^{44},………

a) 2^{-1}

b) 2^{-2}

c) 2^{-3}

4) None of the mentioned.

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^{th}term=1 ,the next term would be first fractional term. G

_{n}= 1 = 2

^{50}( 2

^{3(-n+1)}), n=17.66.. therefore at n=18 the first fractional term would occur.G

_{n}= 2

^{50}( 2

^{3(-n+1)}), G

_{18}= 2

^{-1}.

6. State whether the given statement is true or false

1, 1, 1, 1, 1…….. is a GP series .

a) True

b) False

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7. In the given Geometric progression, ‘2^{25}‘ would be a term in it.

32, 256, 2048, 16384,………,2^{50}.

a) True

b) False

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^{th}term = first term(ratio

^{n – 1})., g

_{n}= 2

^{25}= 2

^{5}(2

^{3(n-1)}), n=23/3, n=7.666 not an integer. Thus 2

^{25}is not a term in this series.

8. Which of the following sequeces in GP will have common ratio 3,where n is an Integer?

a) g_{n} = 2n^{2} + 3n

b) g_{n} = 2n^{2} + 3

c) g_{n} = 3n^{2} + 3n

d) g_{n} = 6(3^{n-1})

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_{n}= 6( 3

^{n-1}) it is a geometric expression with coefficient of constant as 3

^{n-1}.So it is GP with common ratio 3.

9. If a, b, c are in GP then relation between a, b, c can be

a) 2b = 2a + 3c

b) 2a = b+c

c) b =(ac)^{1/2}

d) 2c = a + c

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10. Let the multiplication of the 3 consecutive terms in GP be 8 then midlle of those 3 terms would be:

a) 2

b) 3

c) 4

d) 179

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^{1/2}(G M property), b

^{3}= 8, b = 2.

## Discrete Mathematics MCQ Set 2

1. If a_{1}, a_{2}……… are in AP then a_{1}^{-1}, a_{2}^{-1}……… are in:

a) An airthmetic sequence

b) A geometic progression

c) Airthmetico-geometric progression

d) None of the mentioned

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_{1}, a

_{2}……… are in AP, then a

_{1}

^{-1}, a

_{2}

^{-1}……… are in Harmonic Progression.

2. The ninth term of ^{1}⁄_{3}, ^{1}⁄_{7}, ^{1}⁄_{11}, ^{1}⁄_{15}, ^{1}⁄_{19},……… is given by:

a) ^{1}⁄_{35}

b) ^{1}⁄_{36}

c) ^{1}⁄_{39}

d) None of the mentioned

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_{1}

^{-1}, a

_{2}

^{-1}……… are in AP thus a

_{9}= 3 + (9-1)4 = 35,

^{1}⁄

_{35}is h

_{9}term of the series.

3. If for some number a and d,if first term is ^{1}⁄_{a}, second term is 1/(a+d) ,thrid term is 1/(a+2d) and so on,then 5^{th} term of the sequence is :

a) a+4d

b) a-4d

c) 1/(a+4d)

d) None of the mentioned

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^{th}term will be (a+(5-1)d) – 1.

4. If a, b, c are in hp then a^{-1}, b^{-1}, c^{-1} are in:

a) GP

b) HP

c) AP

d) None of the mentioned

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_{1}, a

_{2}……… are in AP then a

_{1}

^{-1}, a

_{2}

^{-1}……… are in Harmonic Progression.

5. If a, b, c are in hp, then b is related with a and c as :

a) 2(^{1}⁄_{b}) = (^{1}⁄_{a} + ^{1}⁄_{c})

b) 2(^{1}⁄_{c}) = (^{1}⁄_{b} + ^{1}⁄_{c})

c) 2(^{1}⁄_{a}) = (^{1}⁄_{a} + ^{1}⁄_{b})

d) None of the mentioned

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^{1}⁄

_{a},

^{1}⁄

_{b},

^{1}⁄

_{c}willl be in airthmentic series and

^{1}⁄

_{b}will be the AM of a, c.

6. State whether the given statement is true or false

For number A, C if H is harmonic mean ,G is geometric mean then H>=G.

a) True

b) False

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7. State whether the given statement is true or false

For number B, C if H is harmonic mean, A is the airthmetic mean then H>=A.

a) True

b) False

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8. Which of the following gives the right inequality for AM, GM, HM?

a) AM>=HM>=GM

b) GM>=AM>=HM

c) AM>=GM>=HM

d) GM>=HM>=AM

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9. For two number a,b HM between them is given by:

a) (2b+2a )/3b

b) 2ab/(a+b)

c) (a+b)/2ab

d) 2b/(a+b)

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^{2}⁄

_{c}=

^{1}⁄

_{a}+

^{1}⁄

_{b}(AM property), c = 2b/(a+b).

10. If A, G, H are the AM, GM, HM between a and b respectively then:

a) A, G, H are in hp

b) A, G, H are in gp

c) A, G, H are in ap

d) None of the mentioned

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^{1/2}, H = 2b/(a+b), clearly AxH = G

^{2}thus A, G, H are in gp.

## Discrete Mathematics MCQ Set 3

1. Which rule of inference is used in each of these arguments, “If it is Wednesday, then the Smartmart will be crowded. It is Wednesday. Thus, the Smartmart is crowded.”

a) Modus tollens

b) Modus ponens

c) Disjunctive syllogism

d) Simplification

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2. Which rule of inference is used in each of these arguments, “If it hailstoday, the local office will be closed. The local office is not closed today. Thus, it did not hailed today.”

a) Modus tollens

b) Conjunction

c) Hypothetical syllogism

d) Simplification

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3. Which rule of inference is used,”Bhavika will work in an enterprise this summer. Therefore, this summer Bhavika will work in an enterprise or he will go to beach.”

a) Simplification

b) Conjunction

c) Addition

d) Disjunctive syllogism

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4. What rule of inference is used here?

“It is cloudy and drizzling now. Therefore, it is cloudy now.”?

a) Addition

b) Simplification

c) Resolution

d) Conjunction

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5. What rule of inference is used in this argument?

“If I go for a balanced diet, then I will be fit. If I will be fit, then I will remain healthy. Therefore, if I go for a balanced diet, then I will remain healthy.”

a) Modus tollens

b) Modus ponens

c) Disjunctive syllogism

d) Hypothetical syllogism

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6. What rules of inference are used in this argument?

“All students in this science class has taken a course in physics” and “Marry is a student in this class” imply the conclusion “Marry has taken a course in physics.”

a) Universal instantiation

b) Universal generalization

c) Existential instantiation

d) Existential generalization

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7. What rules of inference are used in this argument?

“It is either colder than Himalaya today or the pollution is harmful. It is hotter than Himalaya today. Therefore, the pollution is harmful.”

a) Conjunction

b) Modus ponens

c) Disjunctive syllogism

d) Hypothetical syllogism

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8. The premises (p ∧ q) ∨ r and r → s imply which of the conclusion?

a) p ∨ r

b) p ∨ s

c) q ∨ s

d) q ∨ r

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9. What rules of inference are used in this argument?

“Jay is an awesome student .Jay is also a good dancer. Therefore, Jay is an awesome student and a good dancer.”

a) Conjunction

b) Modus ponens

c) Disjunctive syllogism

d) Simplification

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10. “Parul is out for a trip or it is not snowing” and “It is snowing or Raju is playing chess” imply that

a) Parul is out for trip.

b) Raju is playing chess

c) Parul is out for a trip and Raju is playing chess.

d) Parul is out for a trip or Raju is playing chess.

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## Discrete Mathematics MCQ Set 4

1. For a matrix A, B and identity matrix I, if a matrix AB=I=BA then:

a) B is inverse of A

b) A is inverse of B

c) A^{-1} = B, B^{-1} = A

d) All of the mentioned

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^{-1}Similarly A is the inverse of B.

2. For matrix A,(A^{3}) = I, A^{-1} is equals to:

a) A^{2}

b) A^{-2}

c) Can’t say

d) None of the mentioned

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^{2}) = I this implies A

^{-1}= A

^{2}.

3. Let A = [0 1 0 0 ], A^{-1} is equal to:

a) Null matrix

b) Identity matrix

c) Does not exist

d) None of the mentioned

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4. If A is an invertible square matrix then:

a) (A^{T})^{-1} = (A^{-1})^{T}

b) (A^{T})^{T} = (A^{-1})^{T}

c) (A^{T})^{-1} = (A^{-1})^{-1}

d) None of the mentioned

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^{T}is also inveritble.

5. If matrix A, B and C are invertible matrix of same order then (ABC)^{-1}=

a) CBA

b) C^{-1} B^{-1} A^{-1}

c) C^{T} B^{-1} A^{T}

4) None of the mentioned

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6. State True or False?

If A is non singular matrix then AB = AC implies B = C.

a) True

b) False

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^{-1}we get B = C.

7. State True or False:

For a matrix A of order n, the det(adj(A)) = (det(A))^{n}, where adj() is adjoint of matrix.

a) True

b) False

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^{n-1}.

8. For a non-singular matrix A, A^{-1} is equal to:

a) (adj(A))/det(A)

b) det(A)*(adj(A))

c) det(A)*A

d) None of the mentioned

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^{-1}= (adj(A))/det(A).

9. Let I_{3} be the Identity matrix of order 3 then (I_{3})^{-1} is equal to:

a) 0

b) 3I_{3}

c) I_{3}

d) None of the mentioned.

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_{3}x I

_{3}= I

_{3}.

10. If for a square matrix A(non-singular) and B, null matrix O, AB = O then:

a) B is a null matrix

b) B is a non singular matrix

c) B is a identity matrix

d) All of the mentioned

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^{-1}(AB) = O, B = O.

## Discrete Mathematics MCQ Set 5

1. A Least Common Multiple of a,b is defined as:

a) It is the smallest integer divisible by both a and b

b) It is the greatest integer divisible by both a and b

c) It is the sum of the number a and b

d) None of the mentioned

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2. The LCM of two number 1, b(integer) are

a) b + 2

b) 1

c) b

d) None of the mentioned

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3. If a, b are integers such that a > b then lcm(a, b) lies in

a) a>lcm(a, b)>b

b) a>b>lcm(a, b)

c) lcm(a, b)>=a>b

d) None of the mentioned

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4. LCM of 6, 10 is:

a) 60

b) 30

c) 10

d) 6

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5. The product of two numbers are 12 and there Greatest common divisior is 2 then LCM is:

a) 12

b) 2

c) 6

d) None of the mentioned.

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6. If LCM of two number is 14 and GCD is 1 then the product of two numbers is :

a) 14

b) 15

c) 7

d) 49

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7. If a number is 2^{2} x 3^{1} x 5^{0} and b is 2^{1} x 3^{1} x 5^{1} then lcm of a, b is:

a) 2^{2} x 3^{1} x 5^{1}

b) 2^{2} x 3^{2} x 5^{2}

c) 2^{3} x 3^{1} x 5^{0}

d) 2^{2} x 3^{2} x 5^{0}

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8. State whether the given statement is True or False.

LCM (a, b, c, d) = LCM(a,(LCM(b,(LCM(c, d)))).

a) True

b) False

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9. LCM(a, b) is equals to :

a) ab/(GCD(a, b))

b) (a+b)/(GCD(a, b))

c) (GCD(a, b))/ab

d) None of the mentioned

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10. The lcm of two prime numbers a and b is:

a) ^{a}⁄_{b}

b) ab

c) a + b

d) 1