MCQ's of Maths-I

8/11/2019 MCQ's of Maths-I

http://slidepdf.com/reader/full/mcqs-of-maths-i 1/11

Mathematical Logic:

1.Which of the following is a statement?

(A) Stand up!

(B) Will you help me?

(C)Do you like social studies?

(D) 27 is a perfect cube

2. Which of the following is not a statement?(A) Please do me a favour.

(B) 2 is an even integer.

(C) 2 +1 = 3

(D) The number 17 is a prime.

3. Which of the following is an open statement?

(A) is a natural number.

(B) Give me a glass of water.

(C) Wish you best of luck.

(D) Good morning to all.

4. Which of the following is not a proposition in logic.

(A) √ is a prime.

(B) √ is a irrational.

(C) Mathematics is interesting.

(D) 5 is an even integer.

5. If p: The sun has set

q: The moon has risen,

then the statement ‘The sun has not set or the moon has not risen’ in symbolic form is written as

(A) (B)

(C)

(D)

6. Assuming p: She is beautiful, q: She is clever, the verbal form of is

(A) She is beautiful but not clever

(B) She is beautiful and clever

(C) She is not beautiful not clever

(D) She is beautiful or not clever.

7. Let p: ‘It is hot’ and q: ‘It is raining’. The verbal statement for is(A) If it is hot and not raining, then it is hot.

(B) If it is hot and raining, then it is hot.

(C) If it is hot or not raining, then it is not hot.

(D) If it is hot and not raining, then it is not hot.

8. Use the statements

P: Kiran passed the examination,

q: Kiran is sad.

The statement ‘It is not true that Kiran passes therefore he is sad’ in symbolic form of is

(A)



(B)

(C)

(D)

9. Assuming p: She is beautiful, q: She is clever, the verbal form of is

(A) She is beautiful but not clever

(B) She is beautiful and clever

(C) She is not beautiful not clever

(D) She is beautiful or not clever.

10. The converse of the statement ‘If it is raining then it is cool’ is

(A) If it is cool then it is raining.

(B) If it is not cool then it is raining.

(C) If it is not cool then it is not raining.

(D) If it is not raining then it is not cool.

11. If p and q are simple propositions, then is true when

(A) p is true and q is false.

(B) p is false and q is true.

(C) p is true and q is true.

(D) p is false q is false.

12. Which of the following is logically equivalent to ?(A)

(B)

(C)

(D)

13. The logically equivalent statement of is

(A)

(B)

(C)

(D)

14. The logically equivalent statement of is

(A)

(B)

(C)

(D)

15. The contrapositive of is

(A)

(B)

(C)

(D)

16. Which of the following propositions is true?

(A)

(B)

(C)

(D)

17. When two statements are connected by the connective ‘if and only if’ then the compound statement is called



(A) conjunction of the statement

(B) disjunction of the statement

(C) biconditional statement

(D) conditional statement

18. If p and q be two statements then the conjunction of the statements, is false when

(A) both p and q are true

(B) either p or q are true

(C) either p or q both are false

(D) both p and q are false

19. The negation f the statement, “The question paper is not easy and we shall not pass” is

(A) The question paper is not easy or we shall not pass.

(B) The question paper is not easy implies we shall not pass.

(C) The question paper is easy or we shall pass.

(D) We shall pass implies the question paper is not easy.

20. The statement (pq)

(A) a contradiction.

(B) a tautology.

(C) neither a contradiction nor a tautology.

(D) equivalent to

21. The proposition is a

(A) tautology and contradiction.

(B) contingency.

(C) tautology.

(D) contradiction.

22. The proposition is a

(A) tautology.

(B) contradiction.

(C) contingency.

(D) either (A) or (B)

23. The false statement in the following is

(A) is a contradiction.

(B) is a contradiction.

(C) is a tautology.

(D) is a tautology.

24. Negation

p

q) is

(A) pq

(B) pq

(C) pq

(D) pq

25. A dual of pq) i, (A) (pq)

(B) (pq)

(C)

(D)



26. The symbolic form of the following circuit, where p: switch S1 is closed and q: switch S2 is closed, is-

(A) (pq)

(B)

(C) (pq)

(D)

S1

S2

S1

S2’

Matrices:

1.If A=* +, then adj A

(A) * +

(B) * +

(C)

* +

(D) * +

2. The inverse of the matrix A= is

(A) A

(B) null matrix

(C)

(D)

3. If A=* + then adj A is

(A) * +

(B) * +

(C) *

+



(D) * +

4. Minor and cofactor of the element a22 of the matrix, i i is,

(A) 0,0

(B) -1, 0

(C) 1, 0

(D) 0, 1

5. If A=* +, then A + A-1

=

(A) * +

(B) * +

(C) * +

(D) * +

6. If A=

* +, the (A-1)

3 is equal to

(A) * +

(B) * +

(C) * +

(D) * +

7. If A=* +, then A-1

=

(A)

*

+

(B) * +

(C) * +

(D) * +

8. The inverse of the matrix is

(A)

(B)

(C)

(D)

9. From the matrix equation AB=AC we can conclude that B=C, provided

(A) A is singular matrix

(B) A is non-singular matrix



(C) A is symmetric matrix

(D) A is a square matrix

10. If A=* + be such that A-1

=kA, then k equals

(A) 19

(B)

(C) -19

(D)

11. If * + * + * +

(A) a=1, b=1

(B) , i

(C) i,

(D) a=0, b=1

12. If A=* + and B=*+, AX=B, then X is equal to

(A) (B)

*+

(C) (D) *+

13. If A is non-singular matrix such that A2-A+I=0, then A

-1=

(A) A-2

(B) A+I

(C) A-I

(D) I-A

14. If A=

, then

(A) A-1=AT (B) A-1=A2 (C) A-1=-A (D) A-1 does not exist

15. If A and B are square matrices of the same order and AB=3I, then A-1

is equal to

(A) 3B B) B (C) 3 B

-1 (D)

B-1

16. If A= , then the value of |adj A| is

(A) a27

(B) a9 (C) a

6 (D) a

2

17. The sum of three numbers is 2. If twice the second number is added to the sum of first and third, the sum is 1. By addi

second and third number to five times the first number, we get 6. Then the three numbers are

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

18. If for the matrix A.A3=I, then A-1=

(A) A2 (B) A

3 (C) A (D) A

T

19. If A= i (i=√ ), then A-1

=

(A) i

(B) *i i+

(C) * i i

+



(D) * ii +

20. Solution of equation , is

(A) , (B) , (C) , (D) ,

21. The element in the 1st

row and 1st

column of inverse of the matrix * + is

(A) 1 (B) -1 (C) 2 (D) -5

22. If

, then

is equal to

(A) (B) (C) (D)

23. A trust fund has Rs. 30,000 that must be invested in two different types of bonds. The first type of bond pays 10% inte

per year and the second type pays 12%. Using matrix multiplication, determine how to invest Rs. 30,000 into two types of

bonds so that the total interest received is Rs. 3200.

(A) Rs.25,000 and Rs. 5,000

(B) Rs. 20,000 and Rs. 10,000

(C) Rs. 15,000 and Rs. 15,000

(D) Rs. 22,000 AND Rs. 8,000

24. If A is an invertible symmetric matrix, then A-1 is(A) symmetric

(B) skew symmetric

(c) a diagonal matrix

(D) none of these

25. If A and B are non-singular matrices, then

(A) AB-1

=A-1

B-1

(B) AB=BA

(C) (AB)T=A

TB

T

(D) (AB)-1

=B-1

A-1

26. The inverse matrix of , is

(A)

(B)

(C)

(D)

27. The element in the 2nd

row and 3rd

column of inverse of the matrix is,

(A) 1

(B) 3

(C) 2

(D) 5



28. The solution of the equation

(A) (1, 1, 1)

(B) (0, -1, 2)

(C) (-1, 2, 2)

(D) (-1, 0, 2)

29. If A=

and A

-1=

, thn

(A) a=2, c=

(B) a=1, c=-1

(C) a=-1, c=1

(D) a=, c=

30. Given that (A-6I) (A+3I)=0, thenA-6A

-1=

(A) –I

(B) A-1

(C) 2I

(D) I

31. Adjoint of the matrix N= is

(A) N

(B) 2N

(C) –N

(D) I

32. If A=*

+ then adj(adj A) is equal to

(A) adj A(B) A

(C) AT

(D) –A

Trigonometric Functions:

1. If

√ √ , then the general value of

is

(A)

(B) ( )

(C) ( )

(D) ( )

2. If i , then the general value of is

(A) ,

(B) ,

(C) ,

+



(D) ,

3. The solution of is

(A)

(B)

(C)

(D)

4. If n is any integer, then the general solution of the equation

i

√ is

(A) or

(B)

(C)

(D)

5. In , ,

(A)

(B)

(C)

(D)

6. In , =

(A) 0

(B)

(C)

(D)

7. ABC is a triangle such that

i i i . If A, B and C are in A.P. then ,

(A) , ,

(B) , ,

(C) , ,

(D) , ,

8. In ,

A=5, b=4 and , then side c=

(A) 6

(B) 7

(C) 9(D) 8

9. ( √)

(A)

(B)

(C)

(D)

10. i

(A)



(B) √

(C) 1

(D)

11.

(A)

(B)

(C)

(D)

12. If ,

(A) 0.3

(B)

(C)

(D) ( )

13. [√√√√]

(A)

(B)

(C)

(D)

14. If in a , i i i i , , , are in

(A) A.P.

(B) G.P.

(C) H.P.

(D) both A.P. and G.P

15. In a

, if a=2,

60

o and

=75

o, then b=

(A) √ (B) √

(C) √

(D) 1+√

16. If in a , a= √ cm, b=2cm and 60o, then the other two angles and the third side are

(A) 60o, 70

o and c=√

(B) 65o, 55

o and c=√

(C) 75o, 45

o and c=6

(D)

75

o,

45

o and c=

√

17. The general solution of , where , is(A)

(B)

(C)

(D)

18. If , then the general value of is

(A) (√ )

(B) (√ )



(C) (√ )

(D) (√ )

19. The generals solution of the trigonometric equation is

(A)

(B)

(C)

(D)

20. i i () ()

(A)

(B)

(C)

(D)

21. If ,

(A)

(B) (C) 3

(D) 4

22. In ,() () () is equal to

(A)

(B)

(C)

(D)

23. In , the expression is equal to

(A)

(B)i

(C)

(D)

24. If area of is , then

(A)

(B)

(C) (D)

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MCQ's of Maths-I