JEE Advanced (Single Correct Type): Statistics & Mathematical Reasoning | Chapter-wise Tests for JEE Main & Advanced PDF Download

Q.1. Which of the following is a statement?
(a) Roses are black.
(b) Mind your own business
(c) Be punctual.
(d) Do not tell lies

Correct Answer is option (a)
The sentences in (b), (c), and (d) are neither true nor false. All these sentences are pieces of advice. Sentence (a) is a definite statement.

Q.2. Which of the following is not a statement?
(a) Smoking is injurious to health
(b) 2 + 2 = 4
(c) 2 is the only even prime number
(d) Come here

Correct Answer is option (d)
Smoking is injurious to health. – It is a statement.
2 + 2 = 4; It is a mathematical statement.
2 is the only even prime number. – Mathematical statement.
Come here. – It is not a statement but it is an order.

Q.3. The negation of the statement “7 is greater than 8” is
(a) 7 is equal to 8
(b) 7 is not greater than 8
(c) 8 is less than 7
(d) None of these

Correct Answer is option (b)
Statement: 7 is greater than 8
Negation: 7 is not greater than 8

Q.4. The contrapositive of the statement “If p, then q”, is
(a) If q, then p
(b) If p, then ~ q
(c) If ~ q, then ~ p
(d) If ~ p, then ~ q

Correct Answer is option (c)
The contrapositive of the statement “If p, then q”, is If ~ q, then ~ p.

Q.5. The connective in the statement “Earth revolves around the Sun and Moon is a satellite of earth” is
(a) or
(b) Earth
(c) Sun
(d) And

Correct Answer is option (d)
Given statement: Earth revolves around the Sun and Moon is a satellite of earth Here, the connective word is “and.”

Q.6. The converse of the statement “If x > y, then x + a > y + a” is
(a) If x < y, then x + a < y + a
(b) If x + a > y + a, then x > y
(c) If x < y, then x + a > y + a
(d) If x > y, then x + a < y + a

Correct Answer is option (b)
As we know, the converse of a statement p ⇒ q is the statement q ⇒ p.
So, the converse of the statement “If x > y, then x + a > y + a” is If x + a > y + a, then x > y.

Q.7. Which of the following statements is a conjunction?
(a) Ram and Shyam are friends
(b) Both Ram and Shyam are tall
(c) Both Ram and Shyam are enemies
(d) None of the above

Correct Answer is option (d)
When the word connects two statements “and,” we call the combined statement conjunction.
None of the statements is connected by “and” from the given.

Q.8. The contrapositive of the statement ‘If Chandigarh is the capital of Punjab, then Chandigarh is in India’ is
(a) If Chandigarh is not in India, then Chandigarh is not the capital of Punjab
(b) If Chandigarh is in India, then Chandigarh is the capital of Punjab
(c) If Chandigarh is not the capital of Punjab, then Chandigarh is not the capital of India
(d) If Chandigarh is the capital of Punjab, then Chandigarh is not in India

Correct Answer is option (a)
The contrapositive of a statement p ⇒ q is the statement ∼ q ⇒ ∼p.
Therefore, the contrapositive of the statement ‘If Chandigarh is the capital of Punjab, then Chandigarh is in India’ is “If Chandigarh is not in India, then Chandigarh is not the capital of Punjab.”

Q.9. The method(s) that are used to check the validity of statements is/are
(a) Contrapositive method
(b) Method of contradiction
(c) Using a counter example
(d) All the above

Correct Answer is option (d)
The methods that are used to check the validity of statements include the following.
(i) direct method
(ii) contrapositive method
(iii) method of contradiction
(iv) using a counter example

Q.10. The negation of the statement “Akash or Ankitha lived in Goa” is
(a) Akash did not live in Goa or Ankitha lives in Goa
(b) Akash lives in Goa and Ankitha did not live in Goa
(c) Akash did not live in Goa and Ankitha did not live in Goa
(d) Akash did not live in Goa or Ankitha did not live in Goa

Correct Answer is option (c)
Given,
Statement: Akash or Ankitha lived in Goa
Negation of the above statement is:
Akash did not live in Goa and Ankitha did not live in Goa.