NCERT Solutions for Class 11 Term_policy Chapter 14 Mathematical Reasoning

The remainder left out when 8²ⁿ –(62)²ⁿ⁺¹ is divided by 9 is 

• 0

• 2

• 7

• 8

Statement 1: ~ (p ↔ ~ q) is equivalent to p ↔ q
Statement 2 : ~ (p ↔ ~ q) is a tautology

• Statement–1 is true, Statement–2 is true, Statement–2 is a correct explanation for statement–1

• Statement–1 is true, Statement–2 is true; Statement–2 is not a correct explanation for statement–1.

• Statement–1 is true, statement–2 is false.

• Statement–1 is false, Statement–2 is true

Let p be the statement “x is an irrational number”, q be the statement “y is a transcendental number”, and r be the statement “x is a rational number iff y is a transcendental number”.
Statement –1: r is equivalent to either q or p
Statement –2: r is equivalent to ∼ (p ↔ ∼ q).

• Statement −1 is false, Statement −2 is true

• Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1

• Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1.

• Statement − 1 is true, Statement − 2 is false. 

The statement p → (q → p) is equivalent to

• p → (p → q) 

• p → (p ∨ q)

• p → (p ∧ q)

• p → (p ↔ q) 

Consider the following statements:
(a) Mode can be computed from histogram
(b) Median is not independent of change of scale
(c) Variance is independent of the change of origin and scale. Which of these is/are correct?

• only (a)

• only (b)

• only (a) and (b)

• (a), (b) and (c)

The Boolean expression ~ (p v q )v (-p ∧q ) is equivalent to

• ~q

• ~ p

• p

• q