If the Boolean expression (p $$\Rightarrow$$ q) $$\iff$$ (q * ($$\sim$$p) is a tautology, then the boolean expression (p * ($$\sim$$q)) is equivalent to :

If the Boolean expression $$(p\wedge q)\odot (p\otimes q)$$ is a tautology, then $$\odot$$ and $$\otimes$$ are respectively given by :

If P and Q are two statements, then which of the following compound statement is a tautology?

The Boolean expression $$(p\wedge \sim q)\Rightarrow (q\vee \sim p)$$ is equivalent to :

Consider the following three statements : (A) If 3 + 3 = 7 then 4 + 3 = 8 (B) If 5 + 3 = 8 then earth is flat. (C) If both (A) and (B) are true then 5 + 6 = 17. Then, which of the following statements is correct?

Which of the following Boolean expressions is not a tautology?

The Boolean expression $$(p\Rightarrow q)\wedge (q\Rightarrow \sim p)$$ is equivalent to :

Which of the following is the negation of the statement "for all M > 0, there exists x$$\in$$S such that x $$\ge$$ M" ?

Consider the statement "The match will be played only if the weather is good and ground is not wet". Select the correct negation from the following :

The compound statement $$(P\vee Q)\wedge (\sim P)\Rightarrow Q$$ is equivalent to :

If the truth value of the Boolean expression $$\left(\left(p\vee q\right)\wedge \left(q\to r\right)\wedge \left(\sim r\right)\right)\to \left(p\wedge q\right)$$ is false, then the truth values of the statements p, q, r respectively can be :

Consider the two statements : (S1) : (p $$\to$$ q) $$\vee$$ ($$\sim$$ q $$\to$$ p) is a tautology . (S2) : (p $$\wedge$$ $$\sim$$ q) $$\wedge$$ ($$\sim$$ p $$\wedge$$ q) is a fallacy. Then :

The statement (p $$\wedge$$ (p $$\to$$ q) $$\wedge$$ (q $$\to$$ r)) $$\to$$ r is :

The Boolean expression (p $$\wedge$$ q) $$\Rightarrow$$ ((r $$\wedge$$ q) $$\wedge$$ p) is equivalent to :

Let *, ▢ $$\in$${$$\wedge$$, $$\vee$$} be such that the Boolean expression (p * $$\sim$$ q) $$\Rightarrow$$ (p ▢ q) is a tautology. Then :

Negation of the statement (p $$\vee$$ r) $$\Rightarrow$$ (q $$\vee$$ r) is :

Which of the following is equivalent to the Boolean expression p $$\wedge$$ $$\sim$$ q ?

The work done by a gas molecule in an isolated system is given by, W = \alpha {\beta ^2}{e^{ - {{{x^2}} \over {\alpha kT}}}}, where x is the displacement, k is the Boltzmann constant and T is the temperature. $$\alpha$$ and $$\beta$$ are constants. Then the dimensions of $$\beta$$ will be :

Match List - I with List - II : List I List II (a) h (Planck's constant) (i) $$[ML{T}^{-1}]$$ (b) E (kinetic energy) (ii) $$[M{L}^2{T}^{-1}]$$ (c) V (electric potential) (iii) $$[M{L}^2{T}^{-2}]$$ (d) P (linear momentum) (iv) $$[M{L}^2{I}^{-1}{T}^{-3}]$$ Choose the correct answer from the options given below :

The pitch of the screw gauge is 1 mm and there are 100 divisions on the circular scale. When nothing is put in between the jaws, the zero of the circular scale lies 8 divisions below the reference line. When a wire is placed between the jaws, the first linear scale division is clearly visible while 72nd division on circular scale coincides with the reference line. The radius of the wire is :