The number of choices for $$\Delta \in \{\wedge ,\vee ,\Rightarrow ,\iff \}$$, such that $$(p\Delta q)\Rightarrow ((p\Delta \sim q)\vee ((\sim p)\Delta q))$$ is a tautology, is :

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

Which of the following statements is a tautology ?

Consider the following statements: P : Ramu is intelligent. Q : Ramu is rich. R : Ramu is not honest. The negation of the statement "Ramu is intelligent and honest if and only if Ramu is not rich" can be expressed as:

The statement $$(\sim (\mathrm{p}\iff \sim \mathrm{q}))\wedge \mathrm{q}$$ is :

Negation of the Boolean expression $$p\iff (q\Rightarrow p)$$ is

$$(p\wedge r)\iff (p\wedge (\sim q))$$ is equivalent to $$(\sim p)$$ when $$r$$ is

If the truth value of the statement $$(P\wedge (\sim R))\to ((\sim R)\wedge Q)$$ is F, then the truth value of which of the following is $$\mathrm{F}$$ ?

Let the operations $$\ast ,\odot \in \{\wedge ,\vee \}$$. If $$(\mathrm{p}\ast \mathrm{q})\odot (\mathrm{p}\odot \sim \mathrm{q})$$ is a tautology, then the ordered pair $$(\ast ,\odot )$$ is :

Let $$\mathrm{p}$$ : Ramesh listens to music. $$\mathrm{q}$$ : Ramesh is out of his village. $$\mathrm{r}$$ : It is Sunday. $$\mathrm{s}$$ : It is Saturday. Then the statement "Ramesh listens to music only if he is in his village and it is Sunday or Saturday" can be expressed as

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

The statement $$(p\Rightarrow q)\vee (p\Rightarrow r)$$ is NOT equivalent to

Velocity (v) and acceleration (a) in two systems of units 1 and 2 are related as {v_2} = {n \over {{m^2}}}{v_1} and {a_2} = {{{a_1}} \over {mn}} respectively. Here m and n are constants. The relations for distance and time in two systems respectively are :

The SI unit of a physical quantity is pascal-second. The dimensional formula of this quantity will be :

A silver wire has a mass (0.6 $$\pm$$ 0.006) g, radius (0.5 $$\pm$$ 0.005) mm and length (4 $$\pm$$ 0.04) cm. The maximum percentage error in the measurement of its density will be :

An expression for a dimensionless quantity P is given by P = {\alpha \over \beta }{\log _e}\left( {{{kt} \over {\beta x}}} \right); where $$\alpha$$ and $$\beta$$ are constants, x is distance; k is Boltzmann constant and t is the temperature. Then the dimensions of $$\alpha$$ will be :

The dimension of mutual inductance is :

If Z = {{{A^2}{B^3}} \over {{C^4}}}, then the relative error in Z will be :

Identify the pair of physical quantities that have same dimensions:

Identify the pair of physical quantities which have different dimensions: