Let $$\Delta ,\nabla \in \{\wedge ,\vee \}$$ be such that $$(\mathrm{p}\to \mathrm{q})\mathrm{\Delta }(p\nabla q)$$ is a tautology. Then

The statement $$\left(p\wedge \left(\sim q\right)\right)\Rightarrow \left(p\Rightarrow \left(\sim q\right)\right)$$ is

Let p and q be two statements. Then $$\sim \left(p\wedge (p\Rightarrow \sim q)\right)$$ is equivalent to

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

Negation of $p\wedge (q\wedge \sim (p\wedge q))$ is :

The statement $$(p\wedge (\sim q))\vee ((\sim p)\wedge q)\vee ((\sim p)\wedge (\sim q))$$ is equivalent to _________.

The negation of the statement $$((A\wedge (B\vee C))\Rightarrow (A\vee B))\Rightarrow A$$ is

Among the two statements $$(\mathrm{S}1):(p\Rightarrow q)\wedge (p\wedge (\sim q))$$ is a contradiction and $$(\mathrm{S}2):(p\wedge q)\vee ((\sim p)\wedge q)\vee (p\wedge (\sim q))\vee ((\sim p)\wedge (\sim q))$$ is a tautology

The converse of $$((\sim p)\wedge q)\Rightarrow r$$ is

The statement $$\sim [p\vee (\sim (p\wedge q))]$$ is equivalent to :

The negation of the statement $$(p\vee q)\wedge (q\vee (\sim r))$$ is :

The negation of $$(p\wedge (\sim q))\vee (\sim p)$$ is equivalent to :

Negation of $$(p\Rightarrow q)\Rightarrow (q\Rightarrow p)$$ is :

Statement $$(\mathrm{P}\Rightarrow \mathrm{Q})\wedge (\mathrm{R}\Rightarrow \mathrm{Q})$$ is logically equivalent to :

Among the statements (S1) : $$(p\Rightarrow q)\vee ((\sim p)\wedge q)$$ is a tautology (S2) : $$(q\Rightarrow p)\Rightarrow ((\sim p)\wedge q)$$ is a contradiction

If the velocity of light $$\mathrm{c}$$, universal gravitational constant $$\mathrm{G}$$ and Planck's constant $$\mathrm{h}$$ are chosen as fundamental quantities. The dimensions of mass in the new system is :

Match List I with List II .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-c3ow{border-color:inherit;text-align:center;vertical-align:top} .tg .tg-7btt{border-color:inherit;font-weight:bold;text-align:center;vertical-align:top} .tg .tg-0pky{border-color:inherit;text-align:left;vertical-align:top} LIST I LIST II A. Angular momentum I. $\left[{\mathrm{ML}}^2{\mathrm{T}}^{-2}\right]$ B. Torque II. $\left[{\mathrm{ML}}^{-2}{\mathrm{T}}^{-2}\right]$ C. Stress III $\left[{\mathrm{ML}}^2{\mathrm{T}}^{-1}\right]$ D. Pressure gradient IV. $\left[{\mathrm{ML}}^{-1}{\mathrm{T}}^{-2}\right]$ Choose the correct answer from the options given below:

Match List I with List II: .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-7btt{border-color:inherit;font-weight:bold;text-align:center;vertical-align:top} .tg .tg-0pky{border-color:inherit;text-align:left;vertical-align:top} List I List II A. Torque I. $\mathrm{kg}{\mathrm{m}}^{-1}{\mathrm{s}}^{-2}$ B. Energy density II. $\mathrm{kg}{\mathrm{ms}}^{-1}$ C. Pressure gradient III. $\mathrm{kg}{\mathrm{m}}^{-2}{\mathrm{s}}^{-2}$ D. Impulse IV. $\mathrm{kg}{\mathrm{m}}^2{\mathrm{s}}^{-2}$ Choose the correct answer from the options given below:

The equation of a circle is given by $$x^2+y^2=a^2$$, where a is the radius. If the equation is modified to change the origin other than (0, 0), then find out the correct dimensions of A and B in a new equation : {(x - At)^2} + {\left( {y - {t \over B}} \right)^2} = {a^2}. The dimensions of t is given as $$[{\mathrm{T}}^{-1}]$$.

Match List I with List II : .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-amwm{font-weight:bold;text-align:center;vertical-align:top} .tg .tg-0lax{text-align:left;vertical-align:top} List I (Physical Quantity) List II (Dimensional Formula) A. Pressure gradient I. $$\left[{\mathrm{M}}^{\circ }{\mathrm{L}}^2{\mathrm{T}}^{-2}\right]$$ B. Energy density II. $$\left[{\mathrm{M}}^1{\mathrm{L}}^{-1}{\mathrm{T}}^{-2}\right]$$ C. Electric Field III. $$\left[{\mathrm{M}}^1{\mathrm{L}}^{-2}{\mathrm{T}}^{-2}\right]$$ D. Latent heat IV. $$\left[{\mathrm{M}}^1{\mathrm{L}}^1{\mathrm{T}}^{-3}{\mathrm{A}}^{-1}\right]$$ Choose the correct answer from the options given below: