MHT CET 2025 23RD APRIL EVENING SHIFT

A particle is displaced from point $\mathrm{P}(3 \mathrm{~m}, 4 \mathrm{~m}, 5 \mathrm{~m})$ to a point $\mathrm{Q}(2 \mathrm{~m}, 3 \mathrm{~m}, 4 \mathrm{~m})$ under a constant force $\overrightarrow{\mathrm{F}}=(3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+5 \hat{\mathrm{k}}) \mathrm{N}$. The work done by the force in this process is

If ${ }^{15} \mathrm{C}_4+{ }^{15} \mathrm{C}_5+{ }^{16} \mathrm{C}_6+{ }^{17} \mathrm{C}_7+{ }^{18} \mathrm{C}_8={ }^{19} \mathrm{C}_{\mathrm{r}}$, then the value of $r$ is equal to

The standard emf for cell, ${ }^{\ominus} \mathrm{Cd}_{(\mathrm{s})}\left|{ }^{+2} \mathrm{Cd}(1 \mathrm{M}) \| \stackrel{+2}{\mathrm{Cu}}(1 \mathrm{M})\right| \mathrm{Cu}_{(\mathrm{s})}{ }^{\oplus}$ is 0.74 V .

If concentration of $\mathrm{Cd}_{(\mathrm{aq})}^{+2}$ and $\mathrm{Cu}_{(\mathrm{aq})}^{+2}$ decreases by 10 times at 298 K . Calculate emf of cell.

A particle describes a horizontal circle on smooth inner surface of a cone as shown in figure. If the height of the circle above the vertex is 10 cm . The speed of the particle is $\left(\mathrm{g}\right.$, acceleration due to gravity $\left.=10 \mathrm{~m} / \mathrm{s}^2\right)$

If $\bar{a}=2 \hat{i}+3 \hat{j}+4 \hat{k}, \bar{b}=\hat{i}-2 \hat{j}-2 \hat{k}, \bar{c}=-\hat{i}+4 \hat{j}+3 \hat{k}$ and if $\overline{\mathrm{d}}$ is vector perpendicular to both $\overline{\mathrm{b}}$ and $\overline{\mathrm{c}}, \overline{\mathrm{a}} \cdot \overline{\mathrm{d}}=18$, then $|\overline{\mathrm{a}} \times \overline{\mathrm{d}}|^2=$