5. continuity and differentiation — Maths STD 12 Science — Question

$1.$ One of the two boxes, box $I$ and box $II$, was selected at random and a ball was drawn randomly out of this box. The ball was found to be red. If the probability that this red ball was drawn from box $II$ is $\frac{1}{3}$, then the correct option$(s)$ with the possible values of $n_1, n_2, n_3$ and $n_4$ is(are)

$(A)$ $n_1=3, n_2=3, n_3=5, n_4=15$

$(B)$ $n_1=3, n_2=6, n_3=10, n_4=50$

$(C)$ $n_1=8, n_2=6, n_3=5, n_4=20$

$(D)$ $n_1=6, n_2=12, n_3=5, n_4=20$

$2.$ A ball is drawn at random from box $I$ and transferred to box $II$. If the probability of drawing a red ball from box $I$, after this transfer, is $\frac{1}{3}$, then the correct option$(s)$ with the possible values of $n_1$ and $n_2$ is(are)

$(A)$ $n_1=4, n_2=6$ $(B)$ $n_1=2, n_2=3$

$(C)$ $n_1=10, n_2=20$ $(D)$ $n_1=3, n_2=6$

Give the answer question $1$ and $2.$

1. a - b
2. a + b
3. $\log\text{a}+\log\text{b}$
4. none of these

1. $\sin^{-1}\sqrt{\text{x}}+\text{C}$
   
2. $\sin^{-1}\Big\{\sqrt{\text{x}}-\sqrt{\text{x}(1-\text{x})}\Big\}+\text{C}$
   
3. $\sin^{-1}\Big\{\sqrt{\text{x}(1-\text{x})}\Big\}+\text{C}$
   
4. $\sin^{-1}\sqrt{\text{x}}-\sqrt{\text{x}(1-\text{x})}+\text{C}$
   

1. $\sqrt{\text{b}^2+\text{c}^2}$
   
2. $\sqrt{\text{a}^2+\text{c}^2}$
   
3. $\sqrt{\text{a}^2+\text{b}^2}$
   
4. $\text{none of these}$