2 Marks Questions

Question 12 Marks

If $A$ and $B$ are two events associated with a random experiment such that $P(A)=0.25, P(B)=0.4$ and $P(A$ or $B)$$=0.5$, find the values of
i. P(A and B)
ii. P(A and $\bar{B})$

Answer

i. It is given that
$
: \mathrm{P}(\mathrm{~A})=0.25, \mathrm{P}(\mathrm{~A} \text { or } \mathrm{B})=0.5 \text { and } \mathrm{P}(\mathrm{~B})=0.4
$
To find: $\mathrm{P}(\mathrm{A}$ and B$)$
Formula used: $\mathrm{P}(\mathrm{A}$ or B$)=\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})-\mathrm{P}(\mathrm{A}$ and B$)$
Substituting the value in the above formula we get,
$0.5=0.25+0.4-\mathrm{P}(\mathrm{A}$ and B$)$
$0.5=0.65-\mathrm{P}(\mathrm{A}$ and B$)$
$\mathrm{P}(\mathrm{A}$ and B$)=0.65-0.5$
$P(A$ and $B)=0.15$
ii. Given : $\mathrm{P}(\mathrm{A})=0.25, \mathrm{P}(\mathrm{A}$ and B$)=0.15$ ( from part (i))
To find: $\mathrm{P}(\mathrm{A}$ and $\bar{B})$
Formula used : $\mathrm{P}(\mathrm{A}$ and $\bar{B})=\mathrm{P}(\mathrm{A})-\mathrm{P}(\mathrm{A}$ and B$)$
Substituting the value in the above formula we get,
$\mathrm{P}(\mathrm{A}$ and $\bar{B})=0.25-0.15$
$\mathrm{P}(\mathrm{A}$ and $\bar{B})=0.10$
$\mathrm{P}(\mathrm{A}$ and $\bar{B})=0.10$

View full question & answer→

Question 22 Marks

Differentiate the following functions with respect to $\mathrm{x}: 5^{3-x^{2}}+\left(3-\mathrm{x}^{2}\right)^{5}$

Answer

Let $y=5^{3-x^{2}}+\left(3-x^{2}\right)^{5}$
Differentiating with respect to $x$, we get
$\frac{d y}{d x}=\frac{d}{d x}\left(5^{3-x^{2}}\right)+\frac{d}{d x}\left\{\left(3-x^{2}\right)^{5}\right\}$
$\Rightarrow \frac{d y}{d x}=5^{3-x^{2}} \log _{e} 5 \times \frac{d}{d x}\left(3-\mathrm{x}^{2}\right)+5\left(3-\mathrm{x}^{2}\right)^{5-1} \times \frac{d}{d x}\left(3-\mathrm{x}^{2}\right)$
$\Rightarrow \frac{d y}{d x}=5^{3-x^{2}}$ loge $5 \times(0-2 \mathrm{x})+5\left(3-\mathrm{x}^{2}\right)^{4} \times(0-2 \mathrm{x})$
$\Rightarrow \frac{d y}{d x}=-2 \mathrm{x}\left\{5^{3-x^{2}} \log _{\mathrm{e}} 5+5\left(3-\mathrm{x}^{2}\right)^{4}\right\}$

View full question & answer→

Question 32 Marks

If $\mathrm{y}=\sqrt{x}+\frac{1}{\sqrt{x}}$, prove that $2 \mathrm{x} \frac{d y}{d x}=\sqrt{x}-\frac{1}{\sqrt{x}}$

Answer

We have, $\mathrm{y}=\sqrt{x}+\frac{1}{\sqrt{x}}$
Differentiate with respect to x ,
$\Rightarrow \frac{d y}{d x}=\frac{d}{d x}\left(\sqrt{x}+\frac{1}{\sqrt{x}}\right)$
$\Rightarrow \frac{d y}{d x}=\frac{d}{d x}(\sqrt{x})+\frac{d}{d x}\left(\frac{1}{\sqrt{x}}\right)$
$\Rightarrow \frac{d y}{d x}=\frac{1}{2 \sqrt{x}}+\left(\frac{-\frac{1}{2 \sqrt{x}}}{x}\right)$
$\Rightarrow \frac{d y}{d x}=\frac{1}{2 \sqrt{x}}-\frac{1}{2 x \sqrt{x}}$
$\Rightarrow \frac{d y}{d x}=\frac{x-1}{2 x \sqrt{x}}$
$\Rightarrow 2 x \frac{d y}{d x}=\frac{x-1}{\sqrt{x}}$
$\Rightarrow 2 x \frac{d y}{d x}=\frac{x}{\sqrt{x}}-\frac{1}{\sqrt{x}}$
$\Rightarrow 2 x \frac{d y}{d x}=\sqrt{x}-\frac{1}{\sqrt{x}}$

View full question & answer→

Question 42 Marks

If the second day of April month is a Friday, then find the last day of the next month.

Answer

Given 2nd April is Friday.
From 3rd April to last day of the next month.
Number of days $=28$ April +31 May $=59$
So, the number of odd days $=7 \times 8+3$ i.e. 3 days
Since 2nd April is Friday and there are 3 odd days up to last day of next month i.e. Saturday, Sunday, Monday.
$\therefore$ The last day of the next month is Monday.

View full question & answer→

Question 52 Marks

In a certain language if CORONA is coded as 6 and MALARIA is coded as 5 then how CANCER coded?

Answer

$\mathrm{C}=3, \mathrm{O}=15, \mathrm{R}=18, \mathrm{~N}=14, \mathrm{~A}=1$
CORONA $=3+15+18+15+14+1$
$=\frac{66}{11}=6$
$\mathrm{M}=13, \mathrm{~A}=1, \mathrm{~L}=12, \mathrm{R}=18, \mathrm{I}=9$
MALARIA $=13+1+12+1+18+9+1$
$=\frac{55}{11}=5$
CORONA $\rightarrow 6$
MALARIA $\rightarrow 5$
CANCER
$=3+1+14+3+5+18$
$=\frac{44}{11}=4$
Thus CANCER is coded as '4'

View full question & answer→

Question 62 Marks

Arrange the following words in a logical and meaningful order.
1. Country 2. Furniture 3. Forest 4. Wood 5. Trees

Answer

From the forest, given words, we can say that country contains forest, for has trees, trees have wood that is used to make furniture, Hence, the correct order of the given words is $1,3,5,4,2$.

View full question & answer→

Question 72 Marks

A takes 2 hours more than B to walk $d \mathrm{~km}$, but if A doubles his speed, then he can make it in 1 hour less than $B$. How much time does $B$ require for walking $d \mathrm{~km}$ ?

Answer

Suppose B takes $x$ hours to walk $d$ km. Then A takes $(x+2)$ hours to walk d km.
A's speed $=\left(\frac{d}{x+2}\right) \mathrm{km} / \mathrm{hr}$, B's speed $=\left(\frac{d}{x}\right) \mathrm{km} / \mathrm{hr}$
A's new speed $=\left(\frac{2 d}{x+2}\right) \mathrm{km} / \mathrm{hr}$
It is given that
$\frac{d}{\left(\frac{d}{x}\right)}-\frac{d}{\left(\frac{2 d}{x+2}\right)}=1$
$\Rightarrow x-\left(\frac{x+2}{2}\right)=1 \Rightarrow 2 \mathrm{x}-\mathrm{x}-2=2 \Rightarrow \mathrm{x}=4$

View full question & answer→

Applied Maths 2 Marks Questions

Test yourself on this topic