Correct Answer: 30 ft

Solution :

Let $h$ be the height of the tree and $x$ be the breadth of the river.
From the above figure we get,
$\tan60°=\frac{h}{x}$
⇒ $\sqrt{3}=\frac{h}{x}$
⇒ $x=\frac{h}{\sqrt{3}}$----------(equation 1)
Also, $\tan30°=\frac{h}{x+20\sqrt{3}}$ 
⇒ $\frac{1}{\sqrt{3}}=\frac{h}{x+20\sqrt{3}}$
⇒ $x=h\sqrt{3}–20\sqrt{3}$ ---------(equation 2)
Now equalising the values of $x$ from both

Correct Answer: 30 ft

Solution :

Let $h$ be the height of the tree and $x$ be the breadth of the river.
From the above figure we get,
$\tan60°=\frac{h}{x}$
⇒ $\sqrt{3}=\frac{h}{x}$
⇒ $x=\frac{h}{\sqrt{3}}$----------(equation 1)
Also, $\tan30°=\frac{h}{x+20\sqrt{3}}$ 
⇒ $\frac{1}{\sqrt{3}}=\frac{h}{x+20\sqrt{3}}$
⇒ $x=h\sqrt{3}–20\sqrt{3}$ ---------(equation 2)
Now equalising the values of $x$ from both

Correct Answer: Witness the Night 

Solution : The Correct Answer is Witness the Night 

Witness the Night was written by Kishwar Desai. She followed up Witness the Night, which won the UK's Costa First Novel Award in 2010, with Origins of Love (2012) and Sea of Innocence (2013). In the

Correct Answer: $\sqrt\pi:1$

Solution : Given: A circle and a square have the same area.
We know that the area of the square is $a^2$, where $a$ is its side, and the area of the circle is $\pi\times r^2$, where $r$ is its radius.
According to the question,
$\pi\times r^2=a^2$

Correct Answer: Gram Uday se Bharat Uday Abhiyan

Solution : The correct answer is Gram Uday se Bharat Uday Abhiyan.

The comprehensive scheme aims to promote social harmony and empower people in villages by upgrading Panchayati Raj Institutions with basic amenities such as drinking water, sanitation, etc. This nationwide program

Correct Answer: $5\sqrt{10}$

Solution :

We have, $\mathrm{QT}=25\;\mathrm{cm}$ and $\mathrm{QR=SR}=20\;\mathrm{cm}$
Construction: Join $\mathrm{O_1B}$ and $\mathrm{O_2C}$.
In $\triangle \mathrm{QRT}$,
$⇒\mathrm{QT^2=QR^2+RT^2}$
$⇒\mathrm{RT=15}\;\mathrm{cm}$ 
Inradius of triangle QRT $=\mathrm{\frac{15+20-25}{2} = 5\;\mathrm{cm}}$ 
$⇒\mathrm{O_2C=5\;\mathrm{cm}}$
Since, $\mathrm{O_1B=10}\;\mathrm{cm}$ and $\mathrm{AB=5\;\mathrm{cm}}$
$⇒\mathrm{O_1A= O_1B-AB=5\;\mathrm{cm}}$
$⇒\mathrm{O_2A= O_1B+AB=15\;\mathrm{cm}}$
Use Pythagoras' theorem in $\triangle\mathrm{ AO_1O_2}$
$⇒\mathrm{(O_1O_2)^2=(O_1A)^2+(O_2A)^2=15^2+5^2=250}$
$⇒\mathrm{O_1O_2}=5\sqrt{10}\;\mathrm{cm}$
Hence, the correct answer is $5\sqrt{10}$.

Correct Answer: UQMI

Solution : Given:
DHLP : WSOK :: FJNR : ?

Like, DHLP : WSOK→(DW, HS, LO, PK) are opposite pairs.
Similarly, FJNR : (?)→(FU, JQ, NM, RI) are opposite pairs.

Thus, FJNR is coded as UQMI. Hence, the first option is correct.

Correct Answer: Sincerely

Solution : The correct choice is the fourth option.

Earnestly means with deep sincerity, seriousness, and commitment and sincerely means with genuine and honest intent, truthfulness, or commitment similar in meaning to earnestly.

The meanings of the other options are as follows:

• Wordily: It means an

Correct Answer: 14

Solution : Given: The average of 11 numbers is 7.
Total of 11 numbers = 11 × 7 = 77
If every number is doubled, their total will also be doubled.
So, new total = 77 × 2 = 154
So, new average = $\frac{154}{11}$ = 14

Correct Answer: 73 – 97

Solution : Let's check the options –
First option: 65 – 90→90 – 65 = 25
Second option: 73 – 97→97 – 73 = 24 ≠ 25
Third option: 112 – 137→137 – 112 = 25
Fourth option: 162 – 187→187 – 162 = 25