Correct Answer: $49 \sqrt{3}$ cm²

Solution : Height of an equilateral triangle = $\frac{\sqrt{3}}{2} \times Side$
Area of an equilateral triangle = $\frac{\sqrt{3}}{4} \times Side^2$
So, each side of the triangle = $\frac{7\sqrt{3}}{\frac{\sqrt{3}}{2}}$ = 14 cm
Area of an equilateral triangle = $\frac{\sqrt{3}}{4} \times 14^2$ = $49\sqrt{3}$ cm²

Correct Answer: 200000

Solution : Given: A mask manufacturing company manufactured an ‘$x$’ number of masks in 2018. It increased its manufacturing capacity by 30% in 2019 and further increased its manufacturing by 15% in 2020.
Mask manufactured in 2019 = $x × \frac{130}{100}$ = $\frac{13x}{10}$
Mask manufactured in 2020

Correct Answer: 1

Solution : Given: $xy = -6$ and $x^3+ y^3= 19$ ($x$ and $y$ are integers)
We know the algebraic identity, $(x+y)^3=x^3 + y^3+3xy(x+y)$.
Substitute the given values in the above formula,
⇒ $(x+y)^3=19+3\times(-6)\times(x+y)$
⇒ $(x+y)^3=19-18\times(x+y)$
Let $(x+y)=u$.
⇒ $u^3+18u–19=0$
⇒ $u^3–u^2+u^2–u+19u–19=0$
⇒ $u^2(u–1)+u(u–1)+19(u–1)=0$
⇒ $(u–1)(u^2+u+19)=0$
⇒ $u-1=0$

Correct Answer: Cartographer

Solution : The correct choice is the first option.

A cartographer is an individual who engages in the practice or art of making maps. Therefore, "cartographer" is the appropriate one-word substitute for the underlined group of words.

Correct Answer: Sodium thiosulphate

Solution : The correct option is Sodium thiosulphate.

Sodium thiosulfate is used in photography as a fixing agent, especially in traditional film and darkroom processes. It is used to fix or stabilise the developed image on photographic paper by removing unexposed silver halide.

Correct Answer: # = AOO, % = PAM

Solution : Given:
# : CLQ :: NDK : %

Let's check the options –
First option: # = AJS, % = MAM
AJS : CLQ→A + 2 = C; J + 2 = L; S – 2 = Q 
NDK :

Correct Answer: 105°

Solution :
KI = IT and EK = ET
$\angle$ KET = 150°
In $\triangle$ KEI and $\triangle$ TEI,
KI = IT [Given]
EK = ET [Given]
EI = EI [Common]
So, $\triangle$ KEI $\cong$ $\triangle$ TEI,
⇒ $\angle$ KEI = $\angle$ TEI
Now,
$\angle$ KET +

Correct Answer: FKQDWE

Solution : Given:
SLAIN is written as PKCNU and DENT is written as VPGF.

Follow the pattern to obtain the required code –

Thus, SLAIN is coded as PKCNU.
And, DENT is written as VPGF.

Thus, DENT is coded as VPGF.
Similarly, follow the same pattern for

Correct Answer: Abridgement

Solution : The correct choice is the fourth option.

Abridgement is a term used to describe a version of a larger work that has been condensed. This involves shortening the original work by omitting details while still preserving the essential content and narrative.

The meanings of

Correct Answer: 48

Solution : Given: The ratio of the triangle's sides
$=\frac{1}{2} : \frac{1}{3} : \frac{1}{4}$.
$=\frac{1}{2} × 12 : \frac{1}{3} × 12 : \frac{1}{4} × 12$
$=6: 4: 3$
The perimeter of the triangle is $104$ cm.
$\therefore$ The longest length of the triangle = $\frac{104}{6+4+3}×6= 48$ cm