It's a Question of your Career!

Correct Answer: 18 cm

Solution :
Given: $\triangle ABC$ is an isosceles triangle with $AB = AC = 15$ cm.
$AD \perp BC$ 
So, $AD = 12$ cm.
Also, $BD = DC$.
Using Pythagoras theorem in $\triangle ABD$,
$(BD)^2=(AB)^2–(AD)^2$
$⇒BD=\sqrt{(AB)^2–(AD)^2}$
$⇒BD=\sqrt{(15)^2–(12)^2}$
$⇒BD=\sqrt{(15–12)(15+12)}$
$⇒BD=\sqrt{3\times27}$
$⇒BD=9$ cm
$BC = 2 \times BD

Correct Answer: 3 : 7

Solution : Let's assume that the ratio in which the two types of sugar are mixed is $x:y$
The cost of sugar of Rs. 30 per kg is 30$x$
The cost of sugar of Rs. 40 per kg is 40$y$
The mixture is worth Rs.

Correct Answer: $3x^{2}-6x+3=0$

Solution : An equation has equal roots if its discriminant is zero. The discriminant of a quadratic equation $ax^{2}+bx+c=0$ is given by $b^{2}-4ac$.
Option (i):
$3x^{2}-6x+2=0$
So, $D=(-6)^{2}-4×3×2=36-24$
$\therefore D=12$ > 0
Option (ii):
$3x^{2}-6x+3=0$
So, $D=(-6)^{2}-4×3×3=36-36$
$\therefore D=0$
Option (iii):
$x^{2}-8x+8=0$
So, $D=(-8)^{2}-4×1×8=64-32$
$\therefore D=32$ >

Correct Answer: Raunak Sadhwani

Solution : The correct answer is Raunak Sadhwani.

Raunak Sadhwani became the 65th Indian Grandmaster at the age of 13 years. The Grandmaster is the title award for the chess player by the world chess organisation FIDE (Federation Internationale des Echecs or International Chess Federation). 

Correct Answer: Pneumatic rubber tyre

Solution : The correct option is a Pneumatic rubber tyre.

The pneumatic rubber tyre is said to have been invented by John Boyd Dunlop. Dunlop invented the first workable pneumatic tyre for bicycles in 1887. He placed an air-filled rubber tube around a bicycle

Correct Answer: $4$

Solution :

Given that $AP=QC$, $AB=\operatorname{12 units}$ and $AQ=\operatorname{2 units}$
Let $AP=QC=x\operatorname{ units}$
Since $PQ$ is parallel to $BC$, then,
$\Delta ABC\sim\Delta APQ$
Since the triangles are similar, the ratios of their corresponding sides are equal.
$\frac{AP}{AB}=\frac{AQ}{AC}$
⇒ $\frac{x}{12}=\frac{2}{2+x}$
⇒ $2x+x^2=24$
⇒ $x^2+2x-24=0$
⇒ $(x+6)(x-4)=0$
⇒ $x=4$

Correct Answer: INR 37,500

Solution : Royalty = 15% and Paper cost = 25%
So, 15% is equivalent to INR 22,500
Therefore, 25% is equivalent to $(22500×\frac{25}{15})$ = INR 37,500
Hence, the correct answer is INR 37,500.

Correct Answer: Ministry of Health and Family Welfare

Solution : The correct answer is the Ministry of Health & Family Welfare.

The Ayushman Bharat Digital Mission was implemented by the Ministry of Health & Family Welfare. This mission aims to create unique account numbers for its citizens. The mission

Correct Answer: assume

Solution : The correct choice is the fourth option.

Assume means supposed to be the case, without proof. It helps convey that nature has been suffering mutely for hundreds of years but the problem was not addressed until now.

Correct Answer: in

Solution : The correct choice is the second option.

Explanation: The preposition "in" is the correct choice to indicate the duration within which the action will take place. In this context, it signifies that the person will be joining the office within the time span of