Correct Answer: directly proportional

Solution : The correct option is directly proportional.

Distance is the measure of how far an object has travelled, typically measured in units such as metres or kilometres.

Distance is a scalar quantity, meaning it has only magnitude and no direction.

Correct Answer: 60 km

Solution : Let the distance between the two stations be $x$ km.
So, the speed of the train is $\frac{x}{\frac{45}{60}}=\frac{4x}{3}$ km/hr
According to the question,
$\frac{x}{\frac{4x}{3}-5}=\frac{48}{60}$
⇒ $\frac{x}{\frac{4x-15}{3}}=\frac{48}{60}$
⇒ $\frac{3x}{4x-15}=\frac{4}{5}$
⇒ $16x-60=15x$
⇒ $x=60$ km
Hence, the correct answer is 60 km.

Correct Answer:

Solution : As per mirror image properties, closer things appear close to the mirror in reflection.
According to the information provided, the mirror is placed at the top of the figure (on Line MN). So, the top of the reflected image will appear at the bottom, and the

Correct Answer: Neolithic

Solution : The correct option is Neolithic.

Çatalhöyük was one of the most famous archaeological sites during the Neolithic period, specifically between approximately 7500 and 5700 BCE. It is located in what is now modern-day Turkey.

• Mesolithic: Middle Stone Age Period People were mainly hunters.
• Palaeolithic: Old

Correct Answer: a fact

Solution : The correct solution is the fourth option: a fact.

Explanation: The phrase It is the true fact contains redundancy, as both true and fact convey a similar meaning. The word fact itself implies truth, so the modifier true is unnecessary.

A fact simplifies

Correct Answer: I, II

Solution : The correct answer is I, II.

Soil erosion is a negative environmental phenomenon in which upper fertile layer of soil is washed away. It is exacerbated because of human activities like deforestation, over grazing, extensive farming practices etc.

It could be corrected by steps

Correct Answer: suggest that you

Solution : The correct choice is the second option.

Explanation: The verb "suggest" is often followed by the conjunction "that" when introducing a subordinate clause that contains the proposed action or idea.

In this case, the recommended construction is "I

Correct Answer: Tonight This Savage Rite

Solution : The Correct Answer is Tonight This Savage Rite

This book of love poems was put together by two eminent poets, Kamala Das and Pritish Nandy. Indian author and poet Kamala Das, formerly known by the pen name Madhavikutty, was from Kerala, India.

Correct Answer: United Arab Emirates

Solution : The correct option is United Arab Emirates.

India had entered into a strategic collaboration with the United Arab Emirates for the purpose of storing crude oil in the southern region of India. This agreement granted the Gulf OPEC nation the capacity to store

Correct Answer: 0

Solution : $(x+y)^3+8(x-y)^3=(3 x+A y)\left(3 x^2+B x y+C y^2\right)$
Taking L.H.S.
$(x+y)^3+8(x-y)^3$
$=(x+y)^3+[2(x-y)]^3$
Using identity, $a^3+b^3=(a+b)(a^2-ab+b^2)$
$=[x+y+2(x-y)][(x+y)^2-2(x+y)(x-y)+[2(x-y)]^2]$
$=(3x-y)[(x^2+y^2+2xy) -2(x^2-y^2)+[4(x^2+y^2-2xy]]$
$=(3x-y)[x^2+y^2+2xy -2x^2+2y^2+4x^2+4y^2-8xy]$
$=(3x-y)(3x^2 -6xy+7y^2)$
On comparing the coefficient with R.H.S., we get,
⇒ A = –1
⇒ B =  –6
⇒ C = 7
$\therefore$ (A + B