Correct Answer: (3)

Solution : The third option is the correct choice.

"Dating back to" is a phrasal verb, which means to exist since a particular time. It implies that the artefacts have existed since prehistoric times.

Therefore, the correct sentence is: The museum's collection includes artefacts dating back to

Correct Answer: 44%

Solution : We know,
$\text{Single discount} = (a+b-\frac{a×b}{100}$)%,
where $a,b$ are successive discounts
$\therefore$ Single discount of two successive discounts of 30% and 20% $=30+20-\frac{30×20}{100}=44$%
Hence, the correct answer is 44%.

Correct Answer: 53

Solution : In the diagram, the shaded parts represent the regions representing students playing only one game.

The number of students that play only one game is the region that does not overlap with any other region. So, the number of students who play only chess is

Correct Answer: Dholavira

Solution : The correct answer is Dholavira.

The cities of the Harappan civilisation flourished on the banks of the Indus River, and these are the earliest cities in the Indian subcontinent. The city of Dholavira is located on the Khadir Bet in the Rann of Kutch

Correct Answer: 352

Solution : Given: $2x+3y=4$ and $4x^2+9x^2=64$
To find: $8x^3+27y^3$
Now,
$2x+3y=4$
Squaring both sides, we get:
⇒ $4x^2+9y^2+12xy=16$
Putting the values, we get:
⇒ $64+12xy=16$
⇒ $12xy=-48$
⇒ $xy=-4$
Now again,
$2x+3y=4$
Cubing both sides, we get:
⇒ $8x^3+27y^3+3×2x×3y(2x+3y)=64$
Putting the values, we get:
⇒ $8x^3+27y^3+18×(-4)×4=64$
$\therefore8x^3+27y^3=64+288=

Correct Answer: Angle of Reflection

Solution : The correct option is the Angle of Reflection.

The angle measured from the reflected ray to the normal surface is called the "angle of reflection." The angle of reflection is the angle between the reflected ray and the normal (a line perpendicular

Correct Answer: 1

Solution : Given: $(x^{b+c})^{b–c}(x^{c+a})^{c–a}(x^{a+b})^{a–b}$ $(x\neq 0)$
= $(x^{(b+c)×(b–c)})(x^{(c+a)(c–a)})(x^{(a+b)×(a–b)})$
= $(x^{(b^{2}–c^{2})})(x^{(c^{2}–a^{2})})(x^{(a^{2}–b^{2})})$
= $x^{(b^{2}–c^{2}+c^{2}–a^{2}+a^{2}–b^{2})}$
= $x^{0}$
= 1
Hence, the correct answer is 1.

Correct Answer: Neither conclusion I nor II follows

Solution : The possible Venn diagram according to the statements is as follows –

Let's analyse the conclusions –
Conclusion (I): Some knives are forks – According to the Venn diagram, there is no definite relation between knives and forks. Therefore, this

Correct Answer: pi

Solution : Given:
1. rocket aeroplane sky stars ⇒ ci pi di ki
2. satellite moon sun sky ⇒ ni ci ui li
3. sky sun stars mars ⇒ ui gi ki ci
4. venus aeroplane moon planet ⇒ di qi mi ni

By comparing all the

Correct Answer: ÷ and ×

Solution : Given:
19 – 39 × 3 + 25 ÷ 5 = 131

Let's check the options –
First option: + and ÷
= 19 – 39 × 3 ÷ 25 + 5 
= 19 – 39 × 0.12 + 5
= 19 –