Correct Answer: 30

Solution : Let the numbers be $x, y, z$.
Their average is 40.
Sum = $x + y + z = 40 × 3 = 120$ --(1)
and given that $x = \frac{1}{3}(y+z)$
⇒ $3x = y + z$
Putting the value of $y+z$ in equation 1,

Correct Answer: 18°

Solution :
In $\triangle$ABC, O is the point of intersection of the bisectors of $\angle$B and $\angle$A
$\angle$BOC = 108° 
If the bisector of $\angle$ABC and $\angle$ACB of a triangle ABC meet at a point O then, $\angle$BOC = $90^\circ + \frac{1}{2}$$\angle$A
⇒ $108^\circ = 90^\circ +

Correct Answer: (4)

Solution : The correct option is the fourth option.

In this sentence, the phrase "a good many" is idiomatic and means "a considerable number" or "a large quantity", so it is appropriate in this context. The other options provided do not improve the sentence

Correct Answer: 1

Solution : The correct option is 1.

Earth's crust is its thick outer layer of rock, accounting for less than 1% of the planet's radius and volume. It is the uppermost layer of the lithosphere, which contains the crust and the upper portion of the mantle.

Correct Answer: P.C. Mahalanobis

Solution : The correct option is P.C. Mahalanobis.

P.C. Mahalanobis was the chief architect of the Second Five-Year Plan of India (1956–1961) and was the head of the National Income Committee. He was crucial in shaping India's strategies for economic development and planning.

Correct Answer: 9 : 6 : 7

Solution : The ratio of investment of A, B, and C is = 5 : 7 : 4
The timing ratio of A, B, and C is = x : y : z
The profits distribution ratio is = 45 : 42 :

Correct Answer: 20 cm

Solution : Here, $r_{1} = 25, r_{2} = 4$
Length of a common tangent = $\sqrt{(r_{1}+r_{2})^{2} - (r_{1}-r_{2})^{2}}$
= $\sqrt{29^{2} - 21^{2}}$
= $\sqrt{841-441}$
= $\sqrt{400}$
= $20$ cm
Hence, the correct answer is 20 cm.

Correct Answer: 11

Solution : Given number = 2918245
Divisibility rule for 3: A number is completely divisible by 3 if the sum of its digits is divisible by 3.
Here, 2 + 9 + 1 + 8 + 2 + 4 + 5 = 31, which is not divisible

Correct Answer: 1

Solution : The first option is the correct choice.

Revolutionised means to completely change something, often in a dramatic or transformative way. In the context of technological advancements, especially the internet, "revolutionised" is the most appropriate term to convey the idea that the internet has brought about

Correct Answer: Rs. 61,773

Solution : The selling price of the iPhone at 12% loss = Rs. 46068
We know that loss% = $\frac{\text{Cost price}-\text{Selling Price}}{\text{Cost price}}\times 100$
⇒ $12=\frac{\text{Cost price}-46068}{\text{Cost price}}\times 100$
⇒ Cost price = Rs. 52350
Also, profit% = $\frac{\text{Selling Price}-\text{Cost price}}{\text{Cost price}}\times 100$
⇒ $18=\frac{\text{Selling Price}-52350}{53350}\times