Correct Answer: $20 \sqrt{3}$

Solution : The length of the direct common tangent ($D$) between two circles, where \(d\) is the distance between the centres of the two circles and \(r_1\) and \(r_2\) are the radii of the two circles.
$D=\sqrt{d^2 - (r_1 - r_2)^2}$
Given that \(d \) =

Correct Answer: Equatorial current

Solution : The correct answer is Equatorial current.

There are a few reasons for the excessive cold during the winter season in North India, which are: North India is away from the influence of the sea. The cold beans, which are coming from the Caspian Sea,

Correct Answer: 10 cm

Solution :
In $ΔXYZ$,
$\angle YXZ = 90°$
If $\angle Y = θ$, then $\angle Z = 90° - θ$ 
In $ΔXPY$,
$\angle YPX = 90°$ [Given]
⇒ $\angle Y = \angle YXP = θ$ [As XP = PY]
In $ΔXPZ$,
⇒ $\angle XPZ = 90°$

Correct Answer: (4)

Solution : The correct choice is the fourth option.

The sentence is grammatically accurate and doesn't need any change. The sentence conveys the idea that neither of the two persons knew the way to the school to whom the speaker had asked for directions.

Correct Answer: Urea

Solution : The correct option is Urea.

Urea was the first organic substance synthesised in a laboratory. This was a significant discovery in chemistry since it demonstrated that organic molecules could be synthesised from inorganic starting elements. When ammonium cyanate is heated, it decomposes into urea

Correct Answer: K₁ = 1/K₂

Solution : The correct option is K₁ = 1/K₂.

For the chemical reactions: H₂​ + I₂​ ⇌ 2HI and 2HI ⇌ H₂​ + I_2​

The equilibrium constants are given as K_1​ and

Correct Answer: Subhas Chandra Bose

Solution : The correct option is Subhas Chandra Bose.

Subhas Chandra Bose, an Indian nationalist, formed the Indian National Army (INA). To obtain India's independence from British colonial control with the aid of Imperial Japan during World War II, he founded the INA in

Correct Answer: 38

Solution : Given: 
3, 6, 11, 18, 27, ?

Add consecutive odd numbers starting from 3 to each number of the series to obtain the next number.
3 + 3 = 6; 6 + 5 = 11; 11 + 7 = 18; 18 + 9 = 27;

Correct Answer: 7

Solution : Given:
1. CHAP ⇒ 9756 
2. PACE ⇒ 5963

By comparing the coded words, we find that –
In words 1 and 2, C, A, P and 9, 5, 6 are common.
The remaining letters and code in word 1 are H and 7 and

Correct Answer: Loss = Rs. 2800

Solution : Given:
First watch price = Rs. 12,000
Profit percentage = 10%
⇒ Profit on the first watch = $\frac{10}{100} ×$ 12,000 = Rs. 1,200
Second watch price = Rs. 20,000
Loss percentage = 20%
⇒ Loss on the second watch = $\frac{20}{100}