Explanation

Given:

1. Sum of roots: α + β = 2

2. Sum of cubes of roots: α³ + β³ = 98

Step-by-Step Solution

Step 1: Use the identity for α³ + β³

α³ + β³ = (α + β)³ - 3αβ(α + β)

Step 2: Substitute known values

98 = (2)³ - 3αβ(2)

98 = 8 - 6αβ

Step 3: Solve for αβ

98 - 8 = -6αβ

90 = -6αβ

αβ = -15

Step 4: Form the quadratic equation

x² - (α + β)x + αβ = 0

x² - 2x - 15 = 0

The answer is x² - 2x - 15 = 0.

Explanation

tan θ = sin θ/cos θ and cot θ = cos θ/sin θ

tan θ + cot θ = sin θ/cos θ + cot θ = cos θ/sin θ

= sin^2 θ + cos^2 θ/sin θ cos θ

= 1/sin θ cos θ (since sin² θ + cos² θ = 1)

Now, 1/sin θ cos θ = 1/sin θ × 1/cos θ = cosec θ × sec θ = sec θ cosec θ

The answer is sec θ cosec θ.

Explanation

GPS satellites orbit the Earth at an altitude of approximately 20,200 kilometers (12,550 miles).

They travel in medium Earth orbit (MEO). 

Each satellite orbits the Earth in a circular path, completing one orbit roughly every 12 hours.

The GPS constellation consists of 24 satellites, strategically positioned to provide global coverage. 

Explanation

During soap making, glycerin separates by dissolving in the salty (sodium chloride) water layer.

It does not react with sodium chloride or evaporate with steam.

Explanation

Let's calculate the final selling price after two successive discounts of 10% and 5% on the marked price of Rs. 2000.

Step 1:

First discount = 10% of 2000 = 0.10 × 2000 = Rs. 200

Price after first discount = 2000 - 200 = Rs. 1800

Step 2:

Second discount = 5% of 1800 = 0.05 × 1800 = Rs. 90

Price after second discount = 1800 - 90 = Rs. 1710

Final selling price = Rs. 1710

Explanation

Shirt has the short vowel sound /ɜːr/ (as in "hurt" or "bird").

"Ball" and "Read" have long or different vowel sounds.

Explanation

To find the new quantity of cupcakes, let's calculate based on the given ratio of 7:6.

Initial quantity = 360 cupcakes

Ratio increase = 7:6

New quantity = 360 × (7/6) = 420 cupcakes

Explanation

The report clearly states that sales have increased by 20%.

This sentence directly provides specific information, making its meaning explicit.

It clearly communicates the increase in sales without ambiguity or need for interpretation.

Explanation

In 2020–21, India witnessed a massive protest by farmers against three agricultural laws passed by the central government.

Farmers, mainly from Punjab, Haryana, and Uttar Pradesh, camped on the borders of Delhi for months demanding repeal of the laws, which was later done in November 2021.

Explanation

The correct adjective order in English is: opinion → size → color → material → noun.

"Nice (opinion), long (size), pink (color), cotton (material)" is the right sequence before "Kurta".