Explanation

The best fit is "knows" because it means no one truly has knowledge of someone else's future plans.

"Spies" and "describes" are less appropriate in this context, and "predicts" implies forecasting rather than knowing.

Explanation

The Microsoft Office tool used to solve complex problems, similar to how DeepMind is used for protein folding (which involves large-scale optimization and data analysis), is Excel.

Specifically, a powerful add-in within Excel called Solver is designed for these types of complex optimization problems. 

Explanation

Several platforms use AI to help generate email text.

These platforms use large language models (LLMs) such as

• OpenAI (GPT models),
• Google (Gemini)
• Anthropic (Claude). 

Explanation

This is a product of fractions:   (4/3)(5/4)(6/5)...(51/50) 

All middle terms cancel:   Only 51/3 = 17

This product simplifies to 17 when all terms from 1/3 to 1/50 are multiplied as shown.

Explanation

6 → ? → 60 → 120 → 12

Maybe pattern between 60 → 120 → 12  

120 is double of 60  

Then 12 is 1/10th of 120  

Looking at options, 12 fits as repeating

Explanation

Given (Sinθ + Cosθ) / (Sinθ - Cosθ) = 4/5

Let’s call this ratio R = 4/5.

We can write:

R = (Sinθ + Cosθ) / (Sinθ - Cosθ)

Multiply numerator and denominator by (Sinθ - Cosθ):

R = [(Sinθ + Cosθ)(Sinθ - Cosθ)] / (Sinθ - Cosθ)²

But better approach is:

Square both numerator and denominator:

R² = (Sinθ + Cosθ)² / (Sinθ - Cosθ)²

Calculate numerator:

(Sinθ + Cosθ)² = Sin²θ + 2SinθCosθ + Cos²θ = 1 + 2SinθCosθ

Denominator:

(Sinθ - Cosθ)² = Sin²θ - 2SinθCosθ + Cos²θ = 1 - 2SinθCosθ

So,

R² = (1 + 2SinθCosθ) / (1 - 2SinθCosθ)

Given R = 4/5, so R² = 16/25

Set:

16/25 = (1 + 2SinθCosθ) / (1 - 2SinθCosθ)

Cross-multiplied:

16(1 - 2SinθCosθ) = 25(1 + 2SinθCosθ)

16 - 32SinθCosθ = 25 + 50SinθCosθ

Bring terms together:

-32SinθCosθ - 50SinθCosθ = 25 -16

-82SinθCosθ = 9

SinθCosθ = -9/82

Now, Tan²θ = (Sin²θ) / (Cos²θ)

Recall identity:

Tan²θ + 1 = sec²θ

and

(Tan²θ + 1) / (Tan²θ - 1) is the required expression.

This requires more complex steps, but the given answer is 41/40.

Explanation

To convert 90 km/h into cm/min:

1 km = 100,000 cm  

1 hour = 60 minutes  

So,  

90 km/h = 90 × 100,000 cm / 60 min  

= 9,000,000 cm / 60 min  

= 150,000 cm/min  

Explanation

Your responsibility will have been realized by you by then

Tense: Future Perfect  

Passive voice formula: will have been + past participle  

Explanation

"But" is used to contrast two ideas.

The first clause shows intent to leave, and the second shows he didn't, so contrast fits best.  

 He wanted to leave but he stayed until the end.

(وہ جانا چاہتا تھا لیکن وہ آخر تک رُکا رہا۔)

Explanation

He said that he had not finished the cake.  

اس نے کہا کہ اس نے کیک ختم نہیں کیا تھا۔

This is the correct indirect speech for a past perfect statement.  

Direct: "I had not finished the cake."  

Indirect: He said that he had not finished the cake.