Correct Answer: Personal Income (PI) – Personal tax payments – Non-tax payments

Solution : The correct answer is Personal Income (PI) - Personal tax payments - Non-tax payments.

Disposable income, also known as disposable personal income, refers to the money left over after income taxes are deducted for household consumption, savings, and expenditure. It is calculated to assess the general state of the national economy.

Correct Answer: 20%

Solution : Kartik's marks = 80
Total marks = 80 + 90 + 75 + 70 + 85 = 400
Percentage required = $\frac{80}{400}$ × 100 = 20%
Hence, the correct answer is 20%.

Correct Answer: Wall clock

Solution : As per the graph,
(i) Wristwatch
The sales in 2010 = 28.3 lakhs
The sales in 2005 = 21.3 lakhs
Percentage increase = $\frac{28.3-21.3}{21.3}$ × 100 = 32.71%
(ii) Table clock
The sales in 2010 = 22.3 lakhs
The sales in 2005 = 9.5 lakhs
Percentage increase = $\frac{22.3-9.5}{9.5}$ × 100 = 134.73%
(iii) Wall clock
The sales in 2010 = 32.7 lakhs
The sales in 2005 = 30.7 lakhs
Percentage increase = $\frac{32.7-30.7}{30.7}$ × 100 = 6.51%
During the period 2005-2010, the minimum rate of increase in sales is in the product of wall clock.
Hence, the correct answer is wall clock.

Correct Answer: (1)

Solution : The error lies in the first part of the sentence.

The sentence contains one grammatical error. The definite article the should be used before ordinal numbers and sequence numbers. The addition of the makes the sentence grammatically accurate and conveys the intended meaning of the sentence.

Correct answer: "I was the first to reach the school today."

Correct Answer: Only conclusion II and IV follow

Solution : Let's evaluate the conclusions based on the given statements:

Statements

1. Some cars are buses.
2. All cars are caves.

Venn diagram

Now, let's consider each conclusion:

I. Some caves are not buses.

• This conclusion is not true based on the given statements. Since some cars are buses (Statement 1) and all cars are caves (Statement 2), it does not logically follow that some caves are not buses. Some caves are only for cars and nothing can be said about being buses or not.

II. Some caves are buses.

• This conclusion is also true based on the given statements. Statement 1 states that some cars are buses, and since all cars are caves (Statement 2), it follows that some caves are indeed buses.

III. No cave is a bus.

• This conclusion is not true based on the given statements. Statement 1 explicitly states that some cars are buses, which means there is at least one cave (cars) that is also a bus.

IV. Some caves are cars.

• This conclusion is true based on the given statements. Since all cars are caves (Statement 2) and some cars are buses (Statement 1), it logically follows that some caves are cars.

In summary, conclusions II and IV are true based on the given statements, while conclusions I and III are not true.

Hence, the third option is correct.

Correct Answer: Calcium carbonate

Solution : The correct option is Calcium carbonate.

The interaction between carbon dioxide and calcium hydroxide produces a white precipitate, calcium carbonate (CaCO₃) when carbon dioxide is passed through lime water. This is used to detect the presence of carbon dioxide. The chemical equation for the interaction of carbon dioxide (CO₂) and lime water (calcium hydroxide, Ca(OH)₂) is as follows: Ca(OH)₂ + CO₂ → CaCO₃ + H₂O. Calcium hydroxide combines with carbon dioxide to form calcium carbonate (a white precipitate) and water.

Correct Answer: Only conclusion II follows

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

Let's analyse the conclusions –
Conclusion (I): Some boxes are plates – From the Venn diagram, it is evident that there is no direct relation between boxes and plates. So, no definite relation can be drawn. Therefore, this conclusion does not follow.
Conclusion (II): Some trays are pens – From the Venn diagram, it is evident that some parts of the circle representing trays lie outside the circle representing pens while some lie inside. So, it can be concluded that some trays are pens.
Conclusion (III): Some boxes are pens – From the Venn diagram, it is evident that there is no direct relation between boxes and pens. So, no definite relation can be drawn. Therefore, this conclusion does not follow.
Conclusion (IV): No tray is a plate – From the Venn diagram, it is evident that some parts of the circle representing trays lie outside the circle representing plates while some lie inside. So, this conclusion does not follow.

So, the only conclusion II follows. Hence, the first option is correct.

Correct Answer: Fungal enzymes

Solution : The correct answer is Fungal enzymes​​​​.

Fungal enzymes decompose detritus (dead organic matter) into simpler inorganic substances. Fungi are decomposers in ecosystems, and their enzymes help break down complex organic compounds in detritus into smaller molecules like simple sugars and other organic and inorganic compounds. This process is essential for nutrient cycling in ecosystems.

Correct Answer: 560

Solution : Given:
$a+b-c=20$ and $a^2+b^2+c^2=152$
$ a+b-c = 20$
Squaring both sides, we get,
⇒ $a^2 + b^2+c^2 + 2ab-2bc-2ca = 400$
⇒ $2(ab-bc-ca) = 400-152$
⇒ $ab-bc-ca = 124$
Now to find, $a^3+b^3-c^3+3abc$
$= (a+b-c)(a^2+b^2+c^2-(ab-bc-ca))$
$= 20\times (152-124)$
$= 20\times 28 = 560$
Hence, the correct answer is 560.

Correct Answer: 12.5% gain

Solution : Let the cost price of 1 gm be Rs. 1.
The cost price of 28 gm = Rs. 28
The cost price of 36 gm = Rs. 36
Selling price after 12.5% loss on 36 gm packet = $\frac{100-12.5}{100}\times 36$ = Rs. 31.5
Here the cost price is denoted by CP, the selling price is denoted by SP.
Profit% = $\frac{SP-CP}{CP}\times 100$
= $\frac{31.5-28}{28}\times 100$
= 12.5%
Hence, the correct answer is a 12.5% gain.