Explanation

• Physical (bodily health and well-being)
• Intellectual (mental abilities and knowledge)
• Emotional (feelings and emotional intelligence)
• Social (relationships and social skills)
• Moral (values and character)
• Aesthetic (appreciation for beauty and creativity)
• Spiritual (beliefs and values related to existence and purpose)

Explanation

Volume of tank = 200 m x 150 m x 2 m = 60,000 m³

Volume of water flowing per second = (1.5 m x 1.25 m) x (20 km/h x (1000/3600)) = 208.33/9 m³/s

Time taken to fill the tank = 60,000 m³ / (208.33/9 m³/s) = 2600 seconds

Convert seconds to minutes = 2600 s / 60 = 43.33 minutes

Time taken to fill 2 meters = 43.33 x (2/3) = 96 minutes

Explanation

• Competitions can motivate students to learn by providing a sense of challenge and encouraging them to strive for excellence.
• However, it's important to use competitions judiciously, as they may not be motivating for all students and can have negative consequences if overemphasized.

Explanation

The number of new words that can be formed by rearranging the letters of the word "ALIVE" is:

5! (5 factorial) = 5 × 4 × 3 × 2 × 1 = 120

However, we need to subtract 1 because the original word "ALIVE" is also a possible arrangement.

So, the correct answer is:

120 - 1 = 119

Explanation

Convert the race distance from 1 km to meters: 1 km = 1000 m

Find the distance covered by X in the race: 48 m (given)

Find the distance covered by Y in the race: 42 m (given)

Since X beats Y, X covers the entire race distance (1000 m), while Y covers a shorter distance.

To find the distance by which X beats Y, subtract the distance covered by Y from the race distance: 1000 m - 42 m x (1000/48) = 1000 - 875 = 125 m

So, X beats Y by 125 meters.

Explanation

Principal amount (P) = Rs. 800

Amount after 3 years (A) = Rs. 920

Interest earned (I) = A - P = 920 - 800 = Rs. 120

Rate of interest (R) = (I / P) x (100 / T) = (120 / 800) x (100 / 3) = 5%

New rate of interest (R') = 5% + 3% = 8%

New interest earned (I') = (P x R' x T) / 100 = (800 x 8 x 3) / 100 = Rs. 192

New amount (A') = P + I' = 800 + 192 = Rs. 992

So, if the interest rate is increased by 3%, the amount would be Rs. 992.

Explanation

True Discount (TD) = Rs. 122

Principal (P) = Rs. 2562

Time (T) = 4 months = 1/3 year

Using the formula:

TD = (P x R x T) / 100

where R is the rate percent, we can rearrange the formula to solve for R:

R = (TD x 100) / (P x T)

= (122 x 100) / (2562 x 1/3)

= 15%

So, the rate percent is 15%.

Explanation

When three 6-faced dice are thrown together, the total number of possible outcomes is 6 × 6 × 6 = 216 (since each die has 6 possible outcomes).

The favorable outcomes where all three dice show the same number are:

(1, 1, 1), (2, 2, 2), (3, 3, 3), (4, 4, 4), (5, 5, 5), and (6, 6, 6)

There are 6 favorable outcomes.

The probability of all three dice showing the same number is:

Number of favorable outcomes / Total number of possible outcomes

= 6 / 216

= 1/36

Explanation

Let the principal amount be P.

Simple interest (SI) for 2 years at 8% p.a. = (P x 8 x 2) / 100 = 0.16P

Compound interest (CI) for 2 years at 8% p.a. = P x (1 + 0.08)^2 - P = 0.1664P (approximately)

The difference between CI and SI is Rs. 48, so we can set up the equation:

0.1664P - 0.16P = 48

0.0064P = 48

Now, divide both sides by 0.0064:

P = 48 / 0.0064

P = 7500

So, the principal amount is Rs. 7500.

Explanation

Let the principal amount be P.

Let the original rate of interest be R%.

The interest earned at the original rate for 2 years is (P x R x 2)/100.

If the rate were 4% higher, the interest earned would be (P x (R+4) x 2)/100.

The difference in interest earned is Rs. 60, so we can set up the equation:

(P x (R+4) x 2)/100 - (P x R x 2)/100 = 60

Simplifying the equation:

2P(R+4) - 2PR = 6000

Expanding and simplifying:

8P = 6000

Dividing both sides by 8:

P = 750

So, the sum is Rs. 750.