Explanation

Let's analyze the differences between consecutive terms:

• 20 - 11 = 9
• 35 - 20 = 15
• 56 - 35 = 21
• 83 - 56 = 27

The differences are increasing by 6 each time. So, the next difference should be 27 + 6 = 33.

Therefore, the next term in the series is 83 + 33 = 116.

Explanation

We are given:

• A got more points than B but less than C.
• D got less points than E but more than A.
• C gets less than D.

We know the following:

• C > A > B
• E > D > A
• C < D

Thus, the points order is:

• E has the highest points.

Explanation

We are given:

• 4 boxes with weights: 20 kg, 30 kg, 50 kg, and 70 kg.

We need to determine which total weight cannot be made by combining these boxes.

Let's check the combinations:

1. 20 + 30 + 50 + 70 = 170 kg
2. 20 + 30 + 50 = 100 kg
3. 20 + 30 + 70 = 120 kg
4. 20 + 50 + 70 = 140 kg
5. 30 + 50 + 70 = 150 kg

Now check if 160 kg can be made:

• The possible combinations do not result in 160 kg.

Explanation

We are given:

• A clock is placed on a table such that at 6:00 pm, the hour hand points to North-East.
• We need to find the direction the minute hand points at 9:15 pm.

At 6:00 pm, the clock is rotated, and the hour hand is pointing North-East. This means the clock's orientation is shifted by 45 degrees.

At 9:15 pm:

• The minute hand will be at the 3 o'clock position, which is 15 minutes past.
• Since the clock is rotated by 45 degrees, the minute hand will point in the South-East direction (shifted by 45 degrees from the usual position).

(A) South-East

Explanation

• Saima has more than only Mehak.
• Badar has more than Dawood but less than Adil.

From this, we can conclude that Adil has the highest amount of money.

Answer: (C) Adil

Explanation

Let's analyze the given relationships:

• P is the brother of Q and R.
• S is the mother of R.
• T is the father of P.

From this, we can deduce:

• T is also the father of Q (since P and Q are siblings).
• P is also the son of S (since S is R's mother and P and R are siblings).
• S is also the mother of P (as explained above).

Therefore, all the statements except (D) Q is T's son are true.

Explanation

We are given four words:

1. Apparent
2. Apostate
3. Appoint
4. Apparel

Let's arrange them in the order they appear in a dictionary:

• First, compare the first letter of each word (all start with "A").
• Next, compare the second letters:
  • "p" (for "Apparent", "Appoint", "Apparel", "Apostate")
  • Then, compare the third letter:
    • "p" (Apparent, Appoint, Apparel)
    • "o" (Apostate)
  • "Apparel" comes after "Appoint" and before "Apparent"
  • "Appoint" comes after "Apparent"

So, the correct order is:

1. Apparent
2. Apparel
3. Appoint
4. Apostate

Explanation

There are:

• 8 red toys
• 6 green toys
• 7 blue toys

The total number of toys is:

$$8+6+7=21\text{toys}$$

We are asked to find the probability that the toy picked is neither red nor green, which means it must be blue.

The number of blue toys is 7, so the probability is:

17​/21=1/3​

Explanation

We are given:

• 27 bicycles passed the lights test.
• 21 bicycles passed the brakes test.
• 1 bicycle failed both tests.
• There are 30 bicycles in total.

Let:

• $L$ be the set of bicycles that passed the lights test.
• $B$ be the set of bicycles that passed the brakes test.

We need to find how many bicycles passed both tests, which is the intersection of sets $L$a nd $B$, or $L cap B$.

The formula for the union of two sets is:

$$|L\cup B|=|L|+|B|-|L\cap B|$$

We know:

• $|L cup B| = 30 - 1 = 29$ (since 1 bicycle failed both tests).
• $|L|=27$
• $|B| = 21$

Substitute the values into the formula:

$$29 = 27 + 21 - |L cap B|$$ $$29 = 48 - |L cap B|$$ $$|L cap B| = 48 - 29 = 19$$

Explanation

we use the formula:

$$\text{Total Surface Area}=2\pi r(h+r)$$

Where:

• $r$ is the radius of the cylinder.
• $\mathrm{<span\; style="font-family:\; Overpass,\; sans-serif;\; font-size:\; 0.875rem;"><font\; color="\#0000ff">h\; is\; the\; height\; of\; the\; cylinder.</font></span>}$

• Radius $r = 3.5 , text{cm}$
• Height $h = 5.5 , text{cm}$

1. Plug values into the formula:
   $$\text{Total Surface Area}=2\pi \times 3.5\times (5.5+3.5)$$ $$= 2pi times 3.5 times 9$$=2×3.1416×3.5×9
   =2×3.1416×31.5
   =6.2832×31.5
   ≈198.0cm2