The Correct answer is Option 3

Key Points

If the numbers are 1 and 11, there are two numbers between them that are divisible by 5 (i.e. 5 and 10).

However, if we consider the numbers 5 and 15, there is only one number between them that is divisible by 5 (i.e. 10).

Hence, there can be one or two such numbers in the given range, depending on the range we choose.

Hence the Correct answer is Option 3. 

The Correct answer is Option 1

Key Points

Given that: 0 < x < 1

Statement I: x² > x³

This statement is correct.

For example, let value of x be 0.5.

x² = 0.5² = 0.25

x³ = 0.5³ = 0.125

Statement II: x > √x

Let’s check with the help of an example.

If x = 0.25

Then, √x = √0.25 = 0.5

So, it’s evident that this statement is not correct.

Hence, option (a) is the correct answer.

The Correct answer is Option 1

Key Points

Let p is x more than the average, and q is x less than the average.

So, p = k + x, q = k – x

We also know that, the average of p, q and r is k.

So, (p + q + r)/3 = k

Or {(k + x) + (k - x) + r} / 3 = k

Or 2k + r = 3k

Or, r = k

Hence the Correct answer is Option 1. 

The Correct answer is Option 3

Key Points

Total numbers = 11

For Value I:

Minimum value of average is possible when the numbers being considered are the smallest possible.

Smallest 11 consecutive numbers ≥ -5 are: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5

Their average, Value I = 0

Value II:

Smallest non-negative integer is 0.

So, the minimum possible value of the product of consecutive non-negative integers, Value II = 0

So, Value I = Value II

Hence the Correct answer is Option 3. 

The Correct answer is Option 3

Key Points

Given that p + q = 10, where p and q are integers.

When sum of two numbers is constant, their multiple is the maximum when their values are as close as possible.

So, Value I = 5 × 5 = 25

For p × q to be maximum, they both must be negative or both positive.

The maximum value of p × q, when both numbers are negative = (-6) × (-4) = 24

The maximum value of p × q, when both numbers are positive = 5 × 5 = 25

So, Value II = 25

Hence, Value I = Value II 

Hence the Correct answer is Option 3. 

सही विकल्प 2 है।Key Pointsसही मिलान होगा-

सही विकल्प 3 है।Key Pointsसही मिलान है-

The correct answer is Option 1

Key PointsTo find the remainder when 
⇒ S=1+(1×2)+(1×2×3)+…+(1×2×3×…×500) is divided by 8, so we can analyze the terms in the series.
⇒ The nth term of the series is  n! (n factorial). We need to find the sum of factorials from  1! to 500! and then find the remainder when this sum is divided by 8.
⇒ Calculating the factorials modulo 8:

• 1!=1≡1 mod 8
• 2!=2≡2mod8
• 3!=6≡6 mod 8
• 4!=24≡0 mod8

⇒  For  n≥4 n! will always be divisible by 8 (since  4! and higher factorials include the factors 2 and 4). Thus, we only need to

consider the first three terms:
⇒  S≡1+2+6 mod 8
Calculating this:
⇒  S≡1+2+6=9 ≡1 mod 8
Therefore, the remainder when 
S is divided by 8 is  1.

The Correct answer is Option 1. 

Key Points

• A tree’s trunk grows primarily from the tips (apical meristems) rather than pushing older wood upward. Although the trunk thickens (increases in girth) over time due to lateral growth, any fixed point along its length does not shift significantly up or down.
• Therefore, a nail driven into the trunk at 1 m above the ground will still be at roughly the same height two years later, even though it may become more embedded as the trunk thickens. Hence Correct answer is Option 1. 

The Correct answer is Option 4. 

Key Points

Express each hand’s angle from 12 o’clock:

Minute hand speed: 6° per minute.

Hour hand speed: 0.5° per minute, with a 60° head start at 2:00.

Set up the equation for coincidence:

Let t be the number of minutes after 2:00. We want the minute hand’s angle to equal the hour hand’s angle:

6t  =  60  +  0.5t

Simplifying:

6t − 0.5t = 60 → 5.5t = 60 → t = 60 / 5.5 = 120 / 11 = 10 10⁄11 minutes

Therefore, the hands coincide at 10 10⁄11 minutes past 2, 

Hence Correct answer is Option 4. 

The Correct answer is Option 3. 

Key PointsX/Y = Y/Z ( Equation )​

⇒ XZ = Y²

⇒ Here, Y = 15 , Means XZ = 225 

⇒ Factroize = 3 x 5 x 3 x 5 

⇒ Case 1 = 3 x 3 x 5 x 5 = 9 x 25 

Let Put X = 9 , Y= 15 , Z = 25 , Put in Above Equation 

⇒ 9/15 = 15/25 , This is Perfect as per equation 

⇒ Hence X + Y + Z =  9 + 15 + 25 = 49 

Hence Correct answer is Option 3. 

The correct answer is Option 4. 

Key PointsCalculate the first five multiples of each number:

• For 11:  11,22,33,44,55
• For 12:  12,24,36,48,60
• For 13:  13,26,39,52,65
• For 14:  14,28,42,56,70
• For 15:  15,30,45,60,75
• For 16:  16,32,48,64,80
• For 17:  17,34,51,68,85
• For 18:  18,36,54,72,90
• For 19:  19,38,57,76,95
• For 20:  20,40,60,80,100

Sum the first five multiples for each number:

• Sum for 11:  11+22+33+44+55=165
• Sum for 12:  12+24+36+48+60=180
• Sum for 13:  13+26+39+52+65=195
• Sum for 14:  14+28+42+56+70=210
• Sum for 15:  15+30+45+60+75=225
• Sum for 16:  16+32+48+64+80=240
• Sum for 17:  17+34+51+68+85=255
• Sum for 18:  18+36+54+72+90=270
• Sum for 19:  19+38+57+76+95=285
• Sum for 20:  20+40+60+80+100=300

Total sum of all these sums:
Total Sum=165+180+195+210+225+240+255+270+285+300
Calculating this step-by-step:

• 165+180=345
• 345+195=540
• 540+210=750
• 750+225=975
• 975+240=1215
• 1215+255=1470
• 1470+270=1740
• 1740+285=2025
• 2025+300=2325

Calculate the average: There are 10 numbers (from 11 to 20), and each has 5 multiples, so we divide the total sum by 
10×5=50

Average=232550=46.5
Thus, the average of the first five multiples of each of the numbers from 11 to 20 is  46.5

The Correct answer is Option 1. 

Key Points

Identify the small “inner” triangles:

There are 6 small triangles formed directly by the intersecting lines.

Combine small triangles to form larger ones:

You can form 3 “medium” triangles by joining pairs of those small triangles.

You can form 2 more “medium” triangles by joining three small triangles at once.

Include the outermost triangle: The large boundary triangle itself counts as 1 more.

When you add them all up:

6 (small) + 3 (medium, using 2 small ) + 2 (medium, using 3 small ) + 1 (largest outer triangle) = 12 Triangles 

Hence Correct answer is Option 1. 

सही विकल्प 4 है।Key Points

The Correct answer is Option 4. 

Key Points

Here you can Understand through Given Diagram