Tool By Zeal Point

Competive Exam Math 12

Q. What is the unit digit of 63¹⁰⁴?

A. 4 B. 9 C. 7 D. 1

Trick

Calculate the first few powers: 3¹= 3 → last digit 3, = 9 → last digit 9, = 27→ last digit 7 , = 81 → last digit 1

Then the same pattern repeats: 3 → 9 → 7 → 1 → 3 → 9 → 7 → 1...

So, there are 4 numbers in one cycle.

For 3¹⁰⁴: $104 \div 4 = 26$

There is no remainder, so we take the 4th number in the cycle: $1$

Ans: D. 1

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Q. What is the unit digit of 43³²¹?

A. 3 B. 9 C. 7 D. 1

Short Trick : Calculate the first few powers: 3¹= 3 → last digit 3, = 9 → last digit 9, = 27→ last digit 7 , = 81 → last digit 1

Only the last digit 3 matters: 3³²¹

Pattern: 3 → 9 → 7 → 1

Now,

$321 \div 4$

Remainder = 1

So, take the 1st number in the pattern: $3$

Ans: A. 3

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Q. What is the unit digit of 3⁹³ ?

A. 3 B. 9 C. 7 D. 1

Trick

Unit digit pattern of powers of 3: 3 → 9 → 7 → 1

Now: $93 \div 4 = 23 remainder 1$

Remainder 1 → take the 1st number = 3

Ans: A. 3

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Q. What is the unit digit of 23⁶²?

A. 3 B. 9 C. 7 D. 1

Trick

Only the last digit 3 matters: 23⁶²→ 3⁶²

Pattern: 3 → 9 → 7 → 1

Now divide the power by 4: $62 \div 4 = 15 remainder 2$

Remainder 2 → 2nd number = 9

Ans: B. 9

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Q. The greatest number which divides 2000 and 2200 and leaves 22 and 38 respectively as remainders is:

Solution: Practice

????

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Q. Find: √16%

A) 4% B) 16% C) 40% D) 64%

Solution:

Convert the percentage into a fraction: $16% = 16/100$

Therefore,

$\sqrt16/100 = \sqrt16/\sqrt100 = 4/10 = 0.4$

As a percentage: $0.4 \times 100 = 40%$

Ans: C) 40%

Practice Set: Square Root of Percentage

Q1. Find: $\sqrt25%$

A) 5% B) 25% C) 50% D) 75%

Q2. Find: $\sqrt36%$

A) 6% B) 30% C) 60% D) 36%

Q3. Find: $49%$

A) 7% B) 49% C) 70% D) 14%

Q4. Find: $64%$

A) 8% B) 32% C) 64% D) 80%

Q5. Find: $\sqrt81%$

A) 9% B) 18% C) 81% D) 90%

Trick

$\sqrtx% = \sqrtx/10$

For example: $\sqrt16% = 4 = 40%$

Q. Find the average of the first 10 composite numbers.

First 10 composite numbers are: $4,6,8,9,10,12,14,15,16,18$

1st: Find the sum

2nd: Find the average

Ans: (A) 11.2

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Q. What is the average of the first 15 whole numbers ?

The first 15 whole numbers are: $0,1,2,3,4,5,6,7,8,9,10,11,12,13,14$

Trick

For consecutive numbers: $Average = First number + Last number / 2$ $= 0 + 14/2 = 7$

Ans: (C) 7

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Q.If the average of three consecutive numbers is 42, then find the second smallest number.

A) 41 B) 44 C) 42 D) 43

Trick

For three consecutive numbers, the average is always the middle number.

So: $Middle number = 42$

The three numbers are: $41, 42, 43$

Therefore, the second smallest number = 42.

Ans: (C) 42

Trick: 3 consecutive numbers → Average = 2nd number

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