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11) \begin{aligned} 46^2 - (?)^2 = 4398 - 3066 \end{aligned}

• 1) 23
• 2) 18
• 3) 38
• 4) 28
Ans.   D
Explanation :

12) 1939392 * 6

• 1) 1212120010
• 2) 1212120000
• 3) 1212120011
• 4) 1212121010
Ans.   B
Explanation :
Trick: when multiplying with \begin{aligned} 5^n \end{aligned} then put n zeros to the right of multiplicand and divide the number with \begin{aligned} 2^n \end{aligned} So using this we can solve this question in much less time. \begin{aligned} 1939392 \times 5^4 = \frac {19393920000}{16} = 1212120000 \end{aligned}

13) Simplify (212 * 212 + 312 * 312

• 1) 132288
• 2) 142088
• 3) 142188
• 4) 142288
Ans.   D
Explanation :
Trick: Above equation can be solved by using following formula \begin{aligned} (a^2 + b^2) = \frac{1}{2}((a+b)^2 + (a-b)^2) \end{aligned}

14) Find the unit digit in \begin{aligned} (544)^{102} + (544)^{103} \end{aligned}

• 1) 2
• 2) 4
• 3) 0
• 4) 1
Ans.   C
Explanation :
Required digit is = \begin{aligned} (4)^{102} + (4)^{103} \end{aligned} as \begin{aligned} (4)^2 \end{aligned} gives unit digit 6 so \begin{aligned} (4)^{102} \end{aligned} unit digit is 6 and \begin{aligned} (4)^{103} \end{aligned} unit digit is, unit digit of \begin{aligned} 6 \times 4 \end{aligned}= 4, so answer will be unit digit of 6 + 4 = 0

15) What least value should be replaced by * in 223*431 so the number become divisible by

• 1) 3
• 2) 4
• 3) 5
• 4) 6
Ans.   A
Explanation :
Trick: Number is divisible by 9, if sum of all digits is divisible by 9, so (2+2+3+*+4+3+1) = 15+* should be divisible by 9, 15+3 will be divisible by 9, so that least number is 3.

16) How many terms are there in 2,4,8,16,....,10

• 1) 7
• 2) 8
• 3) 9
• 4) 10
Ans.   D
Explanation :
It is a GP. with r = 2, ie \begin{aligned} 2^1, 2^2, 2^3... \end{aligned} If number of terms is n. Then, \begin{aligned} 2 \times 2^{n-1} = 1024 \end{aligned} => \begin{aligned} 2^{n-1} = 512 \end{aligned} or \begin{aligned} 2 \times 2^{n-1} = 2^9 \end{aligned} so n-1 = 9 => n = 10

17) Which of the following is a prime numb

• 1) 9
• 2) 2
• 3) 4
• 4) 8
Ans.   B
Explanation :
A prime number is a natural number greater than 1 which has no positive divisors other than 1 or itself. So from above options 2 is that number

18) Simplify 586645 * 99

• 1) 5865863355
• 2) 5665863355
• 3) 4865863355
• 4) 4665863355
Ans.   A
Explanation :
Although it is a simple question, but the trick is to save time in solving this. Rather than multiplying it we can do as follows: 586645 * (10000 - 1) = 5866450000 - 586645 = 5865863355

19) What is the largest 4 digit number exactly divisible by

• 1) 9900
• 2) 9999
• 3) 9988
• 4) 9944
Ans.   D
Explanation :
Largest 4 digit number is 9999 After doing 9999 Ã· 88 we get remainder 55 Hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944

20) What is the unit digit in \begin{aligned} (6324)^{1797} \times (615)^{316} \times (341)^{476} \end{aligned}

• 1) 1
• 2) 5
• 3) 7
• 4) 0