11) \begin{aligned}
46^2 - (?)^2 = 4398 - 3066
\end{aligned}
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12) 1939392 * 6
- 1) 1212120010
- 2) 1212120000
- 3) 1212120011
- 4) 1212121010
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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
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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}
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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
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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
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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
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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
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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
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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}
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