1. Evaluate 1^{3} + 2^{3} + 3^{3} + 4^{3} + 5^{3} = ?
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Correct Ans:225
Explanation:
Given
1^{3}+ 2^{3}+ 3^{3}+ 4^{3}+ 5^{3}
= 1 + 8 + 27 + 64 + 125
= 9 + 27 + 64 + 125
= 36 + 64 + 125
= 100 + 125
= 225
2. Evaluate : sqrt(1 + sqrt( 1 + sqrt(64))) = ?
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Correct Ans:2
Explanation:
sqrt(1 + sqrt( 1 + sqrt(64))) = sqrt(1 + sqrt(1+ sqrt(64))) = sqrt(1 + sqrt(1 + 8) ) = sqrt(1 + 3) = 2
3. A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 59.29, the number of the member is the group is:
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Correct Ans:77
Explanation:
Money collected
= (59.29 x 100) paise
= 5929 paise.
Number of members
= sqrt(5929)
= 77.
4. What is the value of sqrt(1.5625) ?
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Correct Ans:1.25
Explanation:
sqrt(1.5625) = sqrt(15625 / 10000) = sqrt(15625) / sqrt(10000) = 125 / 100 = 1.25
5. Find the least four digit number which is a perfect square.
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Correct Ans:1024
Explanation:
1024 = 32^2.
6. If sqrt(2) = 1.414 then find the value of sqrt(20,000) + sqrt(200) = ?
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Correct Ans:155.54
Explanation:
Sqrt (2) = 1.414 =>
Sqrt(20000) = 141.4
Sqrt(200) = 14.14
Adding these two, we get 155.54
7. 1849 students are sitting in an auditorium in such a manner that there are as many students in a row as there columns in the auditorium. Find the number of rows in the auditorium?
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Correct Ans:43
Explanation:
Let k be the number of rows and columns, then k x k = 1849 => k 2 = 1849
k = 43
8. The product of two numbers is 120. The sum of their squares is 289. Find the sum of two numbers
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Correct Ans:23
Explanation:
Let the numbers be x and y. Given x2 + y2 = 289 and xy = 120.
We know that (x+y)2 = x2 + y2 + 2xy = 289 + 2(120) = 289 + 240 = 529
(x+y)2 = 529 => x+y=23
9. Given n = 12, then find the difference between n^{2} and (n+1)^{2}.
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Correct Ans:25
Explanation:
Given n=12, then n+1 = 13.
(n+1)^{2 }– n^{2} = 13^{2} – 12^{2} = 169 – 144 = 25
10. The number 252 is written as a + b where a and b are consecutive natural numbers. Find the maximum of these two values.
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Correct Ans:312
Explanation:
We know that (2n + 1)2 = (2n2+2n) + (2n2+2n+1),
625 = (25)2 = (2 x 12 + 1)2 = ( 2(12)2 + 2(12) ) + (2 x 122 + 2(12)+1) = 312 + 313
Maximum(312,313) = 313
11. How many natural number lie between the square of the following numbers 12 and 13.
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Correct Ans:24
Explanation:
We know that between n2 and (n+1)2 there are 2n non-perfect square numbers.
So, between 122 and 132, there are 2(12) , that is 24 natural numbers.
12. We can express the number 1681 as the sum of first ___?___ odd natural numbers.
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Correct Ans:41
Explanation:
The number 1681 = 412 can always be expressed as sum of first 41 odd natural number
13. Evaluate: 1 + 3+ 5 + 7 + … + 49
SHOW ANSWER
Correct Ans:625
Explanation:
We know that 1 + 3 + 5 + …+ (2n - 1) = n2.
1 + 3 + 5 + 7 + … + 49 = 252 = 625
14. What will be the unit's digit in the number N^2, if N = 1 + 2 + .. + 35
SHOW ANSWER
Correct Ans:0
Explanation:
Given N = 1 + 2 + … + 35 = (35 x 36)/2 = 35 x 18
N is a number which ends with 0, hence N2 also has to end with 0.
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