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- Question
- If n is any odd number greater than 1, then n( n 2 -1 ) is
Options- A. divisible by 96 always
- B. divisible by 48 always
- C. divisible by 24 always
- D. None of these
- Correct Answer
- divisible by 24 always
ExplanationSolving the question by taking two odd numbers greater than 1 i.e. 3 and 5,
for n =3, n( n2 -1 ) = 3( 9 - 1) = 24
for n = 5 n( n2 -1 ) = 5( 25 - 1) = 120
Using option we find that both the number are divisible by 24. - 1. How many factors does 120 contains?
Options- A. 3
- B. 10
- C. 12
- D. 16 Discuss
- 2. A chocolate has 12 equal to pieces Manju gave 1/4 th of it to anju 1/3 th of it to raj and 1/6 th of to fiza The number of pieces of chocolate left with manju is
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
- 3. The sum of two number is 10 Their product is 20. Find the sum of the reciprocals of the two numbers.
Options- A. 1
- B. 3/5
- C. 1/2
- D. 11/6 Discuss
- 4. A man has given one -fourth part of his property to his daughter half part to his sons and one fifth part given as charity. How much part of his his property he has given?
Options- A. 1/20
- B. 19/20
- C. 1/10
- D. 9/10 Discuss
- 5. The positive number, when increased by 10 equals 200 times its reciprocal. What is the number?
Options- A. 100
- B. 10
- C. 20
- D. 200 Discuss
- 6. 7 6n - 6 6n, where n is an integer greater than 0, is divisible by
Options- A. 13
- B. 127
- C. 559
- D. None of these Discuss
- 7. Find the sum of first 25 natural numbers.
Options- A. 432
- B. 315
- C. 325
- D. 335 Discuss
- 8. Find the sum of square of first 35 natural numbers.
Options- A. 14910
- B. 15510
- C. 14510
- D. 16510 Discuss
- 9. Find the sum of cube of first 15 natural numbers.
Options- A. 15400
- B. 14400
- C. 16800
- D. 13300 Discuss
- 10. Find the sum of first 84 even numbers
Options- A. 7140
- B. 7540
- C. 6720
- D. 8832 Discuss
Number System problems
Search Results
Correct Answer: 16
Explanation:
Factors of composite number = (P1 +1)(P2+1)(P3+1)......(Pn+1).
Where P1,P2,P3... Pn are the powers of respective prime factors.
So,
120= 23 x 31 x 51
Factors=(3+1)(1+1)(1+1)=16.
Correct Answer: 3
Explanation:
the number of pieces of chocolate left with manju =1- [(1/4) + (1/3) + (1/6)]
= 1 - [ (3 + 4 + 2)/12)
= 1 - (9/12)
= 3/12
Hence number of piece of chocolate left with in manju is 3
Correct Answer: 1/2
Explanation:
Let the number be a and b Then
a + b = 10 ..........(i)
ab = 20 ........(ii)
Sum of reciprocal = 1/a + 1/b
= (a + b) / ab
= 10/20
= 1/2
Correct Answer: 19/20
Explanation:
Total share given by the person = (1/4) + (1/2) + (1/5)
= (5 + 10 + 4) / 20
=19/20
Correct Answer: 10
Explanation:
Let the positive number be N.
According to the question,
N + 10 = 200 / N
? N2 + 10N = 200
? N2 +10N - 200 =0
? (N - 10)(N + 20) = 0
? N = 10 & N= -20
But N not equal to -20 since N is a positive number
So, the required number is 10
Correct Answer: 127
Explanation:
For n =1
76n - 66n = 76 - 66
? ( 73 )2 - ( 63 )2
? ( 73 - 63 )( 73 + 63 )
= ( 343 - 216 )( 343 + 216 )
= 127 x 559
? it is clearly divisible by 127.
Correct Answer: 325
Explanation:
Sum of first n natural numbers = n(n+1)/2
= 25 ( 25 + 1 ) / 2
= ( 25 x 26 ) / 2
= 325
Correct Answer: 14910
Explanation:
Sum of the square of first n natural numbers = n(n+1)(2n+1) / 6
Given n = 35
? Required sum = ( 35 x 36 x 71 ) / 6
= 14910
Correct Answer: 14400
Explanation:
Sum of cubes of first n natural numbers = [ n(n+1) ]2
Given n = 15
? Required sum = [ ( 15 x 16 ) / 2 ] 2
= (15 x 8 )2
= 1202
= 14400
Correct Answer: 7140
Explanation:
Sum of first n even numbers = n( n +1 )
Given n = 84
? Required sum = 84 ( 84 + 1 )
= 84 x 85
= 7140
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