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Question 1 of 5
1. Question
What is the harmonic mean of 10, 20, 25, 40 and 50?
Correct
Ans: d
Let the numbers be a1 = 10, a2 = 20, a3=25, a4 = 40 and a5 = 50
\Harmonic mean = (Number of observations)/[(1/a1)+(1/a2)+(1/a3)+(1/a4)+(1/a5)]
= 5/[(1/10)+(1/20)+(1/25)+(1/40)+(1/50)] = 5/[20+10+8+5+4]/200
= [(5´ 200)/47] = (1000/47) = 21.27=21.3
Incorrect
Ans: d
Let the numbers be a1 = 10, a2 = 20, a3=25, a4 = 40 and a5 = 50
\Harmonic mean = (Number of observations)/[(1/a1)+(1/a2)+(1/a3)+(1/a4)+(1/a5)]
= 5/[(1/10)+(1/20)+(1/25)+(1/40)+(1/50)] = 5/[20+10+8+5+4]/200
= [(5´ 200)/47] = (1000/47) = 21.27=21.3
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Question 2 of 5
2. Question
Consider the following statements
- Every integer is a rational number
- Every rational number is a real number
Which of the above statement(s) is /are correct?
Correct
Ans: c
- It is true that every integer is a rational number.
E.g. Set of integers, Z = [……..,13/1 , -2/1, -1/1, 0/1, 1/1, 2/1, 3/1,…….]
Which is of the form p/q, which also show rational numbers.
- It is also true that every rational number is a real number because a real number does not contain I (iota).
So, both statements are true.
Incorrect
Ans: c
- It is true that every integer is a rational number.
E.g. Set of integers, Z = [……..,13/1 , -2/1, -1/1, 0/1, 1/1, 2/1, 3/1,…….]
Which is of the form p/q, which also show rational numbers.
- It is also true that every rational number is a real number because a real number does not contain I (iota).
So, both statements are true.
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Question 3 of 5
3. Question
Which one of the following has least number of divisors?
Correct
Ans: b
Here, 88 = 2x 2x 2 x11 = (2)3 x (11)1
91= (7)1 x (13)1
96=2 x2 x2x 2 x2x 3 = (2)5 x (3)1
And 99 = 3 x 3 x 11 = (3)2x (11)1
So, 91 has least number of divisors.
Incorrect
Ans: b
Here, 88 = 2x 2x 2 x11 = (2)3 x (11)1
91= (7)1 x (13)1
96=2 x2 x2x 2 x2x 3 = (2)5 x (3)1
And 99 = 3 x 3 x 11 = (3)2x (11)1
So, 91 has least number of divisors.
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Question 4 of 5
4. Question
Which one of the following is neither prime number nor composite number?
Correct
Ans: a
We know that, a counting number is called a prime number when it has exactly two factors, 1 and itself. A prime number is always greater than 1.
Composite number are non-prime natural numbers. The must have atleast one factor apart from 1 and itself. 1 is not a composite number.
Hence, 1 is neither prime number nor composite number.
Incorrect
Ans: a
We know that, a counting number is called a prime number when it has exactly two factors, 1 and itself. A prime number is always greater than 1.
Composite number are non-prime natural numbers. The must have atleast one factor apart from 1 and itself. 1 is not a composite number.
Hence, 1 is neither prime number nor composite number.
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Question 5 of 5
5. Question
If the sum of an Integer and its reciprocal is 10/3, then the integer is equal to
Correct
Ans: a
Let the integer be x.
Now, by condition
Integer+Its reciprocal = 10/3
X+(1/x) = 10/3 ⇒(x2+1)/x = 10/3
3x2 + 3 = 10x ⇒ 3x2 – 10x +3 =0
3x2-9x-x+3=0 [by splitting the middle term]
3x(x-3)-1(x-3)=0 ⇒ (x-3)(3x-1)=0
∴x = 3 [since, 1/3 is not an integer]
Incorrect
Ans: a
Let the integer be x.
Now, by condition
Integer+Its reciprocal = 10/3
X+(1/x) = 10/3 ⇒(x2+1)/x = 10/3
3x2 + 3 = 10x ⇒ 3x2 – 10x +3 =0
3x2-9x-x+3=0 [by splitting the middle term]
3x(x-3)-1(x-3)=0 ⇒ (x-3)(3x-1)=0
∴x = 3 [since, 1/3 is not an integer]
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