Test: Arithmetic Mean - JEE MCQ

# Test: Arithmetic Mean - JEE MCQ

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## 10 Questions MCQ Test Mathematics (Maths) for JEE Main & Advanced - Test: Arithmetic Mean

Test: Arithmetic Mean for JEE 2024 is part of Mathematics (Maths) for JEE Main & Advanced preparation. The Test: Arithmetic Mean questions and answers have been prepared according to the JEE exam syllabus.The Test: Arithmetic Mean MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Arithmetic Mean below.
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Test: Arithmetic Mean - Question 1

### The three arithmetic mean between – 2 and 10 are:

Detailed Solution for Test: Arithmetic Mean - Question 1

Test: Arithmetic Mean - Question 2

### If a, b, c are in A.P., then

Detailed Solution for Test: Arithmetic Mean - Question 2

If a, b, c are in A.P., then b is the arithmetic mean of a and c.
a b and c are in AP.
∴ b - a = c - b
⇒ 2b = a + c          ........ (1)
The arithmetic mean of a and c
= (a+c)/2
Using equation (1), we get
= 2b/2
= b
∴ The arithmetic mean of a and c = b
Thus, the arithmetic mean of a and c is b.

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Test: Arithmetic Mean - Question 3

### If we want to insert 8 numbers between the numbers 4 and 31 such that the resulting sequence is an AP.The difference between the consecutive numbers will be

Detailed Solution for Test: Arithmetic Mean - Question 3

a = 4, l = 31, n = 8
(l-a)/(n+1) = (31-4)/(8+1)
= 27/9
= 3

Test: Arithmetic Mean - Question 4

For what value of n, is the arithmetic mean (AM) of a and b?

Detailed Solution for Test: Arithmetic Mean - Question 4

(aⁿ⁺¹ + bⁿ⁺¹)/(aⁿ + bⁿ) is mean between a & b
Mean of a & b =  ( a + b)/2
=> (aⁿ⁺¹ + bⁿ⁺¹)/(aⁿ + bⁿ) = ( a + b)/2
=> 2aⁿ⁺¹ + 2bⁿ⁺¹  = aⁿ⁺¹  + bⁿ⁺¹  + baⁿ + bⁿa
=> aⁿ⁺¹ + bⁿ⁺¹ = baⁿ + bⁿa
=> aⁿ(a - b) = bⁿ(a - b)
=> aⁿ = bⁿ
=> (a/b)ⁿ = 1
=> n = 0    or a  = b

Test: Arithmetic Mean - Question 5

The digits of a positive integer having three digits are in AP and sum of their digits is 21. The number obtained by reversing the digits is 396 less than the original number. Find the original number.

Detailed Solution for Test: Arithmetic Mean - Question 5

Let the digits at ones, tens and hundreds place be (a−d)a and (a+d) respectively. The, the number is
(a+d)×100+a×10+(a−d) = 111a+99d
The number obtained by reversing the digits is
(a−d)×+a×10+(a+d) = 111a−99d
It is given that the sum of the digits is 21.
(a−d)+a+(a+d) = 21                        ...(i)
Also it is given that the number obtained by reversing the digits is 594 less than the original number.
∴111a−99d = 111a+99d−396          ...(ii)
⟹ 3a = 21 and 198d = 396
⟹ a = 7 and d = -2
Original number = (a−d)×+a×10+(a+d)
= 100(9) + 10(7) + 5
= 975

Test: Arithmetic Mean - Question 6

A man saved Rs 21700 in 14 years. In each year after the first he saved Rs 100 more than he did in the preceding year. How much did he save in the first year?

Detailed Solution for Test: Arithmetic Mean - Question 6

d = 100
Sn = 21700
n = 14
Sn = n/2[2a + (n-1)d]
21700 = 14/2[2a + (14-1)100]
= 21700 = 7[2a + 1300]
= 3100 = 2a + 1300
⇒ 3100 - 1300 = 2a
⇒ 1800 = 2a
⇒ a = 900

Test: Arithmetic Mean - Question 7

What is the 10th A.M between 2 and 57 if 10 A.M s are inserted between these numbers?

Detailed Solution for Test: Arithmetic Mean - Question 7

2 and 57 have 10 terms between them so including them there would be 12 terms
an = 57, a = 2, n = 12
an = a + (n-1)d
=> 57 = 2 + (12 - 1)d
=> 55 = 11d
d = 5
T10 = a + 10d
=> 2 + 10(5)
= 52

Test: Arithmetic Mean - Question 8

If n numbers are inserted between 15 and 60 such that the ratio of the first to the last is 1 : 3, then the value of n is:

Detailed Solution for Test: Arithmetic Mean - Question 8

Test: Arithmetic Mean - Question 9

The arithmetic mean between 6 and – 12 is:

Detailed Solution for Test: Arithmetic Mean - Question 9

6, x, -12
x = (6-12)/2
x = -6/2
x = -3

Test: Arithmetic Mean - Question 10

If A1, A2, A3,…., An are n numbers between a and b, such that a, A1, A2, A3,…, An, b are in A.P., then nth term from beginning is:

Detailed Solution for Test: Arithmetic Mean - Question 10

A1,A2,......, An are inserted between a and b then the series will become
a, A1,A2,A3,......, An,b. Now a becomes the first term, A1 will be second, A2 will become third term
An will become A(n+1)th term
therefore A(n-1) will become nth term.

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## Mathematics (Maths) for JEE Main & Advanced

209 videos|443 docs|143 tests