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Sia ? 6 years, 3 months ago
1, A1, A2, A3, ----- Am, 31 are in AP.
a = 1
an = 31
{tex}a _ { m + 2 } = 314{/tex}

an = a + (n - 1)d
31 = a + (m + 2 - 1)d
{tex}d = \frac { 30 } { m + 1 }{/tex}
{tex}\frac { A 7 } { A _ { n - 1 } } = \frac { 5 } { 9 }{/tex} (Given)
{tex}\frac { 1 + 7 \left( \frac { 30 } { m + 1 } \right) } { 1 + ( m - 1 ) \left( \frac { 30 } { m + 1 } \right) } = \frac { 5 } { 9 }{/tex}
m = 1
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Gaurav Seth 6 years, 4 months ago
uppose,
A={1,2,3,4,5,6}
B={2,4,6}
In this condition, every element in B is contained in A so,
B(A
But however, B is the set of even numbers and A is the set of natural numbers and thus they are very different in terms of n.
We write even number as 2n whereas natural number just n.
So, B doesn't belong to A.
Rahul Raj 6 years, 4 months ago
Posted by Birendar Kumar 6 years, 4 months ago
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Iram Hasan Hasan 6 years, 3 months ago
Gaurav Seth 6 years, 4 months ago
Any of the ways we can arrange things, where the order is important.
Example: You want to visit the homes of three friends ("a"), ("b") and ("c"), but haven't decided in what order. What choices do you have?
Answer: {a,b,c} {a,c,b} {b,a,c} {b,c,a} {c,a,b} {c,b,a}
Posted by Isha Suryan 6 years, 4 months ago
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Sia ? 6 years, 4 months ago
Let P(n) = a + ar + ar2 + ..... + arn-1{tex} = \frac{{a({r^n} - 1)}}{{r - 1}}{/tex}.
For n = 1
{tex}P(1) = a{r^{1 - 1}} = \frac{{a({r^1} - 1)}}{{r - 1}} \Rightarrow a = a{/tex}
{tex}\therefore {/tex} P(1) is true
Let P(n) be true for n = k
{tex}\therefore P(k) = a + ar + a{r^2} + .... + a{r^{k - 1}}{/tex}{tex} = \frac{{a({r^k} - 1)}}{{r - 1}}{/tex} .... (i)
For n = k + 1
R.H.S. {tex} = \frac{{a({r^{k + 1}} - 1)}}{{r - 1}}{/tex}
L.H.S. {tex} = \frac{{a({r^k} - 1)}}{{r - 1}} + a{r^k}{/tex} [ Using (i)]
{tex} = \frac{{a{r^k}}}{{r - 1}} - \frac{a}{{r - 1}} + a{r^k}{/tex}
{tex} = a{r^k} \cdot \left( {\frac{1}{{r - 1}}+1} \right) - \frac{a}{{r - 1}} = \frac{{a{r^{k + 1}}}}{{r - 1}} - \frac{a}{{r - 1}}{/tex}{tex} = \frac{{a{r^{k + 1}} - a}}{{r - 1}}{/tex}
{tex} = \frac{{a({r^{k + 1}} - 1)}}{{r - 1}}{/tex}
{tex}\therefore {/tex} P(k + 1) is true
Thus P(k) is true {tex} \Rightarrow {/tex} P(k + 1) is true
Hence by principle of mathematical induction, P(n) is true for all {tex}n \in N{/tex}.
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Gaurav Seth 6 years, 4 months ago
NCERT Solutions class-11 Maths Exercise 2.3
Question :
2. Find the domain and range of the following real functions:
(ii) 
Explanation is given below:
(ii) Given:
.
The function is not defined when 
Domain of function = 
=
= 
Range of function = 
Posted by Chitra Verma 6 years, 4 months ago
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Gaurav Seth 6 years, 4 months ago
Let x be the third reading of the pH level.
The acidity of the pool is normal when the average pH reading measurements is between 7.2 and 7.8
The first two measurements are 7.48 and 7.85
The average

Similarly,
The average

Thus the range third reading of the acidity of the pool should be
Posted by Lata Verma 6 years, 4 months ago
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Sia ? 6 years, 3 months ago
The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time.
2Thank You