Ncert Solutions Maths class 11th

3. Here a_n=2ⁿ

Substituting n=1,2,3,4,5 we get,

a₁=2¹=2

a₂=2²=4

a₃=2³=8

a₄=a⁴=16

a₅=2⁵=32.

Hence the first five terns are 2,4,16,32 and 64.

2. Here, a₁= $\frac{n}{n+1}$

Substituting n=1,2,3,4,5 we get,

$a_1=\frac{1}{1+1}=\frac{1}{2}$

$a_2=\frac{2}{2+1}=\frac{2}{3}$

$a_3=\frac{3}{3+1}=\frac{3}{4}$

$a_4=\frac{4}{4+1}=\frac{4}{5}$

$a_5=\frac{5}{5+1}=\frac{5}{6}$ .

Hence the first five terns are $\frac{1}{2},\frac{2}{3},\frac{3}{4},\frac{4}{5}$ and $\frac{5}{6}$ .

1. Since the ordered pairs are equal, the corresponding elements are equal.

$\therefore \frac{x}{3}+1=\frac{5}{3}.$ and $y-\frac{2}{3}=\frac{1}{3}$

$\frac{x}{3}=\frac{5}{3}-1$ $y=\frac{1}{3}+\frac{2}{3}$

$\Rightarrow \frac{x}{3}=\frac{5-3}{3}$ $\Rightarrow y=\frac{1+2}{3}$

$\Rightarrow \frac{x}{3}=\frac{2}{3}$ $\Rightarrow y=\frac{3}{3}$

$\Rightarrow x=2$ y = 1.

This is a  Mathematical Reasoning Solutions Type Questions as classified in NCERT Exemplar

The given statement can be written in five different ways: –

(i) A triangle is equiangular implies that it is an obtuse angled triangle.

(ii) A triangle is equiangular only if the triangle is an obtuse angled triangle.

(iii) For a triangle to be equiangular, it is necessary that the triangle is an obtuse angled triangle.

(iv) For a triangle to be an obtuse angled triangle, it is sufficient that the triangle is equiangular.

(v) If a triangle is an obtuse angled triangle, then the triangle is not equiangular.

This is a  Mathematical Reasoning Solutions Type Questions as classified in NCERT Exemplar

The compound statement with 'And' is as follows 25 is a multiple of 5 and 8.

This is false statement because 25 is not a multiple of 8.

The compound statement with 'Or' is as follows 25 is a multiple of 5 or 8.

This is true statement because 25 is not a multiple of 8 but it is a multiple of 5.

This is a  Mathematical Reasoning Solutions Type Questions as classified in NCERT Exemplar

(i) You watch television if and only if your mind is free.

(ii) You get an A grade if and only if you do all the homework regularly.

(iii) A quadrilateral is equiangular if and only if it is a rectangle.

This is a  Mathematical Reasoning Solutions Type Questions as classified in NCERT Exemplar

(i) The statement p in the form 'if then' is as follows.

If you log on to the server, then you have password.

(ii) The statement q in the form 'if then' is as follows.

If it rains, then there is a traffic jam.

(iii) The statement r in the form 'if them' is as follows.

If you can access the website, then you pay a subscription fee.

This is a  Mathematical Reasoning Solutions Type Questions as classified in NCERT Exemplar

(i) The negation of statement p is as follows.

There exists a positive real number x, such that x – 1 is not positive.

(ii) The negation of statement q is

There exists a CAT that does not scratch.

(iii) The negation of statement r is

There exist a real number x, such that neither x>1 nor x<1.

(iv) The negation of statement s is as follow.

There does not exist a number x, such that 0