Tags Class 11th

Class 11th

Get insights from 8k questions on Class 11th, answered by students, alumni, and experts. You may also ask and answer any question you like about Class 11th

Follow Ask Question

Questions

Discussions

Active Users

Followers

New answer posted

5 months ago

Class 11th Mathematical Reasoning

Show that the statement “For any real numbers a and b, a² = b² implies that a = b” is not true by giving a counter-example.

0 Follower 2 Views

alok kumar singh

Contributor-Level 10

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

Let a = 2, b = –2 be two real numbers.

Clearly, a² = b² (=4) but $a \neq b .$

Thus, the given statement is not true.

0 0

New answer posted

5 months ago

Class 11th Mathematical Reasoning

Show that the statement p: “If x is a real number such that x³ + 4x = 0, then x is 0” is true by

(i) Direct method, (ii) Method of contradiction, (iii) Method of contrapositive

0 Follower 2 Views

alok kumar singh

Contributor-Level 10

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

(i) Direct method:

Let $x^{3} + 4 x = 0, x \in R$

$\Rightarrow x (x^{2} + 4) = 0$

$\Rightarrow$ Either x=0 or x²+4=0

But x² + 4 > 4 because $x \in R$ and hence $\neq 0 .$

Therefore x=0

$∴ x^{3} + 4 x = 0, x \in R \Rightarrow x \neq 0$

This, p is a true statement.

(ii) Method of contradiction

Let $x^{3} + 4 x = 0, x \in R$

Suppose $x \neq 0$

$\Rightarrow x^{2} > 0$

$\Rightarrow x^{2} + 4 > 0$

$\Rightarrow x^{2} + 4 \neq 0$

Now $x \neq 0$ and $x^{2} + 4 \neq 0$

$\Rightarrow x (x^{2} + 4) \neq 0$

$\Rightarrow x^{3} + 4 x \neq 0$ which is a contradiction to given.

$∴$ Our supposition is wrong and hence x = 0

This, p is a true statement.

(iii) Method of contrapositive: The components of the give if… then statement p are:

Let $q : x \in R$ andx³ + 4x = 0 and r:x = 0

$∴$ The given statement p is q $\Rightarrow$ r

Its contra positive is $\sim r \Rightarrow \sim q .$

Let $\sim r$ be true i.e., x

...more

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

(i) Direct method:

Let $x^{3} + 4 x = 0, x \in R$

$\Rightarrow x (x^{2} + 4) = 0$

$\Rightarrow$ Either x=0 or x²+4=0

But x² + 4 > 4 because $x \in R$ and hence $\neq 0 .$

Therefore x=0

$∴ x^{3} + 4 x = 0, x \in R \Rightarrow x \neq 0$

This, p is a true statement.

(ii) Method of contradiction

Let $x^{3} + 4 x = 0, x \in R$

Suppose $x \neq 0$

$\Rightarrow x^{2} > 0$

$\Rightarrow x^{2} + 4 > 0$

$\Rightarrow x^{2} + 4 \neq 0$

Now $x \neq 0$ and $x^{2} + 4 \neq 0$

$\Rightarrow x (x^{2} + 4) \neq 0$

$\Rightarrow x^{3} + 4 x \neq 0$ which is a contradiction to given.

$∴$ Our supposition is wrong and hence x = 0

This, p is a true statement.

(iii) Method of contrapositive: The components of the give if… then statement p are:

Let $q : x \in R$ andx³ + 4x = 0 and r:x = 0

$∴$ The given statement p is q $\Rightarrow$ r

Its contra positive is $\sim r \Rightarrow \sim q .$

Let $\sim r$ be true i.e., x is a non-zero real number

Now $x \neq 0, x \in R$

$\Rightarrow x^{2} > 0$

$\Rightarrow x^{2} + 4 > 4$

$\Rightarrow x^{2} + 4 \neq 0$

$∴ x (x^{2} + 4) \neq 0 \Rightarrow x^{3} + 4 x \neq 0$

$∴ \sim q$ is true

i.e., $\sim r \Rightarrow \sim q$

$∴ q \Rightarrow r$ is true

This, p is a true statement.

less

0 0

New answer posted

5 months ago

Class 11th Mathematical Reasoning

Given statements in (a) and (b). Identify the statements given below as contrapositive or converse of each other.

(a) If you live in Delhi, then you have winter clothes.

(i) If you do not have winter clothes, then you do not live in Delhi.

(ii) If you have winter clothes, then you live in Delhi.

(b) If a quadrilateral is a parallelogram, then its diagonals bisect each other.

(i) If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral is not a parallelogram.

(ii) If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

0 Follower 1 View

alok kumar singh

Contributor-Level 10

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

(a) (i) Contra positive

(ii) Converse

(b) (i) Contra positive

(ii) Converse

0 0

New answer posted

5 months ago

Class 11th Mathematical Reasoning

Write each of the following statements in the form “if-then”

(i) You get a job implies that your credentials are good.

(ii) The Banana trees will bloom if it stays warm for a month.

(iii) A quadrilateral is a parallelogram if its diagonals bisect each other.

(iv) To get an A+ in the class, it is necessary that you do all the exercises of the book.

0 Follower 1 View

alok kumar singh

Contributor-Level 10

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

(i) If you get a job, then your credentials are good.

(ii) If the Banana trees stay warm for a month, then the trees will bloom.

(iii) If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

(iv) If you want to score an A+ in the class, then you do all the exercises in the book.

0 0

New answer posted

5 months ago

Class 11th Mathematical Reasoning

Write the contrapositive and converse of the following statements.

(i) If x is a prime number, then x is odd.

(ii) If the two lines are parallel, then they do not intersect in the same plane.

(iii) Something is cold implies that it has low temperature.

(iv) You cannot comprehend geometry if you do not know how to reason deductively.

(v) x is an even number implies that x is divisible by 4.

0 Follower 1 View

alok kumar singh

Contributor-Level 10

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

(i) Contrapositive

If a number x is not odd, then x is not a prime number.

Converse

If a number x is odd, then it is a prime number.

(ii) Contrapositive

If two lines intersect in the same place, then the two lines are not parallel.

Converse

If two lines do not intersect in the same place, then they are parallel.

(iii) Contrapositive

If something does not have a low temperature, then it is not cold.

Converse

If something is at a low temperature, then it is cold.

(iv) Contrapositive

If you know how to reason deductively, then you can comprehend geo

...more

0 0

New answer posted

5 months ago

Class 11th Mathematical Reasoning

Rewrite the following statement with “if-then” in five different ways conveying the same meaning.

If a natural number is odd, then its square is also odd.

0 Follower 1 View

alok kumar singh

Contributor-Level 10

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

Five different ways are–

(i) A natural number is odd implies that its square is odd.

(ii) A natural number is odd only if its square is odd.

(iii) For a natural number to be odd it is necessary that its square is odd.

(iv) For the square of a natural number to be odd it is sufficient that the number is odd.

(v) If the square of a natural number is not odd, then the natural number is not odd.

0 0

New answer posted

5 months ago

Class 11th Mathematical Reasoning

State whether the “Or” used in the following statements is “exclusive “or” inclusive.

Give reasons for your answer.

(i) Sun rises or Moon sets.

(ii) To apply for a driving licence, you should have a ration card or a passport.

(iii) All integers are positive or negative.

0 Follower 1 View

alok kumar singh

Contributor-Level 10

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

(i) The 'or' in this statement is conclusive because it is not possible for the sun to rise and the moon to set together.

(ii) The 'or' in this statement is inclusive since a person can have both a ration card and a passport to apply for a driving license.

(iii) The 'or' in this statement is exclusive since all integers cannot be both positive and negative.

0 0

New answer posted

5 months ago

Class 11th Chemistry NCERT Exemplar Solutions Class 11th Chapter Four

Assertion (A): Among the two O–H bonds in H2O molecule, the energy required to break the first O–H bond and the other O–H bond is the same.

Reason (R) : This is because the electronic environment around oxygen is the same even after breakage of one O–H bond.

(i) A and R both are correct, and R is correct explanation of A.

(ii) A and R both are correct, but R is not the correct explanation of A.

(iii) A is true but R is false.

(iv) A and R both are false.

0 Follower 1 View

Vishal Baghel

Contributor-Level 10

This is a Assertion Type Questions as classified in NCERT Exemplar

Ans: Option (iv)

Both the statements given in the assertion and reason are false.

The energy required to break the first O-H bond is not same than that of the second O-H bond in water molecule, that means the bond enthalpies of the two O-Hare different. This is because the electronic environment around the oxygen atom in water molecules is not the same even after the O-H bond breaks.

0 0

New answer posted

5 months ago

Class 11th Mathematical Reasoning

Check whether the following pair of statements are negation of each other. Give reasons for your answer.

(i) x + y = y + x is true for every real numbers x and y.

(ii) There exists real numbers x and y for which x + y = y + x.

0 Follower 1 View

alok kumar singh

Contributor-Level 10

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

Negation of statement (i) is:

There exists real numbers x and y for which x + y = y + x.

Now, this statement is not same as statement (ii).

Therefore, the given statements are not negation of each other.

0 0

New answer posted

5 months ago

Class 11th Chemistry NCERT Exemplar Solutions Class 11th Chapter Four

Assertion (A) : Though the central atom of both NH₃ and H₂O molecules are sp³ hybridised, yet H–N–H bond angle is greater than that of H–O–H.

Reason (R) : This is because nitrogen atom has one lone pair and oxygen atom has two lone pairs.

(i) A and R both are correct, and R is the correct explanation of A.

(ii) A and R both are correct, but R is not the correct explanation of A.

(iii) A is true but R is false.

(iv) A and R both are false.

0 Follower 3 Views

Vishal Baghel

Contributor-Level 10

This is a Assertion Type Questions as classified in NCERT Exemplar

Ans: Option (i)

The statements given in the assertion and reason, both are correct and the reason given is the correct explanation for the assertion. In NH₃only one lone pair of electron is present and due to that lone pair-bond pair repulsion occurs which forms a distorted tetrahedral geometry (pyramidal) .

In H₂O two lone pairs of electrons are present on the oxygen atom and due to this lone pairlone pair repulsion occurs which shifts the bonds and forms a bent geometry. The lone pair-lone pair repulsion is more than the lone pair-bond pair repulsion. Thus, bond angle i

...more

0 0

Get authentic answers from experts, students and alumni that you won't find anywhere else

On Shiksha, get access to

65k Colleges
1.2k Exams
679k Reviews
1800k Answers

Community GuidelinesUser Points System

QuestionsDiscussionsTags

Need guidance on career and education? Ask our experts

Your Question

Class 11th

Questions

Discussions

Active Users

Followers

All

Discussions

Unanswered Questions

Share Your College Life Experience