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10 months ago

RSR Rungta College of Engineering and Technology College of Engineering

In which city is RSR, Rungta College of Engineering?

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10 months ago

Maths NCERT Exemplar Solutions Class 12th Chapter One Maths

Functions $f, g : R \to R$ are defined, respectively, by $f (x) = x^{2} + 3 x + 1$ , $g (x) = 2 x - 3$ , find

(i) $f \circ g$

(ii) $g \circ f$

(iii) $f \circ f$

(iv) $g \circ g$

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alok kumar singh

Contributor-Level 10

This is a Long Answer Type Question as classified in NCERT Exemplar

Sol:

$\begin{array}{l} (i) f o g \Rightarrow f [(g (x)] = [g] {(x)}^{2} + 3 [(g (x)] + 1 \\ = {(2 x - 3)}^{2} + 3 (2 x - 3) + 1 \\ = 4 x^{2} + 9 - 12 x + 6 x - 9 + 1 = 4 x^{2} - 6 x + 1 \\ (i i) g o f \Rightarrow g [f (x)] = 2 [x^{2} + 3 x + 1] - 3 \\ = 2 x^{2} + 6 x + 2 - 3 = 2 x^{2} + 6 x + 1 \\ (i i i) f o f \Rightarrow f [(f (x)] = {[f (x)]}^{2} + 3 [f (x)] + 1 \\ = ({x^{2} + 3 x + 1)}^{2} + 3 (x^{2} + 3 x + 1) + 1 \\ = x^{4} + 9 x^{2} + 1 + 6 x^{3} + 6 x + 2 x^{2} + 3 x^{2} + 9 x + 3 + 1 \\ = x^{4} + 6 x^{3} + 14 x^{2} + 15 x + 5 \\ (i v) g o g \Rightarrow g [g (x)] = 2 [g (x)] - 3 = 2 (2 x - 3) - 3 = 4 x - 6 - 3 = 4 x - 9 \end{array}$

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10 months ago

Chemistry NCERT Exemplar Solutions Class 12th Chapter Seven P Block Elements

A black compound of manganese reacts with a halogen acid to give greenish yellow gas. When excess of this gas reacts with NH3 an unstable trihalide is formed. In this process the oxidation state of nitrogen changes from _________.

(i) – 3 to +3

(ii) – 3 to 0

(iii) – 3 to +5

(iv) 0 to – 3

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Payal Gupta

Contributor-Level 10

This is a multiple choice answer as classified in NCERT Exemplar

Correct option is (iv)

MnO₂ ( Black )+4HCl→MnCl₂+2H₂O+Cl₂

Greenish yellow color

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10 months ago

Maths NCERT Exemplar Solutions Class 12th Chapter One Maths

Using the definition, prove that the function $f : A \to B$ is invertible if and only if $f$ is both one-one and onto.

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alok kumar singh

Contributor-Level 10

This is a Long Answer Type Question as classified in NCERT Exemplar

Sol:

$\begin{array}{l} A f u n c t i o n f : X \to Y i s s a i d t o b e i n v e r t i b l e i f t h e r e e x i s t s a \\ f u n c t i o n g : Y \to X s u c h t h a t g o f = I_{X} a n d f o g = I_{Y} a n d t h e n t h e \\ i n v e r s e o f f i s d e n o t e d b y f^{- 1} . \\ A f u n c t i o n f : X \to Y i s s a i d t o b e i n v e r t i b l e i f f f i s a b i j e c t i v e f u n c t i o n . \end{array}$

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10 months ago

Chemistry NCERT Exemplar Solutions Class 12th Chapter Seven P Block Elements

Hot conc. H₂SO₄ acts as moderately strong oxidising agent. It oxidises both metals and nonmetals. Which of the following element is oxidised by conc. H₂SO₄ into two gaseous products?

(i) Cu

(ii) S

(iii) C

(iv) Zn

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Payal Gupta

Contributor-Level 10

This is a multiple choice answer as classified in NCERT Exemplar

Correct option is (iii)

C+2H₂SO₄→CO₂+2SO₂+2H₂O

Conc. H₂SO₄ oxidises C to produce two gaseous products.

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10 months ago

Nehru College of Nursing, Panayur Nehru College

What are the specialisations offered by Nehru College of Nursing, Panayur in the MSc programme?

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saurya snehal

Contributor-Level 10

The specialisations offered by Nehru College of Nursing, Panayur in the MSc programme are:

M.Sc. in Medical Surgical Nursing

Candidates can learn more about the specialisation on the official website of the institute. Candidates are required to make sure that they meet the eligibility criteria of the programme prior to going through the admission process.

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10 months ago

Maths NCERT Exemplar Solutions Class 12th Chapter One Maths

Let $A = {1, 2, 3, \dots, 9}$ and $R$ be the relation in $A \times A$ defined by $(a, b) R (c, d)$ if $a + d = b + c$ for $(a, b), (c, d) i n A \times A$ . Prove that $R$ is an equivalence relation and also obtain the equivalent class $[(2, 5)]$ .

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alok kumar singh

Contributor-Level 10

This is a Long Answer Type Question as classified in NCERT Exemplar

Sol:

$\begin{array}{l} H e r e, A = {1, 2, 3, \dots, 9} \\ a n d R \to A \times A d e f i n e d b y (a, b) R (c, d) \Rightarrow a + d = b + c \\ \forall (a, b), (c, d) \in A \times A \\ F o r r e f l e x i v e : (a, b) R (a, b) = a + b = b + a \forall a, b \in A w h i c h i s t r u e . S o, R i s r e f l e x i v e . \\ F o r s y m m e t r i c : (a, b) R (c, d) = (c, d) R (a, b) \\ L . H . S . a + d = b + c \\ R . H . S . c + b = d + a \\ L . H . S . = R . H . S . S o, R i s s y m m e t r i c . \\ F o r t r a n s i t i v e : (a, b) R (c, d) = (c, d) R (e, f) \Leftrightarrow (a, b) R (e, f) \\ \Rightarrow a + d = b + c a n d c + f = d + e \\ \Rightarrow a + d = b + c a n d d + e = c + f \\ \Rightarrow (a + d) - (d + e) = (b + c) - (c + f) \\ \Rightarrow a - e = b - f \\ \Rightarrow a + f = b + e \\ \Rightarrow (a, b) R (e, f) \\ S o, R i s t r a n s i t i v e . \\ H e n c e, R i s a n e q u i v a l e n c e r e l a t i o n . \\ E q u i v a l e n t c l a s s o f {(2, 5)} i s {(1, 4), (2, 5), (3, 6), (4, 7), (5, 8), (6, 9)} \end{array}$

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10 months ago

Chemistry NCERT Exemplar Solutions Class 12th Chapter Seven P Block Elements

Which of the following are peroxoacids of sulphur?

(i) H₂SO₅ and H₂S₂O₈

(ii) H₂SO₅ and H₂S₂O₇

(iii) H₂S₂O₇ and H₂S₂O₈

(iv) H₂S₂O₆ and H₂S₂O₇

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Payal Gupta

Contributor-Level 10

This is a multiple choice answer as classified in NCERT Exemplar

Correct option is (i)

Peroxy linkage refers to the presence of a bond between oxygen and oxygen (O-O) in a molecule.

Only H₂S₂O₆ and H₂S₂O₇ of the sulphur oxoacids above have a peroxy linkage.

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10 months ago

Maths NCERT Exemplar Solutions Class 12th Chapter One Maths

Each of the following defines a relation on $N$ :

(i) $x$ is greater than $y, x, y \in N$

(ii) $x + y = 10, x, y \in N$

(iii) $x y, i s s q u a r e o f a n i n t e g e r x, y \in N$

(iv) $x + 4 y = 10, x, y \in N$ .

Determine which of the above relations are reflexive, symmetric, and transitive.

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alok kumar singh

Contributor-Level 10

This is a Long Answer Type Question as classified in NCERT Exemplar

Sol:

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10 months ago

Chemistry NCERT Exemplar Solutions Class 12th Chapter Seven P Block Elements

Which of the following is not tetrahedral in shape?

(i) NH₄⁺

(ii) SiCl₄

(iii) SF₄

(iv) SO₄²⁻

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Payal Gupta

Contributor-Level 10

This is a multiple choice answer as classified in NCERT Exemplar

Correct option is (iii)

The C-atom in the CO₃^2- ion undergoes sp2 hybridization. BF₄, NH₄⁺ and SO₄^2- have a tetrahedral structure, whereas it has a triangular planar structure.

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10 months ago

Nehru College of Nursing, Panayur Nehru College

What is the course fee for the MSc programme at Nehru College of Nursing, Panayur?

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saurya snehal

Contributor-Level 10

The course fee for the MSc programme at Nehru College of Nursing, Panayur is INR 2 lakh. The course fee is an amalgamation of various fee componenets such as the tuition fee, hostel fee, and the admission charges. Candidates are required to pay the course fee through the modes offered by the institute.
Candidates who get the admission offer are eligible to pay the course fee.

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10 months ago

Maths NCERT Exemplar Solutions Class 12th Chapter One Maths

Let $A = [- 1, 1]$ , Then, discuss whether the following functions defined on $A$ are one-one, onto, or bijective:

(i) $f (x) = \frac{x}{2}$

(ii) $g (x) = | x |$

(iii) $h (x) = x | x |$

(iv) $k (x) = x^{2}$ .

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alok kumar singh

Contributor-Level 10

This is a Long Answer Type Question as classified in NCERT Exemplar

Sol:

$\begin{array}{l} (i) G i v e n t h a t - 1 \leq x \leq 1 \\ L e t x_{1}, x_{2} \in f (x) \\ f (x_{1}) = \frac{1}{x_{1}} a n d f (x_{2}) = \frac{1}{x_{2}} \\ f (x_{1}) = f (x_{2}) \Rightarrow \frac{1}{x_{1}} = \frac{1}{x_{2}} \Rightarrow x_{1} = x_{2} \\ S o, f (x) i s o n e - o n e f u n c t i o n . \\ L e t f (x) = y = \frac{x}{2} \Rightarrow x = 2 y \\ F o r y = 1, x = 2 \notin [- 1, 1] \\ S o, f (x) i s n o t o n t o . H e n c e, f (x) i s n o t b i j e c t i v e f u n c t i o n . \\ (i i) H e r e, g (x) = | x | \\ g (x_{1}) = g (x_{2}) \Rightarrow | x_{1} | = | x_{2} | \Rightarrow x_{1} = \pm x_{2} \\ S o, g (x) i s n o t o n e - o n e f u n c t i o n . \\ L e t g (x) = y = | x | \Rightarrow x = \pm y \notin A \forall y \in A \\ S o, g (x) i s n o t o n t o f u n c t i o n . \\ H e n c e, g (x) i s n o t b i j e c t i v e f u n c t i o n . \\ (i i i) H e r e, h (x) = x | x | \\ h (x_{1}) = h (x_{2}) \\ \Rightarrow x_{1} | x_{1} | = x_{2} | x_{2} | \Rightarrow x_{1} = x_{2} \\ S o, h (x) i s o n e - o n e f u n c t i o n . \\ N o w, l e t h (x) = y = x | x | = x^{2} o r - x^{2} \\ \Rightarrow &thi \end{array}$

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10 months ago

Design Uttar Pradesh

Which is the best Fashion Designing college in Noida?

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Tasbiya Khan

Contributor-Level 10

As per popularity basis, listed below are the top Fashion Designing colleges in Noida along with their tuition fees:

Top Colleges	Tuition Fee
Amity School of Fashion Technology	INR 3 Lacs - INR 12 lakh
IMS Design and Innovation Academy	INR 1 Lacs - INR 16 lakh
Amity University, Noida	INR 3 lakh
AAFT	INR 2 Lacs - INR 9 lakh
Satyam Fashion Institute	INR 7 lakh

Disclaimer: This information is sourced from official website and may vary.

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10 months ago

Chemistry NCERT Exemplar Solutions Class 12th Chapter Seven P Block Elements

The oxidation state of central atom in the anion of compound NaH₂PO₂ will be ______.

(i) +3

(ii) +5

(iii) +1

(iv) –3

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Payal Gupta

Contributor-Level 10

This is a multiple choice answer as classified in NCERT Exemplar

Correct option is (iii)

Na (H₂)PO₂

1+ (2x+1)+ x +2 (−2)=0

x−1=0

x=1

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10 months ago

Uttar Pradesh Design

How many Fashion Designing colleges are there in Noida?

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Tasbiya Khan

Contributor-Level 10

There are about 15+ best Fashion Design colleges in Noida. Of these, 15 colleges are privately owned and 1 college is owned by public/government organisations. Students can secure admission after passing Class 12 boards. Some of the top Design colleges in Noida offer Fashion Design courses include Amity School of Fashion Technology, IMS Design and Innovation Academy, Amity University, Noida, AAFT, Satyam Fashion Institute (Only for Girls), Apparel Training and Design Centre, and many others.

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10 months ago

Maths NCERT Exemplar Solutions Class 12th Chapter One Maths

Let $A = R - {3}, B = R - {1}$ . Let $f : A \to B$ be defined by $f (x) = \frac{x - 2}{x - 3} \forall x \in A$ . Then Show that $f$ is bijective.

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alok kumar singh

Contributor-Level 10

This is a Long Answer Type Question as classified in NCERT Exemplar

Sol:

$\begin{array}{l} H e r e, A \in R - {3}, B = R - {1} \\ G i v e n t h a t f : A \to B d e f i n e d b y f (x) = \frac{x - 2}{x - 3} \forall x \in A . \\ L e t x_{1}, x_{2} \in f (x) \\ ∴ f (x_{1}) = f (x_{2}) \\ \Rightarrow \frac{x_{1} - 2}{x_{1} - 3} = \frac{x_{2} - 2}{x_{2} - 3} \\ \Rightarrow (x_{1} - 2) (x_{1} - 3) = (x_{2} - 2) (x_{2} - 3) \\ \Rightarrow - x_{1} = - x_{2} \Rightarrow x_{1} = x_{2} \\ S o, i t i s i n j e c t i v e f u n c t i o n . \\ N o w, L e t y = \frac{x - 2}{x - 3} \\ \Rightarrow x y - 3 y = x - 2 \Rightarrow x y - x = 3 y - 2 \\ \Rightarrow x (y - 1) = 3 y - 2 \Rightarrow x = \frac{3 y - 2}{y - 1} \\ f (x) = \frac{x - 2}{x - 3} = \frac{\frac{3 y - 2}{y - 1} - 2}{\frac{3 y - 2}{y - 1} - 3} \Rightarrow \frac{3 y - 2 - 2 y + 2}{3 y - 2 - 3 y + 3} \Rightarrow y \\ \Rightarrow f (x) = y \in B . \\ S o, f (x) i s s u r j e c t i v e f u n c t i o n . \\ H e n c e, f (x) i s b i j e c t i v e f u n c t i o n . \end{array}$

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10 months ago

Guru Nanak Dev University Accounting & Commerce

Are there any govt. job opportunities available after completing BCom from GNDU Gurdaspur?

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Atul Pruthi

Contributor-Level 9

BCom graduates can take up various job roles in the Finance sector of government organisations, such as government banks and regulatory bodies. They are also eligible for competitive exams, such as UPSC, SSC, etc., that lead to various jobs in the government sector. Tabulated below are some of the prospective government jobs for BCom graduates of GNDU Gurdaspur, along with their average salaries:

Job Profile	Average Salary
Bank Probationary Officer (PO)	INR 5 LPA to INR 7 LPA
LIC AAO	INR 3 LPA to INR 4 LPA
IBPS Clerk	INR 2 LPA to INR 3 LPA
RRB NTPC	INR 6 LPA to INR 8 LPA
SSC CHSL	INR 3 LPA to INR 4 LPA
IBPS PO	INR 5 LPA to INR 6 LPA

Note: The above-mentioned are industry-based average payouts. The actual salary may differ from student to student based on their skills and competency.

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10 months ago

Chemistry NCERT Exemplar Solutions Class 12th Chapter Seven P Block Elements

In the preparation of HNO₃, we get NO gas by catalytic oxidation of ammonia. The moles of NO produced by the oxidation of two moles of NH₃will be______.

(i) 2

(ii) 3

(iii) 4

(iv) 6

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Payal Gupta

Contributor-Level 10

This is a multiple choice answer as classified in NCERT Exemplar

Correct option is (i)

The catalytic oxidation of ammonia produces NO gas, which is used to make HNO₃. 4 moles of NH₃ created 4 moles of NO in the equation below. As a result, the moles of NO produced by oxidising two moles of NH₃ will be two moles.

4NH₃ + 5O₂→4NO + 6H₂O.

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10 months ago

Maths NCERT Exemplar Solutions Class 12th Chapter One Maths

Give an example of a map:

(i) which is one-one but not onto

(ii) which is not one-one but onto

(iii) which is neither one-one nor onto.

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