CBSE Class 10: Maths - CH2 - Polynomials (NCERT EX 2.2)

Polynomials

NCERT Solutions Ex 2.2

Q1: Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.
(i)  x²-2x-8
(ii) 4s²-4s+1
(iii) 6x²-3-7x
(iv) 4u²+8u
(v) t²-15
(vi) 3x² - x -4

Answer: (i)  x²-2x-8 = (x - 4)(x +2)
⇒x²-2x-8 = 0 when x - 4= 0 or x + 2 = 0
∴ Zeroes of x²- 2x - 8 are 4 and -2.
Sum of zeroes =
Product of zeroes =
Hence relationship between zeroes and coefficients are verified.

(ii) 4s²-4s+1
= (2s -1 )²
⇒ 4s²-4s+1 = 0 when 2s -1 = 0
⇒ s = 1/2
∴ Zeroes of 4s²-4s+1 are ½ and ½.
Sum of zeroes =
Product of zeroes =
Hence relationship between zeroes and coefficients are verified.

(iii) 6x²-3-7x
= (3x + 1)(2x - 3)
⇒ 6x²-3-7x = 0 when 3x + 1 = 0 OR 2x - 3 = 0
⇒ x = -1/3 or x = 3/2 ∴ Zeroes of 6x²-3-7x are -1/3 and 3/2
Sum of zeroes =
Product of zeroes =
Hence relationship between zeroes and coefficients are verified.

(iv) 4u²+8u
= 4u(u + 2)
⇒ 4u²+8u = 0 when 4u = 0 OR u + 2 = 0
⇒ u = 0 OR u = -2
∴ Zeroes of 4u²+8u are 0 OR -2
Sum of zeroes =
Product of zeroes =

Hence relationship between zeroes and coefficients are verified.

(v) t²-15
= t² - 0t -15 = (t - √15)(t + √15)
⇒ The value of t²-15 is 0 when t - √15 = 0 OR t + √15 = 0
⇒ t = √15 or t = -√15.
Sum of zeroes = √15 -√15 = 0
Product of zeores = (√15) ☓ (-√15) = -15
Hence relationship between zeroes and coefficients are verified.

General Knowledge - First Person In India

First Person in India

Event	Person's Name
First Governor-General of Independent India	Lord Mountbatten
Indian Governor-General of Independent India	Chakravarti Rajgopalachari
First President of India	Dr. Rajendra Prasad
Prime Minister	Pt. Jawahar Lal Nehru.
Vice-President	Dr. Sarvapalli Radhakrishnan
First I. C. S. (Civil Services)	Satyendra Nath Tagore
Raman Magsaysay awardee	Acharya Vinoba Bhave
Nobel prize winner	Rabindra Nath Tagore
First Woman President	Smt. Pratibha Patil
Space traveller	Sqd. Leader Rakesh Sharma
Chairman of Lok Sabha	G. B. Mavlankar
Chief Election Commissioner	Sukumar Sen
Chief Justice of Supreme Court	Justice Hiralal J. Kaniya
Indian Chairman in International Court	Justice Dr. Nagendra Singh

CBSE Class 12- Business Studies - CH2 - Principles Of Management Very Short Q and A

Principles Of Management

Short Q & A

F Taylor - who proposed
scientific management theory
credits: wiki

Q1: What is meant by Management principles?

Answer: Management principles are broad and general guidelines for decision making and behaviour. These are those basic truths which have the ability to predict the result of the managerial activities.

Q2: How are the principles developed?

Answer: These are developed on the basis of observation and experimentation as well as personal experiences of the managers.

Q3: Why is it said that the principles of management are universal?

Answer: Because these principles are intended to apply to all types of organisations, business as well as non-business, small as well large, public sector as well as private sector, manufacturing as well as the services sectors.

Q4: Why are the principles of management are considered contingent?

Answer: The application of principles of management is contingent or dependent upon the prevailing situation at a particular point of time. The
application of principles has to be changed as per requirements.

Q5: Why is it said that principles of management are flexible?

Answer: This is because they can be modified by the managers when the situation so demands.

Q6: The principles of management aren't rigid and can be modified when the situation demands. Which nature of principles is being discussed here?

Answer: Flexibility.

Q7: Which principles of management promotes team spirit?

Answer: Esprict De Corps.

Q8: State one violating effect of the principle of ‘Division of work’.

Answer: Lack of specialization.

Q9: Define scientific management.

Answer: It is the application of a scientific approach to managerial decision making.

Q10: Who was the first to identity functions of management?

Answer: Henri Payol

CBSE Class 12 - Physics - CH3 - Current Electricity (NCERT Solutions)

Current Electricity

NCERT Solution 

Q1: The storage battery of a car has an emf of 12 V. If the internal resistance of the battery is 0.4Ω, what is the maximum current that can be drawn from the battery?

Answer: Emf of the battery, E = 12 V
    Internal resistance of the battery, r = 0.4 Ω
    Maximum current drawn from the battery = I

   According to Ohm’s law,
          E = Ir
          I = E/r  = 12/0.4 = 30 A
   Thus, the maximum current drawn from the given battery is 30 A.


Q2: A battery of emf 10 V and internal resistance 3 Ω is connected to a resistor. If the current in the circuit is 0.5 A, what is the resistance of the resistor? What is the terminal voltage of the battery when the circuit is closed?

Answer: Given,
                Emf of the battery, E = 10 V
                Internal resistance of the battery, r = 3 Ω
                Current in the circuit, I = 0.5 A
                Resistance of the resistor = R
       Applying Ohm’s law,
                I = E/(R + r)
           R + r = E/I  = 10/0.5 = 20 Ω
           ∴ 20 - 3 = 17 Ω

       Terminal voltage of the resistor = V
       According to Ohm’s law,
                    V = IR = 0.5 × 17 = 8.5 V
       ∴ the resistance of the resistor is 17 Ω and the terminal voltage is 8.5 V.

Q3: a) Three resistors 1 Ω, 2 Ω, and 3 Ω are combined in series. What is the total resistance of the combination?
       b) If the combination is connected to a battery of emf 12 V and negligible internal resistance, obtain the potential drop across each resistor.

Answer:
    (a) Three resistors of resistances 1 Ω, 2 Ω, and 3 Ω are combined in series.
         Total resistance of the series combination is the algebraic sum of individual resistances.
         ⇒ Total resistance = 1 + 2 + 3 = 6 Ω

NTSE MAT Quiz - 23

NTSE MAT Quiz

Logical Reasoning

DIRECTIONS. Q1-5: Find the odd one among the choices given for each of these questions

Q1: 
    (a)  Earth
(b)  Venus
(c)  Pluto
(d)  Mars

Q2:
(a) Advise
(b) Suggest
(c) Recommend
(d) Advice

Q3:
(a) Gitar
(b) Piano
(c) Sitar
(d) Veena

Q4:
(a) Apple
(b) Nokia
(c) Dell
(d) Asus

Q5:
(a) 25
(b) 36
(c) 144
(d) 99

NTSE - SAT (Indian History) Quiz - 22

NTSE SAT 

(Indian History - Independence Struggle) Quiz-22

Q1: Who amongst the following was impeached in England for acts committed as Governor-General Of India?

(a) Cornwallis
(b) Bentick
(c) Warrent Hastings
(d) Willingdon

Q2: 'Go back to Vedas' was the motto of

(a) Swami Vivekanand
(b) Swami Dayanand Saraswati
(c) Ramakrishna Paramhansa
(d) Raja Rammohan Roy

Q3: Who was the founder of Muslim League in India?

(a) M. A. Jinnah
(b) Sir Syed Ahmad
(c) Abdul Gaffar Khan
(d) Nawab Salimulla

Q4: Who wrote the book 'Gulamgir'?

(a) Iswarchand Viyasagar
(b) Jytiba Phule
(c) Sir Syed Ahmad
(d) Mahatma Gandhi

Q5: Who founded the Indian National Congress?

NTSE - SAT (Maths) Quiz - 21

NTSE QUIZ 21 (SAT-Maths)

MCQs
Q1: Two trains starting at the same time from two stations 240 km apart and are going in opposite directions cross each other at 160 km from one of the stations. What is the ratio of their speeds?

(a) 2 : 1
(b) 2 : 2
(c) 1 : 3
(d) 1 : 4

Q2: A positive number is by mistake divided by 6 instead of being multiplied by 6. What is the % error on the basis of correct answer?

(a) 3
(b) 97
(c) 17
(d) 83

Q3: The ratio of two numbers is 3 : 8 and their difference is 115. The greater number is

(a) 69
(b) 115
(c) 184
(d) 230

Q4: A person has to cover a distance of 6 km in 45 minutes. If he covers half of the distance in the remaining time, to cover the remaining distance in the remaining time, his speed must be

(a) 6 km/h
(b) 8 km/h
(c) 12 km/h
(d) 15 km/h

Q5: At an examination in which maximum marks are 500, A got 10% less than B, B got 25% more than C, C got 20% less than D. If A got 360 marks, what % of marks was obtained by D?