EXERCISE 20.3 QUESTION 1 Find the sum of the following geometric progressions: (i) to 7 terms; Sol : Here, a=2 and r=3 = 2787 – 1 = 2186 (ii) to 8 terms Sol :[…]

## Geometric progression

EXERCISE 20.2 QUESTION 1 Find three numbers in G.P. whose sum is 65 and whose product is 3375 . Sol : Let the terms of the the given G.P. be , a and Then, product[…]

## Geometric Progressions

EXERCISE 20.1 QUESTION 1 Show that each one of the following progressions is a G.P. Also, find the common ratio in each case: (i) Sol : We have : ,, , , , Thus, ,[…]

## Arithmetic progression

EXERCISE 19.6 QUESTION 1 Find the A.M. between: (i) 7 and 13 Sol : Let be the A.M. between 7 and 13 = 10 (ii) 12 and -8 Sol : Let be the A.M.[…]

## Arithmetic progression

EXERCISE 19.4 QUESTION 1 Find the sum of the following arithmetic progressions: (i) to 10 terms Sol : We have : a = 50 d = (46 -50) = -4 n = 10 = 320[…]

## Arithmetic progression

EXERCISE 19.3 QUESTION 1 The sum of three terms of an A.P. is 21 and the product of the first and the third terms exceeds the second term by 6, find three terms. Sol :[…]

## Arithmetic progression

EXERCISE 19.2 QUESTION 1 Find : (i) 10 th term of the A.P. Sol : We have a = 1 d = 4 – 1 = 3 = 28 (ii) 18 th term[…]

## Arithmetic progression

EXERCISE 19.1 QUESTION 1 If the term of a sequence is given by write down its first five terms. Sol : Given : For = 1 For = 2 For = 3 For = 13[…]

## Circle

EXERCISE 24.3 QUESTION 1 Find the equation of the circle, the end points of whose diameter are $(2,-3)$ and $(-2,4)$ . Find its center and radius. Sol : $(2,-3)$ and $(-2,4)$ are the ends points[…]

## Combination

EXERCISE 17.2 QUESTION 1 From a group of 15 cricket players, a team of 11 players is to be chosen. In how many ways can this be done? Sol : Required number of ways =[…]

## Combination

EXERCISE 17.1 QUESTION 1 Evaluate the following : (i) Sol : (ii) Sol : (iii) Sol : (iv) Sol : (v) Sol : = 31 QUESTION 2 If[…]

## Circle

EXERCISE 24.2 QUESTION 1 Find the co-ordinates of the center and radius of each of the following circles: (i) Sol : The given equation can be rewritten as Center And, radius = 7 (ii)[…]

## Sanskrit translation of chapter 3 स्वावलम्बबम् in hindi class 7

स्वावलम्बबम् कृष्णमूर्ति: श्रीकण्ठश्च मित्रे आस्ताम्। श्रीकण्ठस्य पिता समृद्ध: आसीत। अत: तस्य भवने सर्वविधानि सुख-साधनानि आसन्। तस्मिन् विशाले भवने चत्वारिशत् स्तम्भा: आसन्। तस्य अष्टादश-प्रकोष्ठेषु पञ्चाशत् गवाक्षा:, चतुश्चत्वारिशत् द्वाराणि, षट्त्रिशत् विद्युत-व्यजनानि च आसन्। सरलार्थ- कृष्णमूर्ति और[…]

## Circle

EXERCISE 24.1 QUESTION 1 Find the equation of the circle with : (i) Center $(-2,3)$ and radius 4 Sol : Let $(h, k)$ be the centre of a circle with radius a. Thus, its equation[…]

## Permutation

Exercise 16.2 QUESTION 1 In a class there are 27 boys and 14 girls . The teacher wants to select 1 boy and 1 girl to represent the class in a function . In how[…]

## Rd sharma solution of class 11 chapter 16 permutation

EXERCISE 16.1 QUESTION 1 Compute : (i) Sol : = 870 (ii) Sol : = 100 (iii) L.C.M. Sol : Therefore, and can be rewritten as: LCM of and QUESTION 2 Prove[…]

## complex number

Exercise 13.4 QUESTION 1 Find the modulus and argument of the following complex number and hence express each of them in the polar form : (i) Sol : Let Since point lies in the first[…]

## Quadratic equations

Exercise 14.1 QUESTION 1 Sol : Hence , the roots of the equation are i and -i QUESTION 2 Sol : Hence, the roots of the equation are QUESTION 3 Sol : […]

## Rd sharma solution of class 11 chapter 13 complex number

Exercise 13.3 QUESTION 1 (i) Sol : , and (ii) Sol : , , ṇṇ (iii) Sol : , , (iv) Sol : , , (v) Sol : , ,[…]

## Rd sharma solution of chapter 13 complex number class 11

Exercise 13.2 QUESTION 1 Express the following complex numbers in the standard form a+ib : (i) Sol : (ii) Sol : (iii) Sol : (iv) Sol : (v) Sol[…]

## Rd sharma solution of chapter 13 Complex numbers

Complex numbers Exercise 13.1 QUESTION 1 Evaluate the following: (i) Sol : (ii) Sol : =1 (iii) Sol : = -1 (iv) Sol : (v) Sol : = 0[…]

## Sanskrit translation of chapter 15 प्रहेलिका in hindi class 8

प्रहेलिका पाठ का परिचय पहेलियाँ मनोरंजन का एक प्राचीन विद्या (तरीका) है। ये लगभग संसार की सभी भाषाओं में उपलब्ध् हैं। संस्कृत के कवियों ने इस परम्परा को अत्यन्त समृद्ध किया है। पहेलियाँ हमें आनन्द[…]

## Sanskrit translation of chapter 14 आर्यभटः in hindi class 8

आर्यभटः पाठ का परिचय भारतवर्ष की अमूल्य निधि है ज्ञान-विज्ञान की सुदीर्घ परम्परा। इस परम्परा को सम्पोषित करने वाले प्रबुद्ध मनीषियों में अग्रगण्य थे-आर्यभट। दशमलव प(ति का प्रयोग सबसे पहले आर्यभट ने किया, जिसके कारण[…]

## Sanskrit translation of chapter 13 हिमालयः in hindi class 8

हिमालयः पाठ का परिचय यह पाठ महाकवि कालिदास द्वारा लिखित ‘कुमार सम्भव’ नामक महाकाव्य के प्रथम सर्ग से लिया गया है। इन पद्यों में हिमालय की प्राकृतिक सुषमा का वर्णन किया गया है। (क)[…]

## Sanskrit translation of chapter 12 कः रक्षति कः रक्षितः in hindi class 8

कः रक्षति कः रक्षितः पाठ का परिचय यह पाठ पर्यावरण पर केन्द्रित है। प्लास्टिक पर्यावरण के लिए घातक है, लेकिन इसका हमारे जीवन में इस सीमा तक प्रवेश हो चुका है कि इसके बिना दैनिक[…]

## Sanskrit translation of chapter 11 सावित्री बाई फुले in hindi class 8

सावित्री बाई फुले पाठ का परिचय शिक्षा हमारा अधिकार है। हमारे समाज के कई समुदायों को, जो लम्बे समय तक इससे वंचित रहे, इस अधिकार को पाने के लिए लम्बा संघर्ष करना पड़ा। इसकी प्राप्ति[…]

## Sanskrit translation of chapter 10 अशोक वनिका in hindi class 8

अशोक वनिका पाठ का परिचय यह पाठ आदि कवि वाल्मीकिकृत रामायण के सुन्दरकाण्ड के पन्द्रहवें सर्ग से लिया गया है। हनुमान जी सीता जी की खोज में जब लंका में प्रवेश करते हैं तो वहाँ[…]

## Sanskrit translation of chapter 9 सप्तभगिन्यः in hindi

सप्तभगिन्यः पाठ का परिचय सप्तभगिनी-यह एक उपनाम है। उत्तर-पूर्व के सात राज्य विशेष को उक्त उपाधि दी गई है। इन राज्यों का प्राकृतिक सौन्दर्य अत्यन्त विलक्षण है। इनकी सांस्कृतिक और सामाजिक विशेषता को ध्यान में[…]

## Sanskrit translation of chapter 8 संसारसागरस्य नायकाः in hindi

संसारसागरस्य नायकाः पाठ का परिचय यह पाठ अनुपम मिश्रा द्वारा लिखित ‘आज भी खरे हैं तालाब’ में संकलित ‘संसार सागर के नायक’ नामक अध्याय से लिया गया है। लेखक ने यहाँ पानी के लिए मानव निर्मित[…]

## Sanskrit translation of chapter 6 प्रेमलस्य प्रेमल्याश्च कथा in hindi class 8

प्रेमलस्य प्रेमल्याश्च कथा पाठ का परिचय प्रस्तुत कहानी शिक्षाविद् गिजु भाई (1885-1939) की रचना ‘पेमला पेमली की कहानी’ का अनुवाद है। इस कहानी में एक महिला घरेलू कामों को पूरा करने की अपनी पारम्परिक भूमिका[…]

## Sanskrit translation of chapter 7 जलवाहिनी in hindi class 8

जलवाहिनी पाठ का परिचय यह गीत भोजपुरी लोकगीत का अनुवाद है। इसमें गाँव की पानी भरने वाली स्त्राी का चित्राण किया गया है। कुएँ से घड़े में जल भरकर लाते समय उसके मन में आने[…]

## Sanskrit translation of chapter 5 धर्मे धमनं पापे पुण्यम in hindi class 8

धर्मे धमनं पापे पुण्यम पाठ का परिचय यह कथा पंचतंत्र की शैली में लिखी गई है। यह लोककथा मध्यप्रदेश के डिण्डोरी जिले में परधानों के बीच प्रचलित है। इस कथा में बताया गया है कि[…]

## Sanskrit translation of chapter 4 सदैव पुरतो निधेहि चरणम in hindi class 8

सदैव पुरतो निधेहि चरणम पाठ का परिचय श्रीधरभास्कर वर्णेकर ने अपने इस गीत में चुनौतियों को स्वीकार करते हुए आगे बढ़ने का आह्नान किया है। श्रीधर राष्ट्रवादी कवि हैं जिन्होंने इस गीत के द्वारा जागरण[…]

## Sanskrit translation of chapter 2 दुर्बुद्धि: विनश्यति in hindi class 7

Chapter-दुर्बुद्धि: विनश्यति Chapter-सुभाषितानि दुर्बुद्धि: विनश्यति अस्ति मगधदेशे फुल्लोत्पलनाम सर: । तत्र संकटविकटौ हंसैौ निवसत: । कम्बुग्रवनामक: तयो: मित्रम् एक: कूर्म: अपि तत्रैव प्रतिवसति स्म । अथ एकदा धीवरा: तत्र आगच्छन् । ते अकथयन्[…]

## Sanskrit translation of chapter 3 भगवदज्जुकम in hindi

भगवदज्जुकम पाठ का परिचय भगवदज्जुकम् संस्कृत का एक प्रसिद्ध प्रहसन है। इसकी रचना बोधयन द्वारा की गई है। इसमें एक गणिका जिसका नाम वसन्तसेना है अपनी परभृतिका नामक सेविका के साथ उद्यान में विहार के लिए आती[…]

## Sanskrit translation of chapter 2 बिलस्य वाणी न कदापि मे श्रुता in hindi

बिलस्य वाणी न कदापि मे श्रुता पाठ का परिचय प्रस्तुत पाठ संस्कृत के प्रसिद्ध कथाग्रन्थ ‘पञ्चतन्त्रम्’ के तृतीय तंत्र ‘काकोलूकीयम्’ से संकलित है। पञ्चतंत्र के मूल लेखक विष्णुशर्मा हैं। इसमें पाँच खण्ड हैं जिन्हें ‘तंत्र’[…]

## Sanskrit translation chapter सूभाषितानि class 8 in hindi

सूभाषितानि पाठ का परिचय ‘सुभाषित’ शब्द सु + भाषित दो शब्दों के मेल से बना है। सु का अर्थ है- सुन्दर, मधुर और भाषित का अर्थ है- वचन। इस प्रकार सुभाषित का अर्थ है- सुन्दर/मधुर[…]

## NCERT solution class 9 chapter Surface area and volume

Exercise 13.1 Question 1 A plastic box 1.5 m long, 1.25 m wide and 65 cm deep, is to be made. It is to be open at the top. Ignoring the thickness of the plastic[…]

## Rd sharma solution class 12 chapter continuity

Exercise 9.2 Question 1 Prove that the function is everywhere continuous . Sol : When , we have We know that sin x as well as the identity function x are everywhere continuous . So , the[…]

## Rd sharma solution class 12 chapter 2 functions

Exercise 3.1 Question 1 Give an example of a function (i) which is one-one but not onto Sol : Injectivity : Let x and y be any two elements in the domain (Z) , such that […]

## NCERT solution class 10 chapter 2 polynomials

Exercise 2.2 (working) Question 1 Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. (i) Sol : or or Therefore , the zeroes of are 4[…]

## NCERT solution class 10 chapter 2 polynomials

Exercise 2.1 Question 1 The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x), in each case. (i) Sol : (i) The[…]

## NCERT solution class 10 chapter 1 Real numbers

Exercise 1.1 Exercise 1.2 Exercise 1.3 Exercise 1.4 Exercise 1.4 Question 1 Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating[…]

## NCERT solution class 10 chapter 1 Real numbers

Exercise 1.1 Exercise 1.2 Exercise 1.3 Exercise 1.4 Exercise 1.3 Question 1 Prove that is irrational . Sol : Let is a rational number. Therefore, we can find two integers a , b[…]

## NCERT solution class 10 chapter 1 Real numbers

Exercise 1.1 Exercise 1.2 Exercise 1.3 Exercise 1.4 Exercise 1.2 Question 1 Express each number as product of its prime factors: (i) 140 Sol : (ii) 156 Sol : (iii) 3825[…]

## Rd sharma solution class 12 chapter Relations

Exercise 1.1 Question 1 Let A be the set of all human beings in a town at a particular time. Determine whether each of the following relations are reflexive, symmetric and transitive: (i) R =[…]

## Rd sharma solution class 12 chapter Differentiation

Exercise 11.2 Question 1 Differentiate Sol : Let Differentiating y with respect to x we get, So, Question 2 Differentiate Sol : Let which can be written as Differentiating y with respect to[…]

## Rd sharma solution class 12 chapter Inverse trigonometric functions

Exercise 4.1 Question 1 Find the principal value of each of the following: (i) Sol : (ii) Sol : (iii) Sol : (iv) Sol : […]

## Rd sharma solution class 12 chapter Continuity

Exercise 9.1 Question 1 Test the continuity of the function on at the origin: Sol : Given We observe (LHL at x= 0) =-1 (RHL at x = 0) =1 Hence, is discontinuous at[…]

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## NCERT solution class 10 chapter 1 Real numbers

Exercise 1.1 Exercise 1.2 Exercise 1.3 Exercise 1.4 Exercise 1.1 Question 1 Use Euclid’s division algorithm to find the HCF of: (i) 135 and 225 Sol : (i) 135 and 225 Since 225[…]

## Rd sharma solution class 1 chapter Indefinite integrals

Exercise 19.2 Question 1

## Rd sharma solution class 1 chapter Indefinite integrals

Exercise 19.1 Question 1 Evaluate each of the following integrals: (i) Sol : (ii) Sol : (iii) Sol : (iv) Sol : (v) Sol : (vi) Sol : (vii)[…]

## RD Sharma solution class 12 chapter 28 Straight line in space

Exercise 28.1 Question 1 Find the vector and cartesian equations of the line through the point and which is parallel to the vector Sol : We know that the vector equation of a line[…]

## NCERT solution class 8 chapter 16 Playing with numbers

Exercise 16.1 Exercise 16.2 Exercise 16.2 Question 1 If 21y5 is a multiple of 9, where y is a digit, what is the value of y? Sol : If a number is a multiple of[…]

## NCERT solution class 8 chapter 16 Playing with numbers

Exercise 16.1 Exercise 16.2 Exercise 16.1 Question 1 Find the values of the letters in the following and give reasons for the steps involved. Sol : The addition of A and 5 is giving 2[…]

## NCERT solution class 8 chapter 15 Introduction to Graphs

Exercise 15.1 Exercise 15.2 Exercise 15.3 Exercise 15.3 Question 1 Draw the graphs for the following tables of values, with suitable scales on the axes. (a) Cost of apples Number of apples 1 2 3[…]

## NCERT solution class 8 chapter 15 Introduction to Graphs

Exercise 15.1 Exercise 15.2 Exercise 15.3 Exercise 15.2 Question 1 Plot the following points on a graph sheet. Verify if they lie on a line (a) A(4, 0), B(4, 2), C(4, 6), D(4, 2.5) (b)[…]

## NCERT solution class 8 chapter 15 Introduction to Graphs

Exercise 15.1 Exercise 15.2 Exercise 15.3 Exercise 15.1 Question 1 The following graph shows the temperature of a patient in a hospital, recorded every hour. (a) What was the patient’s temperature at 1 p.m.? (b)[…]

## NCERT solution class 8 chapter 14 Factorisation

Exercise 14.1 Exercise 14.2 Exercise 14.3 Exercise 14.4 Exercise 14.4 Question 1 Find and correct the errors in the statement: 4(x − 5) = 4x − 5 Sol : L.H.S. = 4(x − 5) =[…]

## NCERT solution class 8 chapter 14 Factorisation

Exercise 14.1 Exercise 14.2 Exercise 14.3 Exercise 14.4 Exercise 14.3 Question 1 Carry out the following divisions. (i) 28×4 ÷ 56x (ii) −36y3 ÷ 9y2 (iii) 66pq2r3 ÷ 11qr2 (iv) 34x3y3z3 ÷ 51xy2z3 (v) 12a8b8[…]

## NCERT solution class 8 chapter 14 Factorisation

Exercise 14.1 Exercise 14.2 Exercise 14.3 Exercise 14.4 Exercise 14.2 Question 1 Factorise the following expressions. (i) a2 + 8a + 16 (ii) p2 − 10p + 25 (iii) 25m2 + 30m + 9 (iv)[…]

## NCERT solution class 8 chapter 14 Factorisation

Exercise 14.1 Exercise 14.2 Exercise 14.3 Exercise 14.4 Exercise 14.1 Question 1 Find the common factors of the terms (i) 12x, 36 (ii) 2y, 22xy (iii) 14pq, 28p2q2 (iv) 2x, 3×2, 4 (v) 6abc, 24ab2,[…]

## NCERT solution class 8 chapter 13 Direct and Inverse proportions

Exercise 13.1 Exercise 13.2 Exercise 13.2 Question 1 Which of the following are in inverse proportion? (i) The number of workers on a job and the time to complete the job. (ii) The time taken[…]

## NCERT solution class 8 chapter 13 Direct and Inverse proportions

Exercise 13.1 Exercise 13.2 Exercise 13.1 Question 1 Following are the car parking charges near a railway station up to 4 hours Rs 60 8 hours Rs 100 12 hours Rs 140 24 hours Rs[…]

## NCERT solution class 8 chapter 12 Exponents and Power

Exercise 12.1 Exercise 12.2 Exercise 12.2 Question 1 Express the following numbers in standard form. (i) 0.0000000000085 (ii) 0.00000000000942 (iii) 6020000000000000 (iv) 0.00000000837 (v) 31860000000 Sol : (i) 0.0000000000085 = 8.5 × 10−12 (ii) 0.00000000000942[…]

## NCERT solution class 8 chapter 12 Exponents and Power

Exercise 12.1 Exercise 12.2 Exercise 12.1 Question 1 Evaluate (i) 3−2 (ii) (−4)−2 (iii) Sol : (i) (ii) (iii) Question 2 Simplify and express the result in power notation with positive exponent. (i)[…]

## NCERT solution class 8 chapter 11 Mensuration

Exercise 11.1 Exercise 11.2 Exercise 11.3 Exercise 11.4 Exercise 11.4 Question 1 Given a cylindrical tank, in which situation will you find surface area and in which situation volume. (a) To find how much it[…]

## NCERT solution class 8 chapter 11 Mensuration

Exercise 11.1 Exercise 11.2 Exercise 11.3 Exercise 11.4 Exercise 11.3 Question 1 There are two cuboidal boxes as shown in the adjoining figure. Which box requires the lesser amount of material to make? Sol :[…]

## NCERT solution class 8 chapter 11 Mensuration

Exercise 11.1 Exercise 11.2 Exercise 11.3 Exercise 11.4 Exercise 11.2 Question 1 The shape of the top surface of a table is a trapezium. Find its area if its parallel sides are 1 m and[…]

## NCERT solution class 8 chapter 11 Mensuration

Exercise 11.1 Exercise 11.2 Exercise 11.3 Exercise 11.4 Exercise 11.1 Question 1 A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area?[…]

## NCERT solution class 8 chapter 10 Visualising Solid Shapes

Exercise 10.1 Exercise 10.2 Exercise 10.3 Exercise 10.3 Question 1 Can a polyhedron have for its faces (i) 3 triangles? (ii) 4 triangles? (iii) a square and four triangles? Sol : (i) No, such a polyhedron is[…]

## NCERT solution class 8 chapter 10 Visualising Solid Shapes

Exercise 10.1 Exercise 10.2 Exercise 10.3 Exercise 10.2 Question 1 Look at the given map of a city. Answer the following. (a) Colour the map as follows: Blue − water plant, red − fire station, orange −[…]

## NCERT solution class 8 chapter 10 Visualising Solid Shapes

Exercise 10.1 Exercise 10.2 Exercise 10.3 Exercise 10.1 Question 1 For each of the given solid, the two views are given. Match for each solid the corresponding top and front views. Sol : The given solids, matched[…]

## NCERT solution class 8 chapter 9 Algebraic Expression and Identities

Exercise 9.1 Exercise 9.2 Exercise 9.3 Exercise 9.4 Exercise 9.5 Exercise 9.4 Question 1 Multiply the binomials. (i) (2x + 5) and (4x − 3) (ii) (y − 8) and (3y − 4) (iii) (2.5l − 0.5m) and[…]

## NCERT solution class 8 chapter 9 Algebraic Expression and Identities

Exercise 9.1 Exercise 9.2 Exercise 9.3 Exercise 9.4 Exercise 9.5 Exercise 9.5 Question 1 Use a suitable identity to get each of the following products. (i) (x + 3) (x + 3) (ii) (2y + 5) (2y +[…]

## NCERT solution class 8 chapter 9 Algebraic Expression and Identities

Exercise 9.1 Exercise 9.2 Exercise 9.3 Exercise 9.4 Exercise 9.5 Exercise 9.3 Question 1 Carry out the multiplication of the expressions in each of the following pairs. (i) 4p, q + r (ii) ab, a − b (iii)[…]

## NCERT solution class 8 chapter 9 Algebraic Expression and Identities

Exercise 9.1 Exercise 9.2 Exercise 9.3 Exercise 9.4 Exercise 9.5 Exercise 9.2 Question 1 Find the product of the following pairs of monomials. (i) 4, 7p (ii) − 4p, 7p (iii) − 4p, 7pq (iv) 4p3, − 3p[…]

## NCERT solution class 8 chapter 9 Algebraic Expression and Identities

Exercise 9.1 Exercise 9.2 Exercise 9.3 Exercise 9.4 Exercise 9.5 Exercise 9.1 Question 1 Identify the terms, their coefficients for each of the following expressions. (i) 5xyz2 − 3zy (ii) 1 + x + x2 (iii) 4x2y2 −[…]

## NCERT solution class 8 chapter 8 Comparing quantities

Exercise 8.1 Exercise 8.2 Exercise 8.3 Exercise 8.3 Question 1 Calculate the amount and compound interest on (a) Rs 10800 for 3 years at per annum compounded annually. Sol : (a) Principal (P) = Rs[…]

## NCERT solution class 8 chapter 8 Comparing quantities

Exercise 8.1 Exercise 8.2 Exercise 8.3 Exercise 8.2 Question 1 A man got a 10% increase in his salary. If his new salary is Rs 1,54,000, find his original salary. Sol : Let the original[…]

## NCERT solution class 8 chapter 8 Comparing quantities

Exercise 8.1 Exercise 8.2 Exercise 8.3 Exercise 8.1 Question 1 Find the ratio of the following: (a) Speed of a cycle 15 km per hour to the speed of scooter 30 km per hour. (b)[…]

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## NCERT solution class 8 chapter 7 Cube and Cube roots

Exercise 7.1 Exercise 7.2 Exercise 7.2 Question 1 Find the cube root of each of the following numbers by prime factorization method. (i) 64 Sol : (i) Prime factorization of ∴ (ii) 512 Sol[…]

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## NCERT solution class 8 chapter 7 Cube and Cube roots

Exercise 7.1 Exercise 7.2 Exercise 7.1 Question 1 Which of the following numbers are not perfect cubes? (i) 216 (ii) 128 (iii) 1000 (iv) 100 (v) 46656 Sol : (i) The prime factorization of 216[…]

## NCERT Solutions for class 8 Maths chapter 6 Square and square roots

Exercise 6.1 Exercise 6.2 Exercise 6.3 Exercise 6.4 Exercise 6.3 Question 1 What could be the possible ‘one’s’ digits of the square root of each of the following numbers? (i) 9801 (ii) 99856 (iii) 998001[…]

## NCERT Solutions for class 8 Maths chapter 6 Square and square roots

Exercise 6.1 Exercise 6.2 Exercise 6.3 Exercise 6.4 Exercise 6.4 Question 1 Find the square root of each of the following numbers by division method. (i) 2304 Sol : (i) The square root of 2304[…]

## NCERT Solutions for class 8 Maths chapter 6 Square and square roots

Exercise 6.1 Exercise 6.2 Exercise 6.3 Exercise 6.4 Exercise 6.1 Question 1 What will be the unit digit of the squares of the following numbers? (i) 81 (ii) 272 (iii) 799 (iv) 3853 (v) 1234[…]

## NCERT Solutions for class 8 Maths chapter 6 Square and square roots

Exercise 6.1 Exercise 6.2 Exercise 6.3 Exercise 6.4 Exercise 6.2 Question 1 Find the square of the following numbers (i) 32 (ii) 35 (iii) 86 (iv) 93 (v) 71 (vi) 46 Sol : (i) 322[…]

## NCERT Solutions for class 8 Maths chapter 5 Data handling

Exercise 5.1 Exercise 5.2 Exercise 5.3 Exercise 5.3 Question 1 List the outcomes you can see in these experiments. (a) Spinning a wheel (b) Tossing two coins together Sol : (a) On spinning the given[…]

## NCERT Solutions for class 8 Maths chapter 5 Data handling

Exercise 5.1 Exercise 5.2 Exercise 5.3 Exercise 5.2 Question 1 A survey was made to find the type of music that a certain group of young people liked in a city. Adjoining pie chart[…]

## NCERT Solutions for class 8 Maths chapter 5 Data handling

Exercise 5.1 Exercise 5.2 Exercise 5.3 Exercise 5.1 Question 1 For which of these would you use a histogram to show the data? (a) The number of letters for different areas in a postman’s bag.[…]

## RD sharma solution class 12 chapter determinants

Determinants Exercise 6.1 Question 1 Write the minors and cofactors of each element of the first column of the following matrices and hence evaluate the determinant in each case: (i) A = Sol : In[…]

## NCERT Solutions for class 8 Maths chapter 4 Practical geometry

Exercise 4.1 Exercise 4.2 Exercise 4.3 Exercise 4.4 Exercise 4.5 Exercise 4.5 Question 1 Draw the following: The square READ with RE = 5.1 cm Sol : All the sides of a square are of[…]

## NCERT Solutions for class 8 Maths chapter 4 Practical geometry

Exercise 4.1 Exercise 4.2 Exercise 4.3 Exercise 4.4 Exercise 4.5 Exercise 4.4 Question 1 Construct the following quadrilaterals, (i) Quadrilateral DEAR DE = 4 cm EA = 5 cm AR = 4.5 cm ∠E =[…]

## NCERT Solutions for class 8 Maths chapter 4 Practical geometry

Exercise 4.1 Exercise 4.2 Exercise 4.3 Exercise 4.4 Exercise 4.5 Exercise 4.3 Question 1 Construct the following quadrilaterals. (i) Quadrilateral MORE MO = 6 cm OR = 4.5 cm ∠M = 60° ∠O = 105°[…]

## NCERT Solutions for class 8 Maths chapter 4 Practical geometry

Exercise 4.1 Exercise 4.2 Exercise 4.3 Exercise 4.4 Exercise 4.5 Exercise 4.2 Question 1 Construct the following quadrilaterals. (i) Quadrilateral LIFT LI = 4 cm IF = 3 cm TL = 2.5 cm LF =[…]

## NCERT Solutions for class 8 Maths chapter 4 Practical geometry

Exercise 4.1 Exercise 4.2 Exercise 4.3 Exercise 4.4 Exercise 4.5 Exercise 4.1 Question 1 Construct the following quadrilaterals. (i) Quadrilateral ABCD AB = 4.5 cm BC = 5.5 cm CD = 4 cm AD =[…]

## NCERT Solutions for class 8 Maths chapter 3 Understanding Quadrilaterals

Exercise 3.1 Exercise 3.2 Exercise 3.3 Exercise 3.4 Exercise 3.4 Question 1 State whether True or False. (a) All rectangles are squares. (b) All rhombuses are parallelograms. (c) All squares are rhombuses and also rectangles.[…]

## NCERT Solutions for class 8 Maths chapter 3 Understanding Quadrilaterals

Exercise 3.1 Exercise 3.2 Exercise 3.3 Exercise 3.4 Exercise 3.3 Question 1 Given a parallelogram ABCD. Complete each statement along with the definition or property used. (i) AD = … (ii) ∠DCB = … (iii)[…]

## NCERT Solutions for class 8 Maths chapter 3 Understanding Quadrilaterals

Exercise 3.1 Exercise 3.2 Exercise 3.3 Exercise 3.4 Exercise 3.2 Question 1 Find x in the following figures. (a) Sol : We know that the sum of all exterior angles of any polygon is 360º.[…]

## NCERT Solutions for class 8 Maths chapter 3 Understanding Quadrilaterals

Exercise 3.1 Exercise 3.2 Exercise 3.3 Exercise 3.4 Exercise 3.1 Question 1 Given here are some figures. (1) (2) (3) (4) (5) (6) (7) (8) Classify each of them on the basis of[…]

## Derivative as a rate measure

Derivative as a rate measure Exercise 13.1 1. Find the rate of change of the total surface area of a cylinder of radius r and height h, when the radius varies. Sol : 2.[…]

## NCERT Solutions for class 8 Maths chapter 2 Linear Equation In One Variable

Exercise 2.1 Exercise 2.2 Exercise 2.3 Exercise 2.4 Exercise 2.5 Exercise 2.6 Exercise 2.6 Question 1 : Solve : \( \dfrac{8x-3}{3x}=2 \) Sol : \( \dfrac{8x-3}{3x}=2 \) On multiplying both sides by 3x , we obtain 8x -3 = 6x[…]

## NCERT Solutions for class 8 Maths chapter 2 Linear Equation In One Variable

Exercise 2.1 Exercise 2.2 Exercise 2.3 Exercise 2.4 Exercise 2.5 Exercise 2.6 Exercise 2.5 Question 1 : Solve the linear equation \( \dfrac{x}{2}-\dfrac{1}{5}=\dfrac{x}{3}+\dfrac{1}{4} \) Sol : \( \dfrac{x}{2}-\dfrac{1}{5}=\dfrac{x}{3}+\dfrac{1}{4} \) L.C.M of the denominators 2, 3, 4, and 5 is 60[…]

## NCERT Solutions for class 8 Maths chapter 2 Linear Equation In One Variable

Exercise 2.1 Exercise 2.2 Exercise 2.3 Exercise 2.4 Exercise 2.5 Exercise 2.6 Exercise 2.4 Question 1: Amina thinks a number and subtracts \( \dfrac{5}{2} \) from it . She multiplies the result by 8. The result now obtained is 3 times[…]

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Elon Musk’s Boring Company set to unveil its first Los Angeles-area tunnel The tunnel, an initial proof-of-concept, has been excavated along a path that runs not through Los Angeles but beneath the tiny adjacent[…]

## Light : Reflection and Refraction

Light : is a form of energy which enables us to see objects from which it comes (or from which it reflects.) Luminous objects : Those objects which gives out their own light are called[…]

## NCERT Solutions for class 8 Maths chapter 2 Linear Equation In One Variable

Exercise 2.1 Exercise 2.2 Exercise 2.3 Exercise 2.4 Exercise 2.5 Exercise 2.6 EXERCISE 2.2 Question 1 : If you subtract \( \dfrac{1}{2} \) from a number and multiply the result by \( \dfrac{1}{2} \) , you get \( \dfrac{1}{8} \). What is the[…]

## NCERT Solutions for class 8 Maths chapter 2 Linear Equation In One Variable

Exercise 2.1 Exercise 2.2 Exercise 2.3 Exercise 2.4 Exercise 2.5 Exercise 2.6 EXERCISE 2.3 Question 1 : Solve and check result : 3x = 2x + 18 Sol : 3x = 2x + 18 On transposing 2x to L.H.S ,[…]

## NCERT Solutions for class 8 Maths chapter 2 Linear Equation In One Variable

Exercise 2.1 Exercise 2.2 Exercise 2.3 Exercise 2.4 Exercise 2.5 Exercise 2.6 EXERCISE 2.1 Question 1 : Solve : x-2=7 sol : x-2=7 On transposing 2 to R.H.S , we obtain x=7+2=9 Question 2 : Solve : y+3=10 sol[…]

## NCERT Solution for class 8 chapter 1 RATIONAL NUMBER

Exercise 1.1 Exercise 1.2 EXERCISE 1.2 Question 1 : Represent these numbers on the number line. (i) Sol: can be represented on the number line as follows. (ii) Sol : can be[…]

## NCERT Solution for class 8 chapter 1 RATIONAL NUMBER

Exercise 1.1 Exercise 1.2 EXERCISE 1.1 Question 1 Using appropriate properties find . (i) sol : = 2 (ii) sol : Question 2 : Write the additive inverse of each of the[…]

## WORK AND ENERGY

WORK AND ENERGY Whenever a force makes a body move , then work is said to be done or work is done when force produces motion. And for doing work energy is required. Work done[…]

## PERIODIC CLASSIFICATION OF ELEMENTS

PERIODIC CLASSIFICATION OF ELEMENTS Firstly what is element , an element is a substance containing atoms of only one type e.g Na , Au , Ca , etc . Up till now there are around[…]

## DIFFERENTIATION

Differentiation Exercise 11.1 Differentiate the following functions from first principles : QUESTION 1 Sol : QUESTION 2 Sol : QUESTION 3 Sol : QUESTION 4 Sol : QUESTION 5 Sol : […]

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## Hydrocarbons

HYDROCARBONS Organic compound are composed of only carbons and hydrogen are called hydrocarbons. ON THE BASIS OF STRUCTURE HYDROCARBONS ARE OF TWO TYPES 1. Acyclic or open chain hydrocarbons 2. Cyclic or closed chain hydrocarbons[…]

## Carbon And Its Compound

COAL AND PETROLEUM Firstly what is fuel ,fuel is a material that consist of energy stored in it. Most of the fuel are free carbons (coal , coke ,charcoal) or just carbon compounds (kerosene ,[…]

## WORK, ENERGY AND POWER

WORK, ENERGY AND POWER In your daily life you have seen many things like person pushing heavy box , a teacher teaching students , mom cooking food , all are said to be working .[…]

## REDOX REACTIONS

REDOX REACTIONS Chemical reaction in which electron transfer from one chemical substance to another are termed as oxidation-reduction reactions or redox reactions. You can see many examples from your daily life like production of electricity[…]

## Thermodynamics

Thermodynamics The word “thermodynamics” is derived from Greek words therme (heat) and dinamics (flow or motion) . Thermodynamics mainly deals with the transformation of heat into mechanical energy and vice versa . LIMITATIONS OF THERMODYNAMICS[…]

## straight line

Straight line EXERCISE 23.1 1. Find the slopes of the lines which make the following angles with the positive direction of x-axis : (i) \( -\dfrac{\pi}{4} \) sol: m=tan\( \theta \) =tan(\( -\dfrac{\pi}{4} \)) = -1[…]

## Sanskrit solution chapter 1 सुभाषितानि Class 7 translated in hindi

Chapter-दुर्बुद्धि: विनश्यति Chapter-सुभाषितानि सुभाषितानि पृथिव्यां त्रीणि रत्नानि जलमत्रं सुभाषितम् । मूढै: पाषाणखण्डेषु रत्नसंज्ञा विधीयती ।। 1 ।। सरलार्थ: पृथ्वी पर केवल तीन ही रत्न है। जल, अन्न और मधुर वचन। बुद्धिमान व्यक्ति इनकी समझ[…]

## Chapter Some Basic Concepts of Chemistry

SOME BASIC CONCEPT OF CHEMISTRY Classification of matter on the basis of chemical properties: Matter classified into two groups pure substances and mixtures.Pure substances further divided into elements and compounds. 1. Elements : it is[…]

## Chapter DOS (DISK OPERATING SYSTEM)

DOS (DISK OPERATING SYSTEM) DOS is the most popular example of single user operating system. DOS stands for Disk Operating System. Disk operating system is a ready-made program which provide various computer handling facilities through[…]

## Chapter Software at a glance

SOFTWARE AT A GLANCE As you know, software is a collection of programs and a program is a set of instructions written in a programming language.Using software, user , user interacts with the computer. It[…]

## Chapter Secondary memory

SECONDARY MEMORY As you read in previous lesson that computer have Primary memory or internal memory. Now, let us see the secondary memory.Secondary memory is also called External memory of a computer. We use secondary[…]

## Chapter Primary memory

PRIMARY MEMORY Memory unit of a computer holds (store) all data, instructions and processed data.Memory unit of computer is classified in following two categories: 1. Primary Memory (we study it in this chapter) 2. Secondary[…]

## Chapter Output devices

OUTPUT DEVICES The main function of an output device id to convert the binary information inside computer in numbers and words so as to be easily understood by the user.Whatever we input the data, it[…]

## Chapter Input devices

INPUT DEVICES Input devices is a device through which we feed data into the computer.When data are entered in the form of digits, alphabets and other special character, input devices converts it into their[…]

## Chapter Computer and its components

COMPUTERS AND ITS COMPONENTS COMPUTER-MORE THAN A CALCULATING DEVICE Computer is not mere a calculating device.It is a machine that can perform both arithmetic and non-arithmetic operations like copy, move select, compare etc.It works[…]

## Chapter CHARACTERISTICS OF COMPUTER

CHARACTERISTICS OF COMPUTER Computer have become necessary thing of our lives.Computers are being used almost every field.You can see computers everywhere in banks, schools, railways, airports, laboratories , hospitals shops etc. There are some amazing[…]

## Chapter CLASSIFICATION BY SIZE AND PERFORMANCE

CLASSIFICATION BY SIZE AND PERFORMANCE According to the purpose-wise Digital computer can be classified in to two categories: Special purpose computer Special purpose computers is designed in a way that it could perform special task.Programs[…]

## Chapter CLASSIFICATION OF COMPUTERS BY TYPES

CLASSIFICATION OF COMPUTERS BY TYPES The computer have been classified into three categories according to their types. 1. Analog Computers 2. Digital Computers 3. Hybrid Computers ANALOG COMPUTERS ‘Analog’ is basically a Greek Word, which[…]

## chapter HISTORICAL EVOLUTION OF COMPUTER

HISTORICAL EVOLUTION OF COMPUTER The ascent of computer is very old.It took long duration to mature.Ancient people used stone,bones,beads etc for calculation and to keep record but as a civilization developed, people felt the need[…]

## Blackberry publication class 8 maths chapter comparing quantities

COMPARING QUANTITIES EXERCISE 9(A) 1.Express each of the following ratios in the simplest form: (a) 3 kg 500 g : 4 kg 250 g (b) 8 months : \( 1\dfrac{1}{2} \) years (c) 36 minute : \([…]

## Chapter classification of elements and periodicity in properties

CLASSIFICATION OF ELEMENTS AND PERIODICITY IN PROPERTIES Brief Historical Development Of Periodic Table 1.Johann Dobereiner’s (Law of triads) In between 1815 and 1829 he gave law of triads.According to which group of three elements which[…]

## Blackberry publication class 8 maths chapter rational number

RATIONAL NUMBERS EXERCISE 2(A) 1.Using properties find: (a) \( \dfrac{-4}{7}+\dfrac{-3}{8}+\dfrac{-6}{7}+\dfrac{-14}{14}+\dfrac{1}{56} \) (b) \( \dfrac{-12}{5}+\dfrac{1}{7}+\dfrac{-1}{10}+\dfrac{3}{14}+\dfrac{-7}{20} \) (c) \( \dfrac{-4}{7}+\dfrac{2}{9}+\dfrac{-5}{4}+\dfrac{8}{21} \) (d) \( \dfrac{-3}{16}+\dfrac{14}{8}+\dfrac{-3}{4}+\dfrac{-2}{32}+(-1) \) (e) \( \dfrac{-5}{8}+\dfrac{2}{7}+\dfrac{-5}{2}+\dfrac{8}{56} \) (f) \( \dfrac{-4}{5}\times\dfrac{5}{7}\times\Big(\dfrac{-8}{9}\Big)\times\dfrac{8}{9}\times\dfrac{4}{7} \) (g) \( \dfrac{-3}{2}\times\dfrac{-6}{5}+\dfrac{2}{3}+\dfrac{5}{6}\div\dfrac{7}{6} \) (h) \( \dfrac{-2}{3}\times\Bigg[\dfrac{3}{5}\div\dfrac{-5}{7}\Bigg] \) 2.Write the additive inverse[…]

## Blackberry publications class 8 maths cube and cube root

CUBE AND CUBE ROOTS EXERCISE 8(A) 1.Find the cubes of : (a) 2.4 (b) 0.2.5 (c) 40 (d) 51 (e) 1.4 (f) 0.09 (g) \( 3\dfrac{7}{4} \) (h) \( \dfrac{6}{7} \) (i) \( 2\dfrac{18}{11} \) (j) \( 1\dfrac{6}{17}[…]

## Blackberry publications class 8 maths Square and Square roots

SQUARES AND SQUARE ROOTS EXERCISE 7(A) 1.Write the unit’s digits of the following numbers: (a)93 (b)72 (c)546 (d)931 2.Without actual squaring find the value of: (a)\( 22^2-21^2 \) (b)\( 685^2-684^2 \) (c)\( 108^2-107^2[…]

## Chapter Algebra of matrices

ALGEBRA OF MATRICES EXERCISE 5.1 1.If a matrix has 8 elements, what are the possible orders it can have? What if it has 5 elements? solution: Order of matrix=number of rows \( \times \)number of column[…]

## Chapter Kinematics

KINEMATICS The branch of physics which deals with the study of the objects at rest and in motion is called mechanics. It is further divided into two parts are: 1.Statics Statics is the branch of[…]

## Chapter Unit and measurement

UNIT AND MEASUREMENT Units of measurement are vital parts of any physical quantity. Just as the person is known by his or her name, the physical quantities are known by the units of measurement. System[…]

## S.chand books class 8 maths solution chapter Profit,Loss and Discount

PROFIT,LOSS AND DISCOUNT EXERCISE 8 (A) 1.A person purchased a chair for ₹ 700, spent ₹ 170 on its repairs and ₹ 30 on the cartage.If he sold the chair for ₹ 1080, what is his gain percent ?[…]

## S.chand books class 8 maths solution chapter percentage

PERCENTAGE EXERCISE 7 (A) 1.Write each of these percentages as a fraction and a decimal. (i) 15% (ii) 84% (iii) 12.5% (iv) 120% (v) \( 33\dfrac{1}{3}\% \) 2.Write each of the following as percentages. (i)\( \dfrac{3}{5}[…]

## S.chand books class 8 maths solution chapter playing with numbers

PLAYING WITH NUMBERS EXERCISE 5 (A) 1.The sum of the digits of a 2 digit number is 9.The numbers is 6 times the unit digit.Find the number. 2.The sum of the digits of a 2[…]

## Download NCERT Books from trusted website for free of all classes

NCERT Books download NCERT Books of English Class 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 Class Subject Book Name Download Link 1 English Marigold Download 2 English Marigold Download 3[…]

## S.chand books class 8 maths solution chapter cube and cube roots

CUBE AND CUBE ROOTS EXERCISE 4 (A) 1.Write (T) for True or (F) for false: (i) The cube root of 8000 is 200. (ii) Each prime factor appears 3 times in its cube. (iii) \([…]

## Blue ray books class 8 maths solution chapter cube and cube roots

CUBE AND CUBE ROOTS EXERCISE (A) 1.Find the cube of : (a) 2.4 (b) 0.25 (c) 40 (d) 51 (e) 1.4 (f) 0.09 (g) \( 3\dfrac{4}{5} \) (h) \( \dfrac{6}{7} \) (i) \( 2\dfrac{8}{11} \) (j) \( 1\dfrac{6}{17}[…]

## Blue ray books class 8 maths solution chapter square and square root

Square and Square root EXERCISE (A) 1.Write the unit’s digits of the squares of the following numbers. (a) 93 (b) 72 (c) 546 (d) 931 2.Without actual squaring find the value of: (a) \( 22^2-21^2 \) (b)\( 685^2-684^2 \)[…]

## S.chand books class 8 solution maths Square and Square root

Square and Square root Exercise 3 (A) 1.Find the square of the following numbers : (i) 15 (ii) 48 (iii) \( \dfrac{6}{7} \) (iv) \( \dfrac{21}{25} \) (v) \( 6\dfrac{3}{8} \) (vi) 0.9 (vii) 1.1 (viii) 0.018 2.Determine whether square of[…]

## Class 6 s.chand maths number system

NUMBER SYSTEM Exercise 2 (A) 1.Write down the successor of each of the following numbers : (i) 3008 (ii) 501300708 2.Write down the predecessor of each of the following numbers : (i) 84 (ii) 5000 (iii) 3007000 (iv) 506080301 3.How[…]

## S.chand books solution class 6

Exercise 1 (A) 1.Which of the following collection are sets ? If not a set , give reasons. (a) Planets in our solar system. (b) Interesting books in the library. (c) Colours of the Rainbow.[…]

## C Tokens

C Tokens C Tokens are the basic building block of C language which are constructed together to write a program. Tokens in c language are of seven types: Delimiter Keywords Constants Identifiers Special symbols Operators[…]

## C language

Introduction to C language C language is a programming language. Programming language is just like any another natural language(like English) that we used to share informations and for communication. Natural language is bidirectional but[…]