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Exercise 4.1 Question 1 Find the principal value of each of the following: (i) (ii) (iii) (iv) (v) (vi) Question 2 (i) (ii) Question 3 Find the domain of each of the following functions: (i) (ii) (iii) (iv) Question 4 If , then find the value of Question 5 If…

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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 the origin. Question 2 A function is defined as Show that is continuous that Sol : Given We observe (LHL…

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Read more## NCERT solution class 10 chapter 1 Real numbers

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 > 135, we apply the division lemma to 225 and 135 to obtain 225 = 135 × 1 + 90 Since remainder 90 ≠ 0, we apply the division lemma…

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Exercise 19.2 Question 1

Read more## 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) Sol : (viii) Sol : Question 2 Evaluate : (i) Sol : (ii) Sol : …

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## 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 passing through a point with position vector and parallel to is Here, Vector equation of the required line is given…

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## 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 9, then the sum of its digits will be divisible by 9. Sum of digits of 21y5 = 2 +…

Read more## 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 i.e., a number whose ones digit is 2. This is possible only when digit A is 7. In that case,…

Read more## 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 4 5 Cost (in Rs) 5 10 15 20 25 (b) Distance travelled by a car Time (in hours) 6…

Read more## 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) P(1, 1), Q(2, 2), R(3, 3), S(4, 4) (c) K(2, 3), L(5, 3), M(5, 5), N(2, 5) Sol : (a)…

Read more## 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) When was the patient’s temperature 38.5°C? (c) The patient’s temperature was the same two times during the period given. What…

Read more## 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) = 4 × x − 4 × 5 = 4x − 20 ≠ R.H.S. The correct statement is 4(x − 5)…

Read more## 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 ÷ (−6a6b4) Sol : (i) 28×4 = 2 × 2 × 7 × x × x × x × x…

Read more## 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) 49y2 + 84yz + 36z2 (v) 4×2 − 8x + 4 (vi) 121b2 − 88bc + 16c2 (vii) (l +…

Read more## 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, 12a2b (vi) 16×3, −4×2, 32x (vii) 10pq, 20qr, 30rp (viii) 3x2y3, 10x3y2, 6x2y2z Sol : (i) 12x = 2 ×…

Read more## 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 for a journey and the distance travelled in a uniform speed. (iii) Area of cultivated land and the crop harvested….

Read more## 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 180 Check if the parking charges are in direct proportion to the parking time. Sol : A table of the…

Read more## 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 = 9.42 × 10−12 (iii) 6020000000000000 = 6.02 × 1015 (iv) 0.00000000837 = 8.37 × 10−9 (v) 31860000000 = 3.186…

Read more## 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) (ii) (iii) (iv) (v) Sol : (i) (−4)5 ÷ (−4)8 = (−4)5 − 8 (am ÷ an = am −…

Read more## 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 can hold (b) Number of cement bags required to plaster it (c) To find the number of smaller tanks that…

Read more## 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 : We know that, Total surface area of the cuboid = 2 (lh + bh + lb) Total surface area of…

Read more## 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 1.2 m and perpendicular distance between them is 0.8 m. E Sol : Area of trapezium = (Sum of parallel…

Read more## 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? Sol : Perimeter of square = 4 (Side of the square) = 4 (60 m) = 240 m Perimeter of…

Read more## 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 not possible. A polyhedron has minimum 4 faces. (ii) Yes, a triangular pyramid has 4 triangular faces. (iii) Yes, a…

Read more## 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 − library, yellow − schools, green − park, pink − college, purple − hospital, brown − cemetery. (b) Mark a green…

Read more## 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 to their respective side view and top view, are as follows. Object Side view Top view Question 2 For…

Read more## 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 (2.5l + 0.5m) (iv) (a + 3b) and (x + 5) (v) (2pq + 3q2) and (3pq − 2q2) (vi)…

Read more## 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 + 5) (iii) (2a − 7) (2a − 7) (iv) (v) (1.1m − 0.4) (1.1 m + 0.4) (vi) (a2 +…

Read more## 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) a + b, 7a2b2 (iv) a2 − 9, 4a (v) pq + qr + rp, 0 Sol : (i)…

Read more## 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 (v) 4p, 0 Sol : The product will be as follows. (i) 4 × 7p = 4 × 7 ×…

Read more## 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 − 4x2y2z2 + z2 (iv) 3 − pq + qr − rp (v) (vi) 0.3a − 0.6ab + 0.5b Sol…

Read more## 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 10, 800 Rate (R) = = % (annual) Number of years (n) = 3 Amount, A = C.I. = A…

Read more## 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 salary be x. It is given that the new salary is Rs 1,54,000. Original salary + Increment = New salary…

Read more## 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) 5 m to 10 km (c) 50 paise to Rs 5 Sol : (a) Ratio of the speed of…

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Read more## 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 : (ii) Prime factorization of ∴ (iii) 10648 Sol : (iii) Prime factorization of ∴ (iv) 27000 Sol…

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Read more## 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 is as follows. 2 216 2 108 2 54 3 27 3 9 3 3 1 216 = 2…

Read more## 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 (iv) 657666025 Sol : (i) If the number ends with 1, then the one’s digit of the square root of…

Read more## 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 can be calculated as follows. 48 4 88 704 704 0 ∴ (ii) 4489 Sol : (ii)…

Read more## 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 (vi) 26387 (vii) 52698 (viii) 99880 (ix) 12796 (x) 55555 Sol : We know that if a number has its…

Read more## 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 = (30 + 2)2 = 30 (30 + 2) + 2 (30 + 2) = 302 + 30 × 2…

Read more## 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 wheel, the possible outcomes are A, B, C, D. (b) By tossing two coins together, the possible outcomes are HT,…

Read more## 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 shows the findings of this survey. From this pie chart answer the following − (i) If 20 people liked classical…

Read more## 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. (b) The height of competitors in an athletics meet. (c) The number of cassettes produced by 5 companies. (d) The…

Read more## 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 = (ii) A = (iii) A = (iv) A = (v) A = (vi) A = (vii) A = Question 2 (i) A…

Read more## 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 the same measure and also all the interior angles of a square are of 90º measure. Therefore, the given square…

Read more## 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 = 60° ∠A = 90° Sol : (Step-1)A rough sketch of this quadrilateral can be drawn as follows. (Step-2) Draw…

Read more## 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° ∠R = 105° Sol : (Step-1)A rough sketch of this quadrilateral can be drawn as follows. (Step-2) Draw a line…

Read more## 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 = 4.5 cm IT = 4 cm Sol : A rough sketch of this quadrilateral can be drawn as follows. (Step-1)…

Read more## 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 = 6 cm AC = 7 cm Sol : Firstly, a rough sketch of this quadrilateral can be drawn as follows….

Read more## 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. (d) All squares are not parallelograms. (e) All kites are rhombuses. (f) All rhombuses are kites. (g) All parallelograms are…

Read more## 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) OC = … (iv) m∠DAB + m∠CDA = … Sol : (i) In a parallelogram, opposite sides are equal…

Read more## 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. (a) 125° + 125° + x = 360° 250° + x = 360° x = 110° (b) Sol : We…

Read more## 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 the following. (a) Simple curve (b) Simple closed curve (c) Polygon (d) Convex polygon (e) Concave polygon Sol : (a)…

Read more## 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. Find the rate of change of the volume of a sphere with respect to its diameter. Sol : 3….

Read more## 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 8x – 6x = 3 2x = 3 \( x=\dfrac{3}{2} \) Question 2 : Solve : \( \dfrac{9x}{7-6x}=15 \) Sol…

Read more## 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 Multiplying both sides by 60 , we obtain \( \begin{align*}60\bigg(\dfrac{x}{2}-\dfrac{1}{5}\bigg)&=60\bigg(\dfrac{x}{3}+\dfrac{1}{4}\bigg)\\30x-12&=20x+15\\30x-20x&=15+12\\10x&=27\\x&=\dfrac{27}{10}\end{align*} \) Question 2 : Solve the linear equation \(…

Read more## 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 the same number she thought of . What is the number ? Sol : Let the number be x ….

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Read more## 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 number ? sol : Let the number be x . According to the question , \( \bigg(x-\dfrac{1}{2}\bigg)\times\dfrac{1}{2}=\dfrac{1}{8} \) On multiplying…

Read more## 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 , we obtain 3x – 2x = 18 x = 18 L.H.S \( \begin{align*}&=3x\\&=3\times{}18\\&=54\end{align*} \) R.H.S \( \begin{align*}&=2x+18\\&=2\times{18}+18\\&=36+18\\&=54\end{align*} \) L.H.S = R.H.S Hence,…

Read more## 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 : y+3=10 On transposing 3 to R.H.S , we obtain y= 10-3 = 7 Question 3 : Solve :…

Read more## 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 represented on the number line as follows. Question 2 : Represent on the number line. can be represented on…

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

Read more## 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 by a force on a body depends on the two factors : (i) Magnitude of the force. (ii) Distance through…

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Read more## 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 : Question 6 Sol : Question 7 Sol : Sol : Sol : Sol :

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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 (i) It does not give any direct information about the nature or structure of matter. (ii) It does not give…

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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 (ii) \( \dfrac{2\pi}{3} \) sol: m=tan\( \theta \) =tan(\( \dfrac{2\pi}{3} \)) = tan(\( \pi-\dfrac{\pi}{3} \)) = \( -\sqrt{3} \) (iii) \( \dfrac{3\pi}{4} \)…

Read moreस्वावलम्बनम् कृष्णमूर्तिः श्रीकण्ठश्च मित्रे आस्ताम् । श्रीकण्ठस्य पिता समृद्ध: आसीत् । अत: तस्य भवने सर्वविधानि सुख-साधनानि आसन् । तस्मिन् विशाले भवने चत्वारिंशत् स्तम्भा: आसन । तस्य अष्टादश-प्रकोष्ठेषु पञ्चाशत् गवाक्षा: , चतुश्चत्वारिंशत् स्तम्भा: अासन् । तस्य अष्टादश-प्रकोषठेषु पञ्चाशत् गवाक्षा: चतुश्चत्वारिंशत् द्वाराणि , षट्त्रिंशत् विधुत्-व्यजनानि च अासन् । तत्र दश सेवका: निरन्तरं कार्यं कुर्वन्ति स्म । परं…

Read more## Sanskrit solution chapter सुभाषितानि Class 7

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 रखते है परन्तु मूर्ख लोग पत्थर के टुकड़ों को ही रत्न समझते है। शब्द अर्थ पृथिव्यां पृथ्वी में त्रीणि तीन रत्नानि रत्न…

Read more## 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 a simple individual which has a defined atomic number and has a definite position in periodic table. All the elements…

Read more## 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 its appropriate commands. BOOTING The loading procedure of operating system into computer’s main memory or RAM to make a user…

Read more## 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 controls and governs the operation of a computer system. Software can typically be classified into three categories : 1. System…

Read more## 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 memory devices to store data and information permanently. There are many types of secondary devices available. Some of secondary memory…

Read more## 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 Memory (we will study in the next chapter) Primary memory or main memory is known as computer’s own memory or…

Read more## 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 is processed and comes in front of us in special format which is called output.To showing this output there are…

Read more## 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 respective codes to be used by computer.There are many input devices which can be used for inputing data with different…

Read more## 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 on alphabets, represents symbols and ideas as per the requirements of the user. You can say, a computer is a…

Read more## 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 characteristics of computer like its speed, storage, capacity, accuracy.These characteristics have bothered people to shift to computer working from manual…

Read more## 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 permanently stored at the time of manufacturing for the particular job in special purpose computer. General purpose computer Such type…

Read more## 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 means ‘similar’.Analog Computer works on the principle of measurement.So,analog computers are based on the similarities between any two quantities.These two…

Read more## 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 for calculating devices.The earliest and the simplest device that was used for calculation was the Abacus. THE ABACUS Abacus was…

Read more## 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 : \( 1\dfrac{1}{2} \) hours (d) 14 m : 7 m 35 cm 2.DIivide the number 952 into two parts in the…

Read more## 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 posses similar chemical properties, then the central element mass is equal to the arithmetic mean of atomic masses of the…

Read more## 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 of the following : (a) \( \dfrac{6}{7} \) (b) \( \dfrac{-9}{15} \) (c) \( \dfrac{5}{-26} \) (d) 0 (e) -1 (f) \( \dfrac{-19}{117} \)…

Read more## 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) \( 1\dfrac{6}{17} \) 2.Which of the following are perfect cubes ? (a) 200 (b) 9261 (c) 64 (d) 4095 (e) 864 3.Which…

Read more## 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)\( 108^2-107^2 \) 3.Which of the following numbers are the squares of odd numbers ? (a)9 (b)225 (c)1089 (d)7395 4.Which of the…

Read more## 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 or Total number of elements=number of rows \( \times \)number of column Thus, to find all possible order of a matrix…

Read more## 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 mechanics which deals with the study of objects at rest. An object can be at rest only when all the…

Read more## 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 of unit There are four categories of system of unit. 1.C.G.S : In the CGS system of measurement length is…

Read more## 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 ? 2.Ramesh bought 10 cycles for ₹ 500 each.He spent ₹ 2000 on the repair of all the cycles.He sold five of them…

Read more## 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)\( \dfrac{3}{5} \) (ii) \( \dfrac{19}{20} \) (iii) \( 2\dfrac{2}{3} \) (iv) 0.95 (v) 2.575 3.Express each of the following ratios as percents. (i)…

Read more## 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 digit number is 7.If the digits are reserved, the new number increased by 3 less than 4 times the original…

Read more## 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 English Marigold Download 4 English Marigold Download 5 English Marigold Download 6 English Honeysuckle Download 6 English A Pact With…

Read more## 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) \( \sqrt[3]{27+64}=\sqrt[3]{27}+\sqrt[3]{64} \) (iv) For an integer a, \( a^3 \) is always greater than \( a^2 \). (v) The least number by…

Read more## 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) \( 1\dfrac{6}{17} \) 2.Which of the following are perfect cubes ? (a) 200 (b) 9261 (c) 64 (d) 4095 (e) 864 3.Which…

Read more## 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)\( 685^2-684^2 \) (c) \( 108^2-107^2 \) 3.Which of the following numbers are the squares of odd numbers. (a) 9 (b) 225 (c) 1089 (d) 7395 4.Which of…

Read more## 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 the following numbers will be even or odd.(Do not find the square) (i) 529 (ii) 30976 (iii) 893025 (iv) 6990736 3.Just by looking at…

Read more## 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 many whole numbers are there between 31 and 517 ? 4.Write the next three consecutive natural numbers : (i) 98 (ii) 835…

Read more## 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. (d) All difficult problems in your maths book. (e) Top five wicket takers in test cricket. (f) Intelligent boys of…

Read more## 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 1.Delimiters A delimiter is a unique character or a sequence of characters which signify beginning or ending of a specific…

Read more## 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 programming language is not. Programming language is used to give instructions(commands) to computer or any other devices. Why their is…

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