R.S Aggarwal

R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 10 Chapter 19 Volume and Surface Areas of Solids

Chapter 19 – Volume and Surface Areas of Solids Exercise Ex. 19A Question 1 Two cubes each of volume 27 cm’ are joined end to end to form a solid. Find the surface area of the resulting cuboid. Solution 1 Question 2 Solution 2 Question 3 If the total surface area of a solid hemisphere …

R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 10 Chapter 18 Areas of Circle, Sector and Segment

Chapter 18 – Areas of Circle, Sector and Segment Exercise Ex. 18A Question 1 Solution 1 Question 2 The circumference of a circle is 22 cm. Find the area of its quadrant. Solution 2 Question 3 What is the diameter of a circle whose area is equal to the sum of the areas of two …

R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 10 Chapter 17 Perimeter and Areas of Plane Figures

Chapter 17 – Perimeter and Areas of Plane Figures Exercise Ex. 17A Question 1 Find the area of the triangle whose base measures 24 cm and the corresponding height measures 14. 5 cm. Solution 1 Question 2 Find the area of the triangle whose sides are 42 cm, 34 cm and 20 cm in length. …

R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 10 Chapter 16 Coordinate Geometry

Chapter 16 – Co-ordinate Geometry Exercise Ex. 16A Question 1 Find the distance between the points: (i) A(9,3) and B(15, 11) (ii) A(7, -4) and B(-5, 1) (iii) A(-6, -4) and B(9, -12) (iv) A(1, -3) and B(4, -6) (v) P(a + b, a – b) and Q(a – b, a + b) (vi) P(a …

R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 10 Chapter 15 Probability

Chapter 15 – Probability Exercise Ex. 15A Question 1 Fill in the blanks:  (i) The probability of an impossible event is ……. .  (ii) The probability of a sure event is ……. .  (iii) For any event E, P(E) + P(not E)= …… . (iv) The probability of a possible but not a sure event lies between …… and …

R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 10 Chapter 14 Height and Distance

Chapter 14 – Height and Distance Exercise Ex. 14 Question 1 A tower stands vertically on the ground. From a point on the ground which is 20 m away from the foot of the tower, the angle of elevation of its top is found to be 60°. Find the height of the tower. [Take ] …

R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 10 Chapter 13 Constructions

Chapter 13 – Constructions Exercise Ex. 13A Question 1 Solution 1 Question 2 Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts. Solution 2 Question 3 Solution 3 Question 4 Solution 4   Question 5 Solution 5 Question 6 Construct a ∆ABC in …

R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 10 Chapter 12 Circles

Chapter 12 – Circles Exercise Ex. 12A Question 1 Find the length of tangent drawn to a circle with radius 8 cm from a point 17 cm away from the centre of the circle. Solution 1 PA is the tangent to the circle with center O and radius AO = 8 cm. The point P …

R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 10 Chapter 11 Arithmetic Progressions

Chapter 11 – Arithmetic Progressions Exercise Ex. 11A Question 1 Show that each of the progressions given below is an AP. Find the first term, common difference and next term of each. 9, 15, 21, 27, ….. Solution 1 Question 2 Show that each of the progressions given below is an AP. Find the first …

R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 10 Chapter 10 Quadratic Equations

Chapter 10 – Quadratic Equations Exercise Ex. 10A Question 1 Which of the following are quadratic equations in x? (i) Solution 1 (i)is a quadratic polynomial = 0 is a quadratic equation Question 2 Which of the following are quadratic equations in x? Solution 2 Clearly  is a quadratic polynomial is a quadratic equation. Question 3 …

R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 10 Chapter 9 Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive

Chapter 9 – Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive Exercise Ex. 9A Question 1 If the mean of 5 observation x, x + 2, x + 4, x + 6 and x  + 8 is 11, find the value of x. Solution 1 Question 2 If the mean of 25 …

R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 10 Chapter 8 Trigonometric Identities

Chapter 8 – Trigonometric Identities Exercise Ex. 8A Question 1 Prove the following identities: Solution 1 (i)                     LHS = RHS (ii)       LHS = RHS Question 2 Prove the following identities: (i) (ii) (iii) Solution 2 (i) LHS = RHS (ii) LHS = RHS (iii) LHS = RHS …

R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 10 Chapter 7 Trigonometric Ratios of Complementary Angles

Chapter 7 – Trigonometric Ratios of Complementary Angles Exercise Ex. 7 Question 1 Without using trigonometric tables, evaluate: Solution 1 (i)                         (ii)                           (iii)                         (iv)            (v)            (vi)            Question 2 Without using trigonometric tables, prove that: (i) (ii)  (iii) (iv) (v) (vi) (vii) (viii) (ix) Solution 2 (i)                LHS = cos81° …

R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 10 Chapter 6 TRatios of Some Particular Angles

Chapter 6 – T-Ratios of Some Particular Angles Exercise Ex. 6 Question 1 Evaluate the following: sin 60o cos 30o + cos 60o sin 30o Solution 1 On substituting the value of various T-ratios, we get sin60o cos30o + cos60o sin30o Question 2 Evaluate the following: cos 60o cos 30o – sin 60o sin …

R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 10 Chapter 5 Trigonometric Ratios

R S AGGARWAL AND V AGGARWAL Solutions for Class 10 Maths Chapter 5 – Trigonometric Ratios Chapter 5 – Trigonometric Ratios Exercise Ex. 5 Question 1 If , find the values of all T-ratios of . Solution 1 Given: Let us draw a ABC in which B = 90o and BAC =  Question 2 If …

R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 10 Chapter 4 Triangles

R S AGGARWAL AND V AGGARWAL Solutions for Class 10 Maths Chapter 4 – Triangles Chapter 4 – Triangles Exercise Ex. 4A Question 1 D and E are points on the sides AB and AC respectively of a ABC such that DE || BC. (i) If AD = 3.6 cm, AB = 10 cm and …

R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 10 Chapter 3 Linear equations in two variables

R S AGGARWAL AND V AGGARWAL Solutions for Class 10 Maths Chapter 3 – Linear equations in two variables Chapter 3 – Linear equations in two variables Exercise Ex. 3A Question 1 Solve each of the following systems of equations graphically: 2x + 3y = 2 x – 2y = 8 Solution 1     …

R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 9 Chapter 19 Probability

R S AGGARWAL AND V AGGARWAL Solutions for Class 9 Maths Chapter 19 – Probability Chapter 19 – Probability Exercise Ex. 19 Question 1 A coin is tossed 500 times we get Head: 285 times, Tail: 215 times. When a coin is tossed at random, what is the probability of getting (i) A head? (ii) …

R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 9 Chapter 18 Mean, Median and Mode of Ungrouped Data

R S AGGARWAL AND V AGGARWAL Solutions for Class 9 Maths Chapter 18 – Mean, Median and Mode of Ungrouped Data Chapter 18 – Mean, Median and Mode of Ungrouped Data Exercise Ex. 18A Question 1 Find the arithmetic mean of: The first eight natural numbers Solution 1 first eight natural numbers are: 1,2,3,4,5,6,7and 8 …

R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 9 Chapter 17 Bar Graph, Histogram and Frequency Polygon

R S AGGARWAL AND V AGGARWAL Solutions for Class 9 Maths Chapter 17 – Bar Graph, Histogram and Frequency Polygon Chapter 17 – Bar Graph, Histogram and Frequency Polygon Exercise Ex. 17A Question 1 The following table shows the number of students participating in various games in a school. Game Cricket Football Basketball Tennis Number …

R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 9 Chapter 16 Presentation of Data in Tabular Form

R S AGGARWAL AND V AGGARWAL Solutions for Class 9 Maths Chapter 16 – Presentation of Data in Tabular Form Chapter 16 – Presentation of Data in Tabular Form Exercise Ex. 16 Question 1 Define statistics as a subject. Solution 1 Statistics is a branch of science which deals with the collection, presentation, analysis and …

R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 9 Chapter 15 Volume and Surface Area of Solids

R S AGGARWAL AND V AGGARWAL Solutions for Class 9 Maths Chapter 15 – Volume and Surface Area of Solids Chapter 15 – Volume and Surface Area of Solids Exercise Ex. 15A Question 1 Find the volume, the lateral surface area and the total surface area cuboid whose dimensions are: Length=12 cm,breadth=8 cm and height …

R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 9 Chapter 14 Areas of Triangles and Quadrilaterals

R S AGGARWAL AND V AGGARWAL Solutions for Class 9 Maths Chapter 14 – Areas of Triangles and Quadrilaterals Chapter 14 – Areas of Triangles and Quadrilaterals Exercise Ex. 14 Question 1 Find the area of the triangle whose base measures 24 cm and the corresponding height measures 14.5 cm. Solution 1 Question 2 The …

R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 9 Chapter 13 Geometrical Constructions

R S AGGARWAL AND V AGGARWAL Solutions for Class 9 Maths Chapter 13 – Geometrical Constructions Chapter 13 – Geometrical Constructions Exercise Ex. 13 Question 1 Draw a line segment AB = 5.6 cm and draw its perpendicular bisector. Measure the length of each part. Solution 1 Steps of construction: Draw line segment AB = …

R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 9 Chapter 12 Circles

R S AGGARWAL AND V AGGARWAL Solutions for Class 9 Maths Chapter 12 – Circles Chapter 12 – Circles Exercise Ex. 12A Question 1 A chord of length 16 cm is drawn in a circle of radius 10 cm. Find the distance of a chord from the centre of the circle. Solution 1   Question …

R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 9 Chapter 11 Areas of Parallelograms and Triangles

R S AGGARWAL AND V AGGARWAL Solutions for Class 9 Maths Chapter 11 – Areas of Parallelograms and Triangles Chapter 11 – Areas of Parallelograms and Triangles Exercise Ex. 11 Question 1 Which of the following figures lie on the same base and between the same parallels. In such a case, write the common base …

R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 9 Chapter 10 Quadrilaterals

R S AGGARWAL AND V AGGARWAL Solutions for Class 9 Maths Chapter 10 – Quadrilaterals Chapter 10 – Quadrilaterals Exercise Ex. 10A Question 1 Three angles of a quadrilateral are 75°, 90° and 75°. Find the measure of the fourth angle. Solution 1 Let the measure of the fourth angle = x° For a quadrilateral, …

R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 9 Chapter 9 Congruence of Triangles and Inequalities in a Triangle

R S AGGARWAL AND V AGGARWAL Solutions for Class 9 Maths Chapter 9 – Congruence of Triangles and Inequalities in a Triangle Chapter 9 – Congruence of Triangles and Inequalities in a Triangle Exercise Ex. 9A Question 1 In the given figure, AB ∥ CD and O is the midpoint of AD. Show that (i) …

R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 9 Chapter 8 Triangles

R S AGGARWAL AND V AGGARWAL Solutions for Class 9 Maths Chapter 8 – Triangles Chapter 8 – Triangles Exercise Ex. 8 Question 1 In ABC, if B = 76o and C = 48o, find A. Solution 1 Since, sum of the angles of a triangle is 180o A + B + C = 180o …

R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 9 Chapter 7 Lines and Angles

R S AGGARWAL AND V AGGARWAL Solutions for Class 9 Maths Chapter 7 – Lines And Angles Chapter 7 – Lines And Angles Exercise Ex. 7A Question 1 Define the following terms: (i) Angle (ii) Interior of an angle (iii) Obtuse angle (iv) Reflex angle (v) Complementary angles (vi) Supplementary angles Solution 1 (i) Angle: …

R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 9 Chapter 6 Introduction to Euclid’s Geometry

R S AGGARWAL AND V AGGARWAL Solutions for Class 9 Maths Chapter 6 – Introduction to Euclid’s Geometry Chapter 6 – Introduction to Euclid’s Geometry Exercise Ex. 6 Question 1 What is the difference between a theorem and an axiom? Solution 1 A theorem is a statement that requires a proof. Whereas, a basic fact …

R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 9 Chapter 5 Coordinate Geometry

R S AGGARWAL AND V AGGARWAL Solutions for Class 9 Maths Chapter 5 – Coordinate Geometry Chapter 5 – Coordinate Geometry Exercise Ex. 5 Question 1 On the plane of a graph paper draw X’OX and YOY’ as coordinate axes and plot each of the following points. (i) A(5, 3) (ii) B(6, 2) (iii) C(-5, 3) (iv) D(4, …

R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 9 Chapter 2 Polynomial

R S AGGARWAL AND V AGGARWAL Solutions for Class 9 Maths Chapter 2 – Polynomials Chapter 2 – Polynomials Exercise Ex. 2A Question 1 Which of the following expressions are polynomials? In case of a polynomial, write its degree. Solution 1   The given expression is an expression having only non-negative integral powers of x. …

R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 9 Chapter 1 Number System

R S AGGARWAL AND V AGGARWAL Solutions for Class 9 Maths Chapter 1 – Number Systems Chapter 1 – Number Systems Exercise Ex. 1A Question 1 Is zero a rational number? Justify. Solution 1 A number which can be expressed as , where ‘a’ and ‘b’ both are integers and b ≠ 0, is called …

R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 9 chapter 4 Linear Equations in two variables

R S AGGARWAL AND V AGGARWAL Solutions for Class 9 Maths Chapter 4 – Linear Equations in Two Variables Chapter 4 – Linear Equations in Two Variables Exercise Ex. 4A Question 1 Express each of the following equations in the form ax + by + c = 0 and indicate the values of a, b, …

R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 9 chapter 3 Factorisation of Polynomials

R S AGGARWAL AND V AGGARWAL Solutions for Class 9 Maths Chapter 3 – Factorisation of Polynomials Chapter 3 – Factorisation of Polynomials Exercise Ex. 3A Question 1 Factorize: 9×2 + 12xy Solution 1 9×2 + 12xy = 3x (3x + 4y) Question 2 Factorize: x3 + 2×2 + 5x + 10 Solution 2 x3 …

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2

CBSE Previous Year Question Papers Class 10 Maths 2017 Outside Delhi Term 2 Time Allowed: 3 hours Maximum Marks: 80 General Instructions: All questions are compulsory. This question paper consists of 30 questions divided into four sections- A, B, C and D. Section A contains 6 questions of 1 mark each, Section B contains 6 …

R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 10 Chapter 2 Polynomials

Chapter 2 – Polynomials Exercise Ex. 2A Question 1 Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients: x2 + 7x + 12 Solution 1 Question 2 Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients: …

R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 10 Chapter 1 Real Numbers

Chapter 1 – Real Numbers Exercise Ex. 1A Question 1 What do you mean by Euclid’s division lemma? Solution 1 For any two given positive integers a and b there exist unique whole numbers q and r such that     Here, we call ‘a’ as dividend, b as divisor, q as quotient and r …

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