## Class 11 ML Aggarwal Solutions ISC Mathematics – ML Aggarwal ISC Class 11 Maths Solutions

### ML Aggarwal Class 11 Solutions ISC Volume 1

Section A

ISC Class 11 Maths Solutions Chapter 1 Sets

ISC Mathematics Class 11 Solutions Pdf Chapter 2 Relations and Functions

ISC Maths Class 11 Solutions Chapter 3 Trigonometry

ML Aggarwal Class 11 Maths Solutions Chapter 4 Principle of Mathematical Induction

Understanding ISC Mathematics Class 11 Solutions Chapter 5 Complex Numbers

• Chapter 5 Complex Numbers Ex 5.1
• Chapter 5 Complex Numbers Ex 5.2
• Chapter 5 Complex Numbers Ex 5.3
• Chapter 5 Complex Numbers Ex 5.4
• Chapter 5 Complex Numbers Ex 5.5
• Chapter 5 Complex Numbers Ex 5.6
• Chapter 5 Complex Numbers MCQs
• Chapter 5 Complex Numbers Chapter Test

Class 11 ML Aggarwal Solutions Chapter 6 Quadratic Equations

• Chapter 6 Quadratic Equations Ex 6.1
• Chapter 6 Quadratic Equations Ex 6.2
• Chapter 6 Quadratic Equations Ex 6.3
• Chapter 6 Quadratic Equations Ex 6.4
• Chapter 6 Quadratic Equations Ex 6.5
• Chapter 6 Quadratic Equations MCQs
• Chapter 6 Quadratic Equations Chapter Test

Class 11 ISC Maths Solutions Chapter 7 Linear Inequalities

• Chapter 7 Linear Inequalities Ex 7.1
• Chapter 7 Linear Inequalities Ex 7.2
• Chapter 7 Linear Inequalities Ex 7.3
• Chapter 7 Linear Inequalities Ex 7.4
• Chapter 7 Linear Inequalities Ex 7.5
• Chapter 7 Linear Inequalities Ex 7.6
• Chapter 7 Linear Inequalities MCQs
• Chapter 7 Linear Inequalities Chapter Test

Class 11 Maths ISC Solutions Chapter 8 Permutations and Combinations

• Chapter 8 Permutations and Combinations Ex 8.1
• Chapter 8 Permutations and Combinations Ex 8.2
• Chapter 8 Permutations and Combinations Ex 8.3
• Chapter 8 Permutations and Combinations Ex 8.4
• Chapter 8 Permutations and Combinations Ex 8.5
• Chapter 8 Permutations and Combinations Ex 8.6
• Chapter 8 Permutations and Combinations Ex 8.7
• Chapter 8 Permutations and Combinations Ex 8.8
• Chapter 8 Permutations and Combinations MCQs
• Chapter 8 Permutations and Combinations Chapter Test

ML Aggarwal Class 11 Solutions ICSE Chapter 9 Binomial Theorem

• Chapter 9 Binomial Theorem Ex 9.1
• Chapter 9 Binomial Theorem Ex 9.2
• Chapter 9 Binomial Theorem MCQs
• Chapter 9 Binomial Theorem Chapter Test

ISC 11 Maths Solutions Chapter 10 Sequences and Series

• Chapter 10 Sequences and Series Ex 10.1
• Chapter 10 Sequences and Series Ex 10.2
• Chapter 10 Sequences and Series Ex 10.3
• Chapter 10 Sequences and Series Ex 10.4
• Chapter 10 Sequences and Series Ex 10.5
• Chapter 10 Sequences and Series Ex 10.6
• Chapter 10 Sequences and Series Ex 10.7
• Chapter 10 Sequences and Series Ex 10.8
• Chapter 10 Sequences and Series MCQs
• Chapter 10 Sequences and Series Chapter Test

### ML Aggarwal Class 11 Solutions ISC Volume 2

ML Aggarwal Class 11 Solutions Chapter 11 Straight Lines

• Chapter 11 Straight Lines Ex 11.1
• Chapter 11 Straight Lines Ex 11.2
• Chapter 11 Straight Lines Ex 11.3
• Chapter 11 Straight Lines Ex 11.4
• Chapter 11 Straight Lines Ex 11.5
• Chapter 11 Straight Lines Ex 11.6
• Chapter 11 Straight Lines Ex 11.7
• Chapter 11 Straight Lines Ex 11.8
• Chapter 11 Straight Lines Ex 11.9
• Chapter 11 Straight Lines Ex 11.10
• Chapter 11 Straight Lines Ex 11.11
• Chapter 11 Straight Lines MCQs
• Chapter 11 Straight Lines Chapter Test

ML Aggarwal Maths for Class 11 Solutions Chapter 12 Circles

• Chapter 12 Circles Ex 12.1
• Chapter 12 Circles Ex 12.2
• Chapter 12 Circles Ex 12.3
• Chapter 12 Circles Ex 12.4
• Chapter 12 Circles Ex 12.5
• Chapter 12 Circles MCQs
• Chapter 12 Circles Chapter Test

Maths ISC Class 11 Solutions Chapter 13 Limits and Derivatives

• Chapter 13 Limits and Derivatives Ex 13.1
• Chapter 13 Limits and Derivatives Ex 13.2
• Chapter 13 Limits and Derivatives Ex 13.3
• Chapter 13 Limits and Derivatives Ex 13.4
• Chapter 13 Limits and Derivatives Ex 13.5
• Chapter 13 Limits and Derivatives MCQs
• Chapter 13 Limits and Derivatives Chapter Test

ISC Maths Solutions Class 11 Chapter 14 Statistics

• Chapter 14 Statistics Ex 14.1
• Chapter 14 Statistics Ex 14.2
• Chapter 14 Statistics Ex 14.3
• Chapter 14 Statistics Ex 14.4
• Chapter 14 Statistics Ex 14.5
• Chapter 14 Statistics Ex 14.6
• Chapter 14 Statistics MCQs
• Chapter 14 Statistics Chapter Test

Maths Class 11 ISC Solutions Chapter 15 Probability

• Chapter 15 Probability Ex 15.1
• Chapter 15 Probability Ex 15.2
• Chapter 15 Probability Ex 15.3
• Chapter 15 Probability Ex 15.4
• Chapter 15 Probability MCQs
• Chapter 15 Probability Chapter Test

Section B

11th ISC Maths Solutions Chapter 1 Conic Sections

• Chapter 1 Conic Sections Ex 1.1
• Chapter 1 Conic Sections Ex 1.2
• Chapter 1 Conic Sections Ex 1.3
• Chapter 1 Conic Sections Ex 1.4
• Chapter 1 Conic Sections Ex 1.5
• Chapter 1 Conic Sections Ex 1.6
• Chapter 1 Conic Sections Ex 1.7
• Chapter 1 Conic Sections Ex 1.8
• Chapter 1 Conic Sections MCQs
• Chapter 1 Conic Sections Chapter Test

ISC Maths 11 Solutions Chapter 2 Introduction to Three Dimensional Geometry

• Chapter 2 Introduction to Three Dimensional Geometry Ex 2.1
• Chapter 2 Introduction to Three Dimensional Geometry Ex 2.2
• Chapter 2 Introduction to Three Dimensional Geometry Ex 2.3
• Chapter 2 Introduction to Three Dimensional Geometry MCQs
• Chapter 2 Introduction to Three Dimensional Geometry Chapter Test

ISC Class 11th Maths Solutions Chapter 3 Mathematical Reasoning

• Chapter 3 Mathematical Reasoning Ex 3.1
• Chapter 3 Mathematical Reasoning Ex 3.2
• Chapter 3 Mathematical Reasoning Ex 3.3
• Chapter 3 Mathematical Reasoning Ex 3.4
• Chapter 3 Mathematical Reasoning Ex 3.5
• Chapter 3 Mathematical Reasoning Ex 3.6
• Chapter 3 Mathematical Reasoning Ex 3.7
• Chapter 3 Mathematical Reasoning MCQs
• Chapter 3 Mathematical Reasoning Chapter Test

Section C

Solutions of ISC Mathematics Class 11 Chapter 1 Statistics

• Chapter 1 Statistics Ex 1.1
• Chapter 1 Statistics Ex 1.2
• Chapter 1 Statistics Ex 1.3
• Chapter 1 Statistics Ex 1.4
• Chapter 1 Statistics MCQs
• Chapter 1 Statistics Chapter Test

Class 11th ISC Maths Solutions Chapter 2 Correlation Analysis

• Chapter 2 Correlation Analysis Ex 2.1
• Chapter 2 Correlation Analysis Ex 2.2
• Chapter 2 Correlation Analysis Ex 2.3
• Chapter 2 Correlation Analysis MCQs
• Chapter 2 Correlation Analysis Chapter Test

ISC 11th Maths Solutions Chapter 3 Index Numbers and Moving Averages

• Chapter 3 Index Numbers and Moving Averages Ex 3.1
• Chapter 3 Index Numbers and Moving Averages Ex 3.2
• Chapter 3 Index Numbers and Moving Averages MCQs
• Chapter 3 Index Numbers and Moving Averages Chapter Test

## ICSE Class 10 Home Science Previous Years Question Papers Solved Last 10 Years

APlusTopper.com provides ICSE Class 10 Home Science Previous Year Board Question Papers Solved Pdf Free Download with Solutions, Answers and Marking Scheme. Here we have given ICSE Class 10 Home Science Solved Question Papers Last Ten Years. Students can view or download the ICSE Board 10th Home Science Previous Year Question Papers with Solutions for their upcoming examination.

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Board – Indian Certificate of Secondary Education (ICSE), www.cisce.org
Class – Class 10
Subject – Home Science
Year of Examination – 2020, 2019, 2018, 2017.

## ICSE Class 10 Home Science Solved Question Papers Last Ten Years

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## ICSE Class 10 Physical Education Previous Years Question Papers Solved Last 10 Years

APlusTopper.com provides ICSE Class 10 Physical Education Previous Year Board Question Papers Solved Pdf Free Download with Solutions, Answers and Marking Scheme. Here we have given ICSE Class 10 Physical Education Solved Question Papers Last Ten Years. Students can view or download the ICSE Board 10th Physical Education Previous Year Question Papers with Solutions for their upcoming examination.

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Board – Indian Certificate of Secondary Education (ICSE), www.cisce.org
Class – Class 10
Subject – Physical Education
Year of Examination – 2020, 2019, 2018, 2017.

## ICSE Class 10 Physical Education Solved Question Papers Last Ten Years

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## ICSE Class 10 Commercial Studies Previous Years Question Papers Solved Last 10 Years

APlusTopper.com provides ICSE Class 10 Commercial Studies Previous Year Board Question Papers Solved Pdf Free Download with Solutions, Answers and Marking Scheme. Here we have given ICSE Class 10 Commercial Studies Solved Question Papers Last Ten Years. Students can view or download the ICSE Board 10th Commercial Studies Previous Year Question Papers with Solutions for their upcoming examination.

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Board – Indian Certificate of Secondary Education (ICSE), www.cisce.org
Class – Class 10
Subject – Commercial Studies
Year of Examination – 2020, 2019, 2018, 2017.

## ICSE Class 10 Commercial Studies Solved Question Papers Last Ten Years

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## ICSE Class 10 Commercial Applications Previous Years Question Papers Solved Last 10 Years

APlusTopper.com provides ICSE Class 10 Commercial Applications Previous Year Board Question Papers Solved Pdf Free Download with Solutions, Answers and Marking Scheme. Here we have given ICSE Class 10 Commercial Applications Solved Question Papers Last Ten Years. Students can view or download the ICSE Board 10th Commercial Applications Previous Year Question Papers with Solutions for their upcoming examination.

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Board – Indian Certificate of Secondary Education (ICSE), www.cisce.org
Class – Class 10
Subject – Commercial Applications
Year of Examination – 2020, 2019, 2018, 2017.

## ICSE Class 10 Commercial Applications Solved Question Papers Last Ten Years

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## ICSE Class 10 Computer Applications Previous Years Question Papers Solved Last 10 Years

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Board – Indian Certificate of Secondary Education (ICSE), www.cisce.org
Class – Class 10
Subject – Computer Applications
Year of Examination – 2020, 2019, 2018, 2017.

## ICSE Class 10 Computer Applications Solved Question Papers Last Ten Years

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## Linear Inequations (Solving Linear Inequations in One Variable) Class 10 Maths ICSE Solutions

Get ICSE Solutions for Class 10 Mathematics Chapter 5 Linear Inequations (Solving Linear Inequations in One Variable) for ICSE Board Examinations on ICSESolutions.com. We provide step by step Solutions for ICSE Mathematics Class 10 Solutions Pdf. You can download the Class 10 Maths ICSE Textbook Solutions with Free PDF download option.

## Linear Inequations (Solving Linear Inequations in One Variable) Class 10 Maths ICSE Solutions

### Formulae

Two permissible rules:

If the same number or expression is added to or subtracted from both sides of an inequation, the resulting inequation has the same solution (or solutions) as the original.
2. Multiplication – Division Rule:
(i) If both sides of an inequation are multiplied or divided by the same positive number, the resulting inequation has the same solution (or solutions) as the original.
(ii) If both sides of an inequation are multiplied or divided by the same negative number, the resulting inequation has the same solution (or solutions) as the original if the symbol of the inequality is reversed.
Thus, the only difference between solving a linear equation and solving an inequation concerns multiplying or dividing both sides by a negative number. Therefore, always reverse the symbol of an inequation when multiplying or dividing by a negative number.
3. Properties of absolute values:

### Determine the Following

Question 1. Give that x ∈ I. Solve the inequation and graph the solution on the number line:

Question 2. Graph the solution set for each inequality:

Question 3. Solve the given inequation and graph the solution on the number line

Question 4. Given that x ∈ R, solve the following inequality and graph the solution on the number line:

Question 5. Given:

Question 6. Solve 2 ≤ 2x – 3 ≤ 5, x ∈ R and mark it on a number line.

Question 7. For each inequality, determine which of the given numbers are in the solution set:

Question 8. Graph the solution sets of the following inequalities:

Question 9. Solve the equation and represent the solution set on the number line.

Question 10. Solve the following inequation and represent the solution set on the number line:

Question 11. Solve the following in equalities and graph their solution set

Question 12. Solve the following inequation and graph the solution set,

Question 13. Solve the following inequation and graph the solution on the number line.

Question 14. Solve the following inequalities and represent the solution on a number line:

Question 15. Solve the following inequalities and represent the solution set on a number line:

Question 16. Solve the following inequation, write the solution set and represent it on the number line:

Question 17. Find the values of x, which satisfy the inequation

Question 18. Solve the following inequalities in the given universal set:

Question 19. Find the solution set of the following inequalities and draw the graph of their solutions sets:

Question 20. Solve the following inequalities and graph their solution set:

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## Similarity Class 10 Maths ICSE Solutions

Get ICSE Solutions for Class 10 Mathematics Chapter 13 Similarity for ICSE Board Examinations on ICSESolutions.com. We provide step by step Solutions for ICSE Mathematics Class 10 Solutions Pdf. You can download the Class 10 Maths ICSE Textbook Solutions with Free PDF download option.

## Similarity Class 10 Maths ICSE Solutions

### Formulae

Similarities of triangles: When two triangles are similar, their corresponding angles are equal and corresponding sides are proportional.

Axioms of similarity of triangles: (i.e., three similarity postulates for triangle)

1. If two triangles have a pair of corresponding angles equal and the sides including them proportional; then the triangles are similar (SAS postulate).
2. If two triangles have two pairs of corresponding angles equal; the triangles are similar (AA or AAA postulate).
3. If two triangles have their three pairs of corresponding sides proportional, the triangles are similar (SSS postulate).

Basic Theorem of Proportionality:

1. A line drawn parallel to any side of a triangle, divides the other two sides proportionally. (Basic proportionality theorem).

Conversely: If a line divides two sides of a triangle proportionally, the line is parallel to the third side.
2. Relation between the areas of two triangles: Theorem: The areas of two similar triangles are proportional to the squares on their corresponding sides.

### Determine the Following

Question 1. The model of a building is constructed with scale factor 1:30.
(i) If the height of the model is 80 cm, find the actual height of the building in metres.
(ii) If the actual volume of a tank at the top of the building is 27 m3, find the volume of the tank on the top of the model.

Question 2. Triangles ABC and DEF are similar.

### Prove the Following

Question 3. Prove that the area of the triangle BCE described on one side BC of a square ABCD as base is one half of the area of similar triangle ACF described on the diagonal AC as base.

Question 4. In figure ABC and DBC are two triangles on the same base BC. Prove that

Question 5. In the adjoining figure, the medians BD and CE of a ∆ABC meet at G. Prove that

### Figure Based Questions

Question 2. Two isosceles triangle have equal vertical angles and their areas are in the ratio of 36 : 25. Find the ratio between their corresponding heights.

Question 4. In the given figure, AB and DE are perpendicular to BC.

Question 7. Equilateral triangles are drawn on the sides of a right angled triangle. Show that the area of the triangle on the hypotenuse is equal to the sum of the areas of triangles on the other two sides.

Question 8: On a map drawn to scale of 1 : 2,50,000 a rectangular plot of land ABCD has the following measurement AB = 12 cm, BC = 16 cm angles A, B, C, and D are 900 each. Calculate:
(i) The diagonal distance of the plot of land in
(ii) Actual length of diagonal.

Question 10. In the adjoining figure. BC is parallel to DE, area of ΔABC = 25 sq cm, area of trapezium BCED = 24 sq cm, DE = 14 cm. Calculate the length of BC.

Question 14. In the given figure ABC and CEF are two triangles where BA is parallel to CE and AF : AC = 5 : 8.

Question 16. Triangles ABC and DEF are similar.

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## Loci (Locus and its Constructions) Class 10 Maths ICSE Solutions

Get ICSE Solutions for Class 10 Mathematics Chapter 14 Loci (Locus and its Constructions) for ICSE Board Examinations on ICSESolutions.com. We provide step by step Solutions for ICSE Mathematics Class 10 Solutions Pdf. You can download the Class 10 Maths ICSE Textbook Solutions with Free PDF download option.

## Loci (Locus and its Constructions) Class 10 Maths ICSE Solutions

### Formulae

Theorems on Locus:
(a) The locus of a point equidistant from a fixed point is a circle with the fixed point as centre.
(b) The locus of a point equidistant from two interacting lines is the bisector of the angles between the lines.
(c) The locus of a point equidistant from two given points is the perpendicular bisector of the line joining the points.

### Prove the Following

Question 1. The bisector of ∠ B and ∠C of a quadrilateral ABCD intersect in P, show that P is equidistant from the opposite sides AB and CD.

Question 2. Prove that the common chord of two intersecting circles is bisected at right angles by the line of centres.

Question 4. In Fig. ABCD is a quadrilateral in which AB = BC. E is the point of intersection of the right bisectors of AD and CD. Prove that BE bisects ∠ABC.

### Figure Based Questions

Question 3. State and draw the locus of a swimmer maintaining the same distance from a lighthouse.

Question 4. State and draw the locus of a point equidistant from two given parallel lines.

Question 5. l is the perpendicular bisector of line segment PQ and R is a point on the same side of l as P. The segment QR intersects l at X. Prove that PX + XR = QR.

Question 6. Construct a Δ ABC, with AB = 6 cm, AC = BC = 9 cm; find a point 4 cm from A and equidistant from B and C.

Question 7. Given a Δ ABC with unequal sides. Find a point which is equidistant from B and C as well as from AB and AC.

Question 8. Prove that the common chord of two intersecting circles is bisected at right angles by the line of centres.

Question 9. Find the locus of the centre of a circle of radius r touching externally a circle of radius R.

Question 12. The diagonals of a quadrilateral bisect each other at right angles. Show that the quadrilateral is a rhombus.

Question 13. What is the locus of points which are equidistant from the given non-collinear point A, B and C? Justify your answer.

Question 14. Find the locus of points which are equidistant from three non-collinear points.

Question 15. Show that the locus of the centres of all circles passing through two given points A and B, is the perpendicular bisector of the line segment AB.

From (i) and (ii), it follows that P and Q both lies on the perpendicular bisector of AB.
Hence, the locus of the centres of all the circles passing through A and B is the perpendicular bisector of AB.

Question 16. Using ruler and compasses construct:
(i) a triangle ABC in which AB = 5.5 cm, BC = 3.4 cm and CA = 4.9 cm.
(ii) the locus of point equidistant from A and C.
(iii) a circle touching AB at A and passing through C.

Question 18. ΔPBC and ΔQBC are two isosceles triangles on the same base BC but on the opposite sides of line BC. Show that PQ bisects BC at right angles.

Question 20. Without using set squares or protractor construct:
(i) Triangle ABC, in which AB = 5.5 cm, BC = 3.2 cm and CA = 4.8 cm.
(ii) Draw the locus of a point which moves so that it is always 2.5 cm from B.
(iii) Draw the locus of a point which moves so that it is equidistant from the sides BC and CA.
(iv) Mark the point of intersection of the loci with the letter P and measure PC.

Question 21. Use ruler and compasses only for this question. Draw a circle of radius 4 cm and mark two chords AB and AC of the circle of length f 6 cm and 5 cm respectively.
(i) Construct the locus of points, inside the circle, that are equidistant from A and C. Prove your construction.
(ii) Construct the locus of points, inside the circle, that are equidistant from AB and AC.

Question 22. Draw two intersecting lines to include an angle of 30°. Use ruler and compass to locate points, which are equidistant from these lines and also 2 cm away from these points of intersection. How many such points exist ?

Question 23. How will you find a point equidistant from three given points A, B, C which are not in the same straight line?

Question 24. Without using set squares or protractor.

Question 28. Use ruler and compasses only for this question. Draw a circle of radius 4 cm and mark two chords AB and AC of the circle of length 6 cm and 5 cm respectively.
(i) Construct the locus of points, inside the circle, that are equidistant from A and C. Prove your construction.
(ii) Construct the locus of points, inside the circle, that are equidistant from AB and AC.

With C as centre and the same radius, draw two arcs on opposite sides of AC to intersect the former arcs at P and Q.
Join PQ and produce to cut the circle at D and E.
Join DE. Then chord DE is the locus of points inside the circle that Ls equidistant from A and C.
As chord DE passes through (he centre O of the circle, it is a diameter. To prove the construction take any point S inside the circle on DE.

Question 29. Use ruler and compasses only for the following questions:

Question 30. Ruler and compass only may be used in this question. All construction lines and arcs must be clearly shown, and be of sufficient length and clarity to permit assessment.
(i) Construct Δ ABC, in which BC = 8 cm, AB = 5 cm, ∠ ABC = 60°.

Question 31. Ruler and compasses only may be used in this question. All construction lines and arcs must be clearly shown, and be of sufficient length and clarity to permit assessment.

### Graphical Depiction

Question 1. Use graph paper for this question. Take 2 cm = 1 unit on both axis.
(i) Plot the points A (1, 1), B (5, 3) and C (2, 7);
(ii) Construct the locus of points equidistant from A and B;
(iii) Construct the locus of points equidistant from AB and AC;
(iv) Locate the point P such that PA = PB and P is equidistant from AB and AC;
(v) Measure and record the length PA in cm.

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## Shares and Dividends Class 10 Maths ICSE Solutions

Get ICSE Solutions for Class 10 Mathematics Chapter 4 Shares and Dividends for ICSE Board Examinations on ICSESolutions.com. We provide step by step Solutions for ICSE Mathematics Class 10 Solutions Pdf. You can download the Class 10 Maths ICSE Textbook Solutions with Free PDF download option.

## Shares and Dividends Class 10 Maths ICSE Solutions

### Formulae

1. The nominal value (N.V.) of a share is also called the Register value, printed value, Face value (F.V.), etc.
2. The price of a share at any particular time is called its Market value (M.V.).
3. The market value of a share can be the same, more or less than the nominal value oi the share depending upon the performance and profits of the company.
1. If the market value of a share is the same as its nominal value, the share is said to be at par.
2. If the market value of a share is more than its nominal value, the share is said to be above par or at a premium.
3. If the market value of a share is less than its nominal value, the share is said to be below par or at a discount.
4. The profit, which a share-holder gets (out of the profits of the company) from his investment in the company, is called dividend.
The dividend is always expressed as a percentage of the nominal value, of the share.
5. Sum invested = No, of shares bought × M.V. of 1 share
If the share is at par, market value = nominal value
i.e., M.V. = N.V.

### Formulae Based Questions

Question 1. A man invested Rs. 45,000 in 15% Rs. 100 shares quoted at Rs. 125. When the market value of these share rose to Rs. 140. He sold same shares, just enough to raise Rs. 8,400 calculate.
(i) The number of shares he still holds.
(ii) The dividend due to him on remaining shares.

Question 2. (i) Which in better investment: 7% Rs. 100 shares at Rs.120 or 8% Rs. 10 shares at Rs. 13.50.
(ii) Mamta invested Rs. 10,846 in buying the shares of a company at Rs. 17 each. If the face value of each share be? 10 and company paid 15% dividend at the end of the year, find the dividend earned by her.

Question 3. Ajay owns 560 shares of a company. The face value of each share is Rs. 25. The company declares a dividend of 9%. Calculate:
(i) The dividend that Ajay will get.
(ii) The rate of interest on his investment, if Ajay had paid Rs. 30 for each share.

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## Reflection Class 10 Maths ICSE Solutions

Get ICSE Solutions for Class 10 Mathematics Chapter 7 Reflection for ICSE Board Examinations on ICSESolutions.com. We provide step by step Solutions for ICSE Mathematics Class 10 Solutions Pdf. You can download the Class 10 Maths ICSE Textbook Solutions with Free PDF download option.

## Reflection Class 10 Maths ICSE Solutions

### Formulae

1. Rule to find the reflection of a point in the x-axis:
(i) Retain the abscissa i.e. x-coordinate.
(ii) Change the sign of ordinate i.e. y-coordinate.
2. Rule to find the reflection of a point in the y-axis:
(i) Change the sign of abscissa i.e., x-coordinate.
(ii) Retain the ordinate i.e., y-coordinate.
3. Reflection of a point in a line parallel to x-axis. The reflection of the point P(x, y) in the line y = a is the point P(x, -y+2a).
4. Reflection of a point in a line parallel to y-axis. The reflection of the point P(x, y) in the line x = a is the point P’ (-x+2a, y).
5. Reflection of a point in the origin:
(i) Change the sign of abscissa i.e., x-coordinate.
(ii) Change the sign of ordinate i.e., y-coordinate.
6. A point is called an Invariant point with respect to a given line if and only if lies on the line.

### Determine the Following

Question 1. The triangle A(1, 2), B(4, 4) and C(3, 7) is first reflected in the line y = 0 onto triangle A’B’C’ and then triangle A’B’C’ is reflected in the origin onto triangle A”B”C”. Write down the co-ordinates of:

Question 2. The point P (a, b) is first reflected in the origin and then reflected on the Y-axis to p’. If P’ has co-ordinates (3, – 4), evaluate a, b.

### Figure Based Questions

Question 1. Name the figure formed by a triangle and its reflection, when:
(i) An isosceles right-angled triangle is reflected in its hypotenuse.
(ii) A right-angled triangle is reflected in its hypotenuse.
(iii) An isosceles triangle is reflected in its unequal side.
(iv) A scalene triangle is reflected in its greatest side.
Solution:

### Graphical Depiction

Question 1. Find the co-ordinates of the images of the following under reflection in the origin:

Question 2. The image of a point P under reflection on the X-axis is (5, – 2). Write down the co-ordinates of P.

Question 3. Write down the co-ordinates of the image of (5, – 4).
(i) Reflection in x = 0;
(ii) Reflection in y = 2.

Question 4. Use a graph paper for this question.
(i) The point P (2, – 4) is reflected about the line x = 0 to get the image Q. Find the coordinates of Q.
(ii) Point Q is reflected about the line y = 0 to get the image R. Find the co-ordinates of R.
(iii) Name the figure PQR.
(iv) Find the area of figure PQR.

Question 5. Using a graph paper, plot the points A (6,4) and B (0,4).
(i) Reflect A and B in the origin to get the images A’ and B’.
(ii) Write the co-ordinates of A’ and B’.
(iii) State the geometrical name for. the figure ABA’B’.
(iv) Find its perimeter.

Question 6. (i) Find the reflection of the point (3, 5) on X-axis.
(ii) Find the reflection of the point (- 3, 5) on X-axis.
(iii) Find the reflection of the point (- 3, – 5) on X-axis.
(iv) Find the reflection of the point (3, – 5) on X-axis.

Question 7. P, Q have co-ordinates (-1, 2) and (6, 3) respectively. Reflect P on the X-axis to P’. Find:
(i) The co-ordinate of P’
(ii) Length of P’Q.
(iii) Length of PQ.
(iv) Is P’Q = PQ ?

Question 8. A point P(4, – 1) is reflected to P’ in the line y = 2 followed by the reflection to P” in the line x = -1. Find :
(i) The co-ordinates of P’.
(h) The co-ordinates of P”.
(iii) The length of PP’.
(iv) The length of P’P”.

Question 9. Point A (5, 1) on reflection on X- axis is mapped as A’. Also A on reflection on Y- axis is mapped as A”.
(i) Write the co-ordinates of A’.
(ii) Write the co-ordinates of A”.
(iii) Calculate the distance A’ A”.
(iv) On which coordinate axis does the middle point M of A”A’ lie ?

Question 10. Point A(4, – 1) is reflected as A’ on Y-axis. Point B on refletion on X-axis is mapped as B’ (- 2, 5).
(i) Write the co-ordinates of A’.
(ii) Write the co-ordinates of B.
(iii) Write the co-ordinates of the middle point
M of the segment A’B.
(iv) Write the co-ordinates of the point of reflection A” of A on X-axis.

Question 11. Point A (2, -4) is reflected in origin as A’. Point B (- 3, 2) is reflected on X-axis as B’.
(i) Write the co-ordinates of A’.
(ii) Write the co-ordinates of B’.
(iii) Calculate the distance A’B’.
Give your answer correct to 1 decimal place, (do not consult tables).

Question 12. (i) Point P(a, b) reflected on the X-axis to P'(5, 2). Write down the value of a and b.
(ii) P” is the image of P when reflected on the Y-axis. Write down the co-ordinates of P”.
(iii) Name a single transformation that maps P’ to P”.

Question 13. Points (3, 0) and (-1, 0) are invarient points under reflection in the line L1; point (0, -3) and (0, 1) are invarient points on reflection in line L2.

Question 14. A point P(a, b) is reflected in the X-axis to P'(2, – 3). Write down the value of a & b. P” is the image of P, when reflected on the Y-axis. Write down the co-ordinates of P” when P is reflected in the line parallel to the Y-axis, such that x = 4.

Question 15. Use a graph paper to answer the following questions. (Take 1 cm = 1 unit on both axis):
(i) Plot A (4, 4), B (4, – 6) and C (8, 0), the vertices of a triangle ABC.
(ii) Reflect ABC on the y-axis and name it as A’B’C’.
(iii) Write the coordinates of the images A’, B’ and C’.
(iv) Give a geometrical name for the figure AA’ C’B’ BC.
(v) Identify the line of symmetry of AA’ C’ B’ BC.

Question 16. Use a graph paper for this question. (Take 10 small divisions = 1 unit on both axis). P and Q have co-ordinates (0, 5) (- 2, 4).
(i) P is invariant when reflected in an axis. Name the axis.
(ii) Find the image of Q on reflection in the axis found in (i).
(iii) (0, k) on reflection in the origin is invariant. Write the value of k.
(iv) Write the co-ordinates of the image of Q, obtained by reflecting it in the origin following by reflection in x-axis.

Question 18. The point P(3, 4) is reflected to P’ in the x-axis and O’ is the image of O (the Origin) in the line PP’ Find :
(i) The coordinates of P’ and O’.
(ii) The length of segment PP’ and OO’.
(iii) The perimeter of the quadrilateral POP’O’
(iv) What is the special name of the quadrilateral POP’O’.

Question 19. Use graph paper for this question.
The points A (2, 3), B (4, 5) and C (7, 2) are the ,vertices of A ABC.
(i) Write down the coordinates of A’, B’, C’ if Δ A’B’C’ is the image of Δ ABC, when reflected in the origin.
(ii) Write down the co-ordinates of A”, B”, C” if A”B”C” is the image of Δ ABC, when reflected in the x-axis.
(iii) Mention the special name of the quadrilateral BCC”B” and find its area.

Question 20. Use a graph paper for this question (take 10 small divisions = 1 unit on both axis).
Plot the points P (3, 2) and Q (-3, -2), from P and Q draw perpendicular PM and QN on the X- axis.
(i) Name the image of P on reflection at the origin.
(ii) Assign, the . special name to the geometrical figure. PMQN and find its area.
(iii) Write the co-ordinates of the point to which M is mapped on reflection in (i) X- axis,
(ii) Y-axis, (iii) origin.

Question 21. Using graph paper and taking 1 cm = 1 unit along both x-axis and y-axis.
(i) Plot the points A (- 4, 4) and B (2, 2).
(ii) Reflect A and B in the origin to get the images A’ and B’ respectively.
(iii) Write down the co-ordinates of A’ and B’.
(iv) Give the geometrical name for the figure ABA’B’.
(v) Draw and name its lines of symmetry.

Question 22. Use graph paper for this question.
The point P (5, 3) was reflected in the origin to get the image P’.
(i) Write down the co-ordinates of P’.
(ii) If M is the foot of the perpendicular from of P to the X-axis, find the co-ordinates of M.
(iii) If N is the foot of the perpendicular from of P’ to the X-axis, find the co-ordinates of N.
(iv) Name the figure PMP’N.
(v) Find the area of die figure PMP’N.

Question 23. Use graph paper to answer this question:
(i) Plot the points A (4,6) and B (1, 2).
(ii) A’ is the image of A when reflected in X-axis,
(iii) B’ is the image of B when B is reflected in the line AA’.
(iv) Give the geometrical name for the figure ABA’B’.

Question 24. Use graph paper to answer the following questions. (Take 2 cm = 1 unit on both axis).
(i) Plot the points A (- 4, 2) and B (2, 4).
(ii) A’ is the image of A when reflected in the y-axis. Plot it on the graph paper and write the coordinates of A’.
(iii) B’ is the image of B when reflected in the line AA’. Write the coordinates of B’.
(iv) Write the geometric name of the figure ABA’B’.
(v) Name a line of symmetry of the figure formed.

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## Banking Class 10 Maths ICSE Solutions

Get ICSE Solutions for Class 10 Mathematics Chapter 3 Banking for ICSE Board Examinations on ICSESolutions.com. We provide step by step Solutions for ICSE Mathematics Class 10 Solutions Pdf. You can download the Class 10 Maths ICSE Textbook Solutions with Free PDF download option.

## Banking Class 10 Maths ICSE Solutions

### Formulae

Calculating interest on a savings bank account:

1. Interest for the month is calculated on the minimum balance between the 10th day and the last day of the month.
2. Add all these balances. However, if the same balance continues for n months then multiply this balance by n, rather than writing it n times and then adding.
3. Find simple interest on this sum for one month.
4. If the interest is less than Rs. 1, neglect it.
5. No interest is paid for the month in which the account is closed.

Calculation of maturity amount on recurring deposit:
The interest on the recurring deposit account can be calculated by using the formula:

where S.I. is the simple interest, P is the money deposited per month, n is the number of months for which the money has been deposited and r is the simple interest rate percent per annum.

### Formulae Based Questions

Question 1. Naseem has a 5 years Recurring Deposit account in Punjab National Bank and deposit? Rs. 240 per month. If she receives Rs. 17,694 at the time of maturity find the rate of interest.

Question 2. Zafarullah has a recurring deposit The list price of the television be? 12,500. account in a bank for 3½ years at 9.5% S.I. p.a. If he gets Rs. 78,638 at the time of maturity. Find the monthly instalment.

Question 3. Mohan saves Rs. 25 per month from his pocket allowance and puts this saving every month in a bank recurring deposit scheme for a period of 72 months at 5.25%. What amount does he get on maturity?
Solution: See the table of Recurring deposit scheme. Here the month by instalment is Rs. 25 and the number of instalments is 72.
So the maturity value is the amount given in the table against the row marked 72 and the column marked 25. This amount is 2,721.90.
Hence, on maturity, Mohan gets Rs. 2,721.90.

Question 4. Using R.D., table calculate the values of a R.D., account of Rs. 80 for period of 9 months @ 11.5% p. a.
Solution: In the row of 80 we will locate the value under the column of 9 months which is 755.
So, maturity values of RD., account of 80 for 9 months @ 11.5% p.a Rs. 755.00.

Question 5. Veena deposits Rs. 100 per month in a bank cumulative time deposit scheme for a period of 5 years. What amount does she get on maturity if the rate of interest is 16%?
Solution: See the table of RD. scheme. For a monthly installment of Rs. 1oo per month the maturity values after 5 years is Rs. 8,447.80.

Question 6. Mrs. Goswami deposits Rs. 1000 every month in a recurring deposit account for 3 years at 8% interest per annum. Find the matured value.

Question 7. Amit deposited Rs. 150 per month in a bank for 8 months under the Recurring Deposit Scheme. What will be the maturity value of his deposits, if the rate of interest is 8% per annum and interest is calculated at the end of every month?

Question 8. Kiran deposited  200 per month for 36 months in a bank’s recurring deposit account. If the bank pays interest at the rate of 11% per annum, find the amount she gets on maturity.

### Data Based Questions

Question 1. Given below are the entries in a Savings Bank A/c pass book:

Calculate the interest for six months from February to July at 6% p.a.
Solution:

Question 2. Mr. Dhoni has an account in the Union Bank of India. The following entries are from his pass book:

Question 3. Anita opens an S.B. account in State Bank of India on August 1, 1983 with Rs. 100. She deposits Rs. 100 on the first or second day every month till and including February 1,1984. In between she withdrawal Rs. 200 on October 17,1983 and also on January 13,1984. Write the entries of the passbook.
Solution: The entries in the pass book are given below:

Question 4. Akash, an employee of a bank, has a saving bank account in his bank that pays him
interest at the rate of 5% p.a., which is compounded every June and December. His pass book entries are as follow:

Calculate the interest due at the end of June and find the balance on July 1, if he deposits a cash of ?100 on July 1, which is also entered immediately.
Solution:

Question 5. Mr. Chaudhary opened a Saving’s Bank Account at State Bank of India on 1st April 2007.

If the bank pays interest at the rate of 5% per annum, find the interest paid on 1st April, 2008. Give your answer correct to the nearest rupee.

Question 6. A page of Passbook of Mrs. C. Malik Savings Bank Account in year 2002 is given below:

If the rate of interest decreases from 5% to 4% with effect from June 1st, 2002, compute the interest at the end of the year.
Solution: As per entries of the Passbook page of Mrs. C. Malik, we have:

Question 7. Suresh has joined a factory which pays wages by cheque only. He opens a S.B. account on Feb. 1, and his passbook has the following entries Upto 1st April of the year.

He closes the account on 11th April. Complete the entries for 11th April at the rate of 5% p.a.

Question 8. A page from the passbook of Mrs. Rama Bhalla is given below:
Calculate the interest due to Mrs. Bhalla for the period from January 2004 to December 2004, at the rate of 5% per annum.

Question 9. A page from the Savings Bank Account of Mr. Prateek is given below:

Question 10. Mr. S.K. Mishra had a Savings Bank Account in Punjab National Bank. His Passbook had the following entries:

If the interest is paid at the rate of 5% per annum at the end of September every year, calculate the amount he will get if he closes the account on October 30, of the same year.

Question 11. The entries in the passbook of a Saving Bank Account holder are as follows:

(i) If the account is dosed on Sept 29, 1986, then month of Sept., will not earn interest and principal for one month Rs. 16,800.

Question 12. Mrs. Kapoor opened a Savings Bank Account in State Bank of India on 9th January 2008. Her pass book entries for the year 2008 are given below:

Mrs. Kapoor closes the account on 31st December, 2008. If the bank pays interest at 4% per annum, find the interest Mrs. Kapoor receives on closing the account. Give your answer correct to the nearest rupee.

Question 13. Mr. Ashok has an account in the Central Bank of India. The following entries are from his pass book:

If Mr. Ashok gets Rs. 83.75 as interest at the end of the year where the interest is compounded annually, calculate the rate of interest paid by the bank in his Savings Bank Account on 31st December, 2005.

Question 14. Mr. Mishra has a Savings Bank Account in Allahabad Bank. His pass book entries are as follows:

Rate of interest paid by the bank is 4.5% per annum. Mr. Mishra closes his account on 30th October, 2007. Find the interest he receives.

Question 15. A page from the saving bank account of Priyanka is given below:

If the interest earned by Priyanka for the period ending September, 2006 is Rs. 175, find the rate of interest.

Question 16. Given the following details, calculate the simple interest at the rate of 6% per annum up to June, 30:

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