Tili Kannada Text Book Class 6 Solutions Answers Guide

Expert Teachers at LearnCram.com has created Tili Kannada Text Book Class 6 Solutions Answers Guide Notes Pdf free download is part of KSEEB Solutions for Class 6. Here Learncram has given Karnataka State Board Syllabus 2nd Language Tili Kannada Text Book Class 6th Standard Guide NCERT Solutions Pdf Download. Students can also find Siri Kannada Text Book Class 6 Solutions of 1st language.

Tili Kannada Text Book Class 6 Answers Solutions Guide (2nd Language)

Class 6 Tili Kannada Gadya Bhaga​ Karnataka State Board Solutions

Class 6 Tili Kannada Padya Bhaga​ Karnataka State Board Solutions

Class 6 Tili Kannada Nataka Karnataka State Board Solutions

Class 6 Tili Kannada Puraka Odu Karnataka State Board Solutions

We hope the given Tili Kannada Text Book Class 6 Answers Solutions Guide Notes Pdf free download will help you. If you have any queries regarding Karnataka State Board Syllabus 6th Standard Tili Kannada Textbook NCERT Solutions of 2nd Language, drop a comment below and we will get back to you at the earliest.

Tili Kannada Text Book Class 7 Solutions Answers Guide

Expert Teachers at LearnCram.com has created Tili Kannada Text Book Class 7 Solutions Answers Guide Notes Pdf free download is part of KSEEB Solutions for Class 7. Here Learncram has given Karnataka State Board Syllabus 2nd Language Tili Kannada Text Book Class 7th Standard Guide NCERT Solutions Pdf Download. Students can also find Siri Kannada Text Book Class 7 Solutions of 1st language.

Tili Kannada Text Book Class 7 Answers Solutions Guide (2nd Language)

Class 7 Tili Kannada Gadya Bhaga​ Karnataka State Board Solutions

Class 7 Tili Kannada Padya Bhaga​ Karnataka State Board Solutions

Class 7 Tili Kannada Puraka Odu Karnataka State Board Solutions

We hope the given Tili Kannada Text Book Class 7 Answers Solutions Guide Notes Pdf free download will help you. If you have any queries regarding Karnataka State Board Syllabus 7th Standard Tili Kannada Textbook NCERT Solutions of 2nd Language, drop a comment below and we will get back to you at the earliest.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 16 Perimeter and Area Objective Type Questions

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 16 Perimeter and Area Objective Type Questions

Mental Maths

Class 7 Maths Chapter 16 Perimeter and Area Question 1. Fill in the blanks:
(i) The perimeter of a regular polygon = ……….. × length of a side.
(ii) The unit of measurement of the area is ……….
(iii) The perimeter of a rhombus is = 4 × ………
(iv) An area of 1 km2 = ……… hectare
(v) If the perimeter of a parallelogram is 40 cm and the length of one side is 12 cm, then the length of the adjacent side is ……
(vi) To find the cost of polishing a table-top, we need to find the ………. of the table-top.
(vii) The ratio of circumference to the diameter of a circle is ………..
(viii) If the area of a triangular piece of cardboard is 90 cm2, then the length of the altitude corresponding to 20 cm long base is ………. cm.
Solution:
ICSE Understanding Mathematics Class 7 ML Aggarwal Solutions Chapter 16 Perimeter and Area Objective Type Questions Q1

ML Aggarwal Class 7 Solutions Chapter 16 Question 2. State whether the following statements are true (T) or false (F):
(i) A diagonal of a rectangle divides it into two right-angled triangles of equal areas.
(ii) A diagonal of a parallelogram divides it into two triangles of equal areas.
(iii) If the perimeter of two parallelograms is equal, then their areas are also equal.
(iv) All parallelogram having equal areas have the same perimeters.
(v) The area of a circle of diameter d is πd2.
(vi) Area of a parallelogram = product of lengths of its two adjacent sides.
Solution:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 16 Perimeter and Area Objective Type Questions Q2

Multiple Choice Questions

Choose the correct answer from the given four options (3 to 14):
Question 3.
If the perimeter of a square is 24 cm, then its area is
(a) 16 cm2
(b) 24 cm2
(c) 36 cm2
(d) 36 m2
Solution:
ML Aggarwal Maths for Class 7 Pdf Download Chapter 16 Perimeter and Area Objective Type Questions Q3

ML Aggarwal Class 7 Chapter 16 Question 4. If the area of a parallelogram is 54 cm2 and the length of one side is 7.5 cm, then the corresponding height is
(a) 7.2 cm
(b) 14.4 cm
(c) 3.6 cm
(d) 13.5 cm
Solution:
APC Maths Class 7 ML Aggarwal Solutions Chapter 16 Perimeter and Area Objective Type Questions Q4

Perimeter and Area Class 7 Question 5.
If the base of a triangle is doubled and its height is halved, then the area of the resulting triangle
(a) decreases
(b) increases
(c) doubles
(d) remains the same
Solution:
Class 7 Maths Book By ML Aggarwal Solutions Chapter 16 Perimeter and Area Objective Type Questions Q5

ML Aggarwal Class 7 Question 6. If the height of a parallelogram is doubled and base tripled, then its area becomes
(a) 2 times
(b) 3 times
(c) 6 times
(d) 12 times
Solution:
ML Aggarwal Maths for Class 7 Solutions Pdf Chapter 16 Perimeter and Area Objective Type Questions Q6

Perimeter and Area Class 7 Question 7. The circumference of the circle with diameter 28 cm is
(a) 44 cm
(b) 88 cm
(c) 176 cm
(d) 616 cm
Solution:
ICSE Understanding Mathematics Class 7 ML Aggarwal Solutions Chapter 16 Perimeter and Area Objective Type Questions Q7

ML Aggarwal Class 7 Perimeter and Area Question 8. The ratio of circumference to the area of a circle of radius r units is
(a) 2 : r
(b) r : 2
(c) 1 : r
(d) π : r
Solution:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 16 Perimeter and Area Objective Type Questions Q8

ML Aggarwal Class 9 Solutions ICSE Chapter 16 Question 9. If the area of a circle is numerically equal to its circumference, then the radius of the circle is
(a) 1 unit
(b) 2 units
(c) 3 units
(d) 4 units
Solution:
ML Aggarwal Maths for Class 7 Pdf Download Chapter 16 Perimeter and Area Objective Type Questions Q9

Question 10.
The area of a circle of diameter d is
(a) 2πd2
(b) πd2
(c) \(\frac { \pi { d }^{ 2 } }{ 2 }\)
(d) \(\frac { \pi { d }^{ 2 } }{ 4 }\)
Solution:
APC Maths Class 7 ML Aggarwal Solutions Chapter 16 Perimeter and Area Objective Type Questions Q10

ML Aggarwal Maths for Class 7 Solutions Pdf Question 11. If the ratio of the radii of two circles is 2 then the ratio of their circumferences is
(a) 2 : 3
(b) 3 : 2
(c) 4 : 9
(d) 9 : 4
Solution:
Class 7 Maths Book By ML Aggarwal Solutions Chapter 16 Perimeter and Area Objective Type Questions Q11

Question 12.
If the ratio of the radii of two circles is 3 : 5, then the ratio of their areas is
(a) 3 : 5
(b) 5 : 3
(c) 25 : 9
(d) 9 : 25
Solution:
ML Aggarwal Maths for Class 7 Solutions Pdf Chapter 16 Perimeter and Area Objective Type Questions Q12

Question 13.
The perimeter of a semicircle (including its diameter) of radius 7 cm is
(a) 22 cm
(b) 29 cm
(c) 36 cm
(d) 44 cm
Solution:
Apc Maths Class 7 Solutions

Question 14.
Area of a rectangle and the area of a circle are equal. If the dimensions of the rectangle are 14 cm × 11 cm, then the radius of the circle is
(a) 21 cm
(b) 14 cm
(c) 10.5 cm
(d) 7 cm
Solution:
ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 16 Perimeter and Area Objective Type Questions Q14

Higher Order Thinking Skills (HOTS)

Question 1.
In the given figure, ABDE is a parallelogram, find the area of the trapezium ACDE.
ML Aggarwal Maths for Class 7 Pdf Download Chapter 16 Perimeter and Area Objective Type Questions HOTS 1
Solution:
APC Maths Class 7 ML Aggarwal Solutions Chapter 16 Perimeter and Area Objective Type Questions HOTS 1.1

Question 2.
In the given figure, the length of the rectangle is 28 cm. Find the area of the shaded region.
Class 7 Maths Book By ML Aggarwal Solutions Chapter 16 Perimeter and Area Objective Type Questions HOTS 2
Solution:
ML Aggarwal Maths for Class 7 Solutions Pdf Chapter 16 Perimeter and Area Objective Type Questions HOTS 2.1
ICSE Understanding Mathematics Class 7 ML Aggarwal Solutions Chapter 16 Perimeter and Area Objective Type Questions HOTS 2.2

Question 3.
In the given figure, ABCD is a square of side 14 cm. A, B, C, and D are centers of circular arcs of equal radius. Find the perimeter and the area of the shaded region.
ML Aggarwal Maths for Class 7 Pdf Download Chapter 16 Perimeter and Area Objective Type Questions HOTS 3
Solution:
APC Maths Class 7 ML Aggarwal Solutions Chapter 16 Perimeter and Area Objective Type Questions HOTS 3.1

ML Aggarwal Class 7 Solutions for ICSE Maths

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

ML Aggarwal Class 10 Solutions Arithmetic and Geometric Progression Question 1. Can 0 be a term of a geometric progression?
Solution:
No, 0 is not a term of geometric progression.

ML Aggarwal Class 10 Solutions Question 2.
(i) Find the next term of the list of numbers \(\frac { 1 }{ 6 } ,\frac { 1 }{ 3 } ,\frac { 2 }{ 3 } ,… \)
(ii) Find the next term of the list of numbers \(\frac { 3 }{ 16 } ,-\frac { 3 }{ 8 } ,\frac { 3 }{ 4 } ,-\frac { 3 }{ 2 } ,…\)
(iii) Find the 15th term of the series \(\sqrt { 3 } +\frac { 1 }{ \sqrt { 3 } } +\frac { 1 }{ 3\sqrt { 3 } } +…\)
(iv) Find the nth term of the list of numbers \(\frac { 1 }{ \sqrt { 2 } } ,-2,4\sqrt { 2 } ,-16,…\)
(v) Find the 10th and nth terms of the list of numbers 5, 25, 125, …
(vi) Find the 6th and the nth terms of the list of numbers \(\frac { 3 }{ 2 } ,\frac { 3 }{ 4 } ,\frac { 3 }{ 8 } ,…\)
(vii) Find the 6th term from the end of the list of numbers 3, – 6, 12, – 24, …, 12288.
Solution:
Ap Gp ML Aggarwal Class 10 Solutions
Ap Gp ML Aggarwal
Arithmetic Progression Class 10 ICSE Solutions ML Aggarwal
ML Aggarwal Class 10 Gp Solutions

Question 3.
Which term of the G.P.
(i) 2, 2√2, 4, … is 128?
(ii) \(1,\frac { 1 }{ 3 } ,\frac { 1 }{ 9 } ,…is\quad \frac { 1 }{ 243 } ?\)
(iii) \(\frac { 1 }{ 3 } ,\frac { 1 }{ 9 } ,\frac { 1 }{ 27 } ,…is\quad \frac { 1 }{ 19683 } ? \)
Solution:
ML Aggarwal Ap Gp Solution
ML Aggarwal Class 10 Ap Gp
ML Aggarwal Ap Gp Solutions

Question 4.
Which term of the G.P. 3, -3√3, 9, -9√3, … is 729?
Solution:
Maths Gp

Question 5.
Determine the 12th term of a G.P. whose 8th term is 192 and the common ratio is 2.
Solution:
ML Aggarwal Class 10 Ap Gp Solutions

Question 6.
In a GP., the third term is 24 and 6th term is 192. Find the 10th term
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 7.
Find the number of terms of a G.P. whose first term is \(\\ \frac { 3 }{ 4 } \), common ratio is 2 and the last term is 384.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 8.
Find the value of x such that
(i) \(-\frac { 2 }{ 7 } ,x,-\frac { 7 }{ 2 } \) are three consecutive terms of a G.P.
(ii) x + 9, x – 6 and 4 are three consecutive terms of a G.P.
(iii) x, x + 3, x + 9 are first three terms of a G.P. Find the value of x.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 9.
If the fourth, seventh and tenth terms of a G.P. are x, y, z respectively, prove that x, y, z are in G.P.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 10.
The 5th, 8th and 11th terms of a G.P. are p, q, and s respectively. Show that q² = ps.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 11.
If a, b, c are in G.P., then show that a², b², c² are also in G.P.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 12.
If a, b, c are in A.P., then show that 3a, 3b, 3c are in G.P.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 13.
If a, b, c are in A.P., then show that 10ax + 10, 10bx + 10, 10cx + 10, x ≠ 0, are in G.P.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 14.
If a, a2+ 2 and a3 + 10 are in G.P., then find the values(s) of a.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 15.
If k, 2k + 2, 3k + 3, … are in G.P., then find the common ratio of the G.P.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 16.
The first and the second terms of a GP. are x-4 and xm. If its 8th term is x52, then find the value of m.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 17.
Find the geometric progression whose 4th term is 54 and the 7th Term is 1458.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 18.
The fourth term of a GP. is the square of its second term and the first term is -3. Determine its seventh term.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 19.
The sum of first three terms of a G.P. is \(\\ \frac { 39 }{ 10 } \) and their product is 1. Find the common ratio and the terms.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 20.
Three numbers are in A.P. and their sum is 15. If 1, 4 and 19 are added to these numbers respectively, the resulting numbers are in G.P. Find the numbers.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 21.
Three numbers form an increasing G.P. If the middle term is doubled, then the new numbers are in A.P. Find the common ratio of the G.P.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 22.
Three numbers whose sum is 70 are in GP. If each of the extremes is multiplied by 4 and the mean by 5, the numbers will be in A.P. Find the numbers.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 23.
There are four numbers such that the first three of them form an A.P. and the last three form a GP. The sum of the first and third number is 2 and that of the second and fourth is 26. What are these numbers?
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 24.
(i) If a, b, c are in A.P. as well in G.P., prove that a = b = c.
(ii) If a, b, c are in A.P as well as in G.P., then find the value of ab-c + bc-a + ca-b
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 25.
The terms of a G.P. with first term a and common ratio r are squared. Prove that resulting numbers form a G.P. Find its first term, common ratio, and the nth term.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 26.
Show that the products of the corresponding terms of two G.P.’s a, ar, ar², …, arn-1 and A, AR, AR2, …, ARn-1 form a G.P. and find the common ratio.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 27.
(i) If a, b, c are in G.P. show that \(\frac { 1 }{ a } ,\frac { 1 }{ b } ,\frac { 1 }{ c } \) are also in G.P.
(ii) If K is any positive real number and Ka, Kb Kc is three consecutive terms of a G.P., prove that a, b, c are three consecutive terms of an A.P.
(iii) If p, q, r are in A.P., show that pth, qth and rth terms of any G.P. are themselves in GP.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 28.
If a, b, c are in GP., prove that the following are also in G.P.
(i) a3, b3, c3
(ii) a2 + b2, ab + bc, b2 + c2.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 29.
If a, b, c, d are in G.P., show that
(i) a2 + b2, b2 + c2, c2 + d2 are in G.P.
(ii) (b – c)2 + (c – a)2 + (d – b)2 = (a – d)2.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 30.
The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria present in the culture originally, how many bacteria will be present at the end of the 2nd hour, 4th hour and nth hour?
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

Question 31.
The length of the sides of a triangle form a G.P. If the perimeter of the triangle is 37 cm and the shortest side is of length 9 cm, find the lengths of the other two sides.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 9 Arithmetic and Geometric Progressions Ex 9.4

ML Aggarwal Class 10 Solutions for ICSE Maths

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4

Take π = \(\\ \frac { 22 }{ 7 } \), unless stated otherwise.

ML Aggarwal Class 10 Mensuration Question 1. The adjoining figure shows a cuboidal block of wood through which a circular cylindrical hole of the biggest size is drilled. Find the volume of the wood left in the block.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4

LearnCram.com also covered previous Year argumentative essay topics asked in ICSE board exams.

ML Aggarwal Class 9 Mensuration Solutions Question 2. The given figure shows a solid trophy made of shining glass. If one cubic centimetre of glass costs Rs 0.75, find the cost of the glass for making the trophy.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4

ICSE Class 10 Maths Mensuration Solutions Question 3. From a cube of edge 14 cm, a cone of maximum size is carved out. Find the volume of the remaining material.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4

Mensuration Class 10 ML Aggarwal Question 4. A cone of maximum volume is curved out of a block of wood of size 20 cm × 10 cm × 10 cm. Find the volume of the remaining wood.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4

ML Aggarwal Class 9 Solutions Mensuration Question 5. 16 glass spheres each of radius 2 cm are packed in a cuboidal box of internal dimensions 16 cm × 8 cm × 8 cm and then the box is filled with water. Find the volume of the water filled in the box.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4

Mensuration ML Aggarwal Class 9 Question 6. A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15 cm by 10 cm by 3.5 cm. The radius of each of the depression is 0.5 cm and the depth is 1.4 cm. Find the volume of the wood in the entire stand, correct to 2 decimal places.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4

ML Aggarwal Class 9 Mensuration Solution Question 7. A cuboidal block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter that the hemisphere can have? Also find the surface area of the solid.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4

ML Aggarwal Mensuration Question 8. A wooden article was made by scooping out a hemisphere from each end of a solid cylinder (as shown in the given figure). If the height of the cylinder is 10 cm and its base is of radius 3.5 cm, find the total surface area of the article.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4

ML Aggarwal Mensuration Class 10 Question 9. A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. If the total height of the toy is 15.5 cm, find the total surface area of the toy.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4

Class 10 ML Aggarwal Mensuration Solutions Question 10. A circus tent is in the shape of a cylinder surmounted by a cone. The diameter of the cylindrical portion is 24 m and its height is 11 m. If the vertex of the cone is 16 m above the ground, find the area of the canvas used to make the tent.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4

ML Aggarwal Class 10 Solutions Mensuration Question 11. An exhibition tent is in the form of a cylinder surmounted by a cone. The height of the tent above the ground is 85 m and the height of the cylindrical part is 50 m. If the diameter of the base is 168 m, find the quantity of canvas required to make the tent. Allow 20% extra for folds and stitching. Give your answer to the nearest m².
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4

Mensuration ML Aggarwal Class 10 Solutions Question 12. From a solid cylinder of height 30 cm and radius 7 cm, a conical cavity of height 24 cm and of base radius 7 cm is drilled out. Find the volume and the total surface of the remaining solid.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4

ML Aggarwal Class 10 Mensuration Solutions Question 13. The given figure shows a wooden toy rocket which is in the shape of a circular cone mounted on a circular cylinder. The total height of the rocket is 26 cm, while the height of the conical part is 6 cm. The base of the conical portion has a diameter of 5 cm, while the base diameter of the cylindrical portion is 3 cm. If the conical portion is to be painted green and the cylindrical portion red, find the area of the rocket painted with each of these colours. Also, find the volume of the wood in the rocket. Use π = 3.14 and give answers correct to 2 decimal places.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4

Question 14.
The given figure shows a hemisphere of radius 5 cm surmounted by a right circular cone of base radius 5 cm. Find the volume of the solid if the height of the cone is 7 cm. Give your answer correct to two places of decimal.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4

Question 15.
A buoy is made in the form of a hemisphere surmounted by a right cone whose circular base coincides with the plane surface of the hemisphere. The radius of the base of the cone is 3.5 metres and its volume is \(\\ \frac { 2 }{ 3 } \) of the hemisphere. Calculate the height of the cone and the surface area of the buoy correct to 2 places of decimal
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4

Question 16.
A circular hall (big room) has a hemispherical roof. The greatest height is equal to the inner diameter, find the area of the floor, given that the capacity of the hall is 48510 m³.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4

Question 17.
A building is in the form of a cylinder surmounted by a hemisphere valted dome and contains \(41 \frac { 19 }{ 21 } \) m3 of air. If the internal diameter of dome is equal to its total height above the floor, find the height of the building
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4

Question 18.
A rocket is in the form of a right circular cylinder closed at the lower end and surmounted by a cone with the same radius as that of the cylinder. The diameter and the height of the cylinder are 6 cm and 12 cm respectively. If the slant height of the conical portion is 5 cm, find the total surface area and the volume of the rocket. (Use π = 3.14).
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4

Question 19.
A solid is in the form of a right circular cylinder with a hemisphere at one end and a cone at the other end. Their common diameter is 3.5 cm and the height of the cylindrical and conical portions are 10 cm and 6 cm respectively. Find the volume of the solid. (Take π = 3.14)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4

Question 20.
A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The height and radius of the cylindrical part are 13 cm and 5 cm respectively. The radii of the hemispherical and conical parts are the same as that of the cylindrical part. Calculate the surface area of the toy if the height of the conical part is 12 cm.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4

Question 21.
The given figure shows a model of a solid consisting of a cylinder surmounted by a hemisphere at one end. If the model is drawn to a scale of 1 : 200, find
(i) the total surface area of the solid in π m².
(ii) the volume of the solid in π litres.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 17 Mensuration Ex 17.4

ML Aggarwal Class 10 Solutions for ICSE Maths

Tamilnadu Board Class 10 English Grammar Sentence Pattern

Tamilnadu State Board Class 10 English Grammar Sentence Pattern

There are five components in a sentence.

  1. Subject;
  2. Verb;
  3. Object;
  4. Complement;
  5. Adjunct

1. Subject:
Subject – S – consists of nouns or pronouns – occurs before a verb.

2. Verb:
Verb-
V – consists of
(a) auxiliaries
(b) finite verbs.

(a) Auxiliaries:

  1. am, is are, was, were
  2. has, have, had :
  3. does, do, did
  4. Modals: can, could; will, would; shall, should; may, might; must
  5. Semi-Modals / Quasi Modals: dare to; need to; used to; ought to

(b) Finite verbs – denote action:
e.g.,
sing, play, write, make, dance, leave, create, etc.
verbs occur after the subject (or) before the object.

Examples of S + V pattern:
English Grammar Sentence Pattern

3. Object:
Object – O – consists of nouns or noun phrases or noun clauses.
(a) DO – Direct Object
– answers the question ‘what’ after V
Svc Pattern

(b) IO – Indirect Object
– answers the question ‘whom’
Svo Sentence Pattern Examples

Examples of S V O pattern:
Svc Sentence Pattern Examples

Examples of S V O DO pattern:
Asv Sentence Pattern Examples

Examples of S V O IO pattern:
Tamilnadu Board Class 10 English Grammar Sentence Pattern 12
Sentence Pattern 10 Examples

4. Complement:
Complement – C – from the word ‘complete’
– complete the meaning in the sentence
Sv Sentence Pattern Examples

i) In S V C pattern, the complement C
– complements the subjects
– tells about the subject
– without C, the sentence is incomplete or the sentence changes its meaning.
– “to be” forms, grow, become, seems for a verb.
I Shall Meet You Tomorrow Sentence Pattern
– the same person/thing
– without C, incomplete meaning.

But in
Svoc Sentence Pattern Examples

ii) in S V O C pattern:
– the complement tells about the object
– the complement and object are of the same person or thing.
Sviodo Sentence Pattern Examples

5. Adjunct:
Adjunct – A – answers the questions where? when ? how ? why?
– Absence of ‘A’ does not change the meaning of the sentence.

Examples of Adjuncts:
Svac Sentence Pattern Examples

Examples of Adjuncts in sentences:
1. She / comes I every day. – S V A
2. Sit / here. – V A
3. He / drives / the car / slowly. – S V O A
4. Muthu / has been I an officer / for 10 years. – S V C A
5. We / present I gifts / to our friends / on birthdays. – S V D O IO A
6. This morning / at five / I I heard / a noise. – A A S V O
7. We / rarely I go / to the beach I during weekends. – S A V A A
8. Every year I on New Year’s eve / they / distribute / cake and sweets I to all the guests. – A A S V DO IO
9. Every morning / at five I the Mullah/chants/ prayers / at the mosque I without fail. – A A S V O A A
1o. In the end,) the judge I declared I the accused / innocent, after the trial. – A S V O C A

Exercises
Identify the pattern of the following sentence:

Sentence Pattern Question 1.
He was going to school.
(a) S V O
(b) S V A
(c) S V C A
Answer:
(b) S V A

Question 2.
I met my friend at the market.
(a) S V I O D O
(b) S V O C
(c) S V O A
Answer:
(c) S V O A

Question 3.
Velu grew tired ãfter the match.
(a) S V C A
(b) S V I O D O
(c) S V O C
Answer:
(a) S V C tile n fg[pA

Question 4.
Reading made him a complete man.
(a) S V O C
(b) S V I O D O
(c) S V O A
Sentence Pattern Examples with Answer:
(a) S V O C

Question 5.
They named this child Ria.
(a) S V A C
(b) S V O C
(c) S V C A
Answer:
(b) S V O C

Question 6.
Ram’s father is a lawyer.
(a) S V C
(b) S V A
(c) S V I O D O
Answer:
(a) S V C

Question 7.
He sang me a song melodiously.
(a) S V O C
(b) S V O A
(c) S V IO DO A
Answer:
(c) SV IO DO A

Question 8.
This shoe is large.
(a) S V O
(b) S V C
(c) S V A
Answer:
(b) S V C

Sentence Pattern Exercises for Class 10 Question 9. His father gave him his school bag.
(a) S V C
(b) S V O C
(c) S V IO DO
Answer:
(c) S V IO DO

Question 10.
The player entered the room.
(a) S V O
(b) S V A
(c) S V C
Answer:
(b) S V A

Question 11.
Eve – Teasers must be punished severely.
(a) S V A
(b) S V C
(c) S V O
Answer:
(a) S V A

Question 12.
We wear woolen clothes in winter season.
(a) S V O C
(b) S V IO DO
(c) S V O A
Answer:
(c) S V O A

Question 13.
I shall meet you tomorrow.
(a) S V O
(b) S V IO DO
(c) S V O A
Answer:
(c) S V O A

Question 14.
He answered my question instantly.
(a) S V O A
(b) S V C A
(c) S V IO DO
Answer:
(a) S V O A

Question 15.
They named the child Prem.
(a) S V A C
(b) S V O C
(c) S V C A
Answer:
(c) S V C A

Question 16.
We completed the work on time.
(a) S V O C
(b) S V A C
(c) S V O A
Answer:
(c) S V O A

Question 17.
The meeting ended with a vote of thanks.
(a) S V A
(b) S V C
(c) S V O
Answer:
(a) S V A

Question 18.
I bought a new car yesterday.
(a) S V A O
(b) S V C A
(c) S V O A
Answer:
(c) S V O A

Tamilnadu Board Class 10 English Solutions

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Check Your Progress

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Check Your Progress

ML Aggarwal Class 8 solutions chapter 18 Question 1. A square field of side 65 m and rectangular field of length 75 m have the same perimeter. Which field has a larger area and by how much?
Solution:
ICSE Mathematics Class 8 Solutions Chapter 18 Mensuration Check Your Progress Q1

ML Aggarwal Class 8 solutions Question 2. The shape of a top surface of the table is a trapezium. Find the area if its parallel sides are 1.5 m and 2.5 m and the perpendicular distance between them is 0.8 m.
Solution:
ML Aggarwal Class 8 solutions check your progress

Question 3.
The length and breadth of a hall of a school are 26 m and 22 m respectively. If one student requires 1.1 sq. m area, then find the maximum number of students to be seated in this hall.
Solution:
ML Aggarwal Class 8 Solutions Chapter 18 Mensuration Check Your Progress Q3

Question 4.
It costs ₹936 to fence a square field at ₹7·80 per metre. Find the cost of levelling the field at ₹2.50 per square metre.
Solution:
APC Maths Class 8 Solutions Chapter 18 Mensuration Check Your Progress Q4

Mensuration Class 8 ML Aggarwal Question 5.
Find the area of the shaded portion in the following figures all measurements are given in cm.
apc learning mathematics Class 8 solutions pdf
Solution:
ICSE Class 8 Maths Book Solutions Free Download Pdf Chapter 18 Mensuration Check Your Progress Q5.1
Maths Questions for Class 8 ICSE With Answers Chapter 18 Mensuration Check Your Progress Q5.2

Question 6.
Area of a trapezium is 160 sq. cm. Lengths of parallel sides are in the ratio 1:3. If smaller of the parallel sides is 10 cm in length, then find the perpendicular distance between them.
Solution:
ICSE Mathematics Class 8 Solutions Chapter 18 Mensuration Check Your Progress Q6

ML Aggarwal Class 8 solutions Mensuration Question 7.
The area of a trapezium is 729 cm2 and the distance between two parallel sides is 18 cm. If one of its parallel sides is 3 cm shorter than the other parallel side, find the lengths of its parallel sides.
Solution:
ML Aggarwal Maths for Class 8 Solutions Book Pdf Chapter 18 Mensuration Check Your Progress Q7

Question 8.
Find the area of the polygon given in the figure:
ML Aggarwal Class 8 Solutions Chapter 18 Mensuration Check Your Progress Q8
Solution:
APC Maths Class 8 Solutions Chapter 18 Mensuration Check Your Progress Q8.1
ICSE Understanding Mathematics Class 8 Solutions Chapter 18 Mensuration Check Your Progress Q8.2

ML Aggarwal Class 8 chapter 18 solutions Question 9. The diagonals of a rhombus are 16 m and 12 m, find:
(i) it’s area
(ii) length of a side
(iii) perimeter.
Solution:
ICSE Class 8 Maths Book Solutions Free Download Pdf Chapter 18 Mensuration Check Your Progress Q9

ML Aggarwal Class 8 chapter 18 Question 10.
The area of a parallelogram is 98 cm2. If one altitude is half the corresponding base, determine the base and the altitude of the parallelogram.
Solution:
Maths Questions for Class 8 ICSE With Answers Chapter 18 Mensuration Check Your Progress Q10

Mensuration Questions for Class 8 ICSE Question 11.
Preeti is painting the walls and ceiling of a hall whose dimensions are 18 m × 15 m × 5 m. From each can of paint 120 m2 of area is painted. How many cans of paint does she need to paint the hall?
Solution:
ICSE Mathematics Class 8 Solutions Chapter 18 Mensuration Check Your Progress Q11

Question 12.
A rectangular paper is size 22 cm × 14 cm is rolled to form a cylinder of height 14 cm, find the volume of the cylinder. (Take π = \(\frac{22}{7}\))
Solution:
ML Aggarwal Maths for Class 8 Solutions Book Pdf Chapter 18 Mensuration Check Your Progress Q12

Question 13.
A closed rectangular wooden box has inner dimensions 90 cm by 80 cm by 70 cm. Compute its capacity and the area of the tin foil needed to line its inner surface.
Solution:
ML Aggarwal Class 8 Solutions Chapter 18 Mensuration Check Your Progress Q13

Question 14.
The lateral surface area of a cuboid is 224 cm2. Its height is 7 cm and the base is a square. Find
(i) side of the square base
(ii) the volume of the cuboid.
Solution:
APC Maths Class 8 Solutions Chapter 18 Mensuration Check Your Progress Q14

Question 15.
The inner dimensions of a closed wooden box are 2 m by 1.2 m by 0.75 m. The thickness of the wood is 2.5 cm. Find the cost of wood required to make the box if 1 m3 of wood costs ₹5400.
Solution:
ICSE Understanding Mathematics Class 8 Solutions Chapter 18 Mensuration Check Your Progress Q15

Question 16.
A car has a petrol tank 40 cm long, 28 cm wide and 25 cm deep. If the ful consumption of the car averages 13.5 km per litre, how far can the car travel with a full tank of petrol?
Solution:
ICSE Class 8 Maths Book Solutions Free Download Pdf Chapter 18 Mensuration Check Your Progress Q16

Question 17.
The diameter of a garden roller is 1.4 m and it is 2 m long. How much area it will cover in 5 revolutions?
Solution:
Maths Questions for Class 8 ICSE With Answers Chapter 18 Mensuration Check Your Progress Q17

Question 18.
The capacity of an open cylindrical tank is 2079 m3 and the diameter of its base is 21m. Find the cost of plastering its inner surface at ₹40 per square metre.
Solution:
ICSE Mathematics Class 8 Solutions Chapter 18 Mensuration Check Your Progress Q18

Question 19.
A solid right circular cylinder of height 1.21 m and diameter 28 cm is melted and recast into 7 equal solid cubes. Find the edge of each cube.
Solution:
ICSE Class 8 maths mensuration questions and answers

Question 20.
(i) How many cubic metres of soil must be dug out to make a well 20 m deep and 2 m in diameter?
(ii) If the inner curved surface of the well in part (i) above is to be plastered at the rate of ₹50 per m2, find the cost of plastering.
Solution:
ML Aggarwal Class 8 Solutions Chapter 18 Mensuration Check Your Progress Q20

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1

Question 1.
Using the given information, find the value of x in each of the following figures :
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1

LearnCram.com also covered previous Year argumentative essay topics asked in ICSE board exams.

Question 2.
If O is the centre of the circle, find the value of x in each of the following figures (using the given information):
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1

ML Aggarwal Class 10 Circles Solutions Question 3.
(a) In the figure (i) given below, AD || BC. If ∠ACB = 35°. Find the measurement of ∠DBC.
(b) In the figure (ii) given below, it is given that O is the centre of the circle and ∠AOC = 130°. Find∠ABC
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1

Circles Class 10 ICSE ML Aggarwal Solutions Question 4.
(a) In the figure (i) given below, calculate the values of x and y.
(b) In the figure (ii) given below, O is the centre of the circle. Calculate the values of x and y.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1

Circles ML Aggarwal Class 10 Solutions Question 5.
(a) In the figure (i) given below, M, A, B, N are points on a circle having centre O. AN and MB cut at Y. If ∠NYB = 50° and ∠YNB = 20°, find ∠MAN and the reflex angle MON.
(b) In the figure (ii) given below, O is the centre of the circle. If ∠AOB = 140° and ∠OAC = 50°, find
(i) ∠ACB
(ii) ∠OBC
(iii) ∠OAB
(iv) ∠CBA
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1

ML Aggarwal Class 10 Circle Question 6.
(a) In the figure (i) given below, O is the centre of the circle and ∠PBA = 42°. Calculate the value of ∠PQB
(b) In the figure (ii) given below, AB is a diameter of the circle whose centre is O. Given that ∠ECD = ∠EDC = 32°, calculate
(i) ∠CEF
(ii) ∠COF.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1

Question 7.
(a) In the figure (i) given below, AB is a diameter of the circle APBR. APQ and RBQ are straight lines, ∠A = 35°, ∠Q = 25°. Find (i) ∠PRB (ii) ∠PBR (iii) ∠BPR.
(b) In the figure (ii) given below, it is given that ∠ABC = 40° and AD is a diameter of the circle. Calculate ∠DAC.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1

ML Aggarwal Class 10 Circles Question 8.
(a) In the figure given below, P and Q are centres of two circles intersecting at B and C. ACD is an st. line. Calculate the numerical value of x.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
(b) In the figure given below, O is the circumcentre of triangle ABC in which AC = BC. Given that ∠ACB = 56°, calculate
(i)∠CAB
(ii)∠OAC
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1

Circle ML Aggarwal Question 9.
(a) In the figure (i) given below, chord ED is parallel to the diameter AC of the circle. Given ∠CBE = 65°, calculate ∠DEC.
(b) In the figure (ii) given below, C is a point on the minor arc AB of the circle with centre O. Given ∠ACB = p°, ∠AOB = q°, express q in terms of p. Calculate p if OACB is a parallelogram.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1

ICSE Class 10 Maths Circles Solutions Question 10.
(a) In the figure (i) given below, straight lines AB and CD pass through the centre O of a circle. If ∠OCE = 40° and ∠AOD = 75°, find the number of degrees in :
(i) ∠CDE
(ii) ∠OBE.
(b) In the figure (ii) given below, I is the incentre of ∆ABC. AI produced meets the circumcircle of ∆ABC at D. Given that ∠ABC = 55° and ∠ACB = 65°, calculate
(i) ∠BCD
(ii) ∠CBD
(iii) ∠DCI
(iv) ∠BIC.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1

Question 11.
O is the circumcentre of the triangle ABC and D is mid-point of the base BC. Prove that ∠BOD = ∠A.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1

Question 12.
In the given figure, AB and CD are equal chords. AD and BC intersect at E. Prove that AE = CE and BE = DE.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1

Question 13.
(a) In the figure (i) given below, AB is a diameter of a circle with centre O. AC and BD are perpendiculars on a line PQ. BD meets the circle at E. Prove that AC = ED.
(b) In the figure (ii) given below, O is the centre of a circle. Chord CD is parallel to the diameter AB. If ∠ABC = 25°, calculate ∠CED.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1

Question 14.
In the adjoining figure, O is the centre of the given circle and OABC is a parallelogram. BC is produced to meet the circle at D.
Prove that ∠ABC = 2 ∠OAD.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1

Question 15.
(a) In the figure (i) given below, P is the point of intersection of the chords BC and AQ such that AB = AP. Prove that CP = CQ
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
(b) In the figure (i) given below, AB = AC = CD, ∠ADC = 38°. Calculate :
(i) ∠ABC (ii) ∠BEC.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1

Question 16.
(a) In the figure (i) given below, CP bisects ∠ACB. Prove that DP bisects ∠ADB.
(b) In the figure (ii) given below, BDbisects ∠ABC. Prove that \(\frac { AB }{ BD } =\frac { BE }{ BC } \)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1

Question 17.
(a) In the figure (i) given below, chords AB and CD of a circle intersect at E.
(i) Prove that triangles ADE and CBE are similar.
(ii) Given DC =12 cm, DE = 4 cm and AE = 16 cm, calculate the length of BE.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
(b) In the figure (ii) given below, AB and CD are two intersecting chords of a circle. Name two triangles which are similar. Hence, calculate CP given that AP = 6 cm, PB = 4 cm, and CD = 14 cm (PC > PD).
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1

Question 18.
In the adjoining figure, AE and BC intersect each other at point D. If ∠CDE = 90°, AB = 5 cm, BD = 4 cm and CD = 9 cm, find DE. (2008)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1

Question 19.
(a) In the figure (i) given below, PR is a diameter of the circle, PQ = 7 cm, QR = 6 cm and RS = 2 cm. Calculate the perimeter of the cyclic quadrilateral PQRS.
(b) In the figure (ii) given below, the diagonals of a cyclic quadrilateral ABCD intersect in P and the area of the triangle APB is 24 cm². If AB = 8 cm and CD = 5 cm, calculate the area of ∆DPC.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1

Question 20.
(a) In the figure (i) given below, QPX is the bisector of ∠YXZ of the triangle XYZ. Prove that XY : XQ = XP : XZ,
(b) In the figure (ii) given below, chords BA and DC of a circle meet at P. Prove that:
(i) ∠PAD = ∠PCB
(ii) PA. PB = PC . PD.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 15 Circles Ex 15.1

ML Aggarwal Class 10 Solutions for ICSE Maths

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1

Question 1.
State which pairs of triangles in the figure given below are similar. Write the similarity rule used and also write the pairs of similar triangles in symbolic form (all lengths of sides are in cm):
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1

LearnCram.com also covered previous Year argumentative essay topics asked in ICSE board exams.

Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1

Question 2.
It is given that ∆DEF ~ ∆RPQ. Is it true to say that ∠D = ∠R and ∠F = ∠P ? Why?
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1

Question 3.
If in two right triangles, one of the acute angles of one triangle is equal to an acute angle of the other triangle, can you say that the two triangles are similar? Why?
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1

ML Aggarwal Class 10 Solutions Similarity Question 4. In the given figure, BD and CE intersect each other at the point P. Is ∆PBC ~ ∆PDE? Give reasons for your answer.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1

Question 5.
It is given that ∆ABC ~ ∆EDF such that AB = 5 cm, AC = 7 cm, DF = 15 cm and DE = 12 cm.
Find the lengths of the remaining sides of the triangles.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1

Question 6.
(a) If ∆ABC ~ ∆DEF, AB = 4 cm, DE = 6 cm, EF = 9 cm and FD = 12 cm, then find the perimeter of ∆ABC.
(b) If ∆ABC ~ ∆PQR, Perimeter of ∆ABC = 32 cm, perimeter of ∆PQR = 48 cm and PR = 6 cm, then find the length of AC.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1

ML Aggarwal Similarity Solutions Question 7.
Calculate the other sides of a triangle whose shortest side is 6 cm and which is similar to a triangle whose sides are 4 cm, 7 cm and 8 cm.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1

Question 8.
(a) In the figure given below, AB || DE, AC = , 3 cm, CE = 7.5 cm and BD = 14 cm. Calculate CB and DC.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1
(b) In the figure (2) given below, CA || BD, the lines AB and CD meet at G.
(i) Prove that ∆ACO ~ ∆BDO.
(ii) If BD = 2.4 cm, OD = 4 cm, OB = 3.2 cm and AC = 3.6 cm, calculate OA and OC.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1

ML Aggarwal Class 10 Similarity Question 9.
(a) In the figure
(i) given below, ∠P = ∠RTS.
Prove that ∆RPQ ~ ∆RTS.
(b) In the figure (ii) given below,
∠ADC = ∠BAC. Prove that CA² = DC × BC.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1

Question 10.
(a) In the figure (1) given below, AP = 2PB and CP = 2PD.
(i) Prove that ∆ACP is similar to ∆BDP and AC || BD.
(ii) If AC = 4.5 cm, calculate the length of BD.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1
(b) In the figure (2) given below,
∠ADE = ∠ACB.
(i) Prove that ∆s ABC and AED are similar.
(ii) If AE = 3 cm, BD = 1 cm and AB = 6 cm, calculate AC.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1
(c) In figure (3) given below, ∠PQR = ∠PRS. Prove that triangles PQR and PRS are similar. If PR = 8 cm, PS = 4 cm, calculate PQ.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1

Similarity Class 10 ICSE ML Aggarwal Solutions Question 11.
In the given figure, ABC is a triangle in which AB = AC. P is a point on the side BC such that PM ⊥ AB and PN ⊥ AC. Prove that BM × NP = CN × MP.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1

Question 12.
Prove that the ratio of the perimeters of two similar triangles is the same as the ratio of their corresponding sides.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1

Question 13.
In the given figure, ABCD is a trapezium in which AB || DC. The diagonals AC and BD intersect at O. Prove that \(\frac { AO }{ OC } =\frac { BO }{ OD } \)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1
Using the above result, find the value(s) of x if OA = 3x – 19, OB = x – 4, OC = x – 3 and OD = 4.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1

ML Aggarwal Class 10 Similarity Solutions Question 14.
In ∆ABC, ∠A is acute. BD and CE are perpendicular on AC and AB respectively. Prove that AB x AE = AC x AD.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1

Question 15.
In the given figure, DB ⊥ BC, DE ⊥ AB and AC ⊥ BC. Prove that \(\frac { BE }{ DE } =\frac { AC }{ BC } \)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1

Question 16.
(a) In the figure (1) given below, E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. show that ∆ABE ~ ∆CFB.
(b) In the figure (2) given below, PQRS is a parallelogram; PQ = 16 cm, QR = 10 cm. L is a point on PR such that RL : LP = 2 : 3. QL produced meets RS at M and PS produced at N.
(i) Prove that triangle RLQ is similar to triangle PLN. Hence, find PN.
(ii) Name a triangle similar to triangle RLM. Evaluate RM.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1

ML Aggarwal Class 9 Solutions ICSE Chapter 13 Question 17.
The altitude BN and CM of ∆ABC meet at H. Prove that
(i) CN . HM = BM . HN .
(ii) \(\frac { HC }{ HB } =\sqrt { \frac { CN.HN }{ BM.HM } } \)
(iii) ∆MHN ~ ∆BHC.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1

Question 18.
In the given figure, CM and RN are respectively the medians of ∆ABC and ∆PQR. If ∆ABC ~ ∆PQR, prove that:
(i) ∆AMC ~ ∆PNR
(ii) \(\frac { CM }{ RN } =\frac { AB }{ PQ } \)
(iii) ∆CMB ~ ∆RNQ.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1

Ex 13.1 Class 10 Question 19.
In the given figure, medians AD and BE of ∆ABC meet at the point G, and DF is drawn parallel to BE. Prove that
(i) EF = FC
(ii) AG : GD = 2 : 1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1

Question 20.
(a) In the figure given below, AB, EF and CD are parallel lines. Given that AB =15 cm, EG = 5 cm, GC = 10 cm and DC = 18 cm. Calculate
(i) EF
(ii) AC.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1
(b) In the figure given below, AF, BE and CD are parallel lines. Given that AF = 7.5 cm, CD = 4.5 cm, ED = 3 cm, BE = x and AE = y. Find the values of x and y.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1

Question 21.
In the given figure, ∠A = 90° and AD ⊥ BC If BD = 2 cm and CD = 8 cm, find AD.
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1

Question 22.
A 15 metres high tower casts a shadow of 24 metres long at a certain time and at the same time, a telephone pole casts a shadow 16 metres long. Find the height of the telephone pole.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1

Question 23.
A street light bulb is fixed on a pole 6 m above the level of the street. If a woman of height casts a shadow of 3 m, find how far she is away from the base of the pole?
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 13 Similarity Ex 13.1

ML Aggarwal Class 10 Solutions for ICSE Maths

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18

Question 1.
If A is an acute angle and sin A = \(\\ \frac { 3 }{ 5 } \) find all other trigonometric ratios of angle A (using trigonometric identities).
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q1.1

Trigonometric Identities Class 10 ML Aggarwal Question 2.
If A is an acute angle and sec A = \(\\ \frac { 17 }{ 8 } \), find all other trigonometric ratios of angle A (using trigonometric identities).
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q2.1

Question 3.
Express the ratios cos A, tan A and sec A in terms of sin A.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q3

Question 4.
If tan A = \(\frac { 1 }{ \sqrt { 3 } } \), find all other trigonometric ratios of angle A.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q4
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q4.1

ML Aggarwal Trigonometry Solutions Question 5.
If 12 cosec θ = 13, find the value of \(\frac { 2sin\theta -3cos\theta }{ 4sin\theta -9cos\theta } \)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q5
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q5.1

Without using trigonometric tables, evaluate the following (6 to 10):

Question 6.
(i) cos² 26° + cos 64° sin 26° + \(\frac { tan{ 36 }^{ ° } }{ { cot54 }^{ ° } } \)
(ii) \(\frac { sec{ 17 }^{ ° } }{ { cosec73 }^{ ° } } +\frac { tan68^{ ° } }{ cot22^{ ° } } \) + cos² 44° + cos² 46°
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q6

Question 7.
(i) \(\frac { sin65^{ ° } }{ { cos25 }^{ ° } } +\frac { cos32^{ ° } }{ sin58^{ ° } } \) – sin 28° sec 62° + cosec² 30° (2015)
(ii) \(\frac { sin29^{ ° } }{ { cosec61 }^{ ° } } \) + 2 cot 8° cot 17° cot 45° cot 73° cot 82° – 3(sin² 38° + sin² 52°).
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q7

ML Aggarwal Trigonometry Question 8.
(i) \(\frac { { sin }35^{ ° }{ cos55 }^{ ° }+{ cos35 }^{ ° }{ sin }55^{ ° } }{ { cosec }^{ 2 }{ 10 }^{ ° }-{ tan }^{ 2 }{ 80 }^{ ° } } \)
(ii) \({ sin }^{ 2 }{ 34 }^{ ° }+{ sin }^{ 2 }{ 56 }^{ ° }+2tan{ 18 }^{ ° }{ tan72 }^{ ° }-{ cot }^{ 2 }{ 30 }^{ ° }\)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q8

Question 9.
(i) \({ \left( \frac { { tan25 }^{ ° } }{ { cosec }65^{ ° } } \right) }^{ 2 }+{ \left( \frac { { cot25 }^{ ° } }{ { sec65 }^{ ° } } \right) }^{ 2 }+{ 2tan18 }^{ ° }{ tan }45^{ ° }{ tan72 }^{ ° } \)
(ii) \(\left( { cos }^{ 2 }25+{ cos }^{ 2 }65 \right) +cosec\theta sec\left( { 90 }^{ ° }-\theta \right) -cot\theta tan\left( { 90 }^{ ° }-\theta \right) \)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q9

Question 10.
(i) 2(sec² 35° – cot² 55°) – \(\frac { { cos28 }^{ ° }cosec{ 62 }^{ ° } }{ { tan18 }^{ ° }tan{ 36 }^{ ° }{ tan30 }^{ ° }{ tan54 }^{ ° }{ tan72 }^{ ° } } \)
(ii) \(\frac { { cosec }^{ 2 }(90-\theta )-{ tan }^{ 2 }\theta }{ 2({ cos }^{ 2 }{ 48 }^{ ° }+{ cos }^{ 2 }{ 42 }^{ ° }) } -\frac { { 2tan }^{ 2 }{ 30 }^{ ° }{ sec }^{ 2 }{ 52 }^{ ° }{ sin }^{ 2 }{ 38 }^{ ° } }{ { cosec }^{ 2 }{ 70 }^{ ° }-{ tan }^{ 2 }{ 20 }^{ ° } } \)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q10
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q10.1

ML Aggarwal Class 9 Chapter 18 Solutions Question 11.
Prove that following:
(i) cos θ sin (90° – θ) + sin θ cos (90° – θ) = 1
(ii) \(\frac { tan\theta }{ tan({ 90 }^{ ° }-\theta ) } +\frac { sin({ 90 }^{ ° }-\theta ) }{ cos\theta } ={ sec }^{ 2 }\theta \)
(iii) \(\frac { cos({ 90 }^{ ° }-\theta )cos\theta }{ tan\theta } +{ cos }^{ 2 }({ 90 }^{ ° }-\theta )=1\)
(iv) sin (90° – θ) cos (90° – θ) = \(\frac { tan\theta }{ { 1+tan }^{ 2 }\theta } \)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q11
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q11.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q11.2

Prove that following (12 to 30) identities, where the angles involved are acute angles for which the trigonometric ratios as defined:

Trigonometry ML Aggarwal Class 10 Question 12.
(i) (sec A + tan A) (1 – sin A) = cos A
(ii) (1 + tan2 A) (1 – sin A) (1 + sin A) = 1.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q12

Question 13.
(i) tan A + cot A = sec A cosec A
(ii) (1 – cos A)(1 + sec A) = tan A sin A.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q13
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q13.1

ML Aggarwal Class 10 Trigonometry Solutions Question 14.
(i) \(\frac { 1 }{ 1+cosA } +\frac { 1 }{ 1-cosA } =2{ cosec }^{ 2 }A\)
(ii) \(\frac { 1 }{ secA+tanA } +\frac { 1 }{ secA-tanA } =2{ sec }A\)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q14

Question 15.
(i) \(\frac { sinA }{ 1+cosA } =\frac { 1-cosA }{ sinA } \)
(ii) \(\frac { 1-{ tan }^{ 2 }A }{ { cot }^{ 2 }A-1 } ={ tan }^{ 2 }A\)
(iii) \(\frac { sinA }{ 1+cosA } =cosecA-cotA\)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q15
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q15.1

Trigonometric Identities Class 10 Question 16.
(i) \(\frac { secA-1 }{ secA+1 } =\frac { 1-cosA }{ 1+cosA } \)
(ii) \(\frac { { tan }^{ 2 }\theta }{ { (sec\theta -1) }^{ 2 } } =\frac { 1+cos\theta }{ 1-cos\theta } \)
(iii) \({ (1+tanA) }^{ 2 }+{ (1-tanA) }^{ 2 }=2{ sec }^{ 2 }A\)
(iv) \({ sec }^{ 2 }A+{ cosec }^{ 2 }A={ sec }^{ 2 }A{ .cosec }^{ 2 }A\)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q16
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q16.1

Question 17.
(i) \(\frac { 1+sinA }{ cosA } +\frac { cosA }{ 1+sinA } =2secA \)
(ii) \(\frac { tanA }{ secA-1 } +\frac { tanA }{ secA+1 } =2cosecA\)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q17
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q17.1

Question 18.
(i) \(\frac { cosecA }{ cosecA-1 } +\frac { cosecA }{ cosecA+1 } =2{ sec }^{ 2 }A\)
(ii) \(cotA-tanA=\frac { { 2cos }^{ 2 }A-1 }{ sinA-cosA } \)
(iii) \(\frac { cotA-1 }{ 2-{ sec }^{ 2 }A } =\frac { cotA }{ 1+tanA } \)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q18
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q18.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q18.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q18.3

ML Aggarwal Class 10 Solutions Question 19.
(i) \({ tan }^{ 2 }\theta -{ sin }^{ 2 }\theta ={ tan }^{ 2 }\theta { sin }^{ 2 }\theta \)
(ii) \(\frac { cos\theta }{ 1-tan\theta } -\frac { { sin }^{ 2 }\theta }{ cos\theta -sin\theta } =cos\theta +sin\theta \)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q19
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q19.1

Question 20.
(i) cosec4 θ – cosec2 θ = cot4 θ + cot2 θ
(ii) 2 sec2 θ – sec4 θ – 2 cosec2 θ + cosec4 θ = cot4 θ – tan4 θ.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q20

Question 21.
(i) \(\frac { 1+cos\theta -{ sin }^{ 2 }\theta }{ sin\theta (1+cos\theta ) } =cot\theta \)
(ii) \(\frac { { tan }^{ 3 }\theta -1 }{ tan\theta -1 } ={ sec }^{ 2 }\theta +tan\theta \)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q21

Question 22.
(i) \(\frac { 1+cosecA }{ cosecA } =\frac { { cos }^{ 2 }A }{ 1-sinA } \)
(ii) \(\sqrt { \frac { 1-cosA }{ 1+cosA } } =\frac { sinA }{ 1+cosA } \)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q22
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q22.1

Question 23.
(i) \(\sqrt { \frac { 1+sinA }{ 1-sinA } } =tanA+secA\)
(ii) \(\sqrt { \frac { 1-cosA }{ 1+cosA } } =cosecA-cotA\)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q23
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q23.1

Question 24.
(i) \(\sqrt { \frac { secA-1 }{ secA+1 } } +\sqrt { \frac { secA+1 }{ secA-1 } } =2cosecA\)
(ii) \(\frac { cotAcotA }{ 1-sinA } =1+cosecA \)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q24
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q24.1

Question 25.
(i) \(\frac { 1+tanA }{ sinA } +\frac { 1+cotA }{ cosA } =2(secA+cosecA)\)
(ii) \({ sec }^{ 4 }A-{ tan }^{ 4 }A=1+2{ tan }^{ 2 }A \)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q25
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q25.1

Question 26.
(i) cosec6 A – cot6 A = 3 cot2 A cosec2 A + 1
(ii) sec6 A – tan6 A = 1 + 3 tan2 A + 3 tan4 A
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q26

Question 27.
(i) \(\frac { cot\theta -cosec\theta -1 }{ cot\theta -cosec\theta +1 } =\frac { 1+cos\theta }{ sin\theta } \)
(ii) \(\frac { sin\theta }{ cot\theta +cosec\theta } =2+\frac { sin\theta }{ cot\theta -cosec\theta } \)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q27
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q27.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q27.2

Question 28.
(i) (sinθ + cosθ)(secθ + cosecθ) = 2 + secθ cosecθ
(ii) (cosecA – sinA)(secA – cosA) sec2A = tanA
(iii) (cosecθ – sinθ)(secθ – cosθ)(tan θ + cotθ) = 1
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q28
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q28.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q28.2

Question 29.
(i) \(\frac { { sin }^{ 3 }A+{ cos }^{ 3 }A }{ sinA+cosA } +\frac { { sin }^{ 3 }A-{ cos }^{ 3 }A }{ sinA-cosA } =2\)
(ii) \(\frac { { tan }^{ 2 }A }{ { 1+tan }^{ 2 }A } +\frac { cot^{ 2 }A }{ 1+{ cot }^{ 2 }A } =1\)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q29
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q29.1

Question 30.
(i) \(\frac { 1 }{ secA+tanA } -\frac { 1 }{ cosA } =\frac { 1 }{ cosA } -\frac { 1 }{ secA-tanA } \)
(ii) \({ (sinA+secA) }^{ 2 }+{ (cosA+cosecA) }^{ 2 }={ (1+secA\quad cosecA) }^{ 2 }\)
(iii) \(\frac { tanA+sinA }{ tanA-sinA } =\frac { secA+1 }{ secA-1 } \)
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q30
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q30.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q30.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q30.3

Question 31.
If sin θ + cos θ = √2 sin (90° – θ), show that cot θ = √2 + 1
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q31

Question 32.
If 7 sin2 θ + 3 cos2 θ = 4, 0° ≤ θ ≤ 90°, then find the value of θ.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q32

Question 33.
If sec θ + tan θ = m and sec θ – tan θ = n, prove that mn = 1.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q33

Question 34.
If x – a sec θ + b tan θ and y = a tan θ + b sec θ, prove that x2 – y2 = a2 – b2.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q34

ICSE Maths Solutions For Class 10 Chapter 18 Question 35.
If x = h + a cos θ and y = k + a sin θ, prove that (x – h)2 + (y – k)2 = a2.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 18 Trigonometric Identities Ex 18 Q35

ML Aggarwal Class 10 Solutions for ICSE Maths