In this page, each and every question originate with a step-wise solution. Moreover, it is a perfect guide to help you to score good marks in CBSE board examination. With the aim of imbibing skills and hard work among the students, the 10th class maths NCERT solutions have been designed.

Real Numbers Class 10 has total of four exercises consists of 18 Problems. Other topics included are Fundamental Theorem of **Concise mathematics class tenth,** important properties of positive integers, fraction to decimals and decimals to a fraction. Polynomials Class **concise mathematics class tenth** has total of four exercises consists of 13 Questions. Problems related to finding polynomials, Properties zeros and coefficient, long division of polynomials, finding a quadratic polynomial, finding zeros of polynomials are scoring topics.

Pair of Linear Equations Class 10 has total of seven exercises consists of 55 Problems. The problems will **concise mathematics class tenth** based mathemaics concepts like linear equations in two variables, algebraic methods for solving linear equations, elimination method, cross-multiplication method Time and Work, Age, Boat Stream and equations reducible to a pair of linear equations these answers will give you ease in solving problems related to linear equations.

Quadratic Equations Class 10 has total of four exercises consists of 24 Problems. The Questions **concise mathematics class tenth** related to find roots of quadratic equations and convert world problem into quadratic equations are easily scoring topics in board exams.

Arithmetic Progressions Class 10 has total of four exercises consists of 49 Problems. Triangles Class 10 has total of six exercises consists of 64 Problems. The Questions are based on properties of triangles and 9 important theorems which are important in scoring good marks in CBSE Class 10 Exams.

Coordinate Geometry Class 10 has total of four exercises consists of 33 Problems. The Questions related to finding the distance between two points using their coordinates, Area of Triangle, Line divided in Ratio Section Formula are important models in class 10 boards.

Introduction to Tenht Class 10 has conicse of four exercises consists of 27 Problems. The questions based on trigonometric ratios of specific angles, trigonometric identities and trigonometric ratios of complementary angles are the main topics you will learn in this chapter. Some Applications of Trigonometry Class 10 has one exercise **concise mathematics class tenth** tejth 16 Problems.

In this chapter, you will be studying about mathematicz life applications of trigonometry and questions are based on the practical applications of trigonometry.

Circle Class 10 has total of two exercises consists of 17 Problems. Understand concepts such as tangent, secant, number tangents from a point to a circle and **concise mathematics class tenth.** Constructions Class 10 has total of four exercises consists of 14 Problems.

The Questions are based on drawing tangents and draw similar triangles are important topics. Areas Related to Circles Class 10 has total of three exercises consists of 35 Problems. Surface Areas concisr Volumes Class 10 **concise mathematics class tenth** total of five exercises consists of 36 Problems. The problems are based on finding areas and volumes of different solids such as cube, cuboid and cylinder, frustum, combination of solids.

Statistics Class 10 has total of four exercises consists of 25 Problems. Problems related to find mean, mode or median of grouped data will be studied in this chapter.

Solve questions by understanding the concept of cumulative frequency distribution. Probability Class 10 has total of two exercises consists of 30 Problems. Questions based on the concept of theoretical probability will be **concise mathematics class tenth** in this chapter.

Class 10 maths is having 15 chapters to learn by the students in this academic year. NCERT Solutions are designed in a way that every student can quickly understand the concept into their minds and clarifies all their doubts within a few seconds.

The book is self-explanatory and helps students to Mathematics Class 10 Cbse Sample Papers Case innovate and explore in maths. What are the best reference books for class 10 CBSE? If you have any **concise mathematics class tenth,** ping us through the comment section below and we will mayhematics back to you as soon as possible. RD Sharma Class 12 Solutions. Watch **Concise mathematics class tenth** Videos.

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Let the length of the tower be h m. Hence the length of the tower is Hence the length of the shadow is Hence the length of the shadow is 15 m. Two vertical poles are on either side of a road. A 30 m long ladder is placed between the two poles. When the ladder rests against one pole, it makes angle 32 o 24' with the pole and when it is turned to rest against another pole, it makes angle 32 o 24' with the road.

Calculate the width of the road. Two climbers are at points A and B on a vertical cliff face. To an observer C, 40m from the foot of the cliff, on the level ground, A is at an elevation of 48 o and B of 57 o. What is the distance between the climbers? Let P be the foot of the cliff on level ground. A man stands 9 m away from a flag-pole. He observes that angle of elevation of the top of the pole is 28 o and the angle of depression of the bottom of the pole is 13 o.

Calculate the height of the pole. Let AB be the man and PQ be the flag-pole. From the top of a cliff 92 m high, the angle of depression of a buoy is 20 o. Calculate, to the nearest metre, the distance of the buoy from the foot of the cliff. Let AB Mathematics Class 12 Rd Sharma Solutions be the cliff and C be the buoy. Hence, the buoy is at a distance of m from the foot of the cliff.

Without using tables, find X. Find the height of a tree when it is found that on walking away from it 20 m, in a horizontal line through its base, the elevation of Dinesh Mathematics Class 10 Solutions its top changes from 60 o to 30 o. Let AB be the tree of height h m. Hence, height of the tree is Find the height of a building, when it is found that on walking towards it 40 m in a horizontal line through its base the angular elevation of its top changes from 30 o to 45 o.

Let AB be the building of height h m. Hence, height of the building is From the top of a light house m high, the angles of depression of two ships are observed as 48 o and 36 o respectively.

Find the distance between the two ships in the nearest metre if:. Let AB be the lighthouse. Two pillars of equal heights stand on either side of a roadway, which is m wide. At a point in the roadway between the pillars the elevations of the tops of the pillars are 60 o and 30 o ; find the height of the pillars and the position of the point. Let AB and CD be the two towers of height h m.

Hence, height of the pillars is The point is from the first pillar. That is the position of the point is from the first pillar. The position of the point is From the figure, given below, calculate the length of CD.

The angle of elevation of the top of a tower is observed to be 60 o. At a point, 30 m vertically above the first point of observation, the elevation is found to be 45 o. Let AB be the tower of height h m. Hence, height of the tower is From the top of a cliff, 60 metres high, the angles of depression of the top and bottom of a tower are observed to be 30 o and 60 o.

Let AB be the cliff and CD be the tower. Hence, height of the tower is 40 m. A man on a cliff observes a boat, at an angle of depression 30 o , which is sailing towards the shore to the point immediately beneath him. Three minutes later, the angle of depression of the boat is found to be 60 o. Assuming that the boat sails at a uniform speed, determine:. Let speed of the boat be x metre per minute and let the boat reach the shore after t minutes more.

Hence, the boat takes an extra 1. And, if the height of cliff is m, the speed of the boat is 3. A man in a boat rowing away from a lighthouse m high, takes 2 minutes to change the angle of elevation of the top of the lighthouse from 60 o to 45 o. Find the speed of the boat. Let speed of the boat be x metre per minute. Hence, the speed of the boat is 0. A person standing on the bank of a river observes that the angle of elevation of the top of a tree standing on the opposite bank is 60 o.

When he moves 40 m away from the bank, he finds the angle of elevation to be 30 o. Let AB be the tree of height 'h' m and BC be the width of the river. The horizontal distance between two towers is 75 m and the angular depression of the top of the first tower as seen from the top of the second, which is m high, is 45 o. Find the height of the first tower. Let AB and CD be the two towers. The horizontal distance between the two towers is.

Hence, height of the other tower is 85 m. The length of the shadow of a tower standing on level plane is found to be 2y metres longer when the sun's altitude is 30 o than when it was 45 o.

Prove that the height of the tower is metres. Hence, height of the tower is m. An aeroplane flying horizontally 1 km above the ground and going away from the observer is observed at an elevation of 60 o. After 10 seconds, its elevation is observed to be 30 o ; find the uniform speed of the aeroplane in km per hour. Let A be the aeroplane and B be the observer on the ground. After 10 seconds, let the aeroplane be at point D.

Hence, speed of the aeroplane is From the top of a hill, the angles of depression of two consecutive kilometer stones, due east, are found to be 30 o and 45 o respectively. Find the distances of the two stones from the foot of the hill. Hence, the two stones are at a distance of 1. Find AD:. Calculate the length of the board AB. Calculate BC. Calculate AB. The radius of a circle is given as 15 cm and chord AB subtends an angle of o at the centre C of the circle.

Using trigonometry, calculate:. At a point on level ground, the angle of elevation of a vertical tower is found to be such that its tangent is. On walking metres towards the tower, the tangent of the angle is found to be. Hence, the height of the tower is m. A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height h metre. At a point on the plane, the angle of elevation of the bottom of the flagstaff is and at the top of the flagstaff is.

Prove that the height of the tower is. Let AB be the tower of height x metre, surmounted by a vertical flagstaff AD. With reference to the given figure, a man stands on the ground at point A, which is on the same horizontal plane as B, the foot of the vertical pole BC. The height of the pole is 10 m. The man's eye s 2 m above the ground. Give your answer to the nearest degree.

The angles of elevation of the top of a tower from two points on the ground at distances a and b metres from the base of the tower and in the same line are complementary. Prove that the height of the tower is metre. Let AB be the tower of height h metres. Calculate the height CD of the tower in metres.

A vertical tower is 20 m high. A man standing at some distance from the tower knows that the cosine of the angle of elevation of the top of the tower is 0. How far is he standing from the foot of the tower? Let AB be the tower of height 20 m. Let be the angle of elevation of the top of the tower from point C.

A man standing on the bank of a river observes that the angle of elevation of a tree on the opposite bank is 60 o.

When he moves 50 m away from the bank, he finds the angle of elevation to be 30 o. Let AB be the tree and AC be the width of the river. Given that. A 20 m high vertical pole and a vertical tower are on the same level ground in such a way that the angle of elevation of the top of the tower, as seen from the foot of the pole is 60 o and the angle of elevation of the top of the pole, as seen from the foot of the tower is 30 o.

A vertical pole and a vertical tower are on the same level ground in such a way that from the top of the pole, the angle of elevation of the top of the tower is 60 o and the angle of depression of the bottom of the tower is 30 o. Enter the OTP sent to your number Change. Resend OTP. Starting early can help you score better! Avail Offer. Question 2. Question 3. Question 4. Question 5. Question 6. Question 7. Question 8. Question 9.

Question Prove that: i ii iii iv v vi vii viii ix. Given: and. Without using trigonometric tables, show that: i ii iii. Show that: i ii. For triangle ABC, show that: i ii. Evaluate: i ii iii iv v vi vii viii ix. Find in each case, given below the value of x if: i ii iii iv v vi vii. In each case, given below, find the value of angle A, where i ii.

Prove that: i ii. Use tables to find the acute angle , if the value of sin is: i 0. Use tables to find the acute angle , if the value of cos is: i 0. Use tables to find the acute angle , if the value of tan q is: i 0. Prove the following identities: i ii iii iv v vi vii viii ix x xi xii xiii xiv xv xvi xvii.

Evaluate: i ii iii iv v vi vii viii. Prove that: i ii iii iv v. Have an account? Sign In. Verify mobile number.

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