NCERT would welcome suggestions from students, teachers and parents which . development of Exemplar Problems in Physics for Class XI. . 1 http://www. medical-site.info~ maria/mathfest_education medical-site.info Download all chapters of Class 11 Physics NCERT Exemplar book in PDF format . There are 15 chapters in NCERT Exemplar for Class Exemplar Problems from Class 6 to Class VI; Class VII; Class VIII; Class IX; Class X; Class XI; Class XII. Mathematics. Unit 1 (Number System) · Unit 2.
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IX and XI were released in and for Classes X and XII in Overall comprehension ncert exemplar maths - Pioneer Mathematics. Download PDF. L.K. Gupta (Mathematics Classes) medical-site.info MOBILE: , . The cost of a Video game i Contact for Online Tutoring in Physics, Math, Chemistry. Download PDF . Section B Question numbers 11 to 18 carry 2 marks each. . ncert exemplar maths - Pioneer Mathematics. For maths there r mainly two books first is RS Aggarwal n Which reference book is the best for class 11? . Use NCERT exemplar solution for better practice ; Math – Solve as many best book for physics— SCHAND publication.
Find the present ages of both Asha and Nisha. Find the length and breadth of the pond. At t minutes past 2 pm, the time needed by the minutes hand of a clock to show 3 pm was found to be 3 minutes less than t2 minutes. Find t. The fixed number d is called its common difference.
Note that a1 a. The 10th term of the AP: Answer A Sample Question 2: A 9th 9. C If the 2nd term of an AP is 13 and the 5 th term is 25, what is its 7th term?
Two APs have the same common difference. The first term of one of these is —1 and that of the other is — 8. Then the difference between their 4th terms is A —1 B — 8 C 7 D —9 If 7 times the 7th term of an AP is equal to 11 times its 11 th term, then its 18th term will be A 7 B 11 C 18 D 0 The 4th term from the end of the AP: The sum of first 16 terms of the AP: In the AP: Justify whether the above statement is true or false.
The amounts at the end of first year, second year, third year, So, the amount in Rs at the end of 1st year, 2nd year, 3rd year, Here, 5 — 2 10—5, so it does not form an AP. Alternative Solution 1: So, an n 2 1 cannot be the n th term of an AP. Alternative Solution 2: We observe that an is a linear polynomial in n.
Here, an n 2 1 is not a linear polynomial in n. So, it cannot be the nth term of an AP. Which of the following form an AP? Justify whether it is true to say that —1, — 3 5 , —2, , For the AP: The first term of one AP is 2 and that of the other is 7.
The difference between their 10th terms is the same as the difference between their 21st terms, which is the same as the difference between any two corresponding terms. Is 0 a term of the AP: The taxi fare after each km, when the fare is Rs 15 for the first km and Rs 8 for each additional km, does not form an AP as the total fare in Rs after each km is 15, 8, 8, 8, In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers.
Justify whether it is true to say that the following are the n th terms of an AP. Find the value of the middle most term s of the AP: The sum of the first three terms of an AP is If the product of the first and the third term exceeds the second term by 29, find the AP. Match the APs given in column A with suitable common differences given in column B.
Column A Column B A1 2, — 2, — 6, — 10, Verify that each of the following is an AP, and then write its next three terms. Write the first three terms of the APs when a and d are as given below: Find a, b and c such that the following numbers are in AP: Determine the AP whose fifth term is 19 and the difference of the eighth term from the thirteenth term is The 26th, 11th and the last term of an AP are 0, 3 and — 1 , respectively. Find the 5 common difference and the number of terms.
The sum of the 5th and the 7th terms of an AP is 52 and the 10th term is Find the AP. Find the 20th term of the AP whose 7th term is 24 less than the 11 th term, first term being If the 9th term of an AP is zero, prove that its 29th term is twice its 19th term.
Find whether 55 is a term of the AP: If yes, find which term it is. Split into three parts such that these are in AP and the product of the two smaller parts is The angles of a triangle are in AP. The greatest angle is twice the least. Find all the angles of the triangle. If the nth terms of the two APs: Also find that term. If sum of the 3rd and the 8th terms of an AP is 7 and the sum of the 7th and the 14th terms is —3, find the 10th term.
Find the 12th term from the end of the AP: Which term of the AP: How many numbers lie between 10 and , which when divided by 4 leave a remainder 3? Find the sum of the two middle most terms of the AP: The first term of an AP is —5 and the last term is If the sum of the terms of the AP is , then find the number of terms and the common difference.
Find the sum: Find the sum of this AP upto the term — Also find S Find the sum of first 17 terms of an AP whose 4th and 9th terms are —15 and —30 respectively. If sum of first 6 terms of an AP is 36 and that of the first 16 terms is , find the sum of first 10 terms. Find the sum of all the 11 terms of an AP whose middle most term is Find the sum of last ten terms of the AP: Find the sum of first seven numbers which are multiples of 2 as well as of 9.
Take the LCM of 2 and 9] How many terms of the AP: Explain the reason for double answer. The sum of the first n terms of an AP whose first term is 8 and the common difference is 20 is equal to the sum of first 2n terms of another AP whose first term is — 30 and the common difference is 8.
Find n. Kanika was given her pocket money on Jan 1st, She puts Re 1 on Day 1, Rs 2 on Day 2, Rs 3 on Day 3, and continued doing so till the end of the month, from this money into her piggy bank.
She also spent Rs of her pocket money, and found that at the end of the month she still had Rs with her.
How much was her pocket money for the month? Yasmeen saves Rs 32 during the first month, Rs 36 in the second month and Rs 40 in the third month. If she continues to save in this manner, in how many months will she save Rs ? The sum of four consecutive numbers in an AP is 32 and the ratio of the product of the first and the last terms to the product of the two middle terms is 7: Solve the equation: Here, 1, 4, 7, 10, Alternative solution: The sum of the first five terms of an AP and the sum of the first seven terms of the same AP is If the sum of the first ten terms of this AP is , find the sum of its first twenty terms.
Find the i sum of those integers between 1 and which are multiples of 2 as well as of 5. These numbers will be: The eighth term of an AP is half its second term and the eleventh term exceeds one third of its fourth term by 1.
Find the 15th term. An AP consists of 37 terms. The sum of the three middle most terms is and the sum of the last three is Find the sum of the integers between and that are i divisible by 9 ii not divisible by 9 [Hint ii: Total numbers — Total numbers divisible by 9] 6. The ratio of the 11 th term to the 18th term of an AP is 2: Find the ratio of the 5th term to the 21st term, and also the ratio of the sum of the first five terms to the sum of the first 21 terms.
Show that the sum of an AP whose first term is a, the second term b and the last term c, is equal to a c b c — 2a 2 b —a 8. Jaspal Singh repays his total loan of Rs by paying every month starting with the first instalment of Rs If he increases the instalment by Rs every month, what amount will be paid by him in the 30th instalment?
What amount of loan does he still have to pay after the 30th instalment? The students of a school decided to beautify the school on the Annual Day by fixing colourful flags on the straight passage of the school.
They have 27 flags to be fixed at intervals of every 2 m. The flags are stored at the position of the middle most flag. Ruchi was given the responsibility of placing the flags. Ruchi kept her books where the flags were stored. She could carry only one flag at a time. How much distance did she cover in completing this job and returning back to collect her books?
What is the maximum distance she travelled carrying a flag? If in Fig 6. Answer D Sample Question 2: Then, length of DE in cm is A 2. In Fig. FD B AB. DE C BC. EF D BC. Then, the length of the side of the rhombus is A 9 cm 3. Then, the following is true: Is this triangle a right triangle? ST TU Why? Is the triangle with sides 25 cm, 5 cm and 24 cm a right triangle? In Fig 6. Is the following statement true? Two sides and the perimeter of one triangle are respectively three times the corresponding sides and the perimeter of the other triangle.
Are the two triangles similar? 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 will be similar? The ratio of the corresponding altitudes of two similar triangles is correct to say that ratio of their areas is 6? Is it true to say that if in two triangles, an angle of one triangle is equal to an angle of another triangle and two sides of one triangle are proportional to the two sides of the other triangle, then the triangles are similar?
Legs sides other than the hypotenuse of a right triangle are of lengths 16cm and 8 cm. Find the length of the side of the largest square that can be inscribed in the triangle. Hypotenuse of a right triangle is 25 cm and out of the remaining two sides, one is longer than the other by 5 cm. Find the lengths of the other two sides.
Let one side be x cm. Find the altitude of an equilateral triangle of side 8 cm. Corresponding sides of two similar triangles are in the ratio of 2: If the area 2 of the smaller triangle is 48 cm , find the area of the larger triangle.
If PN. Areas of two similar triangles are 36 cm 2 and cm2. If the length of a side of the larger triangle is 20 cm, find the length of the corresponding side of the smaller triangle. A 15 metres high tower casts a shadow 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. Foot of a 10 m long ladder leaning against a vertical wall is 6 m away from the base of the wall. Find the height of the point on the wall where the top of the ladder reaches. OC — OA. OB — OA. OC or OB. Prove that if in a triangle square on one side is equal to the sum of the squares on the other two sides, then the angle opposite the first side is a right angle. See proof of Theorem 6. How far apart the two aeroplanes would be after 1 Solution: Find the lengths of the remaining sides of the triangles.
Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides, then the two sides are divided in the same ratio. A 5 m long ladder is placed leaning towards a vertical wall such that it reaches the wall at a point 4 m high. If the foot of the ladder is moved 1. It is proposed to construct a 26 km highway which directly connects the two cities A and B.
Find how much distance will be saved in reaching city B from city A after the construction of the highway. A flag pole 18 m high casts a shadow 9.
Find the distance of the top of the pole from the far end of the shadow. A street light bulb is fixed on a pole 6 m above the level of the street. If a woman of height 1. In fig. Prove that CD CE [Hint: Prove that the area of the semicircle drawn on the hypotenuse of a right angled triangle is equal to the sum of the areas of the semicircles drawn on the other two sides of the triangle.
Prove that the area of the equilateral triangle drawn on the hypotenuse of a right angled triangle is equal to the sum of the areas of the equilateral triangles drawn on the other two sides of the triangle. If the distance between the points 2, —2 and —1, x is 5, one of the values of x is A —2 B 2 C —1 D 1 Solution: Answer C Sample Question 3: The distance of the point P 2, 3 from the x-axis is A 2 B 3 C 1 2.
The distance of the point P —6, 8 from the origin is 4. The point which divides the line segment joining the points 7, —6 and 3, 4 in ratio 1: The point which lies on the perpendicular bisector of the line segment joining the points A —2, —5 and B 2, 5 is A 0, 0 B 0, 2 C 2, 0 D —2, 0 The perpendicular bisector of the line segment joining the points A 1, 5 and B 4, 6 cuts the y-axis at A 0, 13 B 0, —13 C 0, 12 D 13, 0 A circle drawn with origin as the 13 centre passes through ,0.
A line intersects the y-axis and x-axis at the points P and Q, respectively. If 2, —5 is the mid-point of PQ, then the coordinates of P and Q are, respectively A 0, — 5 and 2, 0 B 0, 10 and — 4, 0 C 0, 4 and — 10, 0 D 0, — 10 and 4, 0 The points A —1, 0 , B 3, 1 , C 2, 2 and D —2, 1 are the vertices of a parallelogram.
The coordinates of the mid-points of both the diagonals AC and BD are 1 ,1 , i. The points 4, 5 , 7, 6 and 6, 3 are collinear. Since the area of the triangle formed by the points is 4 sq. Point P 0, —7 is the point of intersection of y-axis and perpendicular bisector of line segment joining the points A —1, 0 and B 7, —6.
P 0, —7 lies on the y -axis. It is at a distance of points —1, 0 and 7, —6. The points 0, 5 , 0, —9 and 3, 6 are collinear. Point P 0, 2 is the point of intersection of y—axis and perpendicular bisector of line segment joining the points A —1, 1 and B 3, 3. Points A 3, 1 , B 12, —2 and C 0, 2 cannot be the vertices of a triangle.
Points A 4, 3 , B 6, 4 , C 5, —6 and D —3, 5 are the vertices of a parallelogram. A circle has its centre at the origin and a point P 5, 0 lies on it. The point Q 6, 8 lies outside the circle.
The point A 2, 7 lies on the perpendicular bisector of line segment joining the points P 6, 5 and Q 0, — 4. Point P 5, —3 is one of the two points of trisection of the line segment joining the points A 7, — 2 and B 1, — 5.
The point P —2, 4 lies on a circle of radius 6 and centre C 3, 5. The points A —1, —2 , B 4, 3 , C 2, 5 and D —3, 0 in that order form a rectangle. Find the area of the triangle ABC with A 1, —4 and the mid-points of sides through A being 2, — 1 and 0, — 1. Let the coordinates of B and C be a, b and x, y , respectively. Sample Question 4: Find the coordinates of the fourth vertex D in terms of x1, x2 , x3, y1, y2 and y3. Let the coordinates of D be x, y. We know that diagonals of a parallelogram bisect each other.
Name the type of triangle formed by the points A —5, 6 , B —4, —2 and C 7, 5. Find the points on the x—axis which are at a distance of 2 5 from the point 7, —4.
How many such points are there? What type of a quadrilateral do the points A 2, —2 , B 7, 3 , C 11, —1 and D 6, —6 taken in that order, form? Find the value of a , if the distance between the points A —3, —14 and B a, —5 is 9 units. Find a point which is equidistant from the points A —5, 4 and B —1, 6? Find the coordinates of the point Q on the x—axis which lies on the perpendicular bisector of the line segment joining the points A —5, —2 and B 4, —2.
Name the type of triangle formed by the points Q, A and B. Find the value of m if the points 5, 1 , —2, —3 and 8, 2m are collinear. If the point A 2, — 4 is equidistant from P 3, 8 and Q —10, y , find the values of y.
Also find distance PQ. Find the area of the triangle whose vertices are —8, 4 , —6, 6 and —3, 9. In what ratio does the x—axis divide the line segment joining the points — 4, — 6 and —1, 7? Find the coordinates of the point of division. The centre of a circle is 2a, a — 7. Find the values of a if the circle passes through the point 11, —9 and has diameter 10 2 units. The line segment joining the points A 3, 2 and B 5,1 is divided at the point P in the ratio 1: Find the value of k.
Also find the coordinates of the point of division. Find the coordinates of the vertices of the triangle. Let the coordinates of B be x, y. Thus, the coordinates of the vertices of the triangle are A 1, 2 , B 5,6 and C 11, If — 4, 3 and 4, 3 are two vertices of an equilateral triangle, find the coordinates of the third vertex, given that the origin lies in the interior of the triangle.
Find the coordinates of the point D. If the points A 1, —2 , B 2, 3 C a, 2 and D — 4, —3 form a parallelogram, find the value of a and height of the parallelogram taking AB as base. Students of a school are standing in rows and columns in their playground for a drill practice.
A, B, C and D are the positions of four students as shown in figure 7. Is it possible to place Jaspal in the drill in such a way that he is equidistant from each of the four students A, B, C and D? If so, what should be his position? Ayush starts walking from his house to office. What is the extra distance travelled by Ayush in reaching his office? Assume that all distances covered are in straight lines. If the house is situated at 2, 4 , bank at 5, 8 , school at 13, 14 and office at 13, 26 and coordinates are in km.
Trigonometric ratios of complementary angles: The angle of depression of an object viewed, is the angle formed by the line of sight with the horizontal when it is below the horizontal level. The height or length of an object or the distance between two distinct objects can be determined with the help of trigonometric ratios.
The value of A 1 2 B tan 30 is cot 60 1 3 C 3 Solution: Answer D Sample Question 3: If a Case 2. If the length of the shadow of a tower is increasing, then the angle of elevation of the sun is also increasing.
If a man standing on a platform 3 metres above the surface of a lake observes a cloud and its reflection in the lake, then the angle of elevation of the cloud is equal to the angle of depression of its reflection.
If the height of the tower is doubled, then the angle of elevation of its top will also be doubled. Find the angle of elevation of the sun when the shadow of a pole h metres high is 3 h metres long. A ladder 15 metres long just reaches the top of a vertical wall. An observer 1. Determine the angle of elevation of the top of the tower from the eye of the observer. Let the height of the centre of the balloon be h. If the cars are m apart, find the height of the balloon. Let the height of the balloon at P be h meters see Fig.
Let A and B be the two cars. Let P be the cloud and Q be its reflection in the lake see Fig. Find the height of the tower. The angle of elevation of the top of a tower from two points distant s and t from its foot are complementary. Prove that the height of the tower is st.
A vertical tower stands on a horizontal plane and is surmounted by a vertical flag staff of height h. Find the distance between the two towers and also the height of the other tower. Find the distance between the two objects. The angle of elevation of the top of a vertical tower from a point on the ground is 60o.
From another point 10 m vertically above the first, its angle of elevation is 45o. A window of a house is h metres above the ground. The lower window of a house is at a height of 2 m above the ground and its upper window is 4 m vertically above the lower window. At certain instant the angles of elevation of a balloon from these windows are observed to be 60o and 30o respectively.
Find the height of the balloon above the ground. Tangent is perpendicular to the radius through the point of contact. Only two tangents can be drawn to a circle from an external point. Lengths of tangents from an external point to a circle are equal.
Then the radius of the circle is A 10 cm B 7. Answer C [Hint: If radii of two concentric circles are 4 cm and 5 cm, then the length of each chord of one circle which is tangent to the other circle is A 3 cm C 9 cm 2. The length of tangent from an external point on a circle is always greater than the radius of the circle. The length of tangent from an external point P on a circle with centre O is always less than OP.
If a number of circles touch a given line segment PQ at a point A, then their centres lie on the perpendicular bisector of PQ. If a number of circles pass through the end points P and Q of a line segment PQ, then their centres lie on the perpendicular bisector of PQ. Let AB be a chord of a circle which touches the other circle at C. Therefore, Sample Question 2: If a, b, c are the sides of a right triangle where c is the hypotenuse, prove that the radius r of the circle which touches the sides of the triangle is given by r a b 2 c.
Out of the two concentric circles, the radius of the outer circle is 5 cm and the chord AC of length 8 cm is a tangent to the inner circle. Find the radius of the inner circle. Prove that QORP is a cyclic quadrilateral. Prove that the centre of a circle touching two intersecting lines lies on the angle bisector of the lines. A chord PQ of a circle is parallel to the tangent drawn at a point R of the circle. Prove that R bisects the arc PRQ. Prove that the tangents drawn at the ends of a chord of a circle make equal angles with the chord.
Prove that a diameter AB of a circle bisects all those chords which are parallel to the tangent at the point A. ON is perpendicular on the chord AB.
Prove that: See Fig. By Theorem Two circles with centres O and O' of radii 3 cm and 4 cm, respectively intersect at two points P and Q such that OP and O'P are tangents to the two circles. Find the length of the common chord PQ.
Prove that the tangent to the circle at P bisects BC. A chord RS is drawn parallel to the tangent PQ. Draw a line through Q and perpendicular to QP. The tangent at C intersects extended AB at a point D. Prove that the tangent drawn at the mid-point of an arc of a circle is parallel to the chord joining the end points of the arc.
Prove that the points O, E, O' are collinear. Join C with centre O. A is a point at a distance 13 cm from the centre O of a circle of radius 5 cm. Construction of a triangle similar to a given triangle as per given scale factor which may be less than 1 or greater than 1. To divide a line segment AB in the ratio p: To divide a line segment AB in the ratio 5: C 11 D 12 To divide a line segment AB in the ratio 4: Then locate points B1, B2, B3, Sample Questions 1: By geometrical construction, it is possible to divide a line segment in the ratio 2 3: By geometrical construction, it is possible to divide a line segment in the ratio 3: The points B1, B2, Finally, line segment A'C' is drawn parallel to AC.
A pair of tangents can be constructed from a point P to a circle of radius 3. Draw an equilateral triangle ABC of each side 4 cm. Construct a triangle similar to it and of scale factor 3. Is the new triangle also an equilateral? Follow the similar steps as given in Mathematics Textbook for Class X. Yes, the new triangle is also equilateral. Draw a line segment of length 7 cm. Find a point P on it which divides it in the ratio 3: Construct a triangle similar to it and of scale factor also a right triangle?
Is AB'C'D' a rhombus? Join P and Q and measure the length PQ. Is A'BC'D' a parallelogram? Draw two concentric circles of radii 3 cm and 5 cm. Taking a point on outer circle construct the pair of tangents to the other. Measure the length of a tangent and verify it by actual calculation. Also justify the construction. Draw a circle of radius 4 cm. Measure the distance between the centre of the circle and the point of intersection of tangents.
Construct 3. Justify the construction. Are 2 the two triangles congruent? Note that all the three angles and two sides of the two triangles are equal. Circumference and area of a circle. What is the average acceleration of this sprinter?
The ISM has had to be removed. Chapter 2: Motion in a Straight Line. Distance And Displacement 1. Introduction to Physics of Charging and Discharging. Eugene is Section 2 Learning Objectives. Computer algebra systems began to appear in the s, and evolved out of two quite different sources - the requirements of theoretical physicists and research into artificial intelligence. Answer Key Interaction Forces 1.
Chapter 3: Motion in Two and Three Dimensions.
You may not use any resources other than those provided by your teacher. Solve: Model: The car is represented by the particle model as a dot. So here you can get the Preparations Online for the Exams. Refraction- the wave changes direction as it enters a different medium.
Chapter 1 discussed the statistical thermodynamics of an isolated polymer chain in a solvent. Physics: Principles with Applications 7th Edition answers to Chapter 2 - Describing Motion: Kinematics in One Dimension - Misconceptual Questions 4 including work step by step written by community members like you. Quickly memorize the terms, phrases and much more. Chapter 2 — Units and Measurements; Chapter 3 — Motion in a Straight Line; Chapter 4 — Motion in a plane Learn and revise with easy physics tutorial, revision questions and model answers.
Chapter 2: Motion in One Dimension. There are a lots of chapters in 10th class physics which contains many chapters. What is the speed of an object at rest? Physics Gallery. In class 11 physics syllabus, the chapter 2 i. FHSST is a project that aims to provide free science and mathematics textbooks for Grades 10 to 12 science learners. Covers a wide range of topics for juniors and seniors! Chapter 2 Physics In Action.
Mechanics Study of the motion of objects Kinematics Description of how objects move Dynamics Force and why objects move as they do. All Chapter 2 - Units and Measurement Exercises Questions with Solutions to help you to revise complete Syllabus and boost your score more in examinations.
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