SAMPLE PAPER TERM 2 CLASS 10 MATHS

For more updates follow us at our Facebook page: https://www.facebook.com/GYAANIKEEDA915

Sample Paper-1 Class-X Exam 2021-2022 (Term-2) Mathematics Time Allowed: 120 minutes Maximum Marks: 40 General Instructions: 1. The question paper consists of 14 questions divided into 3 sections A, B, C. 2. All questions are compulsory. 3. Section A comprises of 6 questions of 2 marks each. Internal choice has been provided in two questions. 4. Section B comprises of 4 questions of 3 marks each. Internal choice has been provided in one question. 5. Section C comprises of 4 questions of 4 marks each. An internal choice has been provided in one question. It contains two case study based questions. SECTION A Q1. Find the 10th term the end of the A.P 6, 13, 20 …216? OR In an A.P. ������ = 21, ������ = −3 and ������������ = 0, then what is the value of ������. Q2. If 2 is a root of the equation ������2 + ������������ + 12 = 0 and the equation ������2 + ������������ + ������ = 0 has equal roots. Find the value of ������. Q3. Prove that the parallelogram circumscribing a circle is a rhombus? Q4. Find the curved surface area of hemisphere of radius 7 cm. Q5. Find the mode of the following frequency distribution: CI 25-30 30-35 35-40 40-45 45-50 50-55 Frequency 25 34 50 42 38 14 Q6. Find the value of m so that the quadratic equation ������������(������ − 7) + 49 − 0 has two equal roots. OR Find the nature of roots of quadratic equation 2������² − 4������ + 3 = 0. SECTION B Q7. Draw a circle of radius 3 cm and from a point 8 cm away from its centre. Construct the pair of tangents to the circle and measure their lengths. Q8. As observed from the top of a 100 m high light house from sea level house, the angles of depression of two ships are 300 and 45°. If one ship is exactly behind the other on the same side of light house. Find the distance between the two ships. (������������������ √3 = 1.732) For more updates follow us at our Facebook page: https://www.facebook.com/GYAANIKEEDA915

OR The shadow of a tower standing on a level ground is found to be 40 m longer when the Sun's altitude is 30° than when it was 60°.Find the height of the tower. Q9. Calculate the mean of the following frequency distribution: Class 10-30 30-50 50-70 70-90 90-110 110-130 Frequency 5 8 12 20 32 Q10. The mean of the following distribution is 18. Find the frequency f of the class 19-21. Class 11-13 13-15 15-17 17-19 19-21 21-23 23-25 Frequency 7 6 9 13 ������ 5 4 SECTION C Q11. In figure, a quadrilateral ABCD is drawn to circumscribe a circle, with centre O in such a way that sides AB, BC, CD and DA touch the circle at the points P.Q.R and S respectively Prove that AB+CD=BC+ DA. Q12. A cone of maximum size is carved out from a cube of edge 14 cm. Find the surface area of the remaining solid after the cone is carved out. OR Water in a canal, 6m wide and 1.5m deep, is flowing with a speed of 10km/h. How much area will it irrigate in 30 minutes, if 8 cm of standing water is needed? Q13. CASE STUDY-1 In a Orchard .mango trees are planted in such a way that there are 21 trees in the first row, 19 trees in the second row, 17 trees in the third row and so on. For more updates follow us at our Facebook page: https://www.facebook.com/GYAANIKEEDA915

(a) Do you observe that the number of trees in rows form an A.P? IF yes what is the common difference of this A.P. (b) What is the number of mango trees in the 7th row? Q14. CASE STUDY-2 When an eagle sees a rat or any its prey on the ground, it does not attack it directly. Instead, it takes into account the speed of the prey and the direction in which it is moving. An eagle is sitting on the top of the tree of height 180 m. It observes that angle of depression of a rat from its place is 45° and the rat is moving away from the tree at the certain speed. The eagle starts flying downward with an angle of 30⁰ from the horizontal and catches the rat in 20 seconds. (a) The horizontal distance between the tree and the initial position of rat is (i) 240m (ii) 180 m (iii) 120m (iv) 90m (b) Distance travelled by the eagle to catch the rat is? (i) 180m (ii) 360m (iii) 480m (iv) 540m ANSWER’S Q9. 65.6 Q10. 20 Q1. 153 OR 8 Q12. 1366.35 OR 56.25 hectare Q2. 16 Q13. (i) Yes (ii) 9 Q4. 308 cm2 Q14. (i) 180 (ii) 360 Q5. 38.33 Q6. 4 OR No Real Roots Q8. 73.2 m OR 34.64 For more updates follow us at our Facebook page: https://www.facebook.com/GYAANIKEEDA915

Sample Paper-2 Class-X Exam 2021-2022 (Term-2) Maximum Marks: 40 Mathematics Time Allowed: 120 minutes General Instructions: 1. The question paper consists of 14 questions divided into 3 sections A, B, C. 2. All questions are compulsory. 3. Section A comprises of 6 questions of 2 marks each. Internal choice has been provided in two questions. 4. Section B comprises of 4 questions of 3 marks each. Internal choice has been provided in one question. 5. Section C comprises of 4 questions of 4 marks each. An internal choice has been provided in one question. It contains two case study based questions. SECTION A Q1. If 3.4.p & 7p are in A.P. find the value of p? OR What is the common difference of an A.P. in which a21-a7=84? Q2. Solve for ������: ������������������² + (������² − ������������)������ − ������������ = 0. Q3. From a point P, two tangents PA & PB are drawn to a circle C (0, r). If OP=2r then find∠������������������. What type of triangle is APB? Q4. A largest sphere is carved out of a cube of side 14 cm. Find the volume of the sphere. Q5. If the mean of the following distribution is 54, find the missing frequency x. CI 0-20 20-40 40-60 60-80 80-100 Frequency 16 14 24 16 ������ Q6. Find the positive numerical difference of the roots of the equation ������2 − 7������ − 18 = 0. OR Solve the equation ������2 − 5 ������ = − 13, using the Quadratic formula. 3 For more updates follow us at our Facebook page: https://www.facebook.com/GYAANIKEEDA915

SECTION B Q7. Find the mode of the given data. CI 0-20 20-40 40-60 60-80 80-100 100-120 120-140 Frequency 6 8 10 12 6 53 Q8. PQ is a line segment of length 6.4 cm. geometrically obtain point R on PQ such that ������������ = 58. ������������ Q9. The following frequency distribution shows the survey of heights of 50 girls & their median is given to be 151.5. Find the missing frequencies? Height 120-130 130-140 140-150 150-160 160-170 Frequency 2 ������1 12 ������2 8 Q10. The angle of elevation of the top of the first storey of a building is 30° from a point on the ground at a distance of 15 m from its foot. How high its second storey will be, if the angle of elevation of the top of the second storey from the same point is 45°? OR The angle of elevation of the top B of a tower AB from a point X on the ground is 60°. From a point Y, 40 m vertically above X. the angle of elevation of the top is 45°.Find the height of the tower AB & the distance XB. SECTION C Q11. In summer vacations, a summer camp is organised for students, where they stay in conical tens of radius 12 m. Each tent has 2 m wide path around it for movement. If the land where these tents are erected is a rectangular field of dimension 1.4 kmx200m, how many tents are possible in this field? (������������������ ������ = 272) OR Water in flowing at the rate of 15 km/h through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long & 44 m wide. In what time will the level of water in the pond rise by 21 cm? Q12. In water in flowing at the rate of 15 km/h through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long & 44 m wide. In what time will the level of water in the pond rise by 21 cm? For more updates follow us at our Facebook page: https://www.facebook.com/GYAANIKEEDA915

Q13. CASE STUDY-1 Your elder brother wants to buy a car & plans to take loan from a bank for his car. He repays his total loan of Rs 1.18.000 by paying every month starting with the first instalment of Rs 1000.If he increases the instalment by Rs 100 every month. (a) The amount paid by him in 30th instalment is (i) 3900 (ii) 3500 (iii) 3700 (iv) 3600 (b) The ratio of the 1st instalment to the last instalment is (i) 1:49 (ii) 10:49 (iii) 10:39 (iv)39:10 Q14. CASE STUDY-2 Radio & TV towers are used for transmitting a number communication services. A TV tower was built consisting of two sections AB & BC as shown in the figure. This tower is supported by wires connected from a point O on the ground, which is at a distance of 72 m from the base of the tower. From the point O, the angle of elevation of the top of the section AB is 45° & that of the section BC is 30°. (a) Height BC is (i) 16√2 m (ii) 23√2 m (iii) 16√3 m (iv) 24√3 m (iii) 72√2 m (iv) 56√3 m (b) Length OA is (i) 48√3 m (ii) 64√2 m ANSWER’S Q1. P= ������ OR 6 Q9. ������������ = ������, ������������ = ������������ ������ Q10. 6.35 m OR AB=20(√������ + ������)������, XB=������������(√������ + ������)������ Q2. ������ = −������ , ������ = ������ Q11. 454 OR 2 Hours ������ ������ Q12. r=6 cm Q13. (i) 3900 (ii) 10:49 Q3. 60°, APB is an equilateral ∆ Q14. (i) ������������√������ m (ii) ������������√������ m Q4. 1437.3 cm3 Q5. ������ = ������������ Q6. 11 OR ������ = ������ ±√������ ������ Q7. 65 For more updates follow us at our Facebook page: https://www.facebook.com/GYAANIKEEDA915

Sample Paper-3 Class-X Exam 2021-2022 (Term-2) Maximum Marks: 40 Mathematics Time Allowed: 120 minutes General Instructions: 1. The question paper consists of 14 questions divided into 3 sections A, B, C. 2. All questions are compulsory. 3. Section A comprises of 6 questions of 2 marks each. Internal choice has been provided in two questions. 4. Section B comprises of 4 questions of 3 marks each. Internal choice has been provided in one question. 5. Section C comprises of 4 questions of 4 marks each. An internal choice has been provided in one question. It contains two case study based questions. SECTION A Q1. If the common difference of an A.P is 5 then what is the value of a18-a13? OR Two AP have the same common difference. The first term of one of these is −1 and that of the other is -8. Then find the difference between their 4th terms. Q2. If the quadratic equation ������������2 + 2������ + ������ = 0, has two equal and real roots, then find the value of m? Q3. From a point P, two tangents PA and PB are drawn to a circle C (O, r). If OP= 2r, then find angle APB. What type of triangle is APB? Q4. From a solid right circular cylinder of height 14cm and base radius 6cm, a right circular cone of same height and same base radius is removed. Find the volume of the remaining solid. Q5. Find the mode of the following frequency distribution: - Class 15-20 20-25 25-30 30-35 35-40 40-45 Frequency 3 8 9 10 3 2 Q6. The sum of areas of two squares is 157 sq. m. If the sum of their perimeters is 68m, find the sides of the squares. OR Solve for ������: − 6������2������2 − 7������������������ − 3������2 = 0 For more updates follow us at our Facebook page: https://www.facebook.com/GYAANIKEEDA915

SECTION B Q7. Find the median: - Classes 500-600 600-700 700-800 800-900 900-1000 Frequency 36 32 32 20 30 Q8. Divide a line segment AB of length 7cm in the ratio 2:3. Also measure the two parts with steps on constructions. OR Draw a line segment AB of length 8cm. taking A as centre, draw a circle of radius 4cm and taking B as centre, draw another circle of radius 3cm. Construct tangents to each circle from the centre of the other circle. Also write steps of constructions. Q9. The daily income of a sample of 50 employees are tabulated as follows: - Find the mean income of the employee Income 1-200 201-400 401-600 601-800 No. of employee 14 15 14 7 Q10. A vertical tower stands on a horizontal plane and surmounted by a flagstaff of height 5m. From a point on the ground, the angles of elevation of the top and bottom of the flagstaff are 60 and 30 respectively. Find the height of the tower and the distance of the point from the tower. (take √3=1.732) OR At a point A, 20 meters above the level of water in a lake, the angle of elevation of a cloud is 30. The angle of depression of the reflection of the cloud in the lake at A is 60. Find the distance of the cloud from A. SECTION C Q11. A circus tent is in the shape of a cylinder surmounted by a conical top of the same diameter. If their common diameter is 56m, the height of the cylindrical part is 6m and the total height of the tent above the ground is 27m, find the area of canvas used in making the tent. Q12. In the fig., a triangle ABC is drawn to circumscribe a circle of radius 3cm, such that the segments BD and DC respectively of lengths 6cm and 9cm. If the area of ABC is 54 sq.cm, then find the length of sides AB and AC. Q13. The horizontal distance between a towers AB and a building CD is 120m. The angle of elevation of the top of the tower AB from the top and bottom of the building CD are 45 and 60 respectively. i Find the height of tower AB? ii Find the height of building CD? For more updates follow us at our Facebook page: https://www.facebook.com/GYAANIKEEDA915

14. Push-ups are a fast and effective exercise for the building strength. These are helpful in almost all sports including athletics. While the push-up primarily targets the muscles of the chest, arm and shoulders, support required from other muscles helps in toning up the whole body. Nitesh wants to participate in the push-up challenge. He can currently make 3000 push-ups in one hour. But he wants to achieve a target of 3900 push-ups in 1 hour for which he practices regularly. With each day of practice, he is able to make 5 more push-ups in one hour as compared to the previous day. If on first day of practice he makes 3000 push-ups and continues to practice regularly till his target is achieved. Keeping the above situation in mind answer the following questions: (i) Form an A.P representing the number of push-ups per day and hence find the minimum number of days he needs to practice before the day his goal is accomplished (ii) Find the total number of push-ups performed by Nitesh up to the day his goal is achieved. ANSWER’S Q1. 25 OR 7 Q9. 356.5 Q10. H= 2.5m, Dis. = 4.33 m OR 40 m Q2. ������ = ±������ Q11. 4136 m2 Q12. AB=9 cm, AC=12 cm Q3. 60°, APB is an equilateral ∆ Q13. (i) 120√������ m, (ii) 120(√������ − ������)m Q14. (i) 180 (ii) 6,21,000 Q4. 1056 cm3 Q5. 30.625 Q6. 6, 11 OR ������ = ������������ , ������ = −������ ������������ ������������ Q7. 721.8 For more updates follow us at our Facebook page: https://www.facebook.com/GYAANIKEEDA915

Sample Paper-4 Class-X Exam 2021-2022 (Term-2) Maximum Marks: 40 Mathematics Time Allowed: 120 minutes General Instructions: 1. The question paper consists of 14 questions divided into 3 sections A, B, C. 2. All questions are compulsory. 3. Section A comprises of 6 questions of 2 marks each. Internal choice has been provided in two questions. 4. Section B comprises of 4 questions of 3 marks each. Internal choice has been provided in one question. 5. Section C comprises of 4 questions of 4 marks each. An internal choice has been provided in one question. It contains two case study based questions. SECTION A Q1. The sum of n terms of an AP is 3n2 + 5n. Find AP. Hence find its 15th term. OR 5 times 5th term of an A. P. is equal to 8 times its 8th term. Show its 13th term is zero. Q2. For what value of k, the root of quadratic kx (x - 2√5) + 10 = 0 are equal? Q3. In. fig. PQ is tangent at point C to circle with center O, if AB is a diameter and ∠CAB = 30°, Find ∠PCA. Q4. A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area. Q5. Marks obtained by class 10th students is recorded in the given table .The model marks of the students is 36, but one frequency is missing, find the missing frequency. C.I. 1-10 10-20 20-30 30-40 40-50 50-60 60-70 Frequency 8 10 X 16 12 6 7 Q6. A chess board contains 64 squares and area of each square is 6.25 cm2. A border round the board is 2cm wide. Find the length of the side of the chess board. OR Solve for x: 4x2 - 4ax + a2 - b2 = 0 For more updates follow us at our Facebook page: https://www.facebook.com/GYAANIKEEDA915

SECTION B Q7. An aircraft has 120 passenger seats. The number of seats occupied during 90 flight is given in the following table: No. of seats 100-104 104-108 108-112 112-116 116-120 No. of flights 15 20 32 18 15 Determine the mean number of seats occupied over the flight. Q8. Construct a circle of radius 5cm. Draw two tangents to the circle perpendicular to each other. Q9. Find the unknown entries a, b, c, d, e and f in the following distribution of height of Students in the class. Height Frequency Cumulative (in cm) frequency 150-155 12 b A 155-160 10 160-165 d 25 165-170 e c 170-175 2 43 175-180 50 48 f Q10. A TV tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is 60°. From another point 20 m away from this point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is 30°. Find the height of the tower and the width of the canal. OR An aeroplane when flying at a height of 5000 m from ground passes vertically above another aeroplane at an instance when the angles of elevation of the two planes from the same point on the ground are 60° and 45° respectively. Find the vertical distance between the aeroplanes at the instance. SECTION C Q11. Two tangents TP and TQ are drawn to a circle with centre O from the external point .Prove that ∠PTQ = 2 ∠OPQ. Q12. A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment. OR A container, shaped like a right circular cylinder having diameter 12 cm and height 15cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream. For more updates follow us at our Facebook page: https://www.facebook.com/GYAANIKEEDA915

Q13. CASE STUDY-1 Minar is a tower or turret found especially in India. It is the famous monument of tourist attractions including other places near it. Tourists from all over the world come here every year to see the beauty of these Historical monuments. One day a 1.5m tall boy went for an excursion trip. He saw a beautiful Minar and he asked about the height of the Minar from the local guide. The local guide told him that the height of The Minar is 30 m approximately. He is standing at some distance from the Minar and observes the angle of elevation from his eyes to the top of the building increases from α to β as he walks towards it such that Sin (α + β) =1 and Cos (β - α) = √3/2. i) Find the value of α and β ii) Find the distancehe walked towards the building. Q14. CASE STUDY-2 On the occasion of the world environment day 5th June there is plantation in the School campus. All the students with counsel of students and teachers decided to plant trees in and around the school building to reduce air pollution. It was decided that the number of trees, that each section of each class will plant will be double of the class in which they are studying. If there are 1 to 12 classes in the school and each class have 2 sections. (i) Form an AP representing number of trees planted by each class. (ii) Find total number of trees planted by students. ANSWER’S Q1. A.P. 8, 14, 20…. OR ������������������ = ������������ Q7. 109.92 Q2. ������ = ������ Q9. a=12, b=13, c=35, d=8, e=5, f= 50 Q3. 60° Q10. Height = 10√������ m, width=������������ ������ OR 211.2493 Q4. 220 mn2 Q5. F=10 Q12. H=1.125 m OR 10 ice cream Q6. 24 cm OR ������ = ������±������ Q13. (i) ������ = ������������°, ������ = ������������° (ii) ������������√������������ ������ Q14. (i) 4, 8, 12… (ii) 312 plants For more updates follow us at our Facebook page: https://www.facebook.com/GYAANIKEEDA915

Sample Paper-5 Class-X Exam 2021-2022 (Term-2) Maximum Marks: 40 Mathematics Time Allowed: 120 minutes General Instructions: 1. The question paper consists of 14 questions divided into 3 sections A, B, C. 2. All questions are compulsory. 3. Section A comprises of 6 questions of 2 marks each. Internal choice has been provided in two questions. 4. Section B comprises of 4 questions of 3 marks each. Internal choice has been provided in one question. 5. Section C comprises of 4 questions of 4 marks each. An internal choice has been provided in one question. It contains two case study based questions. SECTION A Q1. The first term of an A.P. is 2 and its tenth term is 47. Find its ������������ℎ term. Q2. The life time of 50 bulbs is given in the following table: Life time (in hour) Number of bulbs 0-100 6 14 100-200 12 200-300 10 300-400 8 400-500 Calculate modal life time. OR The table below shows the salaries of 280 persons: Salary (in thousand Rs.) Number of Person 5-10 49 10-15 133 15-20 63 20-25 15 25-30 6 30-35 7 35-40 4 40-45 2 45-50 1 Calculate the median salary of the above data Q3. Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact. For more updates follow us at our Facebook page: https://www.facebook.com/GYAANIKEEDA915

Q4. Find the sum of the first 15 multiples of 6. OR How many two-digit numbers are divisible by 3 and 5? Q5. Which of the following is a quadratic equation? (������) (������ + 1)2 = 2(������ − 3) (������������) (������ + 2)3 = 2������ (������2 − 1) (������������������) (������ − 2) (������ + 1) = (������ − 1)(������ + 3) (������������) ������2 − 2������ = (−2) (3 − ������) Q6. The following table shows the cumulative frequency distribution of marks obtained by 200 students in an examination: Marks Number of students Below 10 7 Below 20 19 Below 30 40 Below 40 62 Below 50 98 Below 60 132 Below 70 157 Below 80 173 Below 90 190 Below 100 200 Construct a frequency distribution table for the above data. SECTION B Q7. Draw a circle of radius 4 ������������. Construct a pair of tangents to it, the angle between which is 60°. Q8. Water in a canal, 6 ������ wide and 1.5 ������ deep, is flowing with a speed of 10 km/hour. How much area will it irrigate in 30 minutes if 8 ������������ standing water is needed? OR A tent is in the shape of a right circular cylinder upto a height of 3 m and conical above it. The total height of the tent is 13.5 m and radius of base is 14 m. find the cost of cloth required to make the tent at the rate of Rs. 80 per m2 Q9. In a violent storm, a tree got bent by the wind. The top of the tree meets the ground at the angle of 30°, at a distance of 40 meters from the root. What was the original height of the tree? ������������������������ √2 = 1.414 And √3 = 1.732 For more updates follow us at our Facebook page: https://www.facebook.com/GYAANIKEEDA915

Q10. The difference between outer and inner curved surface areas of a hollow right circular cylinder, 14 cm long is 88 cm2. The volume of the metal used in making the cylinder is 176 cm3. Find the outer and inner diameters of the cylinder. SECTION C Q11. Two tangents PA and PB are drawn to a circle with centre O from an external point P. Prove that ∠������������������ = 2 ∠������������������. OR Prove that the parallelogram circumscribing a circle is a rhombus. Q12. The median of the following frequency distribution is 28.5 and the sum of all the frequencies is 60. Class interval Frequency 0-10 5 10-20 p 20-30 20 30-40 15 40-50 q 50-60 5 Find the values of ������ and ������ Q13. CASE STUDY-1 Mohan and Sohan went on a vacation to a seaside. They spotted an island at a certain distance from the sea shore. The two friends planned to stand at a distance of 50 m from each other such that the angle of elevation from Mohan to the island is 30° while that from Sohan is 45° as shown in the figure above. ������������������������ √2 = 1.414 and √3 = 1.732 (i) What is the approximate perpendicular distance of the island from the line joining Mohan and Sohan? (ii) What is the distance of the island from Mohan from the point where he is standing? For more updates follow us at our Facebook page: https://www.facebook.com/GYAANIKEEDA915

Q14. CASE STUDY-1 In a class test, the sum of Ranjita's marks in Mathematics and English is 40. Had she got 3 marks more in Mathematics and 4 marks less in English, the product of the marks would have been 360. On the other hand, Ranjita's friend Malti scored 3 marks less in Mathematics and 2 marks more in English than what Ranjita scored. Based on this information, answer the following questions: (i) How much did Ranjita score in Mathematics? (ii) Find the sum of Malti's marks in both subjects. ANSWER’S Q1. 5n-3 Q2. 180 OR 13.42 Q4. 720 OR 6 Q5. (i) Yes (ii) No (iii) No (iv) Yes Q8. 56.25 hectare OR Rs. 8272 Q9. 69.28 Q10. 2.5, 1.5 Q12. P=8, q= 7 Q13. (i) 18.3 m (ii) 31.7 m Q14. (i) 21 or 12 (ii) 18 or 9 For more updates follow us at our Facebook page: https://www.facebook.com/GYAANIKEEDA915

Sample Paper-6 Class-X Exam 2021-2022 (Term-2) Maximum Marks: 40 Mathematics Time Allowed: 120 minutes General Instructions: 1. The question paper consists of 14 questions divided into 3 sections A, B, C. 2. All questions are compulsory. 3. Section A comprises of 6 questions of 2 marks each. Internal choice has been provided in two questions. 4. Section B comprises of 4 questions of 3 marks each. Internal choice has been provided in one question. 5. Section C comprises of 4 questions of 4 marks each. An internal choice has been provided in one question. It contains two case study based questions. SECTION A Q1. If one root of the quadratic equation 2������² + ������������ − 6 = 0 is 2, find the value of ������ and also find the other root. Q2. Find ‘������’ so that ������ + 3, 2������ + 1 and 5������ + 3 are the consecutive terms of an AP. OR Find the sum of the last ten terms of an AP 8, 10, 12 … . .126. Q3. If the difference of mode and median of a data is 72, find the difference of the median and the mean. Q4. The length of a classroom is double of its breadth. Its height is 4������ and area of four walls (including the door) is 216������². Find its volume. Q5. Find the mode of the following distribution Class 25-30 30-35 35-40 40-45 45-50 50-55 34 50 42 38 14 Frequency 25 Q6. In the given figure ������������ and ������������ are tangents to the circle with centre ������. If ∠������������������ = 65°, then find the value of ������. OR Prove that the lengths of two tangents drawn from an external point to a circle are equal For more updates follow us at our Facebook page: https://www.facebook.com/GYAANIKEEDA915

SECTION B Q7. Draw two concentric circles of radii 3������������ and 6������������.Take a point ������ on the outer circle. Construct a pair of tangents ������������ and ������������ to the smaller circle. Q8. The sum of 6������ℎ and 8������ℎ terms of an AP is 68 and its 10������ℎ term is 46. Find the first four terms of the ������������. Q9. From the top of a 150������ high tower, a man observes two cars on the opposite sides of the tower and in a straight line with the base of the tower with the angles of depression as 60° and 45°. Find the distance between two cars. (������������������ √3 = 1.73). Q10. A train takes 3 hours less than a bus for a journey of 600km. If the speed of the bus is 10 ������������/ℎ������ less than that of the train, find the speed of the bus and the train. OR Solve for ������: 4������2 − 4������������ + (������2 − ������2) = 0 SECTION C Q11. The median of the following data is 16. Find the missing frequencies ������ and ������, if the total of the frequencies is 70. Class 0-5 5-10 10-15 15-20 20-25 25-30 30-35 35-40 ������ 12 15 ������ 6 6 4 Frequency 12 Q12. A metallic solid sphere of diameter 21������������ is melted and recast into smaller solid cones and each of diameter 7������������ and height 9cm. How many cones will be made? OR The sum of the height and the radius of the base of a solid right circular cylinder is 74cm. If the total surface area of the cylinder is 3256cm². Find the volume of the cylinder. Q13. CASE STUDY-1 A tangent to a circle is a straight line which touches the circle at only one point. This point is called the point of tangency. In this figure, the wheels are, of course, circles, the spokes are radii, and the ground is a tangent line. The point where each wheel touches the ground is a point of tangency. Keeping the above situation in mind answer the following questions. i. In the given figure ������ is the centre of the circle and ������������ is a tangent. Find the length of ������������. For more updates follow us at our Facebook page: https://www.facebook.com/GYAANIKEEDA915

ii. A point ������ which is at a distance 13cm from the center ������ of a circle of radius 5cm. The pair of tangents ������������ and ������������ is drawn to the circle. Find the area of the quadrilateral ������������������������. Q14. CASE STUDY-2 Ancient astronomers have used trigonometry to calculate the distance from Earth to stars. Maps are constructed with the help of knowledge of trigonometry. It is used in everyday life around us. Sometimes it may not be easily possible to measure with a measuring tape the height of a big tree, tower, the width of a river, distance between a ship and the light-house etc. We can determine these with knowledge of trigonometry. i. An observer 1.5������ tall is 20.5������ away from a tower 22������ high. Determine the angle of elevation of the top of the tower from the eye of the observer. ii. A 10������ flagstaff is fixed on the top of a tower standing on the horizontal plane. From a point on the ground, the angles of elevation of the top and bottom of the flagstaff are 60° and 45° respectively. Find the height of the tower. (������������������ √3 = 1.73). ANSWER’S Q1. -1 Q9. 236.5 Q2. -2 OR 1170 Q3. 36 Q10. 40 km/h OR ������ = ������±������ Q4. 648 cm3 ������ Q5. 38.33 Q6. 50° Q11. X= 8, y= 7 Q8. 10, 14, 18, 22… Q12. 126 OR 10318 cm3 Q13. (i) 9 cm (ii) 60 cm2 Q14. (i) 45° (ii) 13.699 m approx. For more updates follow us at our Facebook page: https://www.facebook.com/GYAANIKEEDA915

Sample Paper-7 Class-X Exam 2021-2022 (Term-2) Maximum Marks: 40 Mathematics Time Allowed: 120 minutes General Instructions: 1. The question paper consists of 14 questions divided into 3 sections A, B, C. 2. All questions are compulsory. 3. Section A comprises of 6 questions of 2 marks each. Internal choice has been provided in two questions. 4. Section B comprises of 4 questions of 3 marks each. Internal choice has been provided in one question. 5. Section C comprises of 4 questions of 4 marks each. An internal choice has been provided in one question. It contains two case study based questions. SECTION A Q1. The following table gives the life time in days of 100 bulbs: Life time in Less than Less than Less than Less than Less than Less than 250 300 days 50 100 150 200 93 100 Number of 8 23 55 81 Bulbs Change the above distribution as frequency distribution. OR From the following frequency distribution, find the median class: Cost of living index 1400-1500 1550-1700 1700-1850 1850-2000 Number of weeks 8 15 21 8 Q2. In figure, a circle touches all the four sides of a quadrilateral ABCD. If AB = 6 cm, BC = 9 cm and CD = 8 cm, then find the length of AD. Q3. How many terms of the AP 65, 60 55.... be taken so that their sum is zero? Q4. Find the sum of the lower limit of the median class and the upper limit of the modal class: Classes 10-20 20-30 30-40 40-50 50-60 60-70 Frequency 1 3 5 9 7 3 For more updates follow us at our Facebook page: https://www.facebook.com/GYAANIKEEDA915

Q5. Two cubes of 5 cm each are kept together joining edge to edge to form a cuboid. Find the surface area of the cuboid so formed. Q6. Solve the quadratic equation, 2������2 + ������������ − ������2 = 0 for ������ OR Find the value of k for which the roots of the equations 3������2 − 10������ + ������ = 0 are reciprocal of each other. SECTION B Q7. The sum of four consecutive number in AP is 32 and the ratio of the product of the first and last term to the product of two middle terms is 7:15. Find the numbers. Q8. Raw a circle of radius 2 cm with centre O and take a point P outside the circle such that OP = 6.5 cm. From P, draw two tangents to the circle. OR Let ABC be a right triangle in which AB = 6 cm, BC = 8 cm and ∠B = 90°. BD is the perpendicular from B on AC. The circle through B, C, D is drawn. Construct the tangents from A to this circle. Q9. Determine the positive value of k for which the equation ������2 + ������������ + 64 = 0 and ������2 − 8������ + ������ = 0 will both have real and equal roots. Q10. A statue 1.6 m tall stands on the top of a pedestal. From a point on the ground the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal. SECTION C Q11. A straight highway leads to the foot of a tower. A man standing on its top observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. 6 seconds later, the angle of depression of the car becomes 60°. Find the time taken by the car to reach the foot of tower from this point. Q12. In figure, a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC , AB, AD and CD at points P, Q, R and S respectively. If AB = 29 cm, AD = 23 cm, ∠B = 90° and DS = 5 cm, then find the radius of the circle (in cm). OR For more updates follow us at our Facebook page: https://www.facebook.com/GYAANIKEEDA915

In Figure the radius of incircle of ∆ABC of area 84 cm2 and the lengths of the segments AP and BP into which side AB is divided by the point of contact are 6 cm and 8 cm. Find the lengths of the sides AC and BC. Q13. CASE STUDY-1 Electric scooters are plug-in electric vehicles with two or three wheels. The electricity is stored on board in a rechargeable battery, which drives one or more electric motors. Leading manufacturer of electric scooter, Hero Scooter Pvt Ltd wants to declare the mileage of their electric scooters. For this, they recorded the mileage (km/ charge) of 50 scooters of the same model. Details of which are given in the following table. Mileage 100-120 120-140 140-160 160-180 (km/charge) Number of scooters 7 12 18 13 Based on the above information, answer the following questions. (i) What is the modal value of mileage? (ii) What is the median value of mileage? Q14. CASE STUDY-2 DK Jain runs a company that makes ball bearings. The bearings are shipped in boxes that are then loaded onto trucks. Each bearing has a diameter of 18 mm. (i) Each box can hold 3888 cm3 π of ball bearings. How many ball bearings can a box hold? For more updates follow us at our Facebook page: https://www.facebook.com/GYAANIKEEDA915

(ii) Each ball bearing has a mass of 4 gm. Determine the mass of each box. ANSWER’S Q1. OR Median Class= 1700-1850 Q2. 5 cm Q3. 27 Q4. 90 Q5. 250 cm2 Q6. ������ = ������ , −������ OR 3 ������ Q7. 2, 6, 10 and 14 Q9. 16 Q10. 2.2 m Q11. 11 cm OR AC=13 cm, BC=15 cm Q12. 3 seconds Q13. (i) 150.91 km/charge (ii) 224.12 km Q14. (i) 4000 (ii) 16 kg For more updates follow us at our Facebook page: https://www.facebook.com/GYAANIKEEDA915

Sample Paper-8 Class-X Exam 2021-2022 (Term-2) Maximum Marks: 40 Mathematics Time Allowed: 120 minutes General Instructions: 1. The question paper consists of 14 questions divided into 3 sections A, B, C. 2. All questions are compulsory. 3. Section A comprises of 6 questions of 2 marks each. Internal choice has been provided in two questions. 4. Section B comprises of 4 questions of 3 marks each. Internal choice has been provided in one question. 5. Section C comprises of 4 questions of 4 marks each. An internal choice has been provided in one question. It contains two case study based questions. SECTION A Q1. How many terms of the AP −6, − 11 , −5, − 9 … are needed to give their sum zero? 2 2 Q2. Find the roots of the quadratic equation 4������2 − 4������������ + (������2 − ������2) = 0 OR Find the nature of the roots of the quadratic equation 4������2 + 4√3������ + 3 = 0. Q3. If the total surface area of a solid hemisphere is 462 cm2, find its volume. Use π =272. Q4. In the figure, quadrilateral ABCD is circumscribing a circle with centre O and AD ⊥ AB. If radius of in circle is 10 cm, then find the value of x. Q5. Calculate the median from the following data: Marks 0-10 10-20 20-30 30-40 40-50 Number of Students 5 15 30 8 2 OR In the following frequency distribution, find the median class Height (in cm) 104-145 145-150 150-155 155-160 160-165 165-170 Frequency 5 15 25 30 15 10 For more updates follow us at our Facebook page: https://www.facebook.com/GYAANIKEEDA915

Q6. Find the unknown values in the following table: Class Frequency Cumulative Interval Frequency 5 0-10 7 5 10-20 ������2 20-30 5 ������1 30-40 ������4 15 40-50 ������3 30 SECTION B Q7. If in an AP, the sum of first ������ terms is ������ and the sum of its first n terms is m, then prove that the sum of its first (m+n) terms is – (m+n). Q8. On a straight line passing through the foot of a tower, two C and D are at distance of 4 m and 16 m from the foot respectively. If the angles of elevation from C and D of the top of the tower are complementary, then find the height of the tower. Q9. Find the value of k for which the quadratic equation (������ − 2)������2 + 2(2������ − 3)������ + (5������ − 6) = 0 has equal roots. Q10. Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths. OR Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle. SECTION C Q11. Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle. OR In figure, PQ is a chord of a circle O and PT is a tangent. If ∠QPT = 60c, find ∠PRQ. Q12. From the top of a hill, the angle of depression of two consecutive kilometer stones due east are found to be 45° and 30° respectively. Find the height of the hill. [Use √3 = 1.73] Q13. CASE STUDY-1 Transport department of a Jaipur wants to buy some Electric buses for the city. For which they wants to analyse the distance travelled by existing public transport buses in a day. For more updates follow us at our Facebook page: https://www.facebook.com/GYAANIKEEDA915

The following data shows the distance travelled by 60 existing public transport buses in a day Daily distance 200-209 210-219 220-229 230-239 239-249 travelled (in km) Number of buses 5 15 30 8 2 Base on the above information, answer the following questions. (i) Find the median of the distance travelled. (ii) If the mode of the distance travelled is 223.78 km, find the mean of the distance travelled by the bus. Q14. CASE STUDY-2 In a toys manufacturing company, wooden parts are assembled and painted to prepare a toy. For the wood processing activity center, the wood is taken out of storage to be sawed, after which it undergoes rough polishing, then is cut, drilled and has holes punched in it. It is then fine polished using sandpaper. For the retail packaging and delivery activity center, the polished wood sub-parts are assembled together, then decorated using paint. One specific toy is in the shape of a cone mounted on a cylinder. The total height of the toy is 110 mm and the height of its conical part is 77 mm. The diameters of the base of the conical part is 72 mm and that of the cylindrical part is 40 mm. (i) If its cylindrical part is to be painted red, the surface area need to be painted is (ii) If its conical part is to be painted blue, the surface area need to be painted is ANSWER’S Q1. 25 Q8. 8 m Q9. K=1, 2 Q2. ������+������ , ������−������ OR ������������ − ������������������ = ������ Q11. OR 120° ������ ������ Q12. 1365 m Q13. (i) 224.12 km (ii) 224.29 km Q3. 718.67 cm3 Q14. (i) 1720������ mm2 (ii) 3956������ mm2 Q4. 21 cm Q5. 23.33 OR 155-160 Q6. ������������ = ������������, ������������ = ������, ������������ = ������������, ������������ = ������ For more updates follow us at our Facebook page: https://www.facebook.com/GYAANIKEEDA915

Sample Paper-9 Class-X Exam 2021-2022 (Term-2) Maximum Marks: 40 Mathematics Time Allowed: 120 minutes General Instructions: 1. The question paper consists of 14 questions divided into 3 sections A, B, C. 2. All questions are compulsory. 3. Section A comprises of 6 questions of 2 marks each. Internal choice has been provided in two questions. 4. Section B comprises of 4 questions of 3 marks each. Internal choice has been provided in one question. 5. Section C comprises of 4 questions of 4 marks each. An internal choice has been provided in one question. It contains two case study based questions. SECTION A 1. If one root of the quadratic equation 6������2 − ������ − ������ = 0 is 2 then find the value of k. 3 OR If quadratic equation 3������2 − 4������ + ������ = 0 has equal roots, then the value of k is........... 2. If five times the fifth term of an AP is equal to eight times its eighth term, show that its 13th term is zero. 3. The fifth term of an AP is 20 and the sum of its seventh and eleventh terms is 64. Find the common difference. 4. Draw a line segment of length 7.6 cm and divide it in the ratio 5: 8. Measure the two parts. 5. A glass cylinder with radius 10 cm has water to a height of 9 cm. A metal cube of 8 cm edge is 22 7 immersed in it completely. Calculate the height by which water will rise in the cylinder. Use ������ = 6. Find the mode of the following frequency distribution Class 0-10 10-20 20-30 30-40 40-50 50-60 60-70 Frequency 8 10 10 16 12 6 7 OR For the following distribution find the sum of lower limits of the median class and modal class Class 0-5 5-10 10-15 15-20 20-25 Frequency 10 15 12 20 9 SECTION B Q7. Two men on either side of a 75 m high building and in line with base of building observe the angles of elevation of the top of the building as 30º and 60º. Find the distance between the two men. (Use √3 = 1.73) For more updates follow us at our Facebook page: https://www.facebook.com/GYAANIKEEDA915

8. Draw a line segment AB of length 7 cm. Taking A as centre, draw a circle of radius 3 cm and taking B as centre, draw another circle of radius 2 cm. Construct tangents to each circle from the centre of the other circle. 9. A hemispherical bowl of internal diameter 36 cm contains liquid is filled into 72 cylindrical bottles of diameter 6 cm. Find the height of the each bottle, if 10% liquid is wasted in this transfer. 10. The mean of the following distribution is 53. Find the missing frequency p: Class 0-20 20-40 40-60 60-80 80-100 Frequency 12 15 32 P 13 OR Find the mean for the following data: Class 24.5-29.5 29.35-34.5 34.5-39-5 39.5-44.5 44.5-49.5 49.5-54.5 54.5-59.5 Frequency 4 14 22 16 653 SECTION C 11. Amit, standing on a horizontal plane, find a bird flying at a distance of 200 m from him at an elevation of 30°. Deepak standing on the roof of a 50 m high building, find the angle of elevation of the same bird to be 45°. Amit and Deepak are on opposite sides of the bird. Find the distance of the bird from Deepak. 12. In figure O is the centre of a circle of radius 5 cm. T is a point such that OT = 13 cm and OT intersects circle at E. If AB is a tangent to the circle at E, find the length of AB , where TP and TQ are two tangents to the circle. OR In the given figure, O is the centre of the circle. Determine ∠APC , if DA and DC are tangents and ∠ADC = 50° 13. Bequests to Charity: At the time our mother left this Earth, she gave Rs 90000 to her children of birth. This we kept and each year added Rs 30000 more, as a lasting memorial from the children she bore. When Rs 4, 20,000 is thusly attained, all goes to charity that her memory be maintained. For more updates follow us at our Facebook page: https://www.facebook.com/GYAANIKEEDA915

(i) What was the balance in the sixth year? (ii) In what year was the goal of Rs 420,000 met? 14. Toll Tax: In India, for every state or national highway/expressway, a fee is charged for raising the cost incurred in constructing as well as for maintaining the roads. This fee is called toll and is a kind of tax. Once the cost of the highway is recovered, the fee is collected at a lessened rate of 40 percent, for the purpose of maintenance of the road On a particular day, National Highway Authority of India (NHAI) checked the toll tax collection of a particular toll plaza in Rajasthan. The following table shows the toll tax paid by drivers and the number of vehicles on that particular day. Toll tax (in rs.) 30-40 40-50 50-60 60-70 70-80 Number of 80 110 120 70 40 vehicles Based on the above information, answer the following questions. (i) What is the mean of toll tax received by NHAI? (ii) What is the mode of toll tax received by NHAI? ANSWER’S Q1. 2 OR ������ Q10. 28 OR 39.36 ������ Q11. 70.7 m Q12. 6.6 cm OR 115° Q3. 3 Q13. (i) 270000 Rs (ii) 11 Years Q14. Rs. 52.14 (ii) 51.67 Q5. 1.629 cm Q6. 36 OR 25 Q7. 173 Q9. 5.4 cm For more updates follow us at our Facebook page: https://www.facebook.com/GYAANIKEEDA915

Sample Paper-10 Class-X Exam 2021-2022 (Term-2) Maximum Marks: 40 Mathematics Time Allowed: 120 minutes General Instructions: 1. The question paper consists of 14 questions divided into 3 sections A, B, C. 2. All questions are compulsory. 3. Section A comprises of 6 questions of 2 marks each. Internal choice has been provided in two questions. 4. Section B comprises of 4 questions of 3 marks each. Internal choice has been provided in one question. 5. Section C comprises of 4 questions of 4 marks each. An internal choice has been provided in one question. It contains two case study based questions. SECTION A 1. The ninth term of an AP is -32 and the sum of its eleventh and thirteenth term is -94. Find the common difference of the AP OR The sum of first 20 terms of the AP 1, 4, 7, 10.... is 2. An observer, 1.7 m tall, is 20√3 m away from a tower. The angle of elevation from the eye of observer to the top of tower is 30º. Find the height of tower. 3. In the given figure, AB is a 6 m high pole and DC is a ladder inclined at an angle of 60° to the horizontal and reaches up to point D of pole. If AD = 2.54 m, find the length of ladder. (use √3 =1 .73) 4. Find the value(s) of k if the quadratic equation 3������2 − ������√3������ + 4 = 0 has real roots. 5. For what values of k, the roots of the equation ������2 + 4������ + ������ = 0 are real? 6. The data regarding marks obtained by 48 students of a class in a class test is given below. Calculate the modal marks of students. Marks 0-5 5-10 10-15 15-20 20-25 25-30 30-35 35-40 40-45 45-50 obtained 1 0 2 0 0 10 25 7 2 1 Number of students For more updates follow us at our Facebook page: https://www.facebook.com/GYAANIKEEDA915

OR If xi’s are the mid-points of the class intervals of grouped data, fi’s are the corresponding frequencies and ������̅ is the mean, then find ∑(������������������������ − ������̅) SECTION B 7. A boy, flying a kite with a string of 90 m long, which is making an angle θ with the ground. Find the height of the kite. (Given tan θ =485 ) 8. From a point P, which is at a distant of 13 cm from the centre O of a circle of radius 5 cm, the pair of tangents PQ and PR are drawn to the circle, then the area of the quadrilateral PQOR (in cm2 ). 9. Weekly income of 600 families is given below: 4000-5000 5000-6000 Income (in Rs.) 0-1000 1000-2000 2000-3000 3000-4000 15 5 No. of Families 250 190 100 40 Find the median. 10. Find the mean for the following data: Class 24.5-29.5 29.5-34.5 34.5-39.5 39.5-44.5 44.5-49.5 49.5-54.5 54.5-59.5 6 5 3 Frequency 4 14 22 16 OR Weekly income of 600 families is given below: Income (in Rs.) 0-1000 1000-2000 2000-3000 3000-4000 4000-5000 5000-6000 250 No. of Families 190 100 40 15 5 Find the median. SECTION C 11. A two digit number is such that product of its digits is 14. If 45 is added to the number, the digits interchange their places. Find the number. 12. Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm, and taking B as centre draw another circle of radius 3 cm. Construct tangents to each circle of radius centre of the other circle. OR Draw two concentric circle of radii 3 cm and 5 cm. taking a point on the outer circle, construct the pair of tangents to the inner circle. 13. Piono: Suppose you practice the piano 45 min on the first day of the semester and increase your practice time by 5 min each day. (i) How much total time will you devote to practicing during the first 15 days of the semester? (ii) How much total time will you devote to practicing during the first 35 days of the semester? For more updates follow us at our Facebook page: https://www.facebook.com/GYAANIKEEDA915

14. Advertising columns are cylindrical outdoor sidewalk structures with a characteristic style that are used for advertising and other purposes. They are common throughout Germany including its capital Berlin, where the first 100 columns were installed in 1855. Advertising columns are typically used to display advertisements in the form of posters, traditionally chiefly theatre, and cinema, nightclub, and concert announcements. Some are motorized and rotate very slowly. Rajesh has been given the task of designing a advertising column for a client. It consist of a cylindrical part surmounted by hemisphere part on top. The base diameter of column is 7 feet and height of cylindrical part is 11 feet. (i) Find the surface area of cylindrical part of column? Find the total surface area of advertising column? (ii) Find the volume of advertising column? ANSWER’S Q1. -5 OR 590 Q7. 79.41 m Q2. 21.7 m Q9. 1263.16 Q3. 4 m Q10. 39.36 OR 1263.16 Q4. ������ ≤ −������ and ������ ≥ ������ Q11. 27 Q5. ������ ≼ ������ Q13. (i) 20 hours (ii) 75 hour 50 min Q6. 32.27 approx. Q14. (i) 319 feet2 (ii) 513.33 feet3 For more updates follow us at our Facebook page: https://www.facebook.com/GYAANIKEEDA915