CBSE Maths Class 10 Sample Paper 01 PDF

Marking Scheme links are given at end of this PDF. CBSE EXAM 2025 Class : 10th Sub : Maths Standard How to see answers or marking scheme ? Go to end of this PDF. Disclaimer: These papers are based on the SQP released by CBSE and published by a private organization just...

Marking Scheme links are given at end of this PDF. CBSE EXAM 2025 Class : 10th Sub : Maths Standard How to see answers or marking scheme ? Go to end of this PDF. Disclaimer: These papers are based on the SQP released by CBSE and published by a private organization just for the practice of the students. CBSE has not released these papers and CBSE is not related to these papers in any manner. Publisher of these papers clearly state that these paeprs are only for practice of students and questions may not be come in main exam. CBSE Maths Class 10 Sample Paper 01 Page 1 Sample Paper 01 Class - 10th Exam - 2024 - 25 Mathematics - Standard Time : 3 Hours Max. Marks : 80 General Instructions : 1. This question paper contains 38 questions. 2. This Question Paper is divided into 5 Sections A, B, C, D and E. 3. In Section A, Questions no. 1-18 are multiple choice questions (MCQs) and questions no. 19 and 20 are Assertion - Reason based questions of 1 mark each. 4. In Section B, Questions no. 21-25 are very short answer (VSA) type questions, carrying 02 marks each. 5. In Section C, Questions no. 26-31 are short answer (SA) type questions, carrying 03 marks each. 6. In Section D, Questions no. 32-35 are long answer (LA) type questions, carrying 05 marks each. 7. In Section E, Questions no. 36-38 are case study based questions carrying 4 marks each with sub parts of the values of 1, 1 and 2 marks each respectively. 8. All Questions are compulsory. However, an internal choice in 2 Question of Section B, 2 Questions of Section C and 2 Questions of Section D has been provided. An internal choice has been provided in all the 2 marks questions of Section E. 9. Draw neat and clean figures wherever required. 10. Take π = 227 wherever required if not stated. 11. Use of calculators is not allowed. Section - A Section A consists of 20 questions of 1 mark each. 1. If x2 + y2 = 25 , xy = 12 , then x is (a) (3, 4) (b) (3, - 3) (c) (3, 4, - 3, - 4) (d) (3, - 3) 2. If the square of difference of the zeroes of the quadratic polynomial x2 + px + 45 is equal to 144, then the value of p is (a) ! 9 (b) ! 12 (c) ! 15 (d) ! 18 3. TABC and TBDE are two equilateral triangle such that D is the mid-point of BC. Ratio of the areas of triangles ABC and BDE is.................. (a) 1 : 4 (b) 4 : 1 (c) 1 : 3 (d) 3 : 1 4. In the adjoining figure, TP and TQ are the two tangents to a circle with centre O. If +POQ = 110c, then +PTQ is

Continue on next page..... https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install Page 2 Sample Paper 01 CBSE Maths Class 10 (a) 60c (b) 70c (c) 80c (d) 90c 5. A set of numbers consists of three 4’s, five 5’s, six 6’s, eight 8’s and seven 10’s. The mode of this set of numbers is (a) 6 (b) 7 (c) 8 (d) 10 6. TABC is an equilateral triangle with each side of length 2p. If AD = BC then the value of AD is (a) 3 (b) 3p (c) 2p (d) 4p 7. The quadratic equation x2 − 4x − 3 2 = 0 has (a) two distinct real roots (b) two equal real roots (c) no real roots (d) more than 2 real roots 8. From an external point P , tangents PA and PB are drawn to a circle with centre O. If CD is the tangent to the circle at a point E and PA = 14 cm. The perimeter of TPCD is (a) 14 cm (b) 21 cm (c) 28 cm (d) 35 cm 9. (cos 4 A - sin 4 A) is equal to (a) 1 - 2 cos2 A (b) 2 sin2 A - 1 (c) sin2 A - cos2 A (d) 2 cos2 A - 1 10. An observer, 1.5 m tall is 20.5 away from a tower 22 m high, then the angle of elevation of the top of the tower from the eye of observer is (a) 30c (b) 45c (c) 60c (d) 90c 11. Which of the following relationship is the correct? (a) P (E ) + P (E ) = 1 (b) P (E ) − P (E ) = 1 (c) P (E ) = 1 + P (E ) (d) None of these

Continue on next page..... https://qrbook.page.link/appInstall NODIA App to See the Solutions. Click Here To Install CBSE Maths Class 10 Sample Paper 01 Page 3 12. The pair of equations x = a and y = b graphically represents lines which are (a) parallel (b) intersecting at (b, a) (c) coincident (d) intersecting at (a, b) 13. A tree casts a shadow 15 m long on the level of ground, when the angle of elevation of the sun is 45c. The height of a tree is (a) 10 m (b) 14 m (c) 8 m (d) 15 m 14. From a solid circular cylinder with height 10 cm and radius of the base 6 cm, a right circular cone of the same height and same base is removed, then the volume of remaining solid is (a) 280 πcm3 (b) 330 πcm3 (c) 240 πcm3 (d) 440 π cm3 15. If median is 137 and mean is 137.05, then the value of mode is (a) 156.90 (b) 136.90 (c) 186.90 (d) 206.90 16. If the circumference of a circle increases from 4 π to 8 π , then its area is (a) halved (b) doubled (c) tripled (d) quadrupled 17. A chord of a circle of radius 10 cm, subtends a right angle at its centre. The length of the chord (in cm) is (a) 5 (b) 5 2 2 (c) 10 2 (d) 10 3 18. If a number x is chosen at random from the numbers - 2, - 1, 0, 1, 2. Then, the probability that x2 1 2 is (a) 2 (b) 4 5 5 (c) 1 (d) 3 5 5 19. Assertion : The value of sin θ = 43 is not possible. Reason : Hypotenuse is the largest side in any right angled triangle. (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). (c) Assertion (A) is true but reason (R) is false. (d) Assertion (A) is false but reason (R) is true.

Continue on next page..... https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install Page 4 Sample Paper 01 CBSE Maths Class 10 20. Assertion : an - an - 1 is not independent of n then the given sequence is an AP. Reason : Common difference d = an − an − 1 is constant or independent of n. (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). (c) Assertion (A) is true but reason (R) is false. (d) Assertion (A) is false but reason (R) is true. Section - B Section B consists of 5 questions of 2 marks each. 21. Find the ratio in which the point ^- 3, k h divides the line segment joining the points ^- 5, - 4h and ^- 2, 3h. Also find the value of k. 22. From an external point P , tangents PA and PB are drawn to a circle with centre O. If +PAB = 50º, then find +AOB. 23. Write a rational number between 2 and 3. 24. Find the 7th term from the end of AP 7, 10, 13,.... 184.

O The fourth term of an AP is 11. The sum of the fifth and seventh terms of the AP is 34. Find the common difference. 25. How many two digits numbers are divisible by 3? Section - C Section C consists of 6 questions of 3 marks each. 26. Two dice are tossed simultaneously. Find the probability of getting (i) an even number on both dice. (ii) the sum of two numbers more than 9. 27. An electric pole is 10 m high. A steel wire tied to top of the pole is affixed at a point on the ground to keep the pole up right. If the wire makes an angle of 45º with the horizontal through the foot of the pole, find the length of the wire. [Use 2 = 1.414 ] 28. Solve for x : 1 − 1 = 11 x !- 4, - 7. x+4 x+7 30 29. Prove that the rectangle circumscribing a circle is a square.

O If O is centre of a circle, PQ is a chord and the tangent PR at P makes an angle of 50c with PQ , find +POQ. https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install CBSE Maths Class 10 Sample Paper 01 Page 5 30. From a solid right circular cylinder of height 14 cm and base radius 6 cm, a right circular cone of same height and same base removed. Find the volume of the remaining solid.

O A metallic cylinder has radius 3 cm and height 5 cm. To reduce its weights, a conical hole is drilled in the cylinder. The conical hole has a radius of 32 cm and its depth 89 cm. Calculate the ratio of the volume of metal left in the cylinder to the volume of metal taken out in conical shape. 31. A fraction becomes 13 when 2 is subtracted from the numerator and it becomes 1 2 when 1 is subtracted from the denominator- Find the fraction. Section - D Section D consists of 4 questions of 5 marks each. 32. In Figure, a square OABC is inscribed in a quadrant OPBQ. If OA = 15 cm , find the area of the shaded region. (Use π = 3.14 ). 33. Find the zeroes of the quadratic polynomial 7y2 - 113 y - 23 and verify the relationship between the zeroes and the coefficients.

O 2 If α and β are the zeroes the polynomial 2x − 4x + 5, find the values of (i) α2 + β2 (ii) 1 + 1 α β (iii) ^α − βh2 (iv) 12 + 12 α β (v) α2 + β2 https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install Page 6 Sample Paper 01 CBSE Maths Class 10 34. In TABC, AD is a median and O is any point on AD. BO and CO on producing meet AC and AB at E and F respectively. Now AD is produced to X such that OD = DX as shown in figure. Prove that : (1) EF || BC (2) AO : AX = AF : AB 35. If sin A = 3 calculate sec A. 4

O Evaluate : 4 ^sin 4 30º + cos 4 60ºh − 3 ^cos2 45 − sin2 90ºh Section - E Section E consists of 3 case study based questions of 4 marks each. 36. Heart Rate : The heart rate is one of the ‘vital signs,’ or the important indicators of health in the human body. It measures the number of times per minute that the heart contracts or beats. The speed of the heartbeat varies as a result of physical activity, threats to safety, and emotional responses. The resting heart rate refers to the heart rate when a person is relaxed. While a normal heart rate does not guarantee that a person is free of health problems, it is a useful benchmark for identifying a range of health issues. After the age of 10 years, the heart rate of a person should be between 60 and 100 beats per minute while they are resting. Thirty women were examined by doctors of AIIMS and the number of heart beats per minute were recorded and summarised as follows. https://qrbook.page.link/appInstall NODIA App to See the Solutions. Click Here To Install CBSE Maths Class 10 Sample Paper 01 Page 7 Number of heart beats per minute Number of women ^ f ih 65-68 2 68-71 4 71-74 3 74-77 8 77-80 7 80-83 4 83-86 2 Based on the above information, answer the following questions. (i) What is the mean heart beats per minute for these women ? (ii) What is the upper limit of median value of heart beats per minute for these women ? (iii) What is the lower limit of mode value of heart beats per minute for these women ?

O How many women are having heart beat in range 68-77? 37. Volume of a Bird Cage. A company makes rectangular shaped bird cages with height b inches and square bottoms. The volume of these cages is given by the function V = b 3 − 6b2 + 9b. (i) Find an expression for the length of each side of the square bottom. (ii) Use the function to find the volume of a cage with a height of 18 inches. (iii) Use the remainder theorem to find the volume of a cage with a height of 15 inches. https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install Page 8 Sample Paper 01 CBSE Maths Class 10 38. Morning assembly is an integral part of the school’s schedule. Almost all the schools conduct morning assemblies which include prayers, information of latest happenings, inspiring thoughts, speech, national anthem, etc. A good school is always particular about their morning assembly schedule. Morning assembly is important for a child’s development. It is essential to understand that morning assembly is not just about standing in long queues and singing prayers or national anthem, but it’s something beyond just prayers. All the activities carried out in morning assembly by the school staff and students have a great influence in every point of life. The positive effects of attending school assemblies can be felt throughout life. Have you noticed that in school assembly you always stand in row and column and this make a coordinate system. Suppose a school have 100 students and they all assemble in prayer in 10 rows as given below. Here A, B, C and D are four friend Amar, Bharat, Colin and Dravid. (i) What is the distance between A and B ? (ii) What is the distance between C and D ? (iii) What is the distance between A and C ?

O What is the distance between D and B ?

****** https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install CBSE Maths Class 10 Sample Paper 02 Page 1 Sample Paper 02 Class - 10th Exam - 2024 - 25 Mathematics - Standard Time : 3 Hours Max. Marks : 80 General Instructions : 1. This question paper contains 38 questions. 2. This Question Paper is divided into 5 Sections A, B, C, D and E. 3. In Section A, Questions no. 1-18 are multiple choice questions (MCQs) and questions no. 19 and 20 are Assertion - Reason based questions of 1 mark each. 4. In Section B, Questions no. 21-25 are very short answer (VSA) type questions, carrying 02 marks each. 5. In Section C, Questions no. 26-31 are short answer (SA) type questions, carrying 03 marks each. 6. In Section D, Questions no. 32-35 are long answer (LA) type questions, carrying 05 marks each. 7. In Section E, Questions no. 36-38 are case study based questions carrying 4 marks each with sub parts of the values of 1, 1 and 2 marks each respectively. 8. All Questions are compulsory. However, an internal choice in 2 Question of Section B, 2 Questions of Section C and 2 Questions of Section D has been provided. An internal choice has been provided in all the 2 marks questions of Section E. 9. Draw neat and clean figures wherever required. 10. Take π = 227 wherever required if not stated. 11. Use of calculators is not allowed. Section - A Section A consists of 20 questions of 1 mark each. 1. If α and β are the roots of ax2 − bx + c = 0 (a ! 0), then value of α + β is (a) b (b) a a b (c) 2a (d) a b 2b 2. What are the values of x and y for the following pair of linear equations ? 99x + 101y = 499 and 101x + 99y = 501 (a) 3 and 6 (b) 3 and 2 (c) 2 and 3 (d) 6 and 3 3. The zeroes of polynomial p ^x h = ax2 + bx + c are reciprocal of each other if (a) b = 2a (b) c = b (c) b = a (d) c = a 4. If - 1 is a zero of the polynomial p ^x h = kx2 − 4x + k, the value of k is (a) –4 (b) –2 (c) 2 (d) 4 https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install Page 2 Sample Paper 02 CBSE Maths Class 10 5. If a number x is chosen at random from the numbers - 3 , - 2 , - 1. 0, 1, 2, 3, then What is the probability of x2 < 4 ? (a) 4 (b) 3 7 7 (c) 1 (d) 2 7 7 6. Which of the following value of k should be selected so that the pair of equations x + 2y = 5 and 3x + ky + 15 = 0 has a unique solution ? (a) k ! 5 (b) k ! 6 (c) k = 5 (d) k = 6 7. The quadratic equation x2 + 3x + 2 2 = 0 has (a) two distinct real roots (b) two equal real roots (c) no real roots (d) more than 2 real roots 8. A ladder 10 m long reaches a window 8 m above the ground. The distance of the foot of the ladder from the base of the wall is................ m. (a) 8 m (b) 2 m (c) 6 m (d) 4 m 9. The value of x for which 2x, (x + 10) and (3x + 2) are the three consecutive terms of an AP, is (a) 6 (b) - 6 (c) 18 (d) - 18 10. If points A (- 3, 12), B (7, 6) and C (x, 9) are collinear, then the value of x is.......... (a) 2 (b) 3 (c) 4 (d) 5 11. If the sum of the circumferences of two circles with radii R1 and R2 is equal to the circumference of a circle of radius R , then (a) R1 + R2 = R (b) R1 + R2 > R (c) R1 + R2 > R (d) R1 + R2 < R 12. The value of sin2 41º + sin2 49º will be (a) 1 (b) 2 (c) 2 (d) 3 13. The number 7 will have - 75 (a) non-terminating repeating decimal expansion. (b) terminating decimal expansion. (c) non-terminating non repeating decimal expansion. (d) terminating non repeating decimal expansion https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install CBSE Maths Class 10 Sample Paper 02 Page 3 14. A tree casts a shadow 15 m long on the level of ground, when the angle of elevation of the sun is 45c. The height of a tree is (a) 10 m (b) 14 m (c) 8 m (d) 15 m 15. The famous mathematician associated with finding the sum of the first 100 natural numbers is (a) Pythagoras (b) Newton (c) Gauss (d) Euclid 16. If the perimeter of one face of a cube is 20 cm, then its surface area is (a) 120 cm2 (b) 150 cm2 (c) 125 cm2 (d) 400 cm2 17. sin2 60c − 2 tan 45c − cos2 30c = ? (a) 2 (b) –2 (c) 1 (d) –1 18. If xi ’s are the mid-points of the class intervals of grouped data, f i ’s are the corresponding frequencies and x is the mean, then / (f i xi - x ) is equal to (a) 0 (b) - 1 (c) 1 (d) 2 19. Assertion : The two tangents are drawn to a circle from an external point, then they subtend equal angles at the centre. Reason : A parallelogram circumscribing a circle is a rhombus. (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). (c) Assertion (A) is true but reason (R) is false. (d) Assertion (A) is false but reason (R) is true. 20. Assertion : The values of x are - a , a for a quadratic equation 2x2 + ax − a2 = 0. 2 Reason : For quadratic equation ax2 + bx + c = 0 2 x = − b ! b − 4ac 2a (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). (c) Assertion (A) is true but reason (R) is false. (d) Assertion (A) is false but reason (R) is true. https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install Page 4 Sample Paper 02 CBSE Maths Class 10 Section - B Section B consists of 5 questions of 2 marks each. 21. The mid-point of the line-segment AB is P (0, 4), if the coordinates of B are (- 2, 3) then find the co- ordinates of A. 22. Two different dice are tossed together. Find the probability : (i) that the number on each die is even. (ii) that the sum of numbers appearing on the two dice is 5. 23. Given that HCF (306, 1314) = 18. Find LCM (306, 1314). 24. If α and β are the zeroes of a polynomial x2 − 4 3 x + 3, then find the value of α + β − αβ.

O If one of the zeroes of the quadratic polynomial f ^x h = 14x2 − 42k2 x − 9 is negative of the other, find the value of ‘k ’. 25. In the given figure, G is the mid-point of the side PQ of TPQR and GH || QR. Prove that H is the mid- point of the side PR or the triangle PQR.

O In the figure of TABC, the points D and E are on the sides CA, CB respectively such that DE || AB, AD = 2x, DC = x + 3, BE = 2x − 1 and CE = x. Then, find x. https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install CBSE Maths Class 10 Sample Paper 02 Page 5 Section - C Section C consists of 6 questions of 3 marks each. 26. Evaluate : 3 tan2 30º + tan2 60º + cosec 30º − tan 45º cot2 45º 27. Prove that the rectangle circumscribing a circle is a square. 28. A solid is in the shape of a cone surmounted on a hemisphere. The radius of each of them being 3.5 cm and the total height of the solid is 9.5 cm. Find the volume of the solid.

O A heap of rice is in the form of a cone of base diameter 24 m and height 3.5 m. Find the volume of the rice. How much canvas cloth is required to just cover the heap? 29. Write the smallest number which is divisible by both 306 and 657. 30. The mean of the following distribution is 48 and sum of all the frequency is 50. Find the missing frequencies x and y. Class 20-30 30-40 40-50 50-60 60-70 Frequency 8 6 x 11 y

O The table below shows the daily expenditure on food of 25 households in a locality. Find the mean daily expenditure on food. Daily expenditure (in R (c) R1 + R2 > R (d) R1 + R2 < R

Continue on next page..... https://qrbook.page.link/appInstall NODIA App to See the Solutions. Click Here To Install CBSE Maths Class 10 Sample Paper 04 Page 3 13. In the given figure, if +A = 90º, +B = 90º, OB = 4.5 cm OA = 6 cm and AP = 4 cm then find QB. (a) 3 cm (b) 6 cm (c) 4.5 cm (d) 3.5 cm 14. Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is (a) 4 cm (b) 3 cm (c) 2 cm (d) 6 cm 15. Consider the following frequency distribution Class 0-5 6-11 12-17 18-23 24-29 Frequency 13 10 15 8 11 The upper limit of the median class is (a) 17 (b) 17.5 (c) 18 (d) 18.5 16. The probability that a number selected at random from the numbers 1, 2, 3,......, 15 is a multiple of 4 is (a) 4 (b) 2 15 15 (c) 1 (d) 1 15 5 17. The zeroes of the quadratic polynomial x2 + kx + k where k ! 0 , (a) cannot both be positive (b) cannot both be negative (c) are always unequal (d) are always equal 18. If the point P (6, 2) divides the line segment joining A (6, 5) and B (4, y) in the ratio 3 : 1 then the value of y is (a) 4 (b) 3 (c) 2 (d) 1

Continue on next page..... https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install Page 4 Sample Paper 04 CBSE Maths Class 10 19. Assertion : The value of sec2 10c - cot2 80c is 1. Reason : The value of sin 30c = 12. (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). (c) Assertion (A) is true but reason (R) is false. (d) Assertion (A) is false but reason (R) is true. 20. Assertion : x3 + x has only one real zero. Reason : A polynomial of n th degree must have n real zeroes. (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). (c) Assertion (A) is true but reason (R) is false. (d) Assertion (A) is false but reason (R) is true. Section - B Section B consists of 5 questions of 2 marks each. 21. In the given figure, BOA is a diameter of a circle and the tangent at a point P meets BA when produced at T. If +PBO = 30º , what is the measure of +PTA ? 22. A bag contains 5 red, 8 green and 7 white balls. One ball is drawn at random from the bag, find the probability of getting : (i) not a white ball, (ii) neither a green nor a red ball.

O Two coins are tossed together. Find the probability of getting both heads or both tails. 23. If tan 2A = cot (A − 18c), where 2A is an acute angle, find the value of A. 24. In TABC, AD = BC, such that AD2 = BD # CD. Prove that TABC is right angled at A.

O In the figure of TABC, the points D and E are on the sides CA, CB respectively such that DE || AB, AD = 2x, DC = x + 3, BE = 2x − 1 and CE = x. Then, find x. https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install CBSE Maths Class 10 Sample Paper 04 Page 5

O In the figure of TABC, DE || AB. If AD = 2x, DC = x + 3, BE = 2x − 1 and CE = x, then find the value of x. 25. In the given figure, TABC ~TPQR. Find the value of y + z. Section - C Section C consists of 6 questions of 3 marks each. 26. The 34 th part of a conical vessel of internal radius 5 cm and height 24 cm is full of water. The water emptied into a cylindrical vessel with internal radius 10 cm. Find the height of water in cylindrical vessel. 27. Find a quadratic polynomial whose zeroes are reciprocals of the zeroes of the polynomial f (x) = ax2 + bx + c , a ! 0, c ! 0.

Continue on next page..... https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install Page 6 Sample Paper 04 CBSE Maths Class 10 28. Two right triangles ABC and DBC are drawn on the same hypotenuse BC and on the same side of BC. If AC and BD intersect at P , prove that AP # PC = BP # DP.

O In the given figure, two triangles ABC and DBC lie on the same side of BC such that PQ || BA and PR || BD. Prove that QR || AD. 29. The rod of TV disc antenna is fixed at right angles to wall AB and a rod CD is supporting the disc as shown in Figure. If AC = 1.5 m long and CD = 3 m , Find (i) tan θ (ii) sec θ + cosec θ. 30. A vessel is in the form of a hemispherical bowl surmounted by a hollow cylinder of same diameter. The diameter of the hemispherical bowl is 14 cm and the total height of the vessel is 13 cm. Find the total surface area of the vessel. Use π = 227

O A sphere of diameter 12 cm, is dropped in a right circular cylindrical vessel, partly filled with water. If the sphere is completely submerged in water, the water level into the cylindrical vessel rises by 3 5 cm. Find 9 the diameter of the cylindrical vessel. 31. Solve the following pair of linear equations : 8x + 5y = 9 3x + 2y = 4

Continue on next page..... https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install CBSE Maths Class 10 Sample Paper 04 Page 7 Section - D Section D consists of 4 questions of 5 marks each. Solve for x : b 2x l + b 2x l − 24 = 0, x ! 5 2 32. x−5 x−5

O Solve for x : x + 3 − 1 − x = 17 ; x ! 0, 2 x−2 x 4 33. To conduct Sports Day activities, in your rectangular school ground ABCD , lines have been drawn with chalk powder at a distance of 1 m each. 100 flower pots have been placed at a distance of 1 m from each other along AD , as shown in Figure. Niharika runs ¼th the distance AD on the 2nd line and posts a green flag. Preet runs 15 th distance AD on the eighth line and posts a red flag. (i) What is the distance between the two flags? (ii) If Rashmi has to post a blue flag exactly half way between the line segment joining the two flags, where should she post the blue flag? 34. If the angle between two tangents drawn from an external point P to a circle of radius a and centre O, is 60º, then find the length of OP. 35. The median of the following data is 525. Find the values of x and y , if total frequency is 100 : Class Frequency 0-100 2 100-200 5 200-300 x 300-400 12 https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install Page 8 Sample Paper 04 CBSE Maths Class 10 Class Frequency 400-500 17 500-600 20 600-700 y 700-800 9 800-900 7 900-1000 4

O On annual day of a school, 400 students participated in the function. Frequency distribution showing their ages is as shown in the following table : Ages (in years) 05-07 07-09 09-11 11-13 13-15 15-17 17-19 Number of students 70 120 32 100 45 28 5 Find mean and median of the above data. Section - E Section E consists of 3 case study based questions of 4 marks each. 36. Box : For the box to satisfy certain requirements, its length must be three unit greater than the width, and its height must be two unit less than the width. (i) If width is taken as x , find the polynomial that represent volume of box. (ii) Find the polynomial that represent the area of paper sheet used to make box. (iii) If it must have a volume of 18 unit, what must be its length and height ?

O (iv) If box is made of a paper sheet which cost is Rs 100 per square unit, what is the cost of paper? 37. MASK : Masks are an additional step to help prevent people from getting and spreading COVID-19. They provide a barrier that keeps respiratory droplets from spreading. Wear a mask and take every day preventive actions in public settings.

Continue on next page..... https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install CBSE Maths Class 10 Sample Paper 04 Page 9 Due to ongoing Corona virus outbreak, Wellness Medical store has started selling masks of decent quality. The store is selling two types of masks currently type A and type B. The cost of type A mask is `15 and of type B mask is` 20. In the month of April, 2020, the store sold 100 masks for total sales of ` 1650. (i) How many masks of each type were sold in the month of April? If the store had sold 50 masks of each type, what would be its sales in the month of April? (ii) Due to great demand and short supply, the store has increased the price of each type by ` 5 from May 1, 2020. In the month of May, 2020, the store sold 310 masks for total sales of ` 6875. How many masks of each type were sold in the month of May? (iii) What percent of masks of each type sale was increased in the month of May, compared with the sale of month April?

O (iv) What extra profit did store earn by increasing price in May month. 38. 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. https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install Page 10 Sample Paper 04 CBSE Maths Class 10 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, what is the surface area need to be painted ? (ii) If its conical part is to be painted blue, what is the surface area need to be painted ? (iii) How much of the wood have been used in making the toy ?

O (iv) If the cost of painting the toy is 2 paise for 8π mm2 , then what is the cost of painting of a box of 100 toys?

****** https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install CBSE Maths Class 10 Sample Paper 05 Page 1 Sample Paper 05 Class - 10th Exam - 2024 - 25 Mathematics - Standard Time : 3 Hours Max. Marks : 80 General Instructions : 1. This question paper contains 38 questions. 2. This Question Paper is divided into 5 Sections A, B, C, D and E. 3. In Section A, Questions no. 1-18 are multiple choice questions (MCQs) and questions no. 19 and 20 are Assertion - Reason based questions of 1 mark each. 4. In Section B, Questions no. 21-25 are very short answer (VSA) type questions, carrying 02 marks each. 5. In Section C, Questions no. 26-31 are short answer (SA) type questions, carrying 03 marks each. 6. In Section D, Questions no. 32-35 are long answer (LA) type questions, carrying 05 marks each. 7. In Section E, Questions no. 36-38 are case study based questions carrying 4 marks each with sub parts of the values of 1, 1 and 2 marks each respectively. 8. All Questions are compulsory. However, an internal choice in 2 Question of Section B, 2 Questions of Section C and 2 Questions of Section D has been provided. An internal choice has been provided in all the 2 marks questions of Section E. 9. Draw neat and clean figures wherever required. 10. Take π = 227 wherever required if not stated. 11. Use of calculators is not allowed. Section - A Section A consists of 20 questions of 1 mark each. 1. In an AP, if a = 3.5 , d = 0 and n = 101, then an will be (a) 0 (b) 3.5 (c) 103.5 (d) 104.5 2. There are 30 cards of the same size in a bag in which the numbers 1 to 30 are written. One card is taken out of the bag at random. What is the probability that the number on the selected card is not divisible by 3? (a) 1 (b) 2 15 3 (c) 1 (d) 1 10 3 3. If the mid-point of the line segment joining the points A (3, 4) and B (k, 6) is P (x, y) and x + y − 10 = 0 , the value of k will be (a) 4 (b) 5 (c) 6 (d) 7
Continue
on next page..... https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install Page 2 Sample Paper 05 CBSE Maths Class 10 4. In the given factor tree what is the composite number x ? (a) 65 (b) 585 (c) 130 (d) 195 5. A tree is broken by the wind. The top struck the ground at an angle of 30c and at distance of 10 m from its root. The whole height of the tree is ( 3 = 1.732) (a) 10 3 m (b) 3 10 m (c) 20 3 m (d) 3 20 m 6. If the equations kx − 2y = 3 and 3x + y = 5 represent two intersecting lines at unique point, then the value of k is............ (a) k =− 6 (b) k !- 6 (c) k = 4 (d) k ! 4 7. What do you say about the lines represented by ? 2x + 3y − 9 = 0 and 4x + 6y − 18 = 0 (a) lines are parallel (b) lines are coincident (c) lines are intersecting (d) can’t say anything 8. What are the values of x and y for the following system of equations. 21 + 47 = 110 , 47 + 21 = 162 , x , y ! 0 x y x y (a) 13 and 12 (b) 13 and 1 1 1 1 (c) 2 and 3 (d) 2 and 1 9. The zeroes of the polynomial p ^x h = 4x2 − 12x + 9 will be (a) 32 and 32 (b) 2 3 and 1 3 2 1 1 1 (c) 3 and 3 (d) 3 and 3 10. The quadratic equation x2 − 4x − 3 2 = 0 has (a) two distinct real roots (b) two equal real roots (c) no real roots (d) more than 2 real roots https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install CBSE Maths Class 10 Sample Paper 05 Page 3 11. The quadratic equation x2 + 4x − 3 2 = 0 has (a) two distinct real roots (b) two equal real roots (c) no real roots (d) more than 2 real roots 12. Two concentric circles are of radii 10 cm and 8 cm, then the length of the chord of the larger circle which touches the smaller circle is (a) 6 cm (b) 12 cm (c) 18 cm (d) 9 cm ar (TABC) 13. If TABC + TPQR , and AB = 1 , then =? PQ 3 ar (TPQR) (a) 1 (b) 1 3 9 (c) 8 (d) 5 9 9 14. If sec θ $ sin θ = 0 , then value of θ will be (a) 0 (b) 90º (c) 45º (d) 3 15. tan 4 θ + tan2 θ = ? (a) sec2 q - 2 sec 4 q (b) 2 sec2 q - sec 4 q (c) sec2 q - sec 4 q (d) sec 4 q - sec2 q 16. Ratio of volumes of two cylinders with equal height is (a) H : h (b) R : r (c) R2 : r2 (d) None of these 17. Which of the following are the zeroes of the polynomial p ^x h = 2x3 − 11x2 + 17x − 6. (a) 2 (b) 3 (c) 12 (d) Above all 18. Consider the following frequency distribution Class 0-5 6-11 12-17 18-23 24-29 Frequency 13 10 15 8 11 The upper limit of the median class is (a) 17 (b) 17.5 (c) 18 (d) 18.5 19. Assertion : If the circumference of a circle is 176 cm, then its radius is 28 cm. Reason : Circumference = 2π # radius (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). (c) Assertion (A) is true but reason (R) is false. (d) Assertion (A) is false but reason (R) is true. https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install Page 4 Sample Paper 05 CBSE Maths Class 10 20. Assertion : Common difference of the AP - 5 , - 1 , 3, 7,.......... is 4. Reason : Common difference of the AP a, a + d, a + 2d,.......... is given by d = a2 − a1 (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). (c) Assertion (A) is true but reason (R) is false. (d) Assertion (A) is false but reason (R) is true. Section - B Section B consists of 5 questions of 2 marks each. 21. A bag contains 3 red, 4 green and 5 white candles, one candle is drawn at random from the bag, find the probability that candle is not red. 22. Find the sum of first ten multiple of 5.

O If the sum of n terms of an AP is 2n2 + 5n, then find the 4th term. 23. If the points A (4, 3) and B (x, 5) are on the circle with centre O (2, 3), then what is the value of x ? 24. From an external point Q , the length of tangent to a circle is 12 cm and the distance of Q from the centre of circle is 13 cm. What is the radius of circle?

O QP is a tangent to a circle with centre O at a point P on the circle. If TOPQ is isosceles, then find +OQR ? 25. Show that 5 6 is an irrational number. Section - C Section C consists of 6 questions of 3 marks each. 26. Prove that : 1 − cos A = cosec A − cot A 1 + cos A 27. In TABC, if X and Y are points on AB and AC respectively such that AX XB = 34 , AY = 5 and YC = 9, then state whether XY and BC parallel or not.
Continue
on next page..... https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install CBSE Maths Class 10 Sample Paper 05 Page 5 28. In figure, two tangents TP and TQ are drawn to circle with centre O from an external point T. Prove that +PTQ = 2+OPQ. 29. A road which is 7 m wide surrounds a circular park whose circumference is 88 m. Find the area of the road.

O Three horses are tied each with 7 m long rope at three corners of a triangular field having sides 20 m, 34 m and 42 m. Find the area of the plot which can be grazed by the horses. 30. Find HCF and LCM of 16 and 36 by prime factorization and check your answer. 31. An integer is chosen between 70 and 100. Find the probability that it is (i) a prime number (ii) divisible by 7

O Find the probability that 5 Sundays occur in the month of November of a randomly selected year. Section - D Section D consists of 4 questions of 5 marks each. 32. Show that the points ^a, a h , ^- a, - a h and `- 3 a, 3 a j are the vertices of an equilateral triangle. 33. Determine graphically the coordinates of the vertices of triangle, the equations of whose sides are given by 2y − x = 8 , 5y − x = 14 and y − 2x = 1.

O Aftab tells his daughter, ‘7 years ago, I was seven times as old as you were then. Also, 3 years from now, I shall be three times as old as you will be.’ Represent this situation algebraically and graphically. 34. In the given figure, DEFG is a square and +BAC = 90c. Show that FG2 = BG # FC.

Continue on next page..... https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install Page 6 Sample Paper 05 CBSE Maths Class 10

O In Figure, if TABC + TDEF and their sides of lengths (in cm) are marked along them, then find the lengths of sides of each triangle. 35. A toy is in the form of a cylinder of diameter 2 2 m and height 3.5 m surmounted by a cone whose vertical angle is 90c. Find total surface area of the toy. Section - E Section E consists of 3 case study based questions of 4 marks each. 36. John and Priya went for a small picnic. After having their lunch Priya insisted to travel in a motor boat. The speed of the motor boat was 20 km/hr. Priya being a Mathematics student wanted to know the speed of the current. So she noted the time for upstream and downstream. She found that for covering the distance of 15 km the boat took 1 hour more for upstream than downstream. (i) Let speed of the current be x km/hr. What will be the speed of the motorboat in upstream ? What is the relation between speed distance and time? (ii) Write the correct quadratic equation for the speed of the current ? (iii) What is the speed of current ? How much time boat took in downstream ? https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install CBSE Maths Class 10 Sample Paper 05 Page 7 37. 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 (km/charge) 100-120 120-140 140-160 160-180 Number of scooters 7 12 18 13 Based on the above information, answer the following questions. (i) What is the average mileage. (ii) What is the modal value of mileage ? (iii) What is the median value of mileage ? (iv) What about the mileage can be claimed by the manufacturer for his scooter ? 38. Height of a Climber : Himalayan Trekking Club has just hiked to the south rim of a large canyon, when they spot a climber attempting to scale the taller northern face. Knowing the distance between the sheer walls of the northern and southern faces of the canyon is approximately 150 meter, they attempt to compute the distance remaining for the climbers to reach the top of the northern rim. https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install Page 8 Sample Paper 05 CBSE Maths Class 10 Using a homemade transit, they sight an angle of depression of 60c to the bottom of the north face, and angles of elevation of 30c and 45c to the climbers and top of the northern rim respectively. (i) How high is the southern rim of the canyon? (ii) How high is the northern rim? (iii) How much farther until the climber reaches the top?

****** https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install CBSE Maths Class 10 Sample Paper 06 Page 1 Sample Paper 06 Class - 10th Exam - 2024 - 25 Mathematics - Standard Time : 3 Hours Max. Marks : 80 General Instructions : 1. This question paper contains 38 questions. 2. This Question Paper is divided into 5 Sections A, B, C, D and E. 3. In Section A, Questions no. 1-18 are multiple choice questions (MCQs) and questions no. 19 and 20 are Assertion - Reason based questions of 1 mark each. 4. In Section B, Questions no. 21-25 are very short answer (VSA) type questions, carrying 02 marks each. 5. In Section C, Questions no. 26-31 are short answer (SA) type questions, carrying 03 marks each. 6. In Section D, Questions no. 32-35 are long answer (LA) type questions, carrying 05 marks each. 7. In Section E, Questions no. 36-38 are case study based questions carrying 4 marks each with sub parts of the values of 1, 1 and 2 marks each respectively. 8. All Questions are compulsory. However, an internal choice in 2 Question of Section B, 2 Questions of Section C and 2 Questions of Section D has been provided. An internal choice has been provided in all the 2 marks questions of Section E. 9. Draw neat and clean figures wherever required. 10. Take π = 227 wherever required if not stated. 11. Use of calculators is not allowed. Section - A Section A consists of 20 questions of 1 mark each. 1. The quadratic polynomial, the sum of whose zeroes is - 5 and their product is 6, is (a) x2 + 5x + 6 (b) x2 − 5x + 6 (c) x2 - 5x - 6 (d) − x2 + 5x + 6 2. The base radii of a cone and a cylinder are equal. If their curved surface areas are also equal, then the ratio of the slant height of the cone to the height of the cylinder is (a) 2 : 1 (b) 1 : 2 (c) 1 : 3 (d) 3 : 1 3. A single letter is selected at random from the word PROBABILITY. The probability that the selected letter is a vowel is (a) 2 (b) 3 11 11 (c) 4 (d) 0 11 4. The probability expressed as a percentage of a particular occurrence can never be (a) less than 100 (b) less than 0 (c) greater than 1 (d) anything but a whole number https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install Page 2 Sample Paper 06 CBSE Maths Class 10 5. The value of k for which the system of linear equations x + 2y = 3 , 5x + ky + 7 = 0 is inconsistent is (a) - 14 (b) 2 3 5 (c) 5 (d) 10 6. The quadratic equation 2x2 − 5 x + 1 = 0 has (a) two distinct real roots (b) two equal real roots (c) no real roots (d) more than 2 real roots 7. The first four terms of an AP whose first term is - 2 and the common difference is - 2 are (a) - 2, 0, 2, 4 (b) - 2, 4, - 8, 16 (c) - 2, - 4, - 6, - 8 (d) - 2, - 4, - 8, - 16 8. In the given figure, if +A = 90º, +B = 90º, OB = 4.5 cm, OA = 6 cm and AP = 4 cm then find QB. (a) 3 cm (b) 6 cm (c) 4.5 cm (d) 3.5 cm 9. In Figure, in TABC , DE z BC such that AD = 2.4 cm, AB = 3.2 cm and AC = 8 cm, then what is the length of AE ? (a) 4 cm (b) 6 cm (c) 8 cm (d) 3 cm

Continue on next page..... https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install CBSE Maths Class 10 Sample Paper 06 Page 3 10. For the following distribution. Class 0-5 5-10 10-15 15-20 20-25 Frequency 10 15 12 20 9 the sum of lower limits of the median class and modal class is (a) 15 (b) 25 (c) 30 (d) 35 11. If TABC is right angled at C , then the value of cos ^A + B h is (a) 0 (b) 1 (c) 1 (d) 3 2 2 12. A pole casts a shadow of length 2 3 m on the ground, when the Sun’s elevation is 60º. Find the height of the pole. (a) 4 m (b) 6 m (c) 2 m (d) 3 m 13. The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters 36 cm and 20 cm is (a) 56 cm (b) 42 cm (c) 28 cm (d) 16 cm 14. The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 2 mm. The length of the wire is (a) 12 m (b) 18 m (c) 36 m (d) 66 m 15. The mean weight of 9 students is 25 kg. If one more student is joined in the group the mean is unaltered, then the weight of the 10th student is (a) 25 kg (b) 24 kg (c) 26 kg (d) 23 kg 16. In the adjoining figure, TP and TQ are the two tangents to a circle with centre O. If +POQ = 110c, then +PTQ is https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install Page 4 Sample Paper 06 CBSE Maths Class 10 (a) 60c (b) 70c (c) 80c (d) 90c 17. 2 3 is (a) an integer (b) a rational number (c) an irrational number (d) a whole number 18. If A ^ m3 , 5h is the mid-point of the line segment joining the points Q (- 6, 7) and R (- 2, 3), then the value of m is (a) - 12 (b) - 4 (c) 12 (d) - 6 19. Assertion : In the figure, if BC = 20 m , then height AB is 11.56 m. perpendicular Reason : tan θ = AB = where θ is the angle +ACB. BC base (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). (c) Assertion (A) is true but reason (R) is false. (d) Assertion (A) is false but reason (R) is true. 20. Assertion : If both zeros of the quadratic polynomial x2 − 2kx + 2 are equal in magnitude but opposite in sign then value of k is ½. Reason : Sum of zeros of a quadratic polynomial ax2 + bx + c is -ab (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). (c) Assertion (A) is true but reason (R) is false. (d) Assertion (A) is false but reason (R) is true. Section - B Section B consists of 5 questions of 2 marks each. 21. Evaluate : cos 45º + 1 sec 30º sec 60º https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install CBSE Maths Class 10 Sample Paper 06 Page 5 22. In the given figure, CB || QR and CA || PR. If AQ = 12 cm, AR = 20 cm, PB = CQ = 15 cm, calculate PC and BR. 23. A box contains 12 balls of which some are red in colour. If 6 more red balls are put in the box and a ball is drawn at random the probability of drawing a red ball doubles than what it was before. Find the number of red balls in the bag.

O Two different dice are tossed together. Find the probability : (i) that the number on each die is even. (ii) that the sum of numbers appearing on the two dice is 5. 24. In the given figure, G is the mid-point of the side PQ of TPQR and GH || QR. Prove that H is the mid- point of the side PR or the triangle PQR.

O In TABC, if X and Y are points on AB and AC respectively such that AX XB = 34 , AY = 5 and YC = 9, then state whether XY and BC parallel or not. 25. In given figure, AB is the diameter of a circle with centre O and AT is a tangent. If +AOQ = 58c, find +ATQ.

Continue on next page..... https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install Page 6 Sample Paper 06 CBSE Maths Class 10 Section - C Section C consists of 6 questions of 3 marks each. 26. In the given +PQR, right-angled at Q, QR = 9 cm and PR − PQ = 1 cm. Determine the value of sin R + cos R. 27. If α and β are the zeroes of the polynomial f (x) = x2 − 4x − 5 then find the value of α2 + β2. 28. Find HCF and LCM of 16 and 36 by prime factorization and check your answer. 29. In the given figure, DB = BC, DE = AB and AC = BC. Prove that BE = AC. DE BC

O A 6 m high tree cast a 4 m long shadow. At the same time, a flag pole cast a shadow 50 m long. How long is the flag pole? https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install CBSE Maths Class 10 Sample Paper 06 Page 7 30. A well of diameter 4 m is dug 14 m deep. The earth taken out is spread evenly all around the well to form a 40 m high embankment. Find the width of the embankment.

O 3 The th part of a conical vessel of internal radius 5 cm and height 24 cm is full of water. The water 4 emptied into a 0cylindrical vessel with internal radius 10 cm. Find the height of water in cylindrical vessel. 31. Solve graphically : 2x − 3y + 13 = 0 ; 3x − 2y + 12 = 0 Section - D Section D consists of 4 questions of 5 marks each. 32. Find the ratio in which the y -axis divides the line segment joining the points ^- 1, - 4h and ^5, - 6h. Also find the coordinates of the point of intersection. 33. Solve, for x : 3 x2 + 10x + 7 3 = 0

O 2 If x =− 2 is a root of the equation 3x + 7x + p = 0 , find the value of k so that the roots of the equation x2 + k ^4x + k − 1h + p = 0 are equal. 34. 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 = 90c and DS = 5 cm, then find the radius of the circle (in cm). 35. The table below show the salaries of 280 persons: Salary (In thousand 1 (c) 0 # P ^Ah # 1 (d) - 1 # P ^Ah # 1 16. If α and β are the zeroes of the polynomial 2x2 − 13x + 6 , then α + β is equal to (a) - 3 (b) 3 (c) 13 (d) - 13 2 2 17. A tree is broken by the wind. The top struck the ground at an angle of 30c and at distance of 10 m from its root. The whole height of the tree is ( 3 = 1.732) (a) 10 3 m (b) 3 10 m (c) 20 3 m (d) 3 20 m 18. A fair die is thrown once. The probability of getting a composite number less than 5 is (a) 1 (b) 1 3 6 (c) 2 (d) 0 3 19. Assertion : sin2 67c + cos2 67c = 1 Reason : For any value of θ, sin2 θ + cos2 θ = 1 (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). (c) Assertion (A) is true but reason (R) is false. (d) Assertion (A) is false but reason (R) is true. 20. Assertion : If sum of the first n terms of an AP is given by Sn = 3n2 − 4n. Then its n th term is an = 6n − 7. Reason : n th term of an AP, whose sum to n terms is Sn , is given by an = Sn − Sn − 1 (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). (c) Assertion (A) is true but reason (R) is false. (d) Assertion (A) is false but reason (R) is true. Section - B Section B consists of 5 questions of 2 marks each. 21. Find the ratio in which the point P ^ 34 , 125 h divides the line segment joining the point A ^ 12 , 32 h and ^2, - 5h. 22. Two tangents PA and PB are drawn from an external point P to a circle inclined to each other at an angle of 70º, then what is the value of +PAB ? https://qrbook.page.link/appInstall NODIA App to See the Solutions. Click Here To Install CBSE Maths Class 10 Sample Paper 15 Page 5 23. If two positive integers p and q are written as p = a2 b3 and q = a3 b, where a and b are prime numbers than verify LCM (p, q) # HCF (q, q) = pq

O Prove that 3 + 5 is an irrational number. 24. The fifth term of an AP is 20 and the sum of its seventh and eleventh terms is 64. Find the common difference.

O For AP show that a p + a p + 2q = 2a p + q. 25. If the sum of first n terms of an AP is n2 , then find its 10th term. Section - C Section C consists of 6 questions of 3 marks each. 1 1 = 2 ; x ! 1 , 2, 3 ^x − 1h^x − 2h ^x − 2h^x − 3h 3 26. Solve for x : + 27. In given figure, two circles touch each other at the point C. Prove that the common tangent to the circles at C , bisects the common tangent at P and Q.

O In the given figure, PA and PB are tangents to a circle from an external point P such that PA = 4 cm and +BAC = 135º. Find the length of chord AB. 28. Solve for x and y : x + 2y =− 1 2 3 y x- =3 3 https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install Page 6 Sample Paper 15 CBSE Maths Class 10 29. Water in a canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/hour. How much area will it irrigate in 30 minutes; if 8 cm standing water is needed?

O The radii of two right circular cylinders are in the ratio of 2 : 3 and their height are in the ratio of 5 : 4. Calculate the ratio of their curved surface area and radio of their volumes. 30. A die is thrown once. Find the probability of getting a number which (i) is a prime number (ii) lies between 2 and 6. 31. A 7 m long flagstaff is fixed on the top of a tower standing on the horizontal plane. From point on the ground, the angles of elevation of the top and bottom of the flagstaff are 60º and 45º respectively. Find the height of the tower correct to one place of decimal. (Use 3 = 1.73) Section - D Section D consists of 4 questions of 5 marks each. 32. If α and β are zeroes of the polynomial p (x) = 6x2 − 5x + k such that α − β = 16 , Find the value of k.

O Polynomial x + 7x + 7x + px + q is exactly divisible by x2 + 7x + 12 , then find the value of p and q. 4 3 2 33. In figure, two circular flower beds have been shown on two sides of a square lawn ABCD of side 56 m. If the centre of each circular flower bed is the point of intersection O of the diagonals of the square lawn, find the sum of the areas of the lawn and flower beds. 34. Prove that in a right triangle, the square of the hypotenuse is equal to sum of squares of other two sides.

O Prove that in a right triangle, the square of the hypotenuse is equal to sum of squares of other two sides. Using the above result, prove that, in rhombus ABCD, 4AB2 = AC2 + BD2. 35. Given that : tan ^A + B h = tan A + tan B , 1 − tan A tan B find the values of tan 75º and tan 90º by taking suitable values of A and B.

O Prove that : tan θ + cot θ = 1 + tan θ + cot θ. 1 − cot θ 1 − tan θ https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install CBSE Maths Class 10 Sample Paper 15 Page 7 Section - E Section E consists of 3 case study based questions of 4 marks each. 36. A garden is in the shape of rectangle. Gardener grew sapling of Ashoka tree on the boundary of garden at the distance of 1 meter from each other. He want to decorate the garden with rose plants. He choose triangular region inside the park to grow rose plants. On the above situation, gardener took help from the students of class 10th. They made a chart for it which looks as the above figure. (i) If A is taken as origin, What are the coordinates of triangle PQR ? (ii) If C is taken as origin, what is the co-ordinate of point P ? (iii) If B is taken as origin, what are the co-ordinate of P ? (iv) What is distance between P and Q if origin is taken A ? 37. Traffic Management : A traffic enforcement camera is a camera which may be mounted beside or over a road or installed in an enforcement vehicle to detect motoring offenses, including speeding, vehicles going through a red traffic light. A worldwide review of studies found that speed cameras led to a reduction of 11% to 44% for fatal and serious injury crashes. The British Medical Journal recently reported that speed cameras were effective at reducing accidents and injuries in their vicinity and recommended wider deployment.

Continue on next page..... https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install Page 8 Sample Paper 15 CBSE Maths Class 10 In order to monitor reckless driving on Mumbai road, special cameras have been installed at many traffic light. The following table shows a frequency distribution table for the speed of 100 vehicles passing through a particular spot on a day. Speed (in km/h) 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100 Number of Vehicles 1 3 7 16 35 29 7 2 Based on the above information, answer the following questions. (i) Find the number of vehicles whose speed is more than 70 km/h and find the number of vehicles whose speed is less than 50 km/h ? (ii) What is the mode value of speed ? (iii) What is the median value of speed ?

O (iv) Find the mean value of speed using empirical relation. 38. Pyramid, in architecture, a monumental structure constructed of or faced with stone or brick and having a rectangular base and four sloping triangular sides meeting at an apex. Pyramids have been built at various times in Egypt, Sudan, Ethiopia, western Asia, Greece, Cyprus, Italy, India, Thailand, Mexico, South America, and on some islands of the Pacific Ocean. Those of Egypt and of Central and South America are the best known. The volume and surface area of a pyramid with a square base of area a2 and height h is given by ha2 V = 3 and S = a2 + 2a ^ a2 h + h2 2 A pyramid has a square base and a volume of 3y 3 + 18y2 + 27y cubic units. (i) If its height is y , then what polynomial represents the length of a side of the square base ? (ii) If area of base is 576 metre, what is the side of base? (iii) What is the height of pyramid at above area of base ? What is the ratio of length of side to the height?

O (iv) What is surface area of pyramid ?

****** https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install CBSE Maths Class 10 Sample Paper 16 Page 1 Sample Paper 16 Class - 10th Exam - 2024 - 25 Mathematics - Standard Time : 3 Hours Max. Marks : 80 General Instructions : 1. This question paper contains 38 questions. 2. This Question Paper is divided into 5 Sections A, B, C, D and E. 3. In Section A, Questions no. 1-18 are multiple choice questions (MCQs) and questions no. 19 and 20 are Assertion - Reason based questions of 1 mark each. 4. In Section B, Questions no. 21-25 are very short answer (VSA) type questions, carrying 02 marks each. 5. In Section C, Questions no. 26-31 are short answer (SA) type questions, carrying 03 marks each. 6. In Section D, Questions no. 32-35 are long answer (LA) type questions, carrying 05 marks each. 7. In Section E, Questions no. 36-38 are case study based questions carrying 4 marks each with sub parts of the values of 1, 1 and 2 marks each respectively. 8. All Questions are compulsory. However, an internal choice in 2 Question of Section B, 2 Questions of Section C and 2 Questions of Section D has been provided. An internal choice has been provided in all the 2 marks questions of Section E. 9. Draw neat and clean figures wherever required. 10. Take π = 227 wherever required if not stated. 11. Use of calculators is not allowed. Section - A Section A consists of 20 questions of 1 mark each. 1. In TABC, DE || BC, find the value of x. (a) 3 (b) 2 (c) 4 (d) 1 2. If the mean of the observation x, x + 3, x + 5, x + 7 and x + 10 is 9, the mean of the last three observation is (a) 10 1 (b) 10 2 3 3 (c) 11 1 (d) 11 2 3 3 https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install Page 2 Sample Paper 16 CBSE Maths Class 10 3. If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel, then the value of k is (a) - 5 (b) 2 4 5 (c) 15 (d) 3 4 2 4. The following data gives the distribution of total household expenditure (in 0. (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). (c) Assertion (A) is true but reason (R) is false. (d) Assertion (A) is false but reason (R) is true. Section - B Section B consists of 5 questions of 2 marks each. 21. There are 30 cards of the same size in a bag in which the numbers 1 to 30 are written. One card is taken out of the bag at random. Find the probability that the number on the selected card is not divisible by 3. 22. Find the zeroes of the quadratic polynomial 3 x2 − 8x + 4 3.

O Find a quadratic polynomial, the sum and product of whose zeroes are 6 and 9 respectively. Hence find the zeroes. 23. What is the distance of point P (3, 4) from x -axis? 24. If triangle ABC is similar to triangle DEF such that 2AB = DE and BC = 8 cm then find EF.

O In the figure, PQ is parallel to MN. If KP = 4 and KN = 20.4 cm then find KQ. PM 13 https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install CBSE Maths Class 10 Sample Paper 23 Page 5 25. Explain why (7 # 13 # 11) + 11 and (7 # 6 # 5 # 4 # 3 # 2 # 1) + 3 are composite numbers. Section - C Section C consists of 6 questions of 3 marks each. cos2 (45c + θ) + cos2 (45c − θ) 26. Show that : =1 tan (60c + θ) tan (30c − θ) 27. If tangents PA and PB drawn from an external point P to a circle with centre O are inclined to each other at an angle of 80c, then find +POA. 28. A right circular cone of radius 3 cm, has a curved surface area of 47.1 cm2. Find the volume of the cone. (Use π = 3.14 )

O The sum of the radius of base and height of a solid right circular cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 sq. cm, find the volume of the cylinder. π = 227. 29. Given that 5 is irrational, prove that 2 5 - 3 is an irrational number. 30. Compute the mode for the following frequency distribution: Size of items (in cm) 0- 4 4- 8 8- 12 12-16 16-20 20-24 24-28 Frequency 5 7 9 17 12 10 6

O The mean of the following frequency distribution is 18. The frequency f in the class interval 19-21 is missing. Determine f. Class interval 11-13 13-15 15-17 17-19 19-21 21-23 23-25 Frequency 3 6 9 13 f 5 4 31. In Figure, DE || BC. Find the length of side AD , given that AE = 1.8 cm, BD = 7.2 cm and CE = 5.4 cm. https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install Page 6 Sample Paper 23 CBSE Maths Class 10 Section - D Section D consists of 4 questions of 5 marks each. 32. Sides of a right triangular field are 25 m, 24 m and 7 m. At the three corners of the field, a cow, a buffalo and a horse are tied separately with ropes of 3.5 m each to graze in the field. Find the area of the field that cannot be grazed by these animals. 33. Solve for x : 1 + 2 = 4 x !- 1, - 2, - 4 x+1 x+2 x+4

O 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. 34. In Figure, PQ is a chord of length 8 cm of a circle of radius 5 cm and centre O. The tangents at P and Q intersect at point T. Find the length of TP.

O A right triangle ABC , right angled at A is circumscribing a circle. If AB = 6 cm and BC = 10 cm, find the radius r of the circle. 35. Find the ratio in which the point ^- 3, k h divides the line segment joining the points ^- 5, - 4h and ^- 2, 3h. Also find the value of k. Section - E Section E consists of 3 case study based questions of 4 marks each. 36. Political survey questions are questions asked to gather the opinions and attitudes of potential voters. Political survey questions help you identify supporters and understand what the public needs. Using such questions, a political candidate or an organization can formulate policies to gain support from these people.

Continue on next page..... https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install CBSE Maths Class 10 Sample Paper 23 Page 7 A survey of 100 voters was taken to gather information on critical issues and the demographic information collected is shown in the table. One out of the 100 voters is to be drawn at random to be interviewed on the India Today News on prime time. Women Men Totals Republican 17 20 37 Democrat 22 17 39 Independent 8 7 15 Green Party 6 3 5 Totals 53 47 100 (i) What is the probability the person is a woman or a Republican ? (ii) What is the probability the person is a Democrat ? (iii) What is the probability the person is a Independent men ? (iv) What is the probability the person is a Independent men or green party men ? 37. Salary : In investigating different job opportunities, you find that firm A will start you at Rs 25,000 per year and guarantee you a raise of Rs 1,200 each year whereas firm B will start you at Rs 28,000 per year but will guarantee you a raise of only Rs 800 each year. (i) Over a period of 15 years, how much would you receive from firm A? (ii) Over a period of 15 years, how much would you receive from firm B? (iii) What would be your annual salary at firm A for the tenth year? (iv) What would be your annual salary at firm B for the tenth year? https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install Page 8 Sample Paper 23 CBSE Maths Class 10 38. From his hotel room window on the fourth floor, Ranjan notices some window washers high above him on the hotel across the street. Curious as to their height above ground, he quickly estimates the buildings are 60 m apart, the angle of elevation to the workers is about 60c , and the angle of depression to the base of the hotel is about 30c. (i) How high above ground is the window of Ranjan’s hotel room? (ii) How high above ground are the workers?

****** https://qrbook.page.link/app Install NODIA App to See the Solutions. Click Here To Install CBSE Maths Class 10 Sample Paper 24 Page 1 Sample Paper 24 Class - 10th Exam - 2024 - 25 Mathematics - Standard Time : 3 Hours Max. Marks : 80 General Instructions : 1. This question paper contains 38 questions. 2. This Question Paper is divided into 5 Sections A, B, C, D and E. 3. In Section A, Questions no. 1-18 are multiple choice questions (MCQs) and questions no. 19 and 20 are Assertion - Reason based questions of 1 mark each. 4. In Section B, Questions no. 21-25 are very short answer (VSA) type questions, carrying 02 marks each. 5. In Section C, Questions no. 26-31 are short answer (SA) type questions, carrying 03 marks each. 6. In Section D, Questions no. 32-35 are long answer (LA) type questions, carrying 05 marks each. 7. In Section E, Questions no. 36-38 are case study based questions carrying 4 marks each with sub parts of the values of 1, 1 and 2 marks each respectively. 8. All Questions are compulsory. Howeve