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CBSE Class 10 Board Exam 2026 : Mathematics

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Series WX1YZ/2 SET~1 Q.P. Code Roll No. 30/2/1 narjmWu Z-n H$moS> >H$mo C ma-nwp VH$m Ho$ _wI-n >na Ad ` {bIo & Candidates must write the Q.P. Code on the title page of the answer-book. J{UV (_mZH$) MATHEMATICS (STANDARD) * :3 Time allowed : 3 hours ZmoQ> / : 80 Maximum Marks : 80 NOTE : (i) 23 Please check that this question paper contains 23 printed pages. (ii) Q.P. Code given on the right hand side of the question paper should be written on the title page of the answer-book by the candidate. (iii) - 38 Please check that this question paper contains 38 questions. (iv) Please write down the serial number of the question in the answer-book before attempting it. (v) 15 10.15 10.30 15 minute time has been allotted to read this question paper. The question paper will be distributed at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the students will read the question paper only and will not write any answer on the answer-book during this period. 30/2/1 10.15 JJJJ Page 1 P.T.O. General Instructions : Read the following instructions very carefully and strictly follow them : (i) This question paper contains 38 questions. All questions are compulsory. (ii) This question paper is divided into five Sections A, B, C, D and E. (iii) In Section A, Questions no. 1 to 18 are multiple choice questions (MCQs) and questions number 19 and 20 are Assertion-Reason based questions of 1 mark each. (iv) In Section B, Questions no. 21 to 25 are very short answer (VSA) type questions, carrying 2 marks each. (v) In Section C, Questions no. 26 to 31 are short answer (SA) type questions, carrying 3 marks each. (vi) In Section D, Questions no. 32 to 35 are long answer (LA) type questions carrying 5 marks each. (vii) In Section E, Questions no. 36 to 38 are case study based questions carrying 4 marks each. Internal choice is provided in 2 marks questions in each case-study. (viii) There is no overall choice. However, an internal choice has been provided in 2 questions in Section B, 2 questions in Section C, 2 questions in Section D and 3 questions in Section E. 22 (ix) Draw neat diagrams wherever required. Take = wherever required, if not 7 stated. (x) Use of calculators is not allowed. SECTION A This section comprises multiple choice questions (MCQs) of 1 mark each. 1. Which of the following quadratic equations has sum of its roots as 4 ? (a) (c) 2. 2x2 4x + 8 = 0 2 x2 4 x+1=0 2 (b) (d) x2 + 4x + 4 = 0 4x2 4x + 4 = 0 What is the length of the arc of the sector of a circle with radius 14 cm and of central angle 90 ? (a) 22 cm (b) 44 cm (c) 88 cm (d) 11 cm 30/2/1 JJJJ Page 3 P.T.O. 3. If ABC B is : A = 32 and R = 65 , then the measure of (a) 32 (b) 65 (c) 83 (d) 97 (a) pq (b ) p (c) q (d) p+q 4. 5. The coordinates of the vertex A of a rectangle ABCD whose three vertices are given as B(0, 0), C(3, 0) and D(0, 4) are : 6. (a) (4, 0) (b) (0, 3) (c) (3, 4) (d) (4, 3) If the pair of equations 3x y + 8 = 0 and 6x ry + 16 = 0 represent coincident lines, then t 7. (a) 1 2 (b) 1 2 (c) 2 (d) 2 A bag contains 100 cards numbered 1 to 100. A card is drawn at random from the bag. What is the probability that the number on the card is a perfect cube ? 8. (a) 1 20 (b) 3 50 (c) 1 25 (d) 7 100 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) 30/2/1 JJJJ Page 5 P.T.O. 9. If one zero of the polynomial 6x2 + 37x (k 2) is reciprocal of the other, then what is the value of k ? (a) 4 (c) 6 (a) 3 (c) 1 2 (b) 6 (d) 4 (b) 2 (d) 3 4 10. 11. 2 d 2 d 2 d 2 d If three coins are tossed simultaneously, what is the probability of getting at most one tail ? 12. (a) 3 8 (b) 4 8 (c) 5 8 (d) 7 8 In the given figure, DE BC. If AD = 2 units, DB = AE = 3 units and EC = x units, then the value of x is : (a) 2 (b) (c) 5 (d) 30/2/1 JJJJ Page 7 3 9 2 P.T.O. 13. The hour-hand of a clock is 6 cm long. The angle swept by it between 7:20 a.m. and 7:55 a.m. is : 35 4 (a) (c) 14. 15. 35 (d) 35 2 70 The zeroes of the polynomial p(x) = x2 + 4x + 3 are given by : (a) 1, 3 (c) 1, 3 (b) 1, 3 (d) 1, 3 In the given figure, the quadrilateral PQRS circumscribes a circle. Here PA + CS is equal to : (a) (c) 16. (b) If QR PS and (b) (d) PR PQ are the zeroes of the quadratic polynomial p(x) = x2 ax b, then the value of 2 + 2 is : 17. (a) a2 2b (b) (c) b 2 2a (d) a2 + 2b 2 b + 2a x y The area of the triangle formed by the line = 1 with the coordinate a b axes is : (a) ab (b) 1 ab 2 (c) 1 ab 4 (d) 2ab 30/2/1 JJJJ Page 9 P.T.O. 18. In the given figure, AB PQ. If AB = 6 cm, PQ = 2 cm and OB = 3 cm, then the length of OP is : (a) 9 cm (b) 3 cm (c) 4 cm (d) 1 cm Questions number 19 and 20 are Assertion and Reason based questions carrying 1 mark each. Two statements are given, one labelled as Assertion (A) and the other is labelled as Reason (R). Select the correct answer to these questions from the codes (a), (b), (c) and (d) as given below. (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A). (b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A). (c) Assertion (A) is true, but Reason (R) is false. (d) Assertion (A) is false, but Reason (R) is true. 19. Assertion (A) : A tangent to a circle is perpendicular to the radius through the point of contact. Reason (R) : 20. The lengths of tangents drawn from an external point to a circle are equal. Assertion (A) : The polynomial p(x) = x2 + 3x + 3 has two real zeroes. Reason (R): 30/2/1 A quadratic polynomial can have at most two real zeroes. JJJJ Page 11 P.T.O. SET ~ 1 Series WX1YZ/4 Z-n H$moS> Q.P. Code amob Z . 30/4/1 narjmWu Z-n H$moS> H$mo C ma-nwp VH$m Ho$ _wI-n > na Ad ` {bI| & Roll No. Candidates must write the Q.P. Code on the title page of the answer-book. J{UV (_mZH$) - g mp VH$ MATHEMATICS (STANDARD) - Theory # {ZYm [aV g_` 3 K Q>o A{YH$V_ A H$ 80 Time allowed : 3 hours Maximum Marks : 80 ZmoQ> / NOTE : (i) H $n`m Om M H$a b| {H$ Bg Z-n _| _w{ V n > 15 h & Please check that this question paper contains 15 printed pages. (ii) Z-n _| Xm{hZo hmW H$s Amoa {XE JE Z-n H$moS> H$mo N>m C ma-nwp VH$m Ho$ _wI-n > na {bI|& Q.P. Code given on the right hand side of the question paper should be written on the title page of the answer-book by the candidate. (iii) H $n`m Om M H$a b| {H$ Bg Z-n _| 38 Z h & Please check that this question paper contains 38 questions. (iv) H $n`m Z H$m C ma {bIZm ew $ H$aZo go nhbo, C ma-nwp VH$m _| Z H$m H $_m H$ Ad ` {bI|& Please write down the Serial Number of the question in the answer-book before attempting it. (v) Bg Z-n H$mo n T>Zo Ho$ {bE 15 {_ZQ> H$m g_` {X`m J`m h & Z-n H$m {dVaU nydm _| 10.15 ~Oo {H$`m OmEJm& 10.15 ~Oo go 10.30 ~Oo VH$ N>m Ho$db Z-n H$mo n T>|Jo Am a Bg Ad{Y Ho$ Xm amZ do C ma-nwp VH$m na H$moB C ma Zht {bI|Jo& 15 minute time has been allotted to read this question paper. The question paper will be distributed at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the students will read the question paper only and will not write any answer on the answer-book during this period. 30/4/1 ~~~~ 1 [P.T.O. GENERAL INSTRUCTIONS : Read the following instructions carefully and follow them : (i) This question paper contains 38 questions. All questions are compulsory. (ii) Question paper is divided into FIVE sections Section A, B, C, D and E. (iii) In section A question number 1 to 18 are multiple choice questions (MCQs) and question number 19 and 20 are Assertion-Reason based questions of 1 mark each. (iv) In section B question number 21 to 25 are Very Short Answer (VSA) type questions of 2 marks each. (v) In section C question number 26 to 31 are Short Answer (SA) type questions carrying 3 marks each. (vi) In section D question number 32 to 35 are Long Answer (LA) type questions carrying 5 marks each. (vii) In section E question number 36 to 38 are case based integrated units of assessment questions carrying 4 marks each. Internal choice is provided in 2 marks question in each case-study. (viii) There is no overall choice. However, an internal choice has been provided in 2 questions in Section B, 2 questions in Section C, 2 questions in Section D and 3 questions in Section E. (ix) Draw neat figures wherever required. Take = 22/7 wherever required if not stated. (x) Use of calculators is NOT allowed. SECTION - A Section - A consists of Multiple Choice type questions of 1 mark each. 1. 2. 3. 4. 5. 6. 30/4/1 The ratio of HCF to LCM of the least composite number and the least prime number is : (a) 1:2 (b) 2:1 (c) 1:1 (d) 1:3 The roots of the equation x2 + 3x 10 = 0 are : (a) 2, 5 (b) 2, 5 (c) 2, 5 The next term of the A.P. : 6 , (a) 60 (b) 96 24 , 54 is : (c) 72 The distance of the point ( 1, 7) from x-axis is : (a) 1 (b) 7 (c) 6 What is the area of a semi-circle of diameter d ? 1 2 1 2 1 d d (a) (b) (c) d 2 16 4 8 1 (d) 2, 5 1 (d) 216 1 (d) 50 1 (d) 1 2 d 2 The empirical relation between the mode, median and mean of a distribution is : (a) Mode = 3 Median 2 Mean (b) Mode = 3 Mean 2 Median (c) Mode = 2 Median 3 Mean (d) Mode = 2 Mean 3 Median 3 1 1 [P.T.O. 7. 8. 9. 10. The pair of linear equations 2x = 5y + 6 and 15y = 6x 18 represents two lines which are : (a) intersecting (b) parallel (c) coincident (d) either intersecting or parallel If , are zeroes of the polynomial x2 1, then value of ( + ) is : (a) 2 (b) 1 (c) 1 (d) 0 If a pole 6 m high casts a shadow 2 3 m long on the ground, then sun s elevation is : (b) 45 o (c) 30 o (d) 90 o (a) 60o sec when expressed in terms of cot , is equal to : 1+cot 2 (a) (b) 1+cot 2 cot 1+cot 2 1 cot 2 (d) cot cot Two dice are thrown together. The probability of getting the difference of numbers on their upper faces equals to 3 is : 1 2 1 1 (a) (b) (c) (d) 9 9 6 12 1 1 1 1 (c) 11. 1 12. In the given figure, ABC ~ QPR. If AC = 6 cm, BC = 5 cm, QR = 3 cm and PR = x; then the value of x is : (a) 3.6 cm (b) 2.5 cm (c) 10 cm (d) 3.2 cm 13. 14. The distance of the point ( 6, 8) from origin is : (a) 6 (b) 6 (c) 8 1 1 (d) 10 In the given figure, PQ is a tangent to the circle with centre O. If OPQ = x, POQ = y, then x + y is : 1 (a) 45o (b) 90 o (c) 60 o (d) 180 o 30/4/1 5 [P.T.O. 15. In the given figure, TA is a tangent to the circle with centre O such that OT = 4 cm, OTA = 30o, then length of TA is : 1 (a) 2 3 cm (b) 2 cm 16. (c) 2 2 cm (d) 3 cm In ABC, PQ || BC. If PB = 6 cm, AP = 4 cm, AQ = 8 cm, find the length of AC. 1 (a) 12 cm (b) 20 cm (c) 6 cm (d) 14 cm 17. 18. If , are the zeroes of the polynomial p(x) = 4x2 3x 7, then 1 1 + is equal to : 7 7 3 3 (a) (b) (c) (d) 3 3 7 7 A card is drawn at random from a well-shuffled pack of 52 cards. The probability that the card drawn is not an ace is : (a) 19. 1 13 (b) 9 13 (c) 4 13 (d) 1 1 12 13 DIRECTIONS : In the question number 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option out of the following : 2 Assertion (A) : The probability that a leap year has 53 Sundays is . 7 5 Reason (R) : The probability that a non-leap year has 53 Sundays is . 7 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 and 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. 30/4/1 7 [P.T.O. 20. Assertion (A) : a, b, c are in A.P. if and only if 2b = a + c. Reason (R) : The sum of first n odd natural numbers is n2. (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 and 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 Very Short Answer (VSA) type questions of 2 marks each. 21. Two numbers are in the ratio 2 : 3 and their LCM is 180. What is the HCF of these numbers ? 22. If one zero of the polynomial p(x) = 6x2 + 37x (k 2) is reciprocal of the other, then find the value of k. 23. (A) Find the sum and product of the roots of the quadratic equation 2x2 9x + 4 = 0. OR (B) Find the discriminant of the quadratic equation 4x2 5 = 0 and hence comment on the nature of roots of the equation. 24. 25. If a fair coin is tossed twice, find the probability of getting atmost one head . 5cos 2 60o + 4sec2 30o tan 2 45o sin 2 30o + cos 2 30o OR (B) If A and B are acute angles such that sin (A B) = 0 and 2 cos (A + B) 1 = 0, then find angles A and B. (A) Evaluate 1 2 2 2 2 2 2 2 SECTION C Section - C consists of Short Answer (SA) type questions of 3 marks each. 26. (A) How many terms are there in an A.P. whose first and fifth terms are 14 and 2, respectively and the last term is 62. OR (B) Which term of the A.P. : 65, 61, 57, 53, .................. is the first negative term ? 27. Prove that 28. Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the linesegment joining the points of contact at the centre. 30/4/1 5 is an irrational number. 9 3 3 3 3 [P.T.O. Series WX1YZ/5 SET~1 Q.P. Code Roll No. 30/5/1 narjmWu Z-n H$moS> >H$mo C ma-nwp VH$m Ho$ _wI-n >na Ad ` {bIo & Candidates must write the Q.P. Code on the title page of the answer-book. J{UV (_mZH$)$ MATHEMATICS (STANDARD) * :3 Time allowed : 3 hours : 80 Maximum Marks : 80 NOTE : (i) 27 Please check that this question paper contains 27 printed pages. (ii) Q.P. Code given on the right hand side of the question paper should be written on the title page of the answer-book by the candidate. 38 (iii) Please check that this question paper contains 38 questions. (iv) Please write down the serial number of the question in the answer-book before attempting it. (v) 15 10.15 10.30 15 minute time has been allotted to read this question paper. The question paper will be distributed at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the students will read the question paper only and will not write any answer on the answer-book during this period. 30/5/1 10.15 JJJJ Page 1 P.T.O. General Instructions : Read the following instructions carefully and follow them : (i) This question paper contains 38 questions. All questions are compulsory. (ii) This question paper is divided into five Sections A, B, C, D and E. (iii) In Section A, Questions no. 1 to 18 are multiple choice questions (MCQs) and questions number 19 and 20 are Assertion-Reason based questions of 1 mark each. (iv) In Section B, Questions no. 21 to 25 are very short answer (VSA) type questions, carrying 2 marks each. (v) In Section C, Questions no. 26 to 31 are short answer (SA) type questions, carrying 3 marks each. (vi) In Section D, Questions no. 32 to 35 are long answer (LA) type questions carrying 5 marks each. (vii) In Section E, Questions no. 36 to 38 are case study based questions carrying 4 marks each. Internal choice is provided in 2 marks questions in each case-study. (viii) There is no overall choice. However, an internal choice has been provided in 2 questions in Section B, 2 questions in Section C, 2 questions in Section D and 3 questions in Section E. 22 (ix) Draw neat diagrams wherever required. Take = wherever required, if not 7 stated. (x) Use of calculators is not allowed. SECTION A This section comprises multiple choice questions (MCQs) of 1 mark each. 1. The number of polynomials having zeroes 3 and 5 is : (a) only one (b) infinite (c) exactly two (d) at most two 2. The pair of equations ax + 2y = 9 and 3x + by = 18 represent parallel lines, where a, b are integers, if : (a) a=b (b) 3a = 2b (c) 2a = 3b (d) ab = 6 3. The common difference of the A.P. whose nth term is given by an = 3n + 7, is : (a) (c) 30/5/1 7 3n JJJJ (b) (d) Page 3 3 1 P.T.O. 4. 5. 6. In the given figure, DE (a) 6 (b ) 12 5 (c) 8 (d) 10 A quadratic equation whose roots are (2 + (a) x2 (c) 4x2 If tan (a) (c) 7. 8. BC. The value of x is : 4x + 1 = 0 3=0 3 ) and (2 3 ) is : (b) x2 + 4x + 1 = 0 (d) x2 1=0 5 sin cos , then the value of is : 12 sin cos 17 17 (b) 7 7 17 7 (d) 13 13 = The distance between the points P 11 , 5 and Q 3 2 , 5 is : 3 (a) 6 units (b) 4 units (c) 2 units (d) 3 units In the given figure, AB = BC = 10 cm. If AC = 7 cm, then the length of BP is : (a) 3 5 cm (b) 7 cm (c) 6 5 cm (d) 5 cm 30/5/1 JJJJ Page 5 P.T.O. 9. Water in a river which is 3 m deep and 40 m wide is flowing at the rate of 2 km/h. How much water will fall into the sea in 2 minutes ? 10. (a) 800 m3 (b) 4000 m3 (c) 8000 m3 (d) 2000 m3 If the mean and the median of a data are 12 and 15 respectively, then its mode is : 11. (a) 13 5 (b) 21 (c) 6 (d) 14 In the given figure, AB is a tangent to the circle centered at O. If OA = 6 cm and OAB = 30 , then the radius of the circle is : (a) 3 cm (b) 3 3 cm (c) 2 cm (d) 3 cm 2 tan 30 12. 1 tan 2 30 is equal to : (a) sin 60 (b) cos 60 (c) tan 60 (d) sin 30 AB DE 13. BC . Which of the following makes the two FD triangles similar ? (a) A= D (b) B= D (c) B= E (d) A= F 30/5/1 JJJJ Page 7 P.T.O. 14. The 11th term from the end of the A.P. : 10, 7, 4, ......., (a) 25 (c) 15. 16. 32 18. 16 (d) 0 Two coins are tossed together. The probability of getting at least one tail is : (a) 1 4 (b) 1 2 (c) 3 4 (d) 1 In the given figure, AC and AB are tangents to a circle centered at O. If COD = 120 , then 17. (b) 62 is : BAO is equal to : (a) 30 (b) 60 (c) 45 (d) 90 Which of the following numbers cannot be the probability of happening of an event ? (a) 0 (b) 7 0 01 (c) 0 07 (d) 0 07 3 If every term of the statistical data consisting of n terms is decreased by 2, then the mean of the data : (a) decreases by 2 (b) remains unchanged (c) decreases by 2n (d) decreases by 1 30/5/1 JJJJ Page 9 P.T.O. Questions number 19 and 20 are Assertion and Reason based questions carrying 1 mark each. Two statements are given, one labelled as Assertion (A) and the other is labelled as Reason (R). Select the correct answer to these questions from the codes (a), (b), (c) and (d) as given below. 19. (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A). (b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A). (c) Assertion (A) is true, but Reason (R) is false. (d) Assertion (A) is false, but Reason (R) is true. Assertion (A) : If the points A(4, 3) and B(x, 5) lie on a circle with centre O(2, 3), then the value of x is 2. Reason (R) : Centre of a circle is the mid-point of each chord of the circle. 20. n Assertion (A) : The number 5 cannot end with the digit 0, where n is a natural number. Reason (R): Prime factorisation of 5 has only two factors, 1 and 5. SECTION B This section comprises very short answer (VSA) type questions of 2 marks each. 21. (a) The line segment joining the points A(4, 5) and B(4, 5) is divided by the point P such that AP : AB = 2 : 5. Find the coordinates of P. OR (b) Point P(x, y) is equidistant from points A(5, 1) and B(1, 5). Prove that x = y. 30/5/1 JJJJ Page 11 P.T.O.

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