Practice Question Papers · with Answers

CBSE / NCERT Class 10 Maths Practice Question Papers

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Brain Grain · braingrain.in
Maths — Practice Paper · Set 1
Class: 10CBSE / NCERTMax Marks: 45
Name: ____________________Reg No: ____________
Part I — Multiple Choice Questions 9 × 1 = 9

Choose the correct answer. (Answer all questions.)

1.From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle isA. 7 cmB. 12 cmC. 15 cmD. 24.5 cm[1]
2.Choose the correct option. Justify your choice. (i) $9\sec^2 A - 9\tan^2 A$A. As listed in the question.B. As listed in the question.C. As listed in the question.D. As listed in the question.[1]
3.Choose the correct choice in the following and justify : (i) 30th term of the AP: 10, 7, 4, . . . , is (A) 97 (B) 77 (C) -77 (D) - 87 (ii) 11th term of the AP: $-3, -\dfrac{1}{2}, 2, . . .$A. As listed in the question.B. As listed in the question.C. As listed in the question.D. As listed in the question.[1]
4.If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of $80^\circ$A. $50^\circ$B. $60^\circ$C. $70^\circ$D. $80^\circ$[1]
5.A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is :A. 12 cmB. 13 cmC. 8.5 cmD. $\sqrt{119}$ cm[1]
6.Choose the correct option and justify your choice : (i) $\dfrac{2\tan30^\circ}{1+\tan^230^\circ}$A. As listed in the question.B. As listed in the question.C. As listed in the question.D. As listed in the question.[1]
7.Tick the correct answer in the following : Area of a sector of angle $p$A. $\dfrac{p}{180}\times2\pi R$B. $\dfrac{p}{180}\times\pi R^2$C. $\dfrac{p}{360}\times\pi R^2$D. $\dfrac{p}{720}\times2\pi R^2$[1]
8.In Fig. 10.11, if TP and TQ are the two tangents to a circle with centre O so that $\angle POQ = 110^\circ$A. $60^\circ$B. $70^\circ$C. $80^\circ$D. $90^\circ$[1]
9.Which of the following cannot be the probability of an event?A. $\dfrac{2}{3}$B. $-1.5$C. $15\%$D. $0.7$[1]
Part II — Short Answer Questions 18 × 2 = 36

Answer briefly. (Answer all questions.)

10.Which term of the AP : 3, 15, 27, 39, . . . will be 132 more than its 54th term?[2]
11.(i) A lot of 20 bulbs contain 4 defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective? (ii) Suppose the bulb drawn in (i) is not defective and is not replaced. Now one bulb is drawn at random from the rest. What is the probability that this bulb is not defective ?[2]
12.In Fig. 6.38, altitudes AD and CE of $\triangle ABC$[2]
13.If $\sin A = \dfrac{3}{4}$[2]
14.Find the roots of the following quadratic equations by factorisation: (i) $x^2 - 3x - 10 = 0$[2]
15.Fill in the blanks using the correct word given in brackets : (i) All circles are ________. (congruent, similar) (ii) All squares are ________. (similar, congruent) (iii) All ________ triangles are similar. (isosceles, equilateral) (iv) Two polygons of the same number of sides are similar, if (a) their corresponding angles are ________ and (b) their corresponding sides are ________. (equal, proportional)[2]
16.It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. What is the probability that the 2 students have the same birthday?[2]
17.In Fig. 6.21, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR.[2]
18.In Fig. 6.18, if LM || CB and LN || CD, prove that $\dfrac{AM}{AB} = \dfrac{AN}{AD}$[2]
19.A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of $₹500$[2]
20.Find the sums given below : (i) $7 + 10\dfrac{1}{2} + 14 + . . . + 84$[2]
21.To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1m each. 100 flower pots have been placed at a distance of 1m from each other along AD, as shown in Fig. 7.12. Niharika runs $\dfrac{1}{4}$[2]
22.Find the sum of the first 40 positive integers divisible by 6.[2]
23.If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.[2]
24.Find the 20th term from the last term of the AP : 3, 8, 13, . . ., 253.[2]
25.The distribution below gives the weights of 30 students of a class. Find the median weight of the students. Weight (in kg): 40 - 45, 45 - 50, 50 - 55, 55 - 60, 60 - 65, 65 - 70, 70 - 75 Number of students: 2, 3, 8, 6, 6, 3, 2[2]
26.Check whether $6^n$[2]
27.100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows: Number of letters: 1 - 4, 4 - 7, 7 - 10, 10 - 13, 13 - 16, 16 - 19 Number of surnames: 6, 30, 40, 16, 4, 4 Determine the median number of letters in the surnames. Find the mean number of letters in the surnames? Also, find the modal size of the surnames.[2]
🔑 Show Answer Key — Set 1
  1. 1. Correct option: (A) 7 cm.
  2. 2. (i) B, 9 (ii) C, 2 (iii) D, cos A (iv) D, $\tan^2 A$
  3. 3. (i) Choice (C), $-77$ . (ii) Choice (B), $22$ .
  4. 4. Correct option: (A) $50^\circ$ .
  5. 5. Correct option: (D) $\sqrt{119}$ cm.
  6. 6. (i) A, sin 60° (ii) D, 0 (iii) A, 0° (iv) C, tan 60°
  7. 7. Correct option: (C) $\dfrac{p}{360}\times\pi R^2$ .
  8. 8. Correct option: (B) $70^\circ$ .
  9. 9. Correct option: (B) $-1.5$ .
  10. 10. The 65th term.
  11. 11. (i) $\dfrac15$ (ii) $\dfrac{15}{19}$
  12. 12. (i) $\triangle AEP \sim \triangle CDP$ (ii) $\triangle ABD \sim \triangle CBE$ (iii) $\triangle AEP \sim \triangle ADB$ (iv) $\triangle PDC \sim \triangle BEC$
  13. 13. $\cos A=\dfrac{\sqrt7}{4}$ and $\tan A=\dfrac{3}{\sqrt7}=\dfrac{3\sqrt7}{7}$ .
  14. 14. (i) $x = 5, -2$ (ii) $x = \dfrac{3}{2}, -2$ (iii) $x = -\sqrt{2}, -\dfrac{5}{\sqrt{2}}$ (or $-\dfrac{5\sqrt{2}}{2}$ ) (iv) $x = \dfrac{1}{4}, \dfrac{1}{4}$ (v) $x = \dfrac{1}{10}, \dfrac{1}{10}$
  15. 15. (i) similar (ii) similar (iii) equilateral (iv) (a) equal, (b) proportional
  16. 16. The probability is $0.008$ .
  17. 17. $BC \parallel QR$ .
  18. 18. $\dfrac{AM}{AB} = \dfrac{AN}{AD}$ .
  19. 19. The canvas area is $44$ m $^2$ , and the cost is $₹22000$ .
  20. 20. (i) $\dfrac{2093}{2}$ or $1046.5$ (ii) $286$ (iii) $-8930$
  21. 21. The distance between the green and red flags is $\sqrt{61}$ m. Rashmi should post the blue flag at $(5,22.5)$ .
  22. 22. The sum is 4920.
  23. 23. $x=6$ and $y=3$ .
  24. 24. The 20th term from the last term is 158.
  25. 25. The median weight is approximately $56.67$ kg.
  26. 26. No. $6^n$ can never end with the digit 0 for any natural number $n$ .
  27. 27. Median $=8.05$ letters, mean $=8.32$ letters, and mode $\approx7.88$ letters.
Brain Grain · braingrain.in
Maths — Practice Paper · Set 2
Class: 10CBSE / NCERTMax Marks: 45
Name: ____________________Reg No: ____________
Part I — Multiple Choice Questions 9 × 1 = 9

Choose the correct answer. (Answer all questions.)

1.Tick the correct answer in the following : Area of a sector of angle $p$A. $\dfrac{p}{180}\times2\pi R$B. $\dfrac{p}{180}\times\pi R^2$C. $\dfrac{p}{360}\times\pi R^2$D. $\dfrac{p}{720}\times2\pi R^2$[1]
2.In Fig. 10.11, if TP and TQ are the two tangents to a circle with centre O so that $\angle POQ = 110^\circ$A. $60^\circ$B. $70^\circ$C. $80^\circ$D. $90^\circ$[1]
3.Which of the following cannot be the probability of an event?A. $\dfrac{2}{3}$B. $-1.5$C. $15\%$D. $0.7$[1]
4.From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle isA. 7 cmB. 12 cmC. 15 cmD. 24.5 cm[1]
5.Choose the correct option. Justify your choice. (i) $9\sec^2 A - 9\tan^2 A$A. As listed in the question.B. As listed in the question.C. As listed in the question.D. As listed in the question.[1]
6.Choose the correct choice in the following and justify : (i) 30th term of the AP: 10, 7, 4, . . . , is (A) 97 (B) 77 (C) -77 (D) - 87 (ii) 11th term of the AP: $-3, -\dfrac{1}{2}, 2, . . .$A. As listed in the question.B. As listed in the question.C. As listed in the question.D. As listed in the question.[1]
7.If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of $80^\circ$A. $50^\circ$B. $60^\circ$C. $70^\circ$D. $80^\circ$[1]
8.A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is :A. 12 cmB. 13 cmC. 8.5 cmD. $\sqrt{119}$ cm[1]
9.Choose the correct option and justify your choice : (i) $\dfrac{2\tan30^\circ}{1+\tan^230^\circ}$A. As listed in the question.B. As listed in the question.C. As listed in the question.D. As listed in the question.[1]
Part II — Short Answer Questions 18 × 2 = 36

Answer briefly. (Answer all questions.)

10.D is a point on the side BC of a triangle ABC such that $\angle ADC = \angle BAC$[2]
11.If AD and PM are medians of triangles ABC and PQR, respectively where $\triangle ABC \sim \triangle PQR$[2]
12.Express each number as a product of its prime factors: (i) 140 (ii) 156 (iii) 3825 (iv) 5005 (v) 7429[2]
13.The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?[2]
14.A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears (i) a two-digit number (ii) a perfect square number (iii) a number divisible by 5.[2]
15.Write first four terms of the AP, when the first term a and the common difference d are given as follows: (i) a = 10, d = 10 (ii) a = -2, d = 0 (iii) a = 4, d = - 3 (iv) a = - 1, d = $\dfrac{1}{2}$[2]
16.A car has two wipers which do not overlap. Each wiper has a blade of length 25 cm sweeping through an angle of $115^\circ$[2]
17.A child has a die whose six faces show the letters as given below: A B C D E A The die is thrown once. What is the probability of getting (i) A? (ii) D?[2]
18.Prove that the parallelogram circumscribing a circle is a rhombus.[2]
19.Find the area of a sector of a circle with radius 6 cm if angle of the sector is $60^\circ$[2]
20.A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is (i) red ? (ii) not red?[2]
21.A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was ₹90, find the number of articles produced and the cost of each article.[2]
22.In Fig. 6.39, ABC and AMP are two right triangles, right angled at B and M respectively. Prove that: (i) $\triangle ABC \sim \triangle AMP$[2]
23.Evaluate the following : (i) $\sin60^\circ\cos30^\circ + \sin30^\circ\cos60^\circ$[2]
24.A die is thrown once. Find the probability of getting (i) a prime number; (ii) a number lying between 2 and 6; (iii) an odd number.[2]
25.ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show that $\dfrac{AO}{BO} = \dfrac{CO}{DO}$[2]
26.Which term of the AP : 121, 117, 113, . . ., is its first negative term?[2]
27.The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.[2]
🔑 Show Answer Key — Set 2
  1. 1. Correct option: (C) $\dfrac{p}{360}\times\pi R^2$ .
  2. 2. Correct option: (B) $70^\circ$ .
  3. 3. Correct option: (B) $-1.5$ .
  4. 4. Correct option: (A) 7 cm.
  5. 5. (i) B, 9 (ii) C, 2 (iii) D, cos A (iv) D, $\tan^2 A$
  6. 6. (i) Choice (C), $-77$ . (ii) Choice (B), $22$ .
  7. 7. Correct option: (A) $50^\circ$ .
  8. 8. Correct option: (D) $\sqrt{119}$ cm.
  9. 9. (i) A, sin 60° (ii) D, 0 (iii) A, 0° (iv) C, tan 60°
  10. 10. $CA^2 = CB \cdot CD$ .
  11. 11. $\dfrac{AB}{PQ} = \dfrac{AD}{PM}$ .
  12. 12. (i) $140 = 2^2 \times 5 \times 7$ (ii) $156 = 2^2 \times 3 \times 13$ (iii) $3825 = 3^2 \times 5^2 \times 17$ (iv) $5005 = 5 \times 7 \times 11 \times 13$ (v) $7429 = 17 \times 19 \times 23$
  13. 13. There are 38 terms and their sum is 6973.
  14. 14. (i) $\dfrac9{10}$ (ii) $\dfrac1{10}$ (iii) $\dfrac15$
  15. 15. (i) $10, 20, 30, 40$ (ii) $-2, -2, -2, -2$ (iii) $4, 1, -2, -5$ (iv) $-1, -\dfrac{1}{2}, 0, \dfrac{1}{2}$ (v) $-1.25, -1.50, -1.75, -2.00$
  16. 16. The total area cleaned is about $1254.96$ cm $^2$ .
  17. 17. (i) $\dfrac13$ (ii) $\dfrac16$
  18. 18. A parallelogram circumscribing a circle is a rhombus.
  19. 19. The area of the sector is $\dfrac{132}{7}$ cm $^2$ (about $18.86$ cm $^2$ ).
  20. 20. (i) $\dfrac{3}{8}$ (ii) $\dfrac{5}{8}$
  21. 21. Number of articles produced $= 6$ ; cost of each article $= ₹15$ .
  22. 22. (i) $\triangle ABC \sim \triangle AMP$ (ii) $\dfrac{CA}{PA} = \dfrac{BC}{MP}$
  23. 23. (i) $1$ (ii) $2$ (iii) $\dfrac{3\sqrt2-\sqrt6}{8}$ (iv) $\dfrac{3\sqrt3-4}{3\sqrt3+4}$ (v) $\dfrac{67}{12}$
  24. 24. (i) $\dfrac12$ (ii) $\dfrac12$ (iii) $\dfrac12$
  25. 25. $\dfrac{AO}{BO} = \dfrac{CO}{DO}$ .
  26. 26. The 32nd term is the first negative term.
  27. 27. The height of the building is $\dfrac{50}{3}$ m.
Brain Grain · braingrain.in
Maths — Practice Paper · Set 3
Class: 10CBSE / NCERTMax Marks: 45
Name: ____________________Reg No: ____________
Part I — Multiple Choice Questions 9 × 1 = 9

Choose the correct answer. (Answer all questions.)

1.If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of $80^\circ$A. $50^\circ$B. $60^\circ$C. $70^\circ$D. $80^\circ$[1]
2.A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is :A. 12 cmB. 13 cmC. 8.5 cmD. $\sqrt{119}$ cm[1]
3.Choose the correct option and justify your choice : (i) $\dfrac{2\tan30^\circ}{1+\tan^230^\circ}$A. As listed in the question.B. As listed in the question.C. As listed in the question.D. As listed in the question.[1]
4.Tick the correct answer in the following : Area of a sector of angle $p$A. $\dfrac{p}{180}\times2\pi R$B. $\dfrac{p}{180}\times\pi R^2$C. $\dfrac{p}{360}\times\pi R^2$D. $\dfrac{p}{720}\times2\pi R^2$[1]
5.In Fig. 10.11, if TP and TQ are the two tangents to a circle with centre O so that $\angle POQ = 110^\circ$A. $60^\circ$B. $70^\circ$C. $80^\circ$D. $90^\circ$[1]
6.Which of the following cannot be the probability of an event?A. $\dfrac{2}{3}$B. $-1.5$C. $15\%$D. $0.7$[1]
7.From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle isA. 7 cmB. 12 cmC. 15 cmD. 24.5 cm[1]
8.Choose the correct option. Justify your choice. (i) $9\sec^2 A - 9\tan^2 A$A. As listed in the question.B. As listed in the question.C. As listed in the question.D. As listed in the question.[1]
9.Choose the correct choice in the following and justify : (i) 30th term of the AP: 10, 7, 4, . . . , is (A) 97 (B) 77 (C) -77 (D) - 87 (ii) 11th term of the AP: $-3, -\dfrac{1}{2}, 2, . . .$A. As listed in the question.B. As listed in the question.C. As listed in the question.D. As listed in the question.[1]
Part II — Short Answer Questions 18 × 2 = 36

Answer briefly. (Answer all questions.)

10.Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of $\triangle PQR$[2]
11.Solve the following pair of linear equations by the substitution method. (i) $x + y = 14$[2]
12.A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find the mode of the data : Number of cars: 0 - 10, 10 - 20, 20 - 30, 30 - 40, 40 - 50, 50 - 60, 60 - 70, 70 - 80 Frequency: 7, 14, 13, 12, 20, 11, 15, 8[2]
13.The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.[2]
14.Solve the problems given in Example 1.[2]
15.Solve the following pair of linear equations by the elimination method and the substitution method: (i) $x + y = 5$[2]
16.The diagonals of a quadrilateral ABCD intersect each other at the point O such that $\dfrac{AO}{BO} = \dfrac{CO}{DO}$[2]
17.A bag contains lemon flavoured candies only. Malini takes out one candy without looking into the bag. What is the probability that she takes out (i) an orange flavoured candy? (ii) a lemon flavoured candy?[2]
18.The table below shows the daily expenditure on food of 25 households in a locality. Daily expenditure (in ₹): 100 - 150, 150 - 200, 200 - 250, 250 - 300, 300 - 350 Number of households: 4, 5, 12, 2, 2 Find the mean daily expenditure on food by a suitable method.[2]
19.If $P(E) = 0.05$[2]
20.A gulab jamun, contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm (see Fig. 12.15).[2]
21.To find out the concentration of $SO_2$[2]
22.If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms.[2]
23.Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, - 3) and B is (1, 4).[2]
24.Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. (i) 2, 4, 8, 16, . . . (ii) $2, \dfrac{5}{2}, 3, \dfrac{7}{2}, . . .$[2]
25.Suppose you drop a die at random on the rectangular region shown in Fig. 14.6. What is the probability that it will land inside the circle with diameter 1 m?[2]
26.For the following APs, write the first term and the common difference: (i) 3, 1, - 1, - 3, . . . (ii) - 5, - 1, 3, 7, . . . (iii) $\dfrac{1}{3}, \dfrac{5}{3}, \dfrac{9}{3}, \dfrac{13}{3}, . . .$[2]
27.A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, . . . as shown in Fig. 5.4. What is the total length of such a spiral made up of thirteen consecutive semicircles? (Take $\pi = \dfrac{22}{7}$[2]
🔑 Show Answer Key — Set 3
  1. 1. Correct option: (A) $50^\circ$ .
  2. 2. Correct option: (D) $\sqrt{119}$ cm.
  3. 3. (i) A, sin 60° (ii) D, 0 (iii) A, 0° (iv) C, tan 60°
  4. 4. Correct option: (C) $\dfrac{p}{360}\times\pi R^2$ .
  5. 5. Correct option: (B) $70^\circ$ .
  6. 6. Correct option: (B) $-1.5$ .
  7. 7. Correct option: (A) 7 cm.
  8. 8. (i) B, 9 (ii) C, 2 (iii) D, cos A (iv) D, $\tan^2 A$
  9. 9. (i) Choice (C), $-77$ . (ii) Choice (B), $22$ .
  10. 10. $\triangle ABC \sim \triangle PQR$ .
  11. 11. (i) $x = 9$ , $y = 5$ (ii) $s = 9$ , $t = 6$ (iii) Infinitely many solutions: $y = 3x - 3$ (iv) $x = 2$ , $y = 3$ (v) $x = 0$ , $y = 0$ (vi) $x = 1$ , $y = \dfrac{11}{3}$
  12. 12. The mode is approximately $44.71$ cars.
  13. 13. $n = 16$ and $d = \dfrac{8}{3}$ .
  14. 14. (i) John and Jivanti had 36 and 9 marbles, respectively, or 9 and 36 marbles, respectively. (ii) The number of toys produced was 25 or 30. The corresponding cost of each toy was ₹30 or ₹25, respectively.
  15. 15. (i) $x = \dfrac{19}{5}$ , $y = \dfrac{6}{5}$ (ii) $x = 2$ , $y = 1$ (iii) $x = \dfrac{9}{13}$ , $y = -\dfrac{5}{13}$ (iv) $x = 2$ , $y = -3$
  16. 16. ABCD is a trapezium.
  17. 17. (i) $0$ (ii) $1$
  18. 18. The mean daily expenditure on food is $₹211$ .
  19. 19. The probability of 'not E' is $0.95$ .
  20. 20. Approximately $338.18$ cm $^3$ of syrup would be found in 45 gulab jamuns.
  21. 21. The mean concentration of $SO_2$ is approximately $0.099$ ppm.
  22. 22. $S_n = n^2$ .
  23. 23. A is $(3,-10)$ .
  24. 24. (i) Not an AP. (ii) AP; $d = \dfrac{1}{2}$ ; next terms $4, \dfrac{9}{2}, 5$ . (iii) AP; $d = -2$ ; next terms $-9.2, -11.2, -13.2$ . (iv) AP; $d = 4$ ; next terms $6, 10, 14$ . (v) AP; $d = \sqrt{2}$ ; next terms $3 + 4\sqrt{2}, 3 + 5\sqrt{2}, 3 + 6\sqrt{2}$ . (vi) Not an AP. (vii) AP; $d = -4$ ; next terms $-16, -20, -24$ . (viii) AP; $d = 0$ ; next terms $-\dfrac{1}{2}, -\dfrac{1}{2}, -\dfrac{1}{2}$ . (ix) Not an AP. (x) AP; $d = a$ ; next terms $5a, 6a, 7a$ . (xi) Not an AP in general. (xii) AP; $d = \sqrt{2}$ ; next terms $\sqrt{50}, \sqrt{72}, \sqrt{98}$ . (xiii) Not an AP. (xiv) Not an AP. (xv) Not an AP.
  25. 25. The probability is $\dfrac{\pi}{24}$ (approximately $0.131$ ).
  26. 26. (i) $a = 3$ , $d = -2$ . (ii) $a = -5$ , $d = 4$ . (iii) $a = \dfrac{1}{3}$ , $d = \dfrac{4}{3}$ . (iv) $a = 0.6$ , $d = 1.1$ .
  27. 27. The total length is 143 cm.

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