ANSWERS NCERT EXERCISE (C) 2. (D) 3. (C) 4. (B) 5. (A) 6. (B) 7. (C) 8. (A) 9. (D) 10. (D) EXERCISE 1.2

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1 ANSWERS EXERCISE.. (C). (D) 3. (C) 4. (B) 5. (A) 6. (B) 7. (C) 8. (A) 9. (D) 0. (D) EXERCISE.. No, because an integer can be written in the form 4q, 4q+, 4q+, 4q+3.. True, because n (n+) will always be even, as one out of n or (n+) must be even. 3. True, because n (n+) (n+) will always be divisible by 6, as atleast one of the factors will be divisible by and atleast one of the factors will be divisible by No. Since any positive integer can be written as 3q, 3q+, 3q+, therefore, square will be 9q = 3m, 9q + 6q + = 3 (3q + q) + = 3m +, 9q + q = 3m No. (3q + ) = 9q + 6q + = 3 (3q + q) = 3m HCF = 75, as HCF is the highest common factor = 7 (3 5 + ) = 7 (6), which has more than two factors. 8. No, because HCF (8) does not divide LCM (380).

2 84 EXEMPLAR PROBLEMS 9. Terminating decimal expansion, because = = = = and Since is a terminating decimal number, so q must be of the form m.5 n ; m, n are natural numbers. EXERCISE cm , EXERCISE.. (A). (C) 3. (D) 4. (D) 5. (B) 6. (A) 7. (B) 8. (A) 9. (C) 0. (A). (D) EXERCISE.. (i) No (ii) 0, ax + bx + c (iii) deg p (x) < deg g (x) (iv) deg g (x) < deg p(x) (v) No.(i) False (ii) False (iii) True (iv) True (v) True (vi) False (vii) False., 6. EXERCISE.3. 7, 3., , 4 7.,. (i), (ii) 5, , EXERCISE.4 (iii) 3 3, 3. a = and b = 3 or a = 5, b = 3. Zeroes are,, , 3, , 5 (iv) 3, 4 0., , 5

3 ANSWERS 85 3., 3 4. k = 3 Zeroes of x 4 + x 3 4x + 5x + 6 are, 3,, Zeroes of x + x 3 are, , 5, 5 6. a =, b = and are the zeroes of q(x) which are not the zeroes of p(x). EXERCISE 3.. (D). (D) 3. (C) 4. (D) 5. (D) 6. (C) 7. (C) 8. (D) 9. (D) 0. (D). (C). (D) 3. (C). (i) Yes (ii) No (iii) No. (i) No (ii) Yes (iii) No EXERCISE (i) No (ii) Yes (iii) Yes (iv) No 4. No 5. False 6. Not true EXERCISE 3.3. (i) λ = (ii) λ = (iii) All real values of λ except +.. k = 6 3. a = 3, b = 4. (i) All real values of p except 0. (ii) p = (iii) All real values of p except 9. (iv) All real values of p except 4. 0 (v) p = 4, q = 8 5. Do not cross each other. 6. x y = 4 x + 3y = 7; infinitely many pairs.

4 86 EXEMPLAR PROBLEMS 7. 3, x =, y = 4 9. (i) x =., y =. (ii) x = 6, y = 8 (iii) x = 3, y = (iv) x = 6, y = 4 (vii) x =, y = 3 0. x = 340, y = 65; (v) x =, y = (vi) x = a, y = b. (i) consistent; x =, y = (ii) inconsistent (iii) consistent. The solution is given by y = 3 x, where x can take any value, i.e., there are infinitely many solutions.. (,0), (0, 4), (0, 4); 8 sq. units. 3. x = y; Infinitely many lines. 4. a = 5, b = º, 85º. 6. Salim s age = 38 years, Daughter s age = 4 years years , students in hall A, 80 students in hall B. 0. Rs 0, Rs x = 0, y = 30, A =30º, B=00º, C= 50º, D=80º EXERCISE 3.4. x =, y = 4; 4:. (0, 0), (4, 4), (6, ) 3. 8 sq. units 4. 4x + 4y = 00,3x = y + 5, where Rs x and Rs y are the costs of a pen and a pencil box respectively; Rs 0, Rs 5 5. (, 0), (, 3), (4, ) 6. 0 km/h, 40 km/h 7..5 km/h 8. 0 km/h, 4 km/h Rs 500, Rs 30. Rs 600, Rs 400. Rs 000 in scheme A, Rs 0000 in scheme B

5 ANSWERS 87 EXERCISE 4.. (D). (C) 3. (C) 4. (A) 5. (B) 6. (D) 7. (B) 8. (C) 9. (B) 0. (A). (C) EXERCISE 4.. (i) No, because discriminant = 7 < 0. (ii) Yes, because discriminant = 9 > 0. (iii) No, because discriminant = 0. (iv) Yes, because discriminant = 4 > 0. (v) No, because discriminant = 64 < 0. (vi) Yes, because discriminant = ( ) 0. (vii) Yes, because discriminant = > 0. (viii) No, because discriminant = 7 < 0. (ix) Yes, because discriminant = > 0. (x) Yes, because discriminant = 8 > 0.. (i) False, for example : x = is a quadratic equation with two roots. (ii) (iii) (iv) (v) (vi) False, for example x + = 0 has no real root. False, for example : x + = 0 is a quadratic equation which has no real roots. True, because every quadratic polynomial has almost two zeroes. True, because if in ax +bx+c = 0, a and c have opposite signs, then ac<0 and so b 4ac > 0. True, because if in ax +bx+c = 0, a and c have same sign and b = 0, then b 4ac = 4ac < x 3x + = 0 is an equation with integral coefficients but its roots are not integers. 4. x 6x 7 0, which has roots 3,3 5. Yes. 3 x 7 3x 3 0, which has roots 3, 4 6. No. 7. Yes

6 88 EXEMPLAR PROBLEMS. (i) 5, (ii), EXERCISE (iii), 3 (iv) 5, 5 3 (v) 3, (vi) 5, 5 (vii) 3, 3 3. (i), 3 (iv) 5, 5 3 (ii),3 (v),. (i) Real roots exist; roots are, 3 4 (ii) Real roots exist; roots are, (iii) Real roots exist; roots are (iii) EXERCISE , (iv) Real roots exist; roots are 4 + 3,4 3 (v) Real roots exist; roots are 7 5, 5. The natural number is 3. The natural number is 8 4. Original speed of the train is 45 km/h 5. Zeba s age now is 4 years 6. Nisha s age is 5 years and Asha s age is 7 years 7. Length of the pond is 34 m and breadth is 4 m 8. 4, 6

7 ANSWERS 89 EXERCISE 5.. (D). (B) 3. (B) 4. (B) 5. (C) 6. (B) 7. (B) 8. (B) 9. (C) 0. (A). (C). (D) 3. (B) 4. (C) 5. (A) 6. (A) 7. (C) 8. (A) EXERCISE 5.. (i), (iv) and (vii) form an AP as in each of these ak a k is the same for different values of k.. False, as a4 a3 a3 a. 3. Yes, a30 a d 0 d The difference between any two corresponding terms of such APs is the same as the difference between their first terms. 5. No. 6. No, as the total fare (in Rs) after each km is 5, 3, 3, 39, (i), (ii) and (iii) form an AP as in the list of numbers formed every succeeding term is obtained by adding a fixed number. 8. (i) Yes (ii) No (iii) No. (A ) (B 4 ) (A ) (B 5 ) (A 3 ) (B ) (A 4 ) (B ) 5 3. (i),, 4 (ii) 0,,3 3 3 EXERCISE 5.3 (iv) (a+) + (b+), (a+) + (b+), (a+3) + (b+) (v) 5a 4, 6a 5, 7a 6 (iii) 4 3,5 3, 6 3

8 90 EXEMPLAR PROBLEMS 3. (i),, 3 6 (ii) 5, 8, (iii) 4. a, b 5, c , 7,, 5, ,, d, n , 6,, 6, Yes, 7 th term.. k = 0. 67, 69, º, 60º, 80º 4. 6 th term; th term n = 6, d = 0. (i) 9400 (ii) 7 n 6 (iii) a b a b. 6 th term; , 3,, k = n = 5, Rs months. EXERCISE (i) 50 (ii) 750 (iii) , 7,, 5, (i) 683 (ii) :3; 5: Rs 3900; Rs m; 6 m. EXERCISE 6.. (C). (B) 3. (C) 4. (A) 5. (D) 6. (B) 7. (B) 8. (A) 9. (B) 0. (C). (A). (C) EXERCISE 6.. No, No, D = R but F P. 3. Yes, because PA PB QA BR 4. Yes, SAS criterion.

9 ANSWERS 9 5. No, ΔQPR ~ ΔSTM 6. No, Corresponding sides must also be proportional. 7. Yes, as the corresponding two sides and the perimeters are equal, their third sides will also be equal. 8. Yes, AAA criterion. 9. No, ratio will be No, For this, P should be 90.. Yes, AA criterion.. No, angles should be included angles between the two pairs of proportional sides. EXERCISE 6.3. x = 4. 9: cm 7. 8 cm 8. : cm cm. cm cm m 5. 8 m EXERCISE cm, cm. BC = 6.5 cm, EF = 6.8 cm m 6. 8 km m 8. 9 m 9. 5 cm, 6 cm 0. 5cm, 5 cm, 3 5cm 4. 8 cm, cm, 6 cm EXERCISE 7.. (B). (B) 3. (C) 4. (B) 5. (C) 6. (B) 7. (C) 8. (B) 9. (D) 0. (A). (B). (D) 3. (B) 4. (A) 5. (A) 6. (D) 7. (D) 8. (B) 9. (B) 0. (C) EXERCISE 7.. True. Because all three sides of both triangles are proportional.. True. The three points lie on the line x = False, since two points lie on the y axis and one point lies in quadrant I. 4. False. PA= and PB= 0, i.e., PA PB. 5. True, since ar (ΔABC) = 0.

10 9 EXEMPLAR PROBLEMS 6. False, since the diagonals donot bisect each other. 7. True, radius of the circle = 5 and OP > 5 8. False, since AP AQ 9. True, since P divides AB in the ratio : 0. True, since B divides AC in the ratio : 7. False, since PC = 6 6, P will lie inside the circle.. True, Mid-points of both the diagonals are the same and the diagonals are of equal length. EXERCISE 7.3. Scalene triangle. (9, 0), (5, 0), points 3. Rectangle 4. a = 3 5. ( 3, 5) the middle point of AB. Infinite number of points. In fact all points which are solutions of the equation x+y + = 0. 6.,0, isosceles triangle y = 3, 5, PQ = 90, :7, 34,0 3. :5. a = b = 3 3. k =, AB= 6 4. a = 5, a =, Area = 6 sq. unit 8. 4, , 0. 8:, 8, 3 9

11 ANSWERS 93 EXERCISE , sq. units (i) x x, y y 3 3 (iii) same as (ii) (iv) same as (ii) 4. a = 3, h 6 3 (ii) 5. Yes, Jaspal should be placed at the point (7, 5) 6. House to Bank = 5 km Bank to school = 0 km School to Office = km Total distance travelled = 7 km Distance from house to office = 4.6 km Extra distance =.4 km EXERCISE 8. x x x, y y y (B). (A) 3. (B) 4. (C) 5. (B) 6. (B) 7. (C) 8. (A) 9. (A) 0. (D). (B). (C) 3. (C) 4. (B) 5. (A) EXERCISE 8.. True. False 3. False [sin 80 sin 0º = positive : as θ increases, value of sin θ increases ] 4. True 5. True 6. False 7. False 8. False 9. False 0. False. False. True

12 94 EXEMPLAR PROBLEMS m EXERCISE EXERCISE m m m; 0 m 4. h (cot α cot β) m 8. 8 m 6. ( ) EXERCISE 9.. (B). (D) 3. (C) 4. (A) 5. (D) 6. (C) 7. (A) 8. (A) 9. (D) 0. (B) EXERCISE 9.. False. False 3. True 4. True 5. True 6. False 7. True 8. False 9. True 0. True. 3 cm EXERCISE 9.3 EXERCISE cm cm º 3. 8 cm 4. 4 cm EXERCISE 0. 0 cm 3. (D). (B) 3. (A) 4. (C) 5. (B) 6. (D) EXERCISE 0.. True. False 3. False 4. True

13 ANSWERS 95 EXERCISE 0.3. Yes 7. No EXERCISE cm. Yes, yes 3. 4 cm 6. 8 cm EXERCISE.. (B). (A) 3. (B) 4. (A) 5. (B) 6. (A) 7. (D) 8. (B) 9. (C) 0. (D). No, radius of the circle is a. Yes, side of the square is a cm EXERCISE. 3. No, side of the outer square = diagonal of the inner square 4. No, it is only true for minor segment. 5. No, it is πd. 6. Yes, distance covered in one revolution = π r 7. No, it will depend on the value of radius. 8. Yes, it will be true for the arcs of the same circle. 9. No, it will be true for the arcs of the same circle. 0. No, it will be true for arcs of the same circle.. Yes, radius of the circle breadth of the rectangle.. Yes, their radii are equal 3. Yes, their radii are equal 4. No, diagonal of the square is p cm. EXERCISE cm. (6π 3 ) cm cm m 6. ( π )cm cm 8. (3 + π )m 9. (48 4π )m

14 96 EXEMPLAR PROBLEMS cm cm cm cm m cm 6. EXERCISE.4. Rs m cm 5. Rs cm cm (approx) cm 9. 4 cm cm. 4.3 m. 800 cm 3. : 3 : 5 60 cm π cm cm, Areas: cm 44, 54 cm ; Arc lengths: cm ; 3 Arc lengths of two sectors of two different circles may be equal, but their area need not be equal π cm EXERCISE. 5π 5 + cm cm. (A). (A) 3. (B) 4. (B) 5. (C) 6. (D) 7. (A) 8. (A) 9. (B) 0. (A). (B). (C) 3. (A) 4. (A) 5. (A) 6. (B) 7. (C) 8. (A) 9. (A) 0. (D) EXERCISE.. False. False 3. False 4. False 5. False 6. True 7. False 8. True EXERCISE.3. 6 cm cm 4. 7: cm cm cm (approx.) 8. 4 cm, 7 cm; 3 cm 3, 66 cm 3 ; 396 cm cm 3

15 ANSWERS EXERCISE cm. 8.6 m cm 3, 9.7 kg words 5. 5 minutes sec m 3,80.6 m 7. Rs hours 9. m cm cm 3. Rs cm, 43.7 cm cm, 377. cm m m cm 9..5 cm cm 3 EXERCISE 3.. (C). (B) 3. (A) 4. (C) 5. (B) 6. (B) 7. (B) 8. (C) 9. (C) 0. (C). (A). (D) 3. (D) 4. (A) 5. (C) 6. (B) 7. (C) 8. (A) 9. (A) 0. (A). (D). (B) 3. (C) 4. (A) 5. (C) 6. (B) EXERCISE 3.. Not always, because for calculating median of a grouped data, the formula used is based on the assumption that the observations in the classes are uniformly distributed (or equally spaced).. Not necessary, the mean of the data does not depend on the choice of a (assumed mean). 3. No, it is not always the case. The values of these three measures can be the same. It depends on the type of data. 4. Not always. It depends on the data. 5. No, the outcomes are not equally likely. For example, outcome one girl means gbb, bgb, bbg three girls means ggg and so on. 6. No, the outcomes are not equally likely. The outcome 3 is more likely than the others. 7. Peehu; probability of Apoorv s getting 36 while probability of Peehu s getting

16 98 EXEMPLAR PROBLEMS 8. Yes, the probability of each outcome is, since the two outcomes are equally likely No, outcomes and not are not equally likely, P() =, P(not) =, No, the outcomes are not equally likely. Outcome no head means TTT ; outcome one head means THT, HTT, TTH and so on. P (TTT) = 8, P (one head) = 3 8 and so on.. No, the outcomes head and tail are equally likely every time regardless of what you get in a few tosses.. It could be a tail or head as both the outcomes are equally likely, in each toss. 3. No, head and tail are equally likely. So, no question of expecting a tail to have a higher chance in the 4th toss. 4. Yes, the outcomes odd number, even number are equally likely in the situation considered. EXERCISE Rs kg km/l; No, the manufacturer is claiming mileage.5 km/h more than the average mileage 9. Weight (in kg) Number of persons Less then 45 4 Less then 50 8 Less then 55 Less then 60 6 Less then 65 3 Less then Less then Less then 80 40

17 ANSWERS Marks Number of students Marks Number of candidates a =, b = 3, c = 35, d = 8, e = 5, f = 50

18 00 EXEMPLAR PROBLEMS 3. (i) Less than type (ii) More than type Ages (in years) Number of Ages (in years) Number of students students Less than 0 0 More than or equal to Less than 0 60 More than or equal to 0 40 Less than 30 0 More than or equal to Less than More than or equal to Less than 50 7 More than or equal to Less than More than or equal to Less than Marks Number of students Rs km/h 7. Rs kg 9. (i) 6 (ii) 5 6. (i) (ii) 9 P()=, P(3)=, P(4)=, (iii) (i) 6 (ii) 5 (iii) 0 7. (i) 5 5. (i) 8 (ii) (ii) 7 P(5)=, P(6)=, P(7)=, P(8)= (iii) 7 P(9)= 8

19 ANSWERS 0 8. (i) (i) 0 3. (i) (ii) 3 49 (ii) 3 0 (ii) (i) 0 49 (iii) (i) P (not defective) = 3 4, P (nd bulb defective) = (i) (i) 8 (ii) 5 9 (ii) 8 (iii) 3 (iii) (i) 5 scores (0,,, 6, 7, ) (ii) (i) 7 8 (ii) (i) (ii) (i) 5 6 (ii) 49 9 (ii) 00 (iv) 5 8 (ii) 3 [Hint : (ii) After first player has won the prize the number of perfect squares greater than 500 will be reduced by ]

20 0 EXEMPLAR PROBLEMS EXERCISE years g 7. Median salary = Rs 340, Modal salary = Rs f = 8, f = 4 9. p = 5, q = 7. Median = 7.8 hectares, Mode = 7.76 hectares. Median rainfall =.5 cm 3. average = 70.3 sec. 4. (i) Distance (in m) No. of students Cummulative frequency (iii) 49.4 m.

CLASS - VIII. Time Allowed: 2 Hours Max. Marks: 100

CLASS - VIII. Time Allowed: 2 Hours Max. Marks: 100 Roll No. A Please check that this questionnaire contains 11 printed pages. Code A, B or C given on the right hand top corner of the questionnaire should be written on the answer sheet in the space provided.