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1       1      1              5       2       3.  (a) 12x  – 15x + 3;  (i) 66  (ii)  –3
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                      6.  (a)       (b)       (c)       (d) 0    (e)       (e)                        2
                           2       6       3             6       3         (b) a  + a  + a + 5;  (i) 5  (ii) 8  (iii) 4
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                           1       3        1                                          2        2      3   3
                      7.  (a)       (b)       (c)       (d) 0            4.  (i) 4ac  (ii) 3x  + 4xy – y   (iii) x  + y
                           2      10       10                              (iv) 2.25x  – 16y 2
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                                                                         5.  (i) a  – 2a b  + b   (ii) 40x  (iii) 98m  + 128n
                          Some NCERT Textbook Questions                    (iv) 41m  + 80m  + 41n   (v) 4p  – 4q
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                                       Chapter 1                           (vi) a b  + b c   (vii) m  + n m 2
                      1.  Associativity                                  6.  Students to do on their own.
                      2.  No, because the product is not 1.              7.  (i) 10404  (ii) 996004  (iii) 6396  (iv) 9.975
                          –1                                             8.  (i) 10712  (ii) 26.52  (iii) 10094  (iv) 95.06
                      3.
                         –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0                              Chapter 6
                         11 11 11 11 11 11 11 11 11 11 11                1.  (i)  x 3   (ii)  x y  (iii) –2a b
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                       –7 –6 –5 –4 –3 –2 –1       1  2                        2     3
                      4.   ,   ,   ,   ,   ,   ,   , 0, …,   ,                                         1
                       20 20 20 20 20 20 20       20 20                  2.  (i) 5(3x + 5)  (ii) 2y(x + 5)  (iii)  r(p + q)
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                        (There can be many more such rational numbers)      (iv) 4(y  + 5y + 3)  (v) (x + 2)(x + 3)
                        97 98 99 100 101 102 103 104 105 106
                      5.   ,   ,   ,   ,   ,   ,   ,   ,   ,                               Chapter 7
                       160 160 160 160 160 160 160 160 160 160
                        (There can be many more such rational numbers)    1.  (i) (x + 8)(x + y)  (ii) (3x + 1)(5y – 2)
                                                                           (iii) (5p + 3)(3q + 5)  (iv) (z –7)(1 – xy)
                                       Chapter 2                         2.  (i) (a + 4)   (ii) (l – m)   (iii) (3xy – 4)(3xy + 4)
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                           1       1               1        1              (iv) (3x – 2)(2y – 3)  (v)  (a – b)(a + b)(a  + b )
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                      1.  (i)     (ii)    (iii) (5 )  (iv)     (v)
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                          (–4) 3   2 6            (3) 2   (–14) 3          (vi) z(2x – z)(2x  – 2xz + z )  (vii) (a – b) (a + b)
                                1               625t 4                     (viii) (p + 8)(p – 2)
                      2.  (i) 5  (ii)    (iii) 29  3.  (i)     (ii) 5 5
                                2                2                                         Chapter 8
                                                         –7
                               –6
                      4.  (i) 1 × 10   (ii) 1.6 × 10 –19   (iii) 5 × 10                                       8
                                   –5
                        (iv) 1.275 × 10   (v) 7 × 10 –2                  1.  (a) x = 9  (b) x = 2  (c) y = 2.4  (d) x = – 5
                                       Chapter 3                         2.   1   3.  19  4.  (a) t = – 1  (b) x = 40  (c) y =  7 3
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                      1.  These numbers ends with                        5.  26 (or 62)  6.  Length = 275 m; breadth = 100 m
                        (i) 7  (ii) 3  (iii) 8  (iv) 2  (v) 0  (vi) 2                              4
                        (vii) 0  (viii) 0                                7.  72  8.  (a) y = –8  (b) y = – 5
                      2.  (i) 1 + 3 + 5 + 7 + 9 + 11 + 13                9.  Hari’s age = 20 years; Harry’s age = 28 years
                        (ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21               Chapter 9
                      3.  (i) 6, 8, 10  (ii) 14, 48, 50  (iii) 16, 63, 65    –4
                        (iv) 18, 80, 82                                  1.  10  cm; 2 cm
                      4.  (i) 7; 42  (ii) 5; 30  (iii) 7; 84  (iv) 3; 78     2.  21 m  7                6
                        (v) 2; 54  (vi) 3; 48                            3.  (i) 2.25 × 10  crystals  (ii) 5.4 × 10  crystals
                      5.  49  6.  (i) 48  (ii) 67  (iii) 59  (iv) 37     4.  4 → 25,000; 5 → 20,000; 8 → 12,500; 10 → 10,000;
                      7.  (i)  1.6  (ii)  2.7  (iii)  7.2  (iv) 6.5  (v) 5.6      20 → 5,000
                                                                            Amount given to a winner is inversely proportional to the
                                       Chapter 4                           number of winners.
                      1.  (i) 3  (ii) 2  (iii) 3  (iv) 5  (v) 10         5.  4  6.  (i) 6 days  (ii) 6 persons
                      2.  (i) 3  (ii) 2  (iii) 5  (iv) 3  (v) 11
                      3.  (i) False  (ii) True  (iii) False  (iv) False                   Chapter 11
                        (v) False  (vi) False  (vii) True                1.  25 matches
                      4.  11, 17, 23, 32                                 2.  ` 2400
                                                                         3.   10%, cricket → 30 lakh; football → 15 lakh;
                                       Chapter 5                           other games → 5 lakh
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                      1.  (i) 0  (ii) ab + bc + ac  (iii) –p q  + 4pq + 9     4.  ` 1,40,000
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                        (iv) 2(l  + m  + n  + lm + mn + nl)                               Chapter 12
                      2.  (a) 8a – 2ab + 2b – 15                         1.  ` 34.80  2.  Gain of 2%  3.  ` 2,835  4.  ` 18,342.50
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                           2
                        (b) p q – 7pq  + 8pq – 18 q + 5p + 28            5.  ` 2,000
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