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r`j]w jyv}r

l[m|b]N] @kt]v]\l vww n`@g`d kUwr. r`j]w jyv}r. (0718005616 @h` 0343341702 ). mGhr]n<br>. Exit. r`j]w jyv}r. XY} Er~mk } r~w ] p]r]@ vn @ p`l vw w pAsl @ k`l l[p]t]y @ k`LB 03 0718005616 @h` 0343341702. Exit. mGhr]n<br>. gN]wy. sm`nwr @XYV] 10 / 11 @XYN] sQh`

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r`j]w jyv}r

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  1. l[m|b]N] @kt]v]\\l vw\w n`@g`d kUwr. r`j]w jyv}r (0718005616 @h`\ 0343341702) mGhr]n\n Exit

  2. r`j]w jyv}r XY} Er~mk}r~w] p]r]@vn @p`l\vw\w pAsl @k`l\l[p]t]y @k`LB 03 0718005616 @h`\ 0343341702 Exit mGhr]n\n

  3. gN]wy sm`n\wr @XY\V] 10 / 11 @XY\N] sQh` r`j]w jyv}r (v]@X\S gN]w p[h[N[) mGhr]n\n Exit

  4. sm`n\wr @XY\V]. (1) hFq]n\v]m. (2) sm`n\wr @XY\V]ykpqyk\ @s””`yn s[wYx`v]wy. (3) sm`n\wr @XY\V]ykpqvlekw;v @s””`yn s[wYx`v]wy. (4) sm`n\wr @XY\V] vlsm`n\wrmE&ny. Exit

  5. sm`n\wr @XY\V] hFq]n\v]m. (1) 2,4,6,8………………………….. .. .. +2 b#g]n\ ekw;v] a#w. (2) -25,-23,-21………………………….. .. .. -2 b#g]n\ ekw;v] a#w. (3) 65,60,55,50………………………….. .. .. -5 b#g]n\ ekw;v] a#w. ihw a`k`ryt ekm agyk\ ekw;v] n]r~m`Ny vn @XY\V] sm`n\wr @XY\V] yn[@vn\ hÀ[n\vy]. wvq Pm ekw; vn agy @p`À[an\wry yn[@vn\ hÀ[n\vy]. G#tU @p`À[ an\wry d= ps{ pqy - @pr pqy pYE`n @mn[vt

  6. sm`n\wr @XY\V] h#q]n\v]m g#tU. an\wry = 5 - 2 =3 an\wry = 8 - 5 =3 an\wry = 11 - 8=3 phw sqhn\ @XY\V]sm`n\wr @XY\V] @v|q @n`@v|q? (1) 2 5 8 11 ……….. @mh] an\wry sm`n n]s`Py sm`n\wr @XY\V]yk\ @v|. • phw e\v` sm`n\wr @XY\V] @v|q @n`@v|q? (2)10.25, 10.50, 10.75 ……….. (3) 7½ , -8 , 8 ½, -9 ……….. (4) -3 , 5 , -7 , ……….. (5) 0.2 , 0.5 , 0.8 , ……….. (6) a , a+d ,a+2d ,a+3d…. p]L]w;r p]L]w;r p]L]w;r pYE`n @mn[vt p]L]w;r p]L]w;r

  7. (2) 10.25, 10.50, 10.75 sm`n\wr @XY\V]yk\ @v|q @n`@v|q? • an\wry = 10.50 –-10.25=0.25 • an\wry = 10.75-10.50 =0.25 • emn]s` @my sm`n\wr @XY\V]yk\ @v]. pYE`n @mn[vt r`j]w jyv}r 0718005616

  8. (3) 7½ , -8 , 8 ½, -9sm`n\wr @XY\V]yk\ @v|q @n`@v|q? an\wry = -8 - 7 ½, = -15½ an\wry = 8 ½ -(-8) = 8 ½ +8=16½ @my sm`n\wr @XY\V]yk\ @n`@v|. pYE`n @mn[vt

  9. (4) -3 , 5 , -7 ,sm`n\wr @XY\V]yk\ @v|q @n`@v|q? an\wry = 5-(-3) = 5+3 =8 an\wry = -7 -5 =-12 @my sm`n\wr @XY\V]yk\ @n`@v]. pYE`n @mn[vt r`j]w jyv}r 0718005616

  10. (5) 0.2 , 0.5 , 0.8sm`n\wr @XY\V]yk\ @v|q @n`@v|q? an\wry = 0.5 - 0.2 = 0.3 an\wry = 0.8 - 0.5 = 0.3 emn]s` @my sm`n\wr @XY\V]yk\ @v]. pYE`n @mn[vt r`j]w jyv}r 0718005616

  11. (6) a , a+d ,a+2d ,a+3dsm`n\wr @XY\V]yk\ @v|q @n`@v|q? an\wry= a+d - a = d an\wry=a+2d–(a+d)=a+2d-a-d = d an\wry=a+3d-(a+2d)=a+3d-a-2d= d emn]s` @my sm`n\wr @XY\V]yk\ @v|. pYE`n @mn[vt

  12. sm`n\wr @XY\V]yk pqyk\ @s`yn s[wYy x`v]wy Тn = а+(n-1)d @mh] Тn = n vn pqy n = pq gnn а = m[l\ pqy d =@p`u[ an\wry pYE`n @mn[vt s[wYy lb` g#n]m g’#tU

  13. pqyk\ @s`yn s{wYy lb`g#n}m • pLm[ pqy a q n vn pqy T nq @p`À[ aAwry d q vn sm`n\wr @XY\V]y slkm[. 1 vn pqy T 1 = a 2 vn pqy T 2 = a + d 3 vn pqy T 3 = a +d +d =a+ 2d 4 vn pqy T 4 = a +d +d +d =a+ 3d 5 vn pqy T 5 =a +d +d +d +d =a+4d n vn pqy T n = a + (n-1) d pYE`n @mn[vt g’#tU Tn = a + (n-1) d

  14. g’#tU p]L]w;r (1) -2,-4,-6……………………….. sm`n\wr @XY\V]@y\ 10 vn pqy @s`yn\n. (2) 1/2…,1 1/2, 2 ½1/2, 3 1/2…………………….. sm`n\wr @XY\V]@y\ 7 vn pqy @s`yn\n. (3) 0.3,0.6,0.9……………………….. sm`n\wr @XY\V]@y\ 6 vn pqy @s`yn\n. (4) 25,20,15……………………….. sm`n\wr @XY\V]@y\ 9 vn pqy @s`yn\n. p]L]w;r p]L]w;r p]L]w;r pYE`n @mn[vt

  15. Tn = a + (n-1) d a`XY]w g#tU qn\n` pqyk\ @sv}m Tn pLm[ pqy @sv}m a @p`À[ an\wry @sv}m d pq gNn @sv}m n sAk}r~ g#tU pYE`n @mn[vt

  16. (1) -2,-4,-6……………………….. sm`n\wr @XY\V]@y\ 10 vn pqy @s`yn\n. a =-2 d = -4-(-2)=-4+2=-2 T10 =? n =10 Tn = a + (n-1) d T10 = -2 + (10-1) -2 T10 = -2 + 9 X -2 T10 = -2 -18 T10 = -20 pYE`n @mn[vt

  17. (2) 1/2…,1 1/2, 2 ½1/2, 3 1/2…………………….. sm`n\wr @XY\V]@y\7 vn pqy @s`yn\n. a =1/2 d = 1 ½ - ½ =1 T7 =? n =7 Tn = a + (n-1) d T7 = ½ + (7-1) 1 T7 = ½ + (6) 1 T7 = ½ + 6 T7 = 6 ½ pYE`n @mn[vt

  18. (3) 0.3,0.6,0.9……………………….. sm`n\wr @XY\V]@y\ 6 vn pqy @s`yn\n. Tn = a + (n-1) d T6 = 0.3 + (6-1) 0.3 T6 = 0.3 + 5 X 0.3 T6 = 0.3 +1.5 T6 = 1.8 a =0.3 d = 0.6-0.3=0.3 T6 =? n =6 pYE`n @mn[vt

  19. (4) 25,20,15……………………….. sm`n\wr @XY\V]@y\ 9 vn pqy @s`yn\n. Tn = a + (n-1) d T9 = 25 + (9-1) -5 T9 = 25 + 8 X -5 T9 = 25 - 40 T9 = -15 a = 25 d = 20-25 = -5 T9 =? n =9 pYE`n @mn[vt

  20. (2) pLm[ pqy @sv}m p]L]w;r (1)10 vn pqy -20 q @p`À[ an\wry -2 q v{ @XY\V]@y\ 1 vn pqy @s`yn\n. (2) 7vn pqy 6 1/2 q @p`À[ an\wry 1 q v{ @XY\V]@y\ 1 vn pqy @s`yn\n. (3) 6 vn pqy 1.8 q @p`À[ an\wry 0.3 q v{ @XY\V]@y\ 1 vn pqy @s`yn\n. (4) 9 vn pqy -15 q @p`À[ an\wry -5 q v{ @XY\V]@y\ 1 vn pqy @s`yn\n. p]L]w;r p]L]w;r pYE`n @mn[vt p]L]w;r

  21. (1)10 vn pqy -20 q @p`À[ an\wry -2 q v{ @XY\V]@y\ 1 vn pqy @s`yn\n. a =? d = -2 T10 =-20 n =10 Tn = a + (n-1) d T10 = a + (10-1) -2 -20= a + 9 X -2 -20= a – 18 -20+18 = a -2=a pYE`n @mn[vt

  22. (2) 7vn pqy 6 1/2 q @p`À[ an\wry 1 q v{ @XY\V]@y\ 1 vn pqy @s`yn\n. a =? d = 1 T7 = 6 ½ n =7 Tn = a + (n-1) d T7 = a + (7-1) 1 6 ½ = a + 6 X 1 6 ½ = a + 6 6 ½ - 6 = a ½ =a pYE`n @mn[vt

  23. (3) 6 vn pqy 1.8 q @p`À[ an\wry 0.3 q v{ @XY\V]@y\ 1 vn pqy @s`yn\n. a =? d = 0.3 T6 =1.8 n =6 Tn = a + (n-1) d T6 = a + (6-1) 0.3 1.8= a +5 X 0.3 1.8= a +1.5 1.8 -1.5= a 0.3 = a pYE`n @mn[vt

  24. (4) 9 vn pqy -15 q @p`À[ an\wry -5 q v{ @XY\V]@y\ 1 vn pqy @s`yn\n. a =? d = -5 T9 = -15 n =9 Tn = a + (n-1) d T9 = a + (9-1) -5 -15= a +8 X -5 -15= a -40 -15+40= a 25 = a pYE`n @mn[vt

  25. (3) @p`À[ an\wry @sv}m p]L]w;r (1)1 vn pqy -2 q 10 vn pqy-20 q v{ @XY\V]@y\ @p`À[ an\wry @s`yn\n. (2)7 vn pqy 6 1/2 q 1 vn pqy 1/2 q v{ @XY\V]@y\ @p`À[ an\wry @s`yn\n. (3)6 vn pqy 1.8 q 1 vn pqy 0.3 q v{ @XY\V]@y\ @p`À[ an\wry @s`yn\n. (4)1 vn pqy 25 q 9 vn pqy-15 q v{ @XY\V]@y\ @p`À[ an\wry @s`yn\n. p]L]w;r p]L]w;r p]L]w;r pYE`n @mn[vt

  26. a =-2 d = ? T10 = -20 n =10 Tn = a+ (n-1) d T10 = -2+(10-1) d -20 = -2+ 9 X d -20 = -2+ 9d -20-2 = 9d -18 = 9d -18 ÷9=d -2=d (1)1 vn pqy -2 q 10 vn pqy-20 q v{ @XY\V]@y\ @p`À[ an\wry @s`yn\n. pYE`n @mn[vt

  27. a = ½ d = ? T7 = 6 ½ n =7 Tn = a+ (n-1) d T7 = ½ +(7-1) d 6 ½ = ½ + 6 X d 6 ½ = ½ + 6d 6½-½= 6d 6 = 6d 6 ÷6 =d 1 =d (2)7 vn pqy 6 1/2 q 1 vn pqy 1/2 q v{ @XY\V]@y\ @p`À[ an\wry @s`yn\n. pYE`n @mn[vt

  28. a = 0.3 d = ? T6 = 1.8 n =6 Tn = a+ (n-1) d T6 = 0.3 +(6-1) d 1.8 = 0.3 + 5 X d 1.8 = 0.3 + 5d 1.8-0.3 = 5d 1.5 = 5d 1.5 ÷5 = d 0.3 = d (3)6 vn pqy 1.8 q 1 vn pqy 0.3 q v{ @XY\V]@y\ @p`À[ an\wry @s`yn\n. pYE`n @mn[vt

  29. a = 25 d = ? T9= -15 n =9 Tn = a+ (n-1) d T9 = 25 +(9-1) d -15 = 25 + 8 X d -15 = 25 + 8d -15-25 = 8d 40 = 8d 40 ÷8 = d 5 = d (4)1 vn pqy 25 q 9 vn pqy-15 q v{ @XY\V]@y\ @p`À[ an\wry @s`yn\n. pYE`n @mn[vt

  30. (4) pq gNn @sv}m p]L]w;r (1) pLm[ pqy -2 q @p`À[ aAwry -2 q v[ @XY\V]@y\ -20 vn\@n\ k}vn pqyq ?’. (2) pLm[ pqy 1/2 q @p`À[ aAwry 1 q v[ @XY\V]@y\ 6 1/2 vn\@n\ k}vn pqyq ?’. (3) pLm[ pqy 0.3 q @p`À[ aAwry 0.3 q v[ @XY\V]@y\ 1.8 vn\@n\ k}vn pqyq ?’. (4) pLm[ pqy 25 q @p`À[ aAwry -5 q v[ @XY\V]@y\ -15 vn\@n\ k}vn pqyq ?’. p]L]w;r p]L]w;r p]L]w;r pYE`n @mn[vt

  31. sn = n (a+l) 2 sn=n{2a+(n-1)d} 2 sm`n\wr @XY\V]yk pqvl ekw;v @s`yn s[wYy x`v]wy g’#tU g’#tU sn= pq n vl ekw;v a = m[l\ pqy l = avsn\ pqy d = @p`À[ aAwry s[wYy 1 lb`g#n}m s[wYy 2 lb`g#n}m pYE`n @mn[vt

  32. sn=n (a+l) s[wYy lb`g#n}m 2 plm[ pqy a q pq n vl ekw;v sn q avsn\ pqy l q vn @XY\V]y slkm[. ev]t @XY\V]y a,a+d,a+2d ………l-2d,l-d,l@v|. @mm @XY\V]@y\ ekw;v sn nm| Sn= a+(a+d)+(a+2d) ……+(l-2d)+(l-d)+l(a+l) (a+l) (a+l) pYE`n @mn[vt

  33. wvq @mh’] pq n a#w’] b#v]n\ a+l pq n/2 k\ a#w. em n]s` pq n vl ekw;v sn = n (a+l) 2 g’#tU pYE`n @mn[vt

  34. sn=n {2a+(n-1)d} s[wYy lb`g#n}m2 sn=n (a+l) s[wYy slkm[. 2 @mm @XY\V]y pq n a#w\nm| avs`n pqy l vn pqy @v|. enm| l = a + (n -1) d @v|. ev]t sn=n {a+a+(n-1)d} 2 sn=n {2a+(n-1)d} 2 g’#tU pYE`n @mn[vt

  35. s n=n {2a+(n-1)d} s[wYy x`v]wy 2 (1) q} a#w] pq gnnk ekw;v @sv}m sn (2) pLm[ pqy @sv}m a (3) @p`À[ an\wry @sv}m d (4) pq gNn @sv}m n pYE`n @mn[vt

  36. (1) q} a#w] pq gnnk ekw;v @sv}m sn p]L]w;r (1) 2,4,6,8….. @XY\V]@y\ pq 8 k ekw;v @s`yn\n. (2) 0.2,0.5,0.8 ….. @XY\V]@y\ pq 7 k ekw;v @s`yn\n. (3) ½ , ¾ ,1….. @XY\V]@y\ pq 5 k ekw;v @s`yn\n. p]L]w;r p]L]w;r pYE`n @mn[vt

  37. (1) pLm[ pqy -2 q @p`À[ aAwry -2 q v[ @XY\V]@y\ -20 vn\@n\ k}vn pqyq ?’. Tn = a+ (n-1) d Tn = -2+(n-1) -2 -20 = -2 -2n + 2 -20 = -2n -20 ÷-2 =n 10 =n a =-2 d = -2 Tn = -20 n =? pYE`n @mn[vt

  38. (2) pLm[ pqy 1/2 q @p`À[ aAwry 1 q v[ @XY\V]@y\ 6 1/2 vn\@n\ k}vn pqyq ?’. Tn = a+ (n-1) d Tn = ½ +(n-1) 1 6 ½ = ½ + n - 1 6 ½ +½ = n 6 =n a = ½ d = 1 Tn = 6 ½ n =? pYE`n @mn[vt

  39. (3) pLm[ pqy 0.3 q @p`À[ aAwry 0.3 q v[ @XY\V]@y\ 1.8 vn\@n\ k}vn pqyq ?’. Tn = a+ (n-1) d 1.8 = 0.3+(n-1) 0.3 1.8 = 0.3 +0.3n-0.3 1.8 = 0.3n 1.8 ÷0.3=n 0.6 =n a = 0.3 d = 0.3 Tn= 1.8 n =? pYE`n @mn[vt

  40. (4) pLm[ pqy 25 q @p`À[ aAwry -5 q v[ @XY\V]@y\ -15 vn\@n\ k}vn pqyq ?’. Tn = a+ (n-1) d -15 = 25+(n-1) (-5) -15 = 25 -5n+5 -15 = 30 -5n -15 -30 = -5n -45 ÷-5 = n 9 = n • a = 25 • d = -5 • Tn = -15 • n =? pYE`n @mn[vt

  41. (1) 2,4,6,8….. @XY\V]@y\ pq 8 k ekw;v @s`yn\n. Sn = n {2a+(n-1)d} 2 S8 = 8 {2 x2+(8-1)2} 2 S8 = 4 {4+7x2} S8 = 4 {4+14} S8 = 4 x 18 S8 = 72 a = 2 d = 4 – 2 = 2 S8 = ? n =8 pYE`n @mn[vt

  42. (2) 0.2,0.5,0.8 ….. @XY\V]@y\ pq 7 k ekw;v @s`yn\n. Sn = n {2a+(n-1)d} 2 S7 = 7{2x0.2+(7-1)0.3} 2 S7 = 3.5 {0.4+6x0.3} S7 = 3.5 {0.4+1.8} S7 = 3.5 x 2.2 S7 = 7.7 a = 0.2 d = 0.5-0.2 = 0.3 S7 = ? n =7 pYE`n @mn[vt

  43. (3) ½ , ¾ ,1….. @XY\V]@y\ pq 5 k ekw;v @s`yn\n. Sn = n {2a+(n-1)d} 2 S5=5{2x½ +(5-1) ¼} 2 S5 = 2.5 {1+4x ¼ } S5 = 2.5 {1+1} S5 = 2.5 x 2 S5 = 5 a = ½ d = ¾ – ½ = ¼ S5= ? n =5 pYE`n @mn[vt

  44. (2) pLm[ pqy @sv}m a p]L]w;r • (1) sm`n\wr @XY\V]yk pq 8 k ekw;v 72 q @p`À[aAwry 2 q vn @XY\V]@y\ pLm[ pqy @s`yn\n. • (2) sm`n\wr @XY\V]yk pq 7 k ekw;v 7.7 q @p`À[aAwry 0.3 q vn @XY\V]@y\ pLm[ pqy @s`yn\n. • (3) sm`n\wr @XY\V]yk pq 5 k ekw;v 5 q @p`À[aAwry ¼ q vn @XY\V]@y\ pLm[ pqy @s`yn\n. p]L]w;r p]L]w;r pYE`n @mn[vt

  45. (1) sm`n\wr @XY\V]yk pq 8 k ekw;v 72 q @p`À[ aAwry 2 q vn @XY\V]@y\ pLm[ pqy @s`yn\n. Sn = n {2a+(n-1)d} 2 72 = 8{2a+(8-1)2} 2 72 = 4 {2a+7x2} 72 = 4 {2a+14} 72 = 8a +56 72-56 = 8a 16÷8 = a 2 = a a = ? d = 2 S8= 72 n =8 pYE`n @mn[vt

  46. (2) sm`n\wr @XY\V]yk pq 7 k ekw;v 7.7 q @p`À[aAwry 0.3 q vn @XY\V]@y\ pLm[ pqy @s`yn\n. Sn = n {2a+(n-1)d} 2 7.7 = 7{2a+(7-1)0.3} 2 7.7 = 3.5 {2a+6x0.3} 7.7 = 3.5 {2a+1.8} 7.7 = 7a +6.3 7.7-6.3 = 7a 1.4÷7 = a 0.2 = a a = ? d = 0.3 S7 = 7.7 n =7 pYE`n @mn[vt

  47. (3) sm`n\wr @XY\V]yk pq 5 k ekw;v 5 q @p`À[aAwry ¼ q vn @XY\V]@y\ pLm[ pqy @s`yn\n. Sn = n {2a+(n-1)d} 2 5 = 5{2a+(5-1) ¼ } 2 5 = 2.5 {2a+4x ¼ } 5 = 2.5 {2a+1} 5 = 5a +2.5 5-2.5 = 5a 2.5÷5 = a 0.5 = a a = ? d = ¼ S5= 5 n =5 pYE`n @mn[vt

  48. (3) @p`À[ an\wry @sv}m d p]L]w;r • (1) sm`n\wr @XY\V]yk pq 8 k ekw;v 72 q pLm[ pqy 2 q vn @XY\V]@y\ @p`À[aAwry @s`yn\n. • (2) sm`n\wr @XY\V]yk pq 7 k ekw;v 7.7 q pLm[ pqy 0.2 q vn @XY\V]@y\ @p`À[aAwry @s`yn\n. • (3) sm`n\wr @XY\V]yk pq 5 k ekw;v 5 q pLm[ pqy ½ q vn @XY\V]@y\ @p`À[aAwry @s`yn\n. p]L]w;r p]L]w;r pYE`n @mn[vt

  49. (1) sm`n\wr @XY\V]yk pq 8 k ekw;v 72 q pLm[ pqy 2 q vn @XY\V]@y\ @p`À[aAwry @s`yn\n. Sn = n {2a+(n-1)d} 2 72 = 8{2x2+(8-1) d} 2 72 = 4 {4+7d } 72 ÷4 = 4+7d 18 = 4 +7d 18-4 = 7d 14÷7 = d 2 = d a = 2 d = ? S8= 8 n =8 pYE`n @mn[vt

  50. (2) sm`n\wr @XY\V]yk pq 7 k ekw;v 7.7 q pLm[ pqy 0.2 q vn @XY\V]@y\ @p`À[aAwry @s`yn\n. Sn = n {2a+(n-1)d} 2 7.7 = 7{2x0.2+(7-1) d} 2 7.7 = 3.5 {0.4+6d } 7.7 ÷3.5 = 0.4+6d 2.2 = 0.4 +6d 2.2-0.4 = 6d 1.8÷6 = d 0.3 = d a = 0.2 d = ? S7 = 7.7 n =7 pYE`n @mn[vt

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