welq †KvW 2 6 6 we G Gd kvnxb K‡jR XvKv
AMÖMwZ g~j¨vqb cixÿv-1 t 2017 Øv`k †kªwY
welq t D”PZi MwYZ 2q cÎ (eûwbe©vPwb)
mgq t 25 wgwbU c~Y©gvb25
[ we‡kl `ªóe¨ t mieivnK…Z eûwbe©vPwb Afxÿvi DËic‡Îi cÖ‡kœi µwgK b¤^‡ii wecix‡Z cÖ`Ë eY©m¤^wjZ e„Ëmg~n n‡Z mwVK/m‡e©vrK…ó Dˇii e„ËwU ejc‡q›U Kjg Øviv m¤ú~Y© fivU Ki| cÖwZwU cÖ‡kœi gvb-1 ]
1. a < b Ges c < d n‡j, wb‡Pi †KvbwU mwVK?
bd < ac a + c < b + d a + c < b d b d < a c 2. |2x + 1| < 7 Gi mgvavb †mU
{x : 5 < x < 3} {x : 2 < x < 3}
{x : 4 < x < 3} {x : 4 < x < 3}
3. cv‡k¦©i wPÎwU jÿ Ki t
i. e¯‘wUi Avw`‡eM 3 GKK ii. e¯‘wUi Z¡iY 1 GKK
iii. 3 GKK `~iZ¡ †k‡l e¯‘wUi †eM 6 GKK wb‡Pi †KvbwU mwVK?
i I ii ii I iii i I iii i, ii I iii 4. 5 < x < 2 Gi ciggvb AvKvi wb‡Pi †KvbwU?
|2x + 3| < 7 |2x 5| < 3
|2x +5 | < 3 |2x 3| < 7 5. x Gi ev¯Íe gv‡bi Rb¨ 4x x2 +4 Gi Mwiô gvb
2 4 6 8
wb‡Pi Z‡_¨i Av‡jv‡K 6 I 7 bs cÖ‡kœi DËi `vI t Lv‡`¨i cÖKvi (‡KwR‡Z) ‡cÖvwUb d¨vU
A 1 3
B 3 2
‰`wbK b~¨bZg cÖ‡qvRb 8 12
A cÖKvi Lvevi cÖ‡qvRb x ‡KwR Ges B cÖKvi Lvevi cÖ‡qvRb y †KwR 6. †cÖvwU‡bi cwigvY wb‡Pi †Kvb AmgZv Øviv †jLv nq
x + 3y ≥ 8 3x + 2y ≥ 12
3x + 2y ≤ 12 x + 3x ≤ 8
7. d¨v‡Ui cwigvY wb‡Pi †Kvb AmgZv Øviv †jLv nq
x + 3y ≥ 8 3x + 2y ≥ 12
3x + 2y ≤ 12 x + 3x ≤ 8
8. sin-1x Gi †jLwPÎ wb‡Pi †KvbwU ?
9. `yBwU wecixZgyLx mgvšÍivj ej؇qi jwä 10 wbDUb Zv‡`i GKwU n‡Z 3 wgUvi AciwU n‡Z 5 wgUvi `~‡i wµqv K‡i| e„nËi e‡ji gvb wb‡Pi †KvbwU?
10 wbDUb 15 wbDUb
20 wbDUb 25 wbDUb
10. 8 6 1 Gi eM©g~j
(1 + 3 1 ) (13 1 )
(1 + 3i) (1 3i) 11. (1+x) (1x)-1 Gi we¯Í…wZ‡Z x9 Gi mnM
2 1
0 2
12. `yBwU Q°v GK‡Î wb‡ÿ‡c MwVZ bgybv we›`yi msL¨v
6 12 24 36
wb‡Pi Z‡_¨i Av‡jv‡K 13 I 14 bs cÖ‡kœi DËi `vI t x2 7x + 12 = 0 GKwU wØNvZ mgxKiY|
13. mgxKiYwU g~jØq n‡e
ev¯Íe I mgvb ev¯Íe I Amgvb RwUj I mgvb RwUj I Amgvb 14. mgxKiYwU g~jØq α I β n‡j 1
α I 1
β g~jwewkó mgxKiY wb‡Pi †KvbwU
12x2 7x + 1 = 0 12x2 + 7x + 1 = 0 12x2 7x 1 = 0 12x2 + 7x 1 = 0 15.
1 x
6
1
2 Gi we¯Í…wZi Awfm„wZi Rb¨ cÖ‡qvRbxq e¨ewa wb‡Pi †KvbwU?
6 < x < 6 6 > x > 6
1
2 > x > 1
2 1
2 < x < 1 2 16.
x22 + 1
x2
4 Gi we¯Í…wZ‡Z c‡`i msL¨v KZ?
5 8 9 11
17. wb‡Pi †KvbwU Dce„‡Ëi mgxKiY?
x2 5 + y2
5 = 1 3x2 + 2y2 = 0 x2
5 y2
4 = 1 9x2 + 25y2 + 64x 64 = 0 18. x2 = 4ay (a > 0) Gi †jLwPÎ wb‡Pi †KvbwU ?
wb‡Pi Z‡_¨i Av‡jv‡K 19 I 20 bs cÖ‡kœi DËi `vI t
GKwU mgevû wÎfy‡Ri GKwU †KŠwYK we›`y‡Z `yBwU wfbœ evû eivei P I 3P gv‡bi `yBwU ej wµqv Ki‡Q|
19. ej `yBwUi jwäi gvb KZ?
P 7 P 10 P 13 P 17
20. P Gi w`K eivei 3P e‡ji j¤^vs‡k gvb KZ?
P 2
3P 2
3 3P
2 P 17
21. x2 y2
4 = 1 GKwU KwY‡Ki mgxKiY|
i. KwYKwUi bvwfj¤^ = 8 ii. KwYKwUi Dr‡Kw›`ªKZv = 3
iii. KwYKwUi wbqvg‡Ki mgxKiY, 5x = 1 wb‡Pi †KvbwU mwVK?
i I iii ii I iii i I ii i, ii I iii
22. GKwU †bŠKv †mªv‡Zi wظY †e‡M P‡j †mvRvmywR b`x cvi nj| †mªv‡Zi mv‡_ †bŠKvwU MwZ KZ?
60 90 120 150
23. GKwU UvIqv‡ii kxl© we›`y n‡Z 19.5 m/sec †e‡M Lvov Dc‡ii w`‡K wbwÿß GKLÛ cv_i 5 sec mg‡q f‚wg‡Z cwZZ nj| wgbv‡ii D”PZv KZ?
18 25
30 40
24. 2a, a, 0, a, 2a Gi msL¨v¸wji †K›`ªxq cÖeYZv
0 6
2a 6a
25. 1+ i 3
2 Gi AvM©y‡g›U
3 2
3
3
2
3
welq †KvW 2 6 5 we G Gd kvnxb K‡jR XvKv
AMÖMwZ g~j¨vqb cixÿv-1 t 2017 Øv`k †kªwY
welq t D”PZi MwYZ 1g cÎ (eûwbe©vPwb)
mgq t 25 wgwbU c~Y©gvb25
[ we‡kl `ªóe¨ t mieivnK…Z eûwbe©vPwb Afxÿvi DËic‡Îi cÖ‡kœi µwgK b¤^‡ii wecix‡Z cÖ`Ë eY©m¤^wjZ e„Ëmg~n n‡Z mwVK/m‡e©vrK…ó Dˇii e„ËwU ejc‡q›U Kjg Øviv m¤ú~Y© fivU Ki| cÖwZwU cÖ‡kœi gvb-1 ]
1. wb‡Pi †KvbwU e„‡Ëi mgxKiY bq?
x2 + y2 + 2x 4y 1 = 0 x2 + y2 3x + 6y + 10 = 0 2x2+ 2y2 3x 6y + 4 = 0 x2 + y2 2x + 6y + 12 = 0 2. cosA = 45 n‡j 1+tan1tan22A
A Gi gvb KZ?
7 25
25 7
16 25
9 25 3. f(x) = 4x2 n‡j f(x) Gi †iÄ
[2, 2] (0, 2) [0, 2] [1, 1]
4. y = x7 n‡j y6 = KZ?
7! x 7x 7! x
5. 15 wU evû wewkó eûfyR K‡Y©i msL¨v KZ?
90 105 195 210
6. y = sec Gi †iÄ
{y : 0 ≤ y ≤ 1 {y : y < 1 or y > 1}
{y : 1 ≤ y ≤ 1} {y : y ≤ 1 or y ≥ 1}
7. ‘SHAHEEN’ kãwUi eY©¸‡jv wb‡q mvRv‡bv msL¨v
i. me¸‡jv GK‡Î wb‡q 5040 ii. cÖ_‡g A _v‡K Giƒc 180 iii. cÖ_‡g I †k‡l E _v‡K Giƒc 60
wb‡Pi †KvbwU mwVK?
i I ii i I iii ii I iii i, ii I iii 8. sin(3x+5) Gi ch©vq Kvj KZ?
3 3
2
2
3 2
9.
[ ]
10 10 xy =
3
2 n‡j y = ?
2 2 3 1
10. r Gi gvb KZ n‡j 10cr Gi gvb e„nËg n‡e?
1 3 5 10
11. wb‡Pi †KvbwU GK-GK Ges mvwe©K?
f(x) = x2 f(x) = |x|
f(x) = sinx f(x) = 3x+25
12. A = [aij] GKwU eM© g¨vwUª· G i ≠ j n‡j aij = 0 Ges i = j n‡j aij = 1 Zvn‡j A g¨vwUª·
A‡f`K mgNvwZ D`NvwZK e¨wZµg©x
wb‡gœi Z‡_¨i Av‡jv‡K 13 I 14 bs cÖ‡kœi DËi `vI t x 3 y + 1 = 0 GKwU mij‡iLvi mgxKiY|
13. †iLvwU x-A‡ÿi mv‡_ abvZ¥K w`‡K †h †KvY Drcbœ K‡i Zvi cwigvY
30 60 150 210
14. Aÿ؇qi ga¨eZ©x LwÐZvs‡ki ˆ`N©¨
4
3 GKK 2
3 GKK
1 GKK 43 GKK
15. y = tanx,
2 < x <
2 Gi †jLwPÎ †KvbwU?
16.
α+3 5 6
α4 g¨vwUª·wU e¨wZµgx n‡j α Gi gvb KZ n‡e?
6, 7 1, 3 3, 1 7, 6
17. A = 2
1 7
4 n‡j A-1 = ?
12 7
4
12 7
4 4
1 7
2
14 7 2 wb‡Pi Z‡_¨i Av‡jv‡K 18 I 19 bs cÖ‡kœi DËi `vI t
mij‡iLvq Pjgvb †Kv‡bv KYvi t mg‡q AwZµvšÍ `~iZ¡, S = 63t 6t2 t3.
18. 1 †m‡KÛ c‡i KYvwUi †eM
0 6 48 GKK 57 GKK
19. _vgvi c~‡e© KYvwU KZ †m. a‡i PjwQ‡jv?
1 †m. 3 †m. 5 †m. 7 †m.
20. cos x
x dx = KZ?
sin x +c sin x +c
2sin x +c 2sin x +c
21. f(x) = x21, g(x) = x n‡j
i. gof(1) = 0 ii. fog (1) = 0 iii. fog(x)= gof(x)
wb‡Pi †KvbwU mwVK?
i I ii i I iii ii I iii i, ii I iii wb‡Pi Z‡_¨i Av‡jv‡K 22 I 23 bs cÖ‡kœi DËi `vI t
x2 + y2 10x + 8y + 16 = 0 GKwU e„‡Ëi mgxKiY|
22. e„ËwU y Aÿ‡K ¯úk© K‡i, ¯úk© we›`yi ¯’vbvsK
(0, 4) (0, 4) (0, 5) (0, 5)
23. e„ËwUi e¨vmva© = ?
3 GKK 3 GKK 2 GKK 4 GKK
24. x2 9 + y2
4 = 1 Dce„‡Ëi †ÿÎdj KZ?
6 eM© GKK 9 eM© GKK
6 eM© GKK 9 eM© GKK
25. hw` 2^i +^jk Ges ^ ^i 2^j 3^k ci¯ú‡ii Dci j¤^ n‡j gvb KZ ? 2
5
2 5
5 2
5 2
