Pre-Test Exam-2022_H. Maths_MCQ_BV_Sample Questions

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Page 1 of 8

we G Gd kvnxb K‡jR XvKv GBP Gm wm-2022

cÖvK-wbe©vPbx

welq : D”PZi MwYZ 1g I2q cÎ (eûwbe©vPbx) bgybv cÖkœ

mgq -25 wgwbU cyb©gvb -25 [ DËi c‡Îi mwVK DË‡ii e„ËwU (0) Kv‡jv Kvwji ej c‡q›U Kjg Øviv fivU Ki ]

1. y = |x + 3| dvsk‡bi †jLwPÎ †KvbwU?

K.

Y

O X

− 3 L.

Y

O 3 X

M.

Y

O X

− 3

N.

Y

O X

3

wb‡Pi wPÎwU jÿ¨ Ki Ges (2-3) bs cÖ‡kœi DËi `vI:

Dc‡ii wP‡Î P, Q we›`y AB †iLv‡K mgvb wZb fv‡M wef³ K‡i|

2. OP †iLvi mgxKiY †KvbwU?

K. x = 6y L. 6x = y M. 2x = 3y N. 3x = 2y 3. AB †iLvi j¤^ mgwØLÛ‡Ki mgxKiY †KvbwU?

K. 3x − y − 16 = 0 L. 3x − y + 16 = 0 M. x − 3y = 16 N. x − 3y + 16 = 0 4. 3x − 4y + 20 = 0 mij‡iLvi mgxKi‡Yi †ÿ‡ÎÑ

i. †iLvwUi Xvj 3 4

ii. g~jwe›`y n‡Z †iLvwUi j¤^ `~iZ¡ 4

iii. †iLvwU y Aÿ‡K (0, 5) we›`y‡Z †Q` K‡i wb‡Pi †KvbwU mwVK?

K. iI ii L. iI iii M. ii I iii N. i,iiI iii 5. (1, 3), (3, 2) we›`yØ‡qi ms‡hvM †iLvsk‡K e¨vm a‡i Aw¼Z

e„‡Ëi mgxKiY †KvbwU?

K. (x + 1) (x + 3) + (y + 3) (y + 2) = 0 L. (x + 1) (x + 3) − (y + 3) (y + 2) = 0 M. (x − 1) (x − 3) + (y − 3) (y − 2) = 0 N. (x − 1) (x −3) − (y −3) (y − 2) = 0 wb‡Pi Z‡_¨i Av‡jv‡K (6 I 7) bs cÖ‡kœi DËi `vI:

x²+ y² = 5 GKwU e„‡Ëi mgxKiY|

6. (−1, 2) we›`y‡Z e„ËwUi ¯úk©‡Ki mgxKiY †KvbwU?

K. 2x + y = 5 L. 2y − x = 5 M. x − 2y = 5 N. y − 2x = 5 7. (2, 3) we›`yMvgx e¨v‡mi mgxKiY †KvbwU?

K. 3x − 2y = 0 L. 3x + 2y = 0

M. 3y + 2x = 0 N. 3y − 2x = 0

8. k Gi gvb KZ n‡j 3x + 4y = k †iLvwU x² + y² = 10x e„Ë‡K ¯úk© Ki‡e?

K. – 40, – 10 L. 40, – 10 M. – 40, 10 N. 40, 10 9.hw` 𝑦 = ln⁡(𝑠𝑒𝑐𝑥) nq Z‡e d²y

dx² = ? K. tan x L. − cot x M. sec²xN. cosec² x 10. (x) = 2x + 1

x dvsk‡bi †ÿ‡Î (1, 3) we›`y‡Z i. ¯úk©‡Ki mgxKiY x − y + 2 = 0

ii. Awfj‡¤^i mgxKiY x + y − 4 = 0 iii.dvskbwUi †Kv‡bv ¸iægvb I jNygvb †bB|

wb‡Pi †KvbwU mwVK?

K. iI ii L. iI iii M. ii I iii N. i,iiI iii 11. GKwU Mvox †mvRv iv¯Ívq t †m‡K‡Û 

 3t + 1

8 t² wgUvi c_

AwZµg K‡i| 5 wgwb‡U Zvi †eM KZ?

K. 4.25m/sec L. 18.125m/sec M. 75m/sec N. 78m/sec 12. lim

x →  

 1 x + 1 

 5x² − 1

x² = KZ?

K. 1 L. 0 M. 5 N. 2 13. cive„‡Ëi Dc‡Kw›`ªK ˆ`N©¨ KZ?

K. 2 L. 1 M. 1

2 N. 1

2 14. y = 2x + c †iLvwU x²

4 + y²

3 = 1 Dce„‡Ëi ¯úk©K n‡j c Gi gvb KZ?

K. 7 L. √19 M. 25 N. ±√19 15. x² = 4(1 − y) cive„‡ËiÑ

i. wbqvgK‡iLvi mgxKiY y = 2 ii. kxl©we›`y (0, 1)

iii. Dc‡Kw›`ªK j‡¤^i ˆ`N©¨ 1 wb‡Pi †KvbwU mwVK?

K. i I ii L.ii I iii M. i I iii N. i, ii I iii

Y

x + 3y − 12 = 0 O

Q P

A X B

bgybv cÖkœ-1

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Page 2 of 8 wb‡Pi DÏxc‡Ki Av‡jv‡K 16 I 17 bs cÖ‡kœi DËi `vI:

16. cive„‡Ëi Aÿ‡iLvi mgxKiY †KvbwU?

K. x + y = 0 L. x – y + 2 = 0 M. x – y – 2 = 0 N. x – y = 0 17. cive„‡Ëi Dc‡Kw›`ªK j‡¤^i ˆ`N©¨ KZ?

K. 2 L. 1 M. 1

2 N. 1 2 18| x²−2x−1=0mgxKi‡Yi-

(i) GKwU g~j 1− 2 (ii) g~jØq Ag~j`

(iii) g~jØq ev¯Íe I Amgvb wb‡Pi †KvbwU mwVK?

K. i I ii L. ii I iii M. i I iii N. i, ii I iii

19| 4x²+3x+7=0mgxKi‡Yi g~jØq I n‡j, +

 1

1 Gi gvb KZ?

(K) 3

−7 (L) 7

−3 (M) 7

3 (N) 3 7 20| 3x²−2x+1=0mgxKi‡Yi g~jØ‡qi e‡M©i mgwó KZ?

(K) 3

−2 (L) 9

−2 (M) 3

2 (N) 9 2

21. ax + bx + c = 0 Gi GKwU g~j k~b¨ n‡j c Gi gvb KZ?

K. 1 L. 0 M. 2 N. 3 22. sin⁻¹x Gi ‡jLwPÎ wb‡Pi †KvbwU ?

(K) (L)

(M) (N)

23. 1

2 cosec^{– 1}1 + x²

2x Gi gvb KZ?

K. 2 tan^{– 1}x L. tan^{– 1}x M. 1

2 sin^{– 1}x N. 1

2 tan^{– 1}x wb‡Pi Z‡_¨i Av‡jv‡K 24 I 25 bs cÖ‡kœi DËi `vI:

A = cos⁻¹x, B = cos⁻¹y 24. A = 0 n‡j wb‡Pi †KvbwU mwVK?

K. x = 1 L. x = 2 M. x = 3 N. x = 4 25. A − B = 

2 n‡j wb‡Pi †KvbwU mwVK?

K. x 1 − y² + y 1 − x² = 1 L. x 1 − y² − y 1 − x² = 1 M. xy + (1 − x²)(1 − y²) = 0 N. xy − (1 − x²)(1 − y²) = 0

z

p(x, y)

x + y + 1 = 0

M

s(−1, 1)

Y x x

Y

x Y

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Page 3 of 8 we G Gd kvnxb K‡jR XvKv

bgybv cÖkœ

cÖvK wbe©vPwb cixÿv Õ 2021

welq : D”PZi MwYZ, 1g I 2q cÎ (eûwbe©vPbx )

mgq : 25 wgwbU| c~Y©gvb : 25 [ DËi c‡Îi mwVK DË‡ii e„ËwU (0) Kv‡jv Kvwji ej c‡q›U Kjg Øviv fivU Ki ]

1|

0 lim

→

x (1+3x)^(3x+7)/x

K. e L. e² M. e²⁷ N. e²¹ 2| y = x² – x + 1 eµ‡iLvi x = 2 we›`y‡Z Awfj‡¤^i Xvj-

K. 3 L. -3 M.

3

1 N.

3

−1 3| ax²+bx+c ivwkwU c~Y©eM© n‡e KLb ?

(K) b² −4ac0 n‡j (L) b²−4ac0 n‡j (M) b²−4ac c~Y©eM© n‡j (N) b²−4ac=0 n‡j

4| tcwieZ©bkxj n‡j, 



 



 + −

t t 1 t, t 1

P Gi mÂvi c‡_i

mgxKiY-

K. mij‡iLv L. e„Ë

M. cive„Ë N. Awae„Ë 5| (−2,3) we›`y n‡Z 4x−3y−10=0 †iLvi j¤^ `~iZ¡ †KvbwU

?

K. 5

23 L.

5

27 M.

5

27 N.

5

13 wb‡Pi Z‡_¨i Av‡jv‡K (6-7) bs c‡Ökœi DËi `vI:

0 7 y 3

x− + = I 2x−9y+8=0`yBwU mij‡iLvi mgxKiY|

6. cÖ_g †iLvwU x-Aÿ‡K †Kvb we›`y‡Z †Q` K‡i ? K. (−7,0) L. (7,0)

M. 



 

− ,0 3

7 N. 



 



 ,0 3

7 7. †iLvØ‡qi †Q` we›`yi ¯’vbv¼ †KvbwU ?

K. (13,2) L. (−13,−2) M. (13,−2) N. (−13,2) 8. x=0,y=0Ges 3x+4y=12 †iLv wZbwU Øviv MwVZ wÎfz‡Ri †ÿÎdj †KvbwU ?

K. 4 eM© GKK L. 6 eM© GKK M. 8 eM© GKK N. 10 eM© GKK 9. 4x−3y=0 GKwU mij‡iLvi mgxKiY n‡j,

) i

( (1, 1) we›`ywU †iLvwUi Dci Aew¯’Z (ii) ‡iLvwU g~j we›`yMvgx

) iii

( (3, 0) we›`y †_‡K †iLvwUi j¤^ `~iZ¡

5 12 GKK Dc‡ii evK¨¸wji g‡a¨ †KvbwU mwVK ?

K. iIii L. iiIiii

M. iIiii N. i,iiI

10. x² + y² + 8x + 2ky + c = 0 e„Ë Dfq Aÿ‡K ¯úk©

Ki‡j

k Ges c Gi gvb wb‡Pi †KvbwU?

K. k = 16, c = 4 L. k = 4, c = 4 M. k = + 4, c = 16 N. k =  4, c = 4

11. (1, −1) we›`y †_‡K 2x² + 2y² − x + 3y + 1 = 0 e„‡Ë Aw¼Z ¯úk©‡Ki ˆ`N©¨ wb‡Pi †KvbwU?

K. 2 2 L. 3

2 M. 1

2 N. 1

2 2 12. 5x² + 5y² – 10x + 30y + 49 = 0 e„ËwUi GKwU

¯úk©K 2x + ky = 4 n‡j, k Gi gvb †KvbwU?

K. 1 L. -2 M. 2 N. -3 13| y = tan⁻¹ 2x

1 − x² n‡j, dy dx mgvb−

K. 1

2(1 − x²) L. 2 (1 − x²)

M. 2

(1 + x²) N. 2 1 − x² 14| lim

x→{ln (2x −1) − ln (x + 5)} Gi gvb KZ?

K. 4 ln3 L. ln3 M. ln2 N. ln(−3)

15| 𝑥 Gi †Kvb ev¯Íe gv‡bi Rb¨ 3𝑥 − 𝑥²+ 4 Gi Mwió gvb -

K. ¹⁷

7 L. ²¹

4 M. ²⁵

4 N.

−15 4

16| 6𝑥²− 5𝑥 + 1 = 0 mgxKi‡Yi gyjØq 𝑎, 𝛽 n‡j ¹

𝑎,¹

𝛽 g~jwewgó mgxKiY †KvbwU?

K. 𝑥²− 5𝑥 + 6 = 0 L. 𝑥² − 4𝑥 + 3 = 0 M. 𝑥²− 11𝑥 + 30 = 0

N. 𝑥²− 2𝑥 + 1 = 0

iii

bgybv cÖkœ-2

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Page 4 of 8 17| ‡Kvb wØNvZ mgxKi‡Yi GKwU g~j 2 + 3𝑖 n‡j, wØNvZ

mgxKiY wb‡¤œi †KvbwU?

K. 𝑥²− 4𝑥 − 13 − 0 L. 𝑥²− 2𝑥 − 3 = 0 M. 𝑥²+ 2𝑥 − 3 = 0 N. 𝑥²+ 2𝑥 + 3 = 0

18| 𝑥²+ 𝑎𝑥 + 𝑏 = 0 mgxKi‡Yi GKwU g~j 1 − 𝑖 n‡j, 𝑎 Ges 𝑏 Gi gvb wb‡¤œi †Kvb `yBwU ?

K. 𝑎 = 2, 𝑏 = 1 L. 𝑎 = −2, 𝑏 = 2 M. 𝑎 = 2, 𝑏 = 2 N. 𝑎 = 2, 𝑏 = −2 19| cive„ËwUi-

(i) ZGi ¯’vbv¼ (-3,-4) (ii) MZ Gi Xvj=

4

−3

(iii) KwYKvwUi mgxKiY 1 9 y 4

x² + ² =

(K) i I ii (L) i I iii

(M) ii I iii (N) i,ii I iii

20| cive„ËwUi mgxKiY y² =−9x n‡j, SP= ? (K) 9 (L) -9 (M)

2

9 (N) 2

−9 21| 5x² +6y² =30 Dce„‡Ëi Dr‡Kw›`ªKZv KZ ? (K) 6 (L)

6

1 (M) 3

2 (N) 3 4

22| sec²(tan⁻¹4)+tan²(sec⁻¹3)Gi gvb KZ ?

(K) 7 (L) 5

(M) 12 (N) 25

23| b

tan a

sin ⁻¹ Gi gvb- K.

2

2 b

a a

+ L.

a b a²+ ²

M. 2 2

b a

b

+ N.

b b q²+ ²

wb‡Pi DÏxc‡Ki Av‡jv‡K 24 I 25 bs cÖ‡kœi DËi `vI:

x 2 cos

sin 3

y= ⁻¹ + ⁻¹ mgxKi‡Y-

24| y=90⁰ n‡j, x Gi gvb †KvbwU ? K.

2

1 L.

2

1 M.

2

3 N.

3

2

25| 31

3

x= 3 n‡j, y Gi gvb †KvbwU ? K.

7 3 tan ¹5

−

− L.

3 tan⁻¹ 11

M.

11

tan⁻¹ 3 N.

3 5

tan⁻¹ 7

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Page 5 of 8 weGGd kvnxb K‡jR XvKv

welq †KvW: 2 6 5

mgq ⎯25 wgwbU D”PZi MwYZ (eûwbe©vPনী) c~Y©gvb ⎯ 25

প্রাক-নির্ বাচিী িমুিা প্রশ্ন

[`ªóe¨: mieivnK…Z eûwbe©vPwb Afxÿvi DËic‡Î cÖ‡kœi µwgK b¤^‡ii wecix‡Z cÖ`Ë eY©m¤^wjZ e„Ëmg~n n‡Z mwVK/ m‡e©vrK…ó DË‡ii e„ËwU () ej c‡q›U Kjg Øviv m¤ú~Y© fivU Ki| cÖwZwU cÖ‡kœi gvb 1|]

wb‡Pi Z‡_¨i Av‡jv‡K (১ I ২) bs cÖ‡kœi DËi `vI

(3k + 1)x² + (11 + k)x + 9 = 0 GKwU wØNvZ mgxKiY,

†hLv‡b k GKwU aªeK|

১. GKwU g~j 1 n‡j k Gi gvb KZ?

A ক) – 21

4 খ) –21 গ) 21

4 ঘ)21

২. g~jØq mgvb n‡j k Gi GKwU gvb KZ?

A ক)–86 খ)–85 গ)85 ঘ)86

৩. x² − 7x + 12 = 0 mgxKi‡Yi g~jØq  I  n‡j  +

 I  g~jwewkó mgxKiY †KvbwU?

A ক) x² − 19x + 84 = 0 খ) x² + 14x − 144 = 0 গ) x² − 14x + 144 = 0 ঘ) x² + 19x − 84 = 0 ৪.

wP‡Îi ⎯

i. dvsk‡bi †Wv‡gb (− , ) ii.dvsk‡bi †iÄ





−  2 

2 e¨ewa‡Z Aew¯’Z iii.y GKwU wecixZ e„Ëxq dvskb

A wb‡Pi †KvbwU mwVK?

ক)i I ii খ)i I iii গ)ii I iii ঘ)i, ii I iii

৫. tan⁻¹x + cot⁻¹x = ?

A ক)0 খ)

4 গ)

3 ঘ)

2

৬. ntan⁻¹x = tan⁻¹nx − xⁿ

1 − nx² n‡j n Gi gvb †KvbwU?

A ক)1 খ)2 গ)3 ঘ)4

৭. tanx + tan2x + tan 3x = 0 mgxKi‡Yi mgvavb bq

†KvbwU?

C ক)0 খ)

4 গ)

3 ঘ)2

3

wb‡Pi Z‡_¨i Av‡jv‡K (৮ I ৯) bs cÖ‡kœi DËi `vI :

৮. AB Gi mgxKiY †KvbwU?

ক)x + y = 2 2 খ)x − y = 2 2 গ)x + y

= 4 ঘ)x − y = 4

৯. OAP Gi †ÿÎdj KZ eM© GKK?

ক)4 2 খ)4 গ)2 2 ঘ)2

1০. d

dx (3^{sin– 1x}) = KZ?

ক)3^{sin– 1x}

1 – x² খ)3^{sin– 1x}.ln3

1 – x² গ)3^sin–

1x.ln3 ঘ) ln3 1 – x²

O X

2 B

O A

45

P

bgybv cÖkœ-3

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Page 6 of 8 ১1. lim

y→0 1 − e

ln (1 + y) = ? [0 < y < 1]

ক)0 খ)1 গ)2 ঘ)

wb‡Pi Z‡_¨i Av‡jv‡K (১2-১৪) bs cÖ‡kœi DËi `vI:

x² − 4x + y² = 140 GKwU e„‡Ëi mgxKiY|

১2. e„‡Ëi e¨vmva© KZ?

ক)2 খ)8 গ)10 ঘ)12

১৩. (15, 0) we›`y †_‡K cÖ`Ë e„‡Ë ¯úk©‡Ki ˆ`N©¨ KZ?

ক)5 খ)10 গ)12 ঘ)13

১৪. cÖ`Ë mgxKiYwUi †ÿ‡ÎÑ

i. e„‡Ëi e¨vm 12 ii. e„ËwUi †K›`ª x-A‡ÿi Dci Aew¯’Z iii. e„ËwU (2, 12) we›`yMvgx

ক)i I ii খ)i I iii গ)ii I iii ঘ)i, ii I iii

১৫. †Kv‡bv mgxKi‡Yi GKwU g~j 1 − i 2 n‡j mgxKiYwU n‡eÑ

ক) x² − 2x + 3 = 0 খ)x²

+ 2x + 3 = 0

গ) x² − 3x + 2 = 0 ঘ)x² + 3x + 2 = 0

১৬. †Kv‡bv we›`yi Kv‡Z©mxq ¯’vbv¼ (− 1, 3) n‡j we›`ywUi

†cvjvi ¯’vbv¼ KZ n‡e?

B ক)

 2 

3 খ)

 2 2

3 গ)

 2 − 

3 ঘ)

 4 2

3

A ক)(x − 2)² + (y − 3)² = 3² খ) (x + 2)² + (y + 3)² = 2 গ) (x + 2)² + (y − 3)² = 2²

ঘ) (x − 2)² + (y + 3)² = 3²

১৮. A (1, −2) I B(−8, 1) we›`yØ‡qi ms‡hvRK †iLvsk BA

A ক) (−5, −1) খ) (−2, −1) গ)

(−2, 0) ঘ) (−5, 0)

1৯. 6x − 8y + 6 = 0 †iLvi Dci j¤^ Ges g~jwe›`y n‡Z 2 GKK `~‡i Aew¯’Z mij‡iLvi mgxKiYÑ

A ক)3x − 4y  10 = 0 খ)4x + 3y  10 = 0 গ) 3x + 4y  10 = 0

ঘ)4x − 3y  10 = 0

†Kv‡Yi mgwØLÐ‡Ki mgxKiYÑ A ক)5x + 5y + 2 = 0

খ)9x − 9y + 8 = 0 গ) 9x − 9y − 8 = 0

ঘ)5x + 5y − 2 = 0

DÏxc‡Ki Av‡jv‡K 2১ I 2২ bs cÖ‡kœi DËi `vI : 25x² − 16y² + 400 = 0 GKwU Awae„‡Ëi mgxKiY|

ক) ( 2, 0) খ) (0,  2)

গ) (0,  5) ঘ) ( 5,

0)

ক) 8

5 খ)5

8 গ)25

2 ঘ)32

5 2৩. (x − 1)²

9 + y²

ক) i I ii খ)ii I iii গ)i I iii ঘ)i, ii I iii

2৪. x² + xy + y² = 1 n‡j, dy dx = ? ক) – 2x

y + 2x খ)– (2x + y)

2y + x গ) – 2x

2y + x ঘ) – x y + 2x 2৫. d

dx

(

tan e^x2

)

= KZ?

A ক)− x e^x2 sec²e^x2

tan e^x2 খ)xe^x2sec²e^x2 2 tane^x2 গ)e^x2sec²e^x2

tane^x2 ঘ)xe^x2sec²e^x2 tane^x2

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Page 7 of 8

mgq-25 wgwbU gvb-25 welq †KvW: 2 6 5

30 45 60 90

3 2 4 10 8

3. d

dx (5^x) = KZ?

A x5^x−1 5^x ln5^x 5^x ln5 x ln5^x

57 4

73

4 61 4 69

4

wb‡Pi Z‡_¨i Av‡jv‡K (5 I 6) bs cÖ‡kœi DËi `vI :

(1, 3) we›`y n‡Z x 3 − y + 8 = 0 mij‡iLvi Dci Aw¼Z j¤^‡iLvi `~iZ¡ P Ges j¤^‡iLvwU x-A‡ÿi mv‡_  †KvY Drcbœ K‡i|

5. P Gi gvb KZ?

2 4 10 20

6.  Gi gvb KZ?

30 60

120 150

7. x Gi †Kvb gv‡bi Rb¨ (x) = 1 3 x³ − 5

2 x² + 6x − 1 Gi Pig gvb cvIqv hvq?

A 2, 3 −2, 3

2, −3 −2, −3

A 4 9

2 18

ii. †K›`ª x A‡ÿi Dci Aew¯’Z

i I ii i I iii ii I iii i, ii I iii

10. lim

x→0 (1 + 5x) 3x + 2

x Gi gvb KZ?

1 

e¹⁰ 6

11. x² + y² = 81 e„‡Ëi GKwU R¨v (− 2, 3) we›`y‡Z সমরিখরিত n‡j R¨v-wUi mgxKiY †KvbwU?

2x − 3y + 13 = 0 2x + 3y − 13 = 0 2x + 3y − 6 = 0 3x + 2y − 13 = 0

12. 2x³ − 3x − 5 = 0 mgxKi‡Yi g~jÎq , ,  n‡j, 

Gi gvb KZ?

−3

2 0 3

2 5 2

y = x + 2 y = x + 1 y = x − 1 y = x − 2 14. cos tan⁻¹ cot sin⁻¹x Gi gvb KZ?

− x 

2 − x x − 

2 x

15. 2 + i 3 g~jwewkó mgxKiYwU n‡eÑ

x² + 4x – 7 = 0 x² – 4x + 7 = 0 x² – 3x + 2 = 0 x² + 3x – 2 = 0 16. sin⁻¹x + cos⁻¹y = 

2 n‡jÑ i. x = y = 1

2 ii. x² + y² = 1

iii. x 1 − y² + y 1 − x² = 1 wb‡Pi †KvbwU mwVK?

i I ii ii I iii i I iii i, ii I iii

−2 0

18. sin⁻¹ (− cos x) + sin⁻¹ (cos 3x) = KZ?

− 2x − 3x

+ 2x 3x

bgybv cÖkœ-4

(8)

Dr‡Kw›`ªKZv KZ?

1 2

2 2

20. sin

 2sin^{– 1}1

2 = ? 1

4

3 4 3

2

5 2

4x² − 8(p − 2)x + 1 = 0 wØNvZ mgxKi‡Yi Av‡jv‡K (21 I 22) bs cÖ‡kœi DËi `vI:

21. DÏxc‡Ki mgxKi‡Yi g~jØq বাস্তব Ges mgvb n‡j, p Gi GKwU gvbÑ

2 5

2 3 4

3

5 2

22. DÏxc‡Ki mgxKi‡Yi g~jØq Ag~j` I Amgvb n‡j p Gi gvb wb‡Pi †KvbwU?

2 7

4 9

4 3

23. x² a² + y²

b² = 1 KwYKwUÑ i. Awae„Ë n‡e hLb a² = b² ii. Dce„Ë n‡e, hLb a  b iii. e„Ë n‡e hLb a = b wb‡Pi †KvbwU mwVK?

i I ii i I iii i, ii I iii ii I iii 24. d

dx {sin⁻¹ (cos x)} = ?

−1 x 1

x 1

25. 4sin⁻¹x + cos⁻¹x =  n‡j, x Gi gvb wb‡Pi †KvbwU?

0 1

2 3

2 1