R - eenadu pratibha

EAMCET (ENGINEERING) MODEL GRAND TEST 

Max.Marks: 160 Questions: 160 Time: 3 Hours 

MATHEMATICS 

1. If f: [0, 3] →R defined by f (x) = [x + [x + [x]]], where [.] denotes greatest 

integer function then the range of f is 

f: [0, 3] →R ´’Jßª· f(x) = [x + [x + [x]]], [.] í∫J≠æe °æ‹®Ωg Ææçêu†’ Ææ÷*ÊÆh f ßÁ·éπ\ 

¢√u°œh 

1) [0, 9] 2) [−3, 3] 3) [0, 1] 4) [−3, 1] 

√ ⎯⎯⎯⎯ 

1 1 1 

1) [ ⎯, 4 ] 2) 

4 [ −4, −⎯ 4 ] ∪ [ ⎯, 4 

4 ] 

2. Domain of f (x) = e sin−1 (log x2 16) is v°æ¢Ë’ßª’ v°æüË¨¡ç 

1 

3) [−4, − ⎯ ] 4) [0, 4] 

4 

3. In the sequence {1}, {2, 3}, {4, 5, 6}, {7, 8, 9, 10}, ... of sets the sum of 

elements in the 5 th set is 3 P − 2 P then P is 

www.eenadupratibha.net 

{1}, {2, 3}, {4, 5, 6}, {7, 8, 9, 10}, ... v¨ÏùÀapple 5´ Ææ´‚-£æ«ç-appleE °æü∆© ¢Á·ûªhç 

3 P − 2 P Å®·ûË P= 

1) 4 2) 3 3) 5 4) 2 

4. If 'O' is circumcentre and 'H' is orthocentre of ∆ABC, then 

∆ABC apple 'O' °æJ-Íéçvü¿ç, 'H' ©ç•-Íéçvü¿ç -Å®·-ûË 

List (-ñ«-G-û√) − I 


1 

A) OA ⎯ + OB ⎯ + OC 

1) ⎯ HO 

2 

B) HA ⎯ + HB 

+ HC ⎯ 

2) 2 HO ⎯ 

C) AH ⎯ + HB ⎯ + HC ⎯ 3) 2 AO 

List (-ñ«-G-û√) − II 

1 

D) OG ⎯ 4) ⎯ OH 

⎯ 

3 

5) OH ⎯ 

The correct matching is 


ÆæÈ®j† ïûª 

A B C D A B C D 

1) 1 5 3 2 2) 5 2 4 3 

3) 5 2 3 4 4) 2 4 3 5 

www.eenadupratibha.net


5. Assertion (A): The torque about the point 3 ⎯ i − ⎯ j + 3 ⎯ k of a force represented by 

4 ⎯ i + 2 ⎯ j + ⎯ k through the point 5 ⎯ i + 2 ⎯ j + 4 ⎯ k is ⎯ i + 2 ⎯ j − 8 ⎯ k. 

(A) : 5 ⎯ i + 2 ⎯ j + 4 ⎯ k ≤ƒn†-C-¨¡í¬ Ö†o Gçü¿’´¤ ü∆y®√ ¢Á∞¡⁄h 3 ⎯ i − ⎯ j + 3 ⎯ k 

≤ƒn†ÆæC¨¡í¬ Ö†o Gçü¿’´¤ ü¿%≥ƒdu 4 ⎯ i + 2 ⎯ j + ⎯ k •©ç ßÁ·éπ\ ö«®˝\ 

⎯ i + 2 

⎯ j − 8 

⎯ k. 

Reason (R): The torque of a force F about a point P is ⎯ r × ⎯ F where ⎯ r is the 

vector from the point P to any point ⎯ a on the line of action of ⎯ F 

(R): F ÅØË •©ç -ßÁ·éπ\ ö«®˝\ P Gçü¿’´¤ ü¿%≥ƒdu ⎯ r × ⎯ F Å´¤-ûª’çC. Ééπ\úø ⎯ r 

ÅØËC P Gçü¿’´¤ †’ç* ⎯ a ≤ƒn†- Ææ-C-¨¡í¬ Ö†o Gçü¿’-´¤éÀ UÆœ† ÆæC¨¡ 

Which of the following is correct? 

1) Both A and R are true and R is the correct explanation of A. 

A, R ÆæÈ®j-†N, A éÀ R ÆæÈ®j-†- N-´-®Ωù. 

2) Both A and R are true but R is not correct explanation of A. 

A, R ÆæÈ®j-†N. A éÀ R ÆæÈ®j† N´-®Ωù é¬ü¿’. 

3) A is true, but R is false. A Ææûªuç, R ÅÆæûªuç. 

4) A is false, but R is true. A ÅÆæûªuç, R Ææûªuç. 


6. Let ⎯ a = ⎯ i + ⎯ j + ⎯ k, ⎯ b = x 1 

⎯ i + x2 

⎯ j + x3 

⎯ k, where x1 , x 2 , x 3 ∈{−3, −2, −1, 0,1, 2} 

then the number of possible vectors ⎯ b such that ⎯ a. ⎯ b = 0 are 

⎯a = ⎯ i + ⎯ j + ⎯ k, ⎯ b = x 1 

⎯ i + x2 

⎯ j + x3 

⎯ k, x1 , x 2 , x 3 ∈{−3, −2, −1, 0, 1, 2} -Å®·-ûË 

⎯ a. 

⎯ b = 0 ÅßË’u Nüµ¿çí¬ ≤ƒüµ¿u-´’ßË’u ⎯ b ÆæC-¨¡© Ææçêu 

1) 5 2) 10 3) 25 4) 1 

7. If ⏐ ⎯ a ⏐ = 3,⏐ ⎯ b ⏐ = 4 and ⏐ ⎯ a + ⎯ b ⏐ = 5 then ⏐ ⎯ a − ⎯ b ⏐ = 

⏐ ⎯ a ⏐ = 3,⏐ ⎯ b ⏐= 4, ⏐ ⎯ a + ⎯ b ⏐ = 5 Å®·ûË ⏐ ⎯ a − ⎯ b ⏐ = 

1) 5 2) 3 3) 1 4) 0 

8. If P is real and ⎯ a = P ⎯ i + sinθ ⎯ j + ⎯ k, ⎯ b = 2 ⎯ i + P ⎯ j + ⎯ k, ⎯ c = ⎯ i + ⎯ j + ⎯ k are three 

coplanar vectors then P = 

P äéπ ¢√Ææh´ Ææçêu, ⎯ a = P ⎯ i + sinθ ⎯ j + ⎯ k, ⎯ b = 2 ⎯ i + P ⎯ j + ⎯ k, ⎯ c = ⎯ i + ⎯ j + ⎯ k Ææûª-Mßª’ 

ÆæC-¨¡©’ Å®·-ûË P= 

9. 


1) 1 2) −1 3) 0 4) 3 

⎯ a 1 , ⎯ b 1 , ⎯ c 1 are reciprocal vectors of ⎯ a, ⎯ b, ⎯ c then [ ⎯ a 1 ⎯ b 1 ⎯ c 1 ][ ⎯ a ⎯ b ⎯ c ] = 

⎯ a 1 , ⎯ b 1 , ⎯ c 1 -©’ ⎯ a, ⎯ b, ⎯ c -ßÁ·éπ\ -Napple´’ ÆæC-¨¡©’ Å®·ûË [ ⎯ a 1 ⎯ b 1 ⎯ c 1 ][ ⎯ a ⎯ b ⎯ c ] N©’´ 

1) 3 2) 1 3) 13 4) 4 



10. Which of the following is possible? éÀçC¢√-öÀapple àC ≤ƒüµ¿uç? 

1 

1) sin θ = x + ⎯ , x ∈ R 

x 

2) cos θ = x 2 + 2x + 2, x ∈ R 

x 

3) 2 

sec θ = ⎯⎯⎯, x ∈ R 

1+ x 2 

4) tan θ = −500π 

11. sin 2 α + cos 2 (α + β) + 2 sinα sin β cos (α + β) = 

1) sin 2 α 2) sin 2 β 3) cos 2 α 4) cos 2 β 

B + 2C + 3A A−B 

12. In ∆ABC (apple) cos (⎯⎯⎯⎯⎯) + cos (⎯⎯) = .. 

2 2 

1) −1 2) 1 3) 0 4) 2 

13. The maximum value of cos 3 A + cos 3 (120° −A) +cos 3 (120° +A) is 

cos 3 A + cos 3 (120° −A) +cos 3 (120° +A) ßÁ·éπ\ í∫J≠æe N©’´ 

3 4 1 1 

1) ⎯ 2) ⎯ 3) ⎯ 4) ⎯ 

4 3 2 4 

14. Period of cos (cos x) +cos (sin x) is 


cos (cos x) +cos (sin x) ßÁ·éπ\ Ç´-®Ωh†ç 

π π 2π 

1) ⎯ 2) 2π 3) ⎯ 4) ⎯ 

2 4 3 

5 11 

√ ⎯⎯ 61 60 

5 11 

2 sin −1 ( ⎯ ) + tan−1 ( ⎯ ) ßÁ·éπ\ N©’´= 

√ ⎯⎯ 61 60 

15. The value of 2 sin −1 ( ⎯ ) + tan−1 ( ⎯ ) = 

π π π 

1) ⎯ 2) ⎯ 3) ⎯ 4) none of these àD-é¬ü¿’ 

4 2 3 

√ ⎯⎯ √ ⎯⎯ π 

16. The number of real solutions of tan −1 x(x + 1) +sin −1 x 2 + x + 1 = ⎯ is 

2 

√ ⎯⎯ √ ⎯⎯ π 

tan −1 x(x + 1) +sin −1 x 2 + x + 1 = ⎯ ßÁ·éπ\ ¢√Ææh´ ≤ƒüµ¿--†© Ææçêu 

2 

1) 0 2) 1 3) 2 4) infinite 


17. If sinx sinhy = cosθ and (´’Jßª·) cosx coshy = sinθ then (Å®·ûË) 

cos h 2 y + cos 2 x = 

1) −1 2) 0 3) 1 4) 2 


18. A man on the top of a 100 meters high tower seen a car moving towards the tower 

at an angle of 30°. After some time the angle of depression becomes 60°. Then 

the distance travelled by the car is 

äéπ ´’E≠œ 100 O’. áûª’happle Ö†o Pê®Ωç †’ç* Pê®Ωç ¢Áj°æ¤ ´Ææ’h†o é¬®Ω’†’ 30° éÓùçapple 

îª÷¨»úø’. éÌç-ûª Ææ´’ßª’ç ûª®√yûª Ç E´’o-éÓùç 60° Öçõ‰ é¬®Ω’ v°æßª÷-ùÀç-*† ü¿÷®Ωç 

200 √ ⎯ 3 100 √ ⎯ 3 

1) 100 √ ⎯ 3 2) ⎯⎯⎯ 3) ⎯⎯⎯ 4) 200 √ ⎯ 3 

3 3 

1° 1° 

19. If base angles of triangle are 22 ⎯, 112 ⎯ then base and height are in the ratio 

2 2 

1° 1° 

äéπ vAµº’ï µº÷N’, éÓù«©’ 22 ⎯, 112 ⎯ Å®·ûË ü∆E µº÷N’éÀ, áûª’h-èπ◊ Ö†o E≠æpAh 

2 2 

1) 1 : 2 2) 1 : 3 3) 3 : 1 4) 2 : 1 

20. In ∆ABC, if the line joining orthocentre and centroid is parallel to ⎯ BC, then 

cot B. cot C = 

ABC vAµº’-ïçapple ©ç•-Íéç-vü∆Eo, í∫’®Ω’-ûªy-Íéç-vü∆Eo éπLÊ° Í®ê ⎯ BC éÀ Ææ´÷ç-ûª-®Ωçí¬ Öçõ‰ 

cot B.cot C ßÁ·éπ\ N©’´ 

1 1 

1) ⎯ 2) 2 3) ⎯ 4) 3 

2 3 

2 

z = 2 then the greatest value of ⏐z⏐ is 

2 

⎥ z − z 

⎯ ⎥ 

= 2 Å®·ûË ⏐z⏐ ßÁ·éπ\ í∫J≠æe N©’´ 

1) √ ⎯ 3 – 1 2) √ ⎯ 3 3) √ ⎯ 3 + 1 4) √ ⎯ 3 + 2 


21. If ⎥ z − ⎯ ⎥ 


22. If cos α+cos β+ cos γ=0 = sin α+sin β+sin γ then (Å®·ûË) 

cos 2 α+cos 2 β+cos 2 γ = 

1) 3 cos (α +β+γ) 2) −3 cos (α +β+γ) 

3 

3) ⎯ 

2 

1 

4) ⎯ 

2 

23. cos 4θ = 

1) 8 sin 4 θ−8 sin 2 θ+1 2) 8 cos 4 θ−8 cos 2 θ+1 

3) 4 cos 3 θ sin θ−4 cos θ sin 3 θ 4) 2 sin 3 θ+2 cos θ sin 2 θ 


24. If the transformed equation of a curve is X 2 + Y 2 + 4X + 6Y + 12 = 0 when the 

axes are translated to the point (2, 3) then the original equation of the curve is 

´‚© Gçü¿’-´¤†’ (2, 3) èπ◊ ´÷®Ωaí¬ X 2 + Y 2 + 4X + 6Y + 12 = 0 ÆæO’-éπ-®Ωùç ÅÆæ©’ ®Ω÷°æç 

1) x 2 + y 2 + 1 = 0 2) x 2 + y 2 − 1 = 0 3) x 2 − y 2 + 1 = 0 4) x 2 − y 2 − 1 = 0 



25. A(7, 3), B(−15, 3) are two vertices of a ∆ABC then locus of third vertex 'C' if 

cotA + cotB = k, where k is constant is 

A(7, 3), B(−15, 3) ©’ vAµº’ïç ABC ßÁ·éπ\ Q®√{©’. cotA + cotB = k (k Æœn®Ω Ææçêu) 

Å®·ûË ´‚úÓ Q®Ω{ç 'C' ßÁ·éπ\ Gçü¿’-°æü∑¿ç 

1) a line parallel to BC. ⎯ 2) a line perpendicular to BC. 

⎯ 

⎯ 

BC éÀ Ææ´÷ç-ûª-®Ωçí¬ ÖçúË Ææ®Ω-∞¡-Í®ê 

⎯ BC éÀ ©ç•çí¬ ÖçúË Ææ®Ω-∞¡-Í®ê 

3) a circle with A, B as ends of diameter. 4) a line parallel to AB. 

⎯ 

A, B ©’ ¢√uÆæç *´-®Ωí¬ ÖçúË ´%ûªh ÆæO’-éπ-®Ωùç 

⎯ AB éÀ Ææ´÷ç-ûª-®Ωçí¬ ÖçúË Ææ®Ω-∞¡-Í®ê 

26. The equation of perpendicular bisector of a line segment ⎯ A ⎯ B is x − y + 5 = 0. 

If A = (1, −2) then AB = 

A= (1, − 2), ⎯ A ⎯ B -ßÁ·éπ\ -©ç• Æǽ ’-Cy-êç-úø† Í®ê ÆæO’-éπ-®Ωùç x − y + 5 = 0 Å®·ûË AB = 

1) 7 √ ⎯ 2 2) 6 √ ⎯ 2 

3) 8 √ ⎯ 2 4) 9 

27. If P, Q are two points on the line 3x + 4y + 15 = 0 such that OP = OQ = 9, then 

the area of ∆OPQ is 


P, Q ©’ 3x + 4y + 15 = 0 Í®êÂ°j ÖçúË È®çúø’ Gçü¿’-´¤©’ OP = OQ = 9, Å®·ûË ∆OPQ 

¢Áj¨»©uç 

1) 6√ ⎯ 2 2) 9 √ ⎯ 2 3) 12√ ⎯ 2 4) 18√ ⎯ 2 

28. The length of the intercept on X − axis cut by the pair of lines 

2x 2 + 5xy + 3y 2 + 6x + 7y + 1 = 0 is 

2x 2 + 5xy + 3y 2 + 6x + 7y + 1 = 0 Ææ®Ω∞¡ Í®ê- ßÁ·éπ\ X − Åçûª®Ω êçúøç §Òúø´¤ 

1) √ ⎯ 5 2) 2 √ ⎯ 5 3) √ ⎯ 7 4) 2√ ⎯ 7 

29. If the slope of one of the lines represented by 2x 2 + 3xy + ky 2 = 0 is 2 then the 

angle between pair of lines is 

2x 2 + 3xy + ky 2 = 0 Ææ®Ω∞¡ Í®êapplex äéπ Ææ®Ω∞¡ Í®ê ¢√©’ 2 Å®·ûË Ç Í®ê© ´’üµ¿u éÓùç 

π π π π 

1) ⎯ 2) ⎯ 3) ⎯ 4) ⎯ 

2 3 6 4 

1 1 

30. If the direction cosines of a line are ⎯, ⎯, n and n < 0 then n = 

3 3 

1 1 

äéπ Í®ê Cé˙ éÌÂÆj-Ø˛©’ ⎯, ⎯ n, n < 0 Å®·ûË n = 

3 3 

√ ⎯ 7 7 3 3 

1) − ⎯⎯ 2) − ⎯⎯ 3) ⎯⎯ 4) − ⎯⎯ 

3 3 7 7 




31. The distance between the parallel planes 

4x − 4y + 2z + 5 = 0, 2x − 2y + z + 3 = 0 is 

4x − 4y + 2z + 5 = 0, 2x − 2y + z + 3 = 0 Ææ´÷ç-ûª®Ω ûª«© ´’üµ¿u ü¿÷®Ωç 

1) 1 unit 2) 2 units 

1 

3) ⎯ units 

6 

4) 3 units 

1 3 

5 5 

respectively then the angle made by the line with Z − axis is 

1 3 

5 5 

32. If a line makes angles cos −1 (⎯), cos −1 (⎯) with X − axis and Y − axis 

äéπ-Í®ê X − Åéπ~ç, Y− Åé~¬-©-ûÓ ´®Ω’-Ææí¬ cos −1 (⎯), cos −1 (⎯) éÓù«©’ îËÆæ’hçC. 

Å®·ûË ÇÍ®ê Z − Åéπ~çûÓ îËÊÆ éÓùç 

1 2 √ ⎯ 3 4 

1) cos −1 (⎯) 2) cos −1 (⎯) 3) cos −1 (⎯) 4) cos 

5 5 5 −1 (⎯) 

5 

1 − √ ⎯ x 

33. Lt ⎯⎯⎯⎯ = 

x→1 (cos −1 x) 2 1 1 

1) 1 2) 4 3) ⎯ 4) ⎯ 

4 2 

1 − tanx π π 

34. Let f(x) = ⎯⎯⎯, x ≠ ⎯ , x ∈ [0, ⎯]. 

4x − π 4 2 


π π 

If f(x) is continuous in [0, ⎯], then f (⎯) is 

2 4 

1 − tanx π π π 

f(x) = ⎯⎯⎯ , x ≠ ⎯, x ∈ [0, ⎯], f(x) v°æ¢Ë’ßª’ç [0, ⎯]apple 

4x − π 4 π 2 

π 

ÅN--*a¥-†oç Å®·ûË f (⎯) N©’´ 

4 

1 1 

1) 1 2) − ⎯ 3) −1 4) ⎯ 

2 2 

1 + x 

√ ⎯⎯ 1 / 2 

1 dy 

1 − x 2 dx 

35. If y = log ( ⎯⎯ ) − ⎯ tan −1 x then (Å®·ûË) ⎯ = 

x 2 x 2 x x 

1) ⎯⎯ 2) ⎯⎯ 3) ⎯⎯ 4) ⎯⎯ 

1 + x 4 1 − x 4 1 − x 2 x 2 − 1 


x n + y n 

∂U 

x e + y e 

∂x 

1) n 2) e 3) n − e 

n 

4) ⎯ e 

36. If U = log (⎯⎯⎯) then (Å®·ûË) Σ x ⎯ = 



37. The radius and height of a cylinder are measured as 5 cm, 10 cm respectively and 

there is an error of 0.02 in both the measurements. The percentage error in 

volume is 

äéπ Ææ÷h°æç ¢√u≤ƒ®Ωl¥ç, áûª’h ´®Ω’-Ææí¬ 5 ÂÆç.O’., 10 ÂÆç.O’., OöÀ éÌ©ûªapplex 0.02 üÓ≠æç Öçõ‰ 

°∂æ’†-°æ-J-´÷-ùçapple ÖçúË üÓ≠æ ¨»ûªç áçûª? 

1) 1 2) 0.01 3) 0.001 4) – 1 

38. The lengths of tangent, sub tangent, normal and subnormal for the curve 

y = x 2 + x − 1 at (1, 1) are A, B, C, D respectively then their increasing order is 

y = x 2 + x − 1 ´véπçÂ°j (1, 1) Gçü¿’´¤ ü¿í∫_®Ω UÆœ† Ææp®Ωz Í®ê, Ö°æ-Ææp®Ωz Í®ê, ÅGµ-©ç• Í®ê, 

Ö°æ-Å-Gµ-©ç• Í®ê-© §Òúø-´¤©’ A, B, C, D Å®·ûË, -¢√-öÀ N©’-´©’ Ç®Ó£æ«ù véπ´’çapple.... 

1) B, D, A, C 2) B, A, C, D 

3) A, B, C, D 4) B, A, D, C 

39. If a 2 x 4 + b 2 y 4 = c 6 , then the maximum value of xy is 

a 2 x 4 + b 2 y 4 = c 6 , Å®·ûË xy í∫J≠æe N©’´ 

c 3 c 3 c 3 c 

1) ⎯⎯ 2) ⎯⎯ 3) ⎯⎯ 4) ⎯⎯ 

3 

2ab √ ⎯ 2ab ab √ ⎯ ab 


40. The relation between displacement 'S' and time 't' of a particle is given by 

1 

S = 6 t − ⎯ t 2 then its maximum velocity is 

2 

äéπ éπùç v°æßª÷-ùÀçîË ü¿÷®Ωç (S), é¬©ç (t) ´’üµ¿u Ææç•çüµ¿ç 

1 

S = 6 t −⎯ t 2 Å®·ûË ü∆E í∫J≠æe ¢Ëí∫ç 

2 

1) 1 unit/sec 2) 6 units/sec 3) 3 units/sec 4) 11 units/sec 

41. If y = log (x 2 − a 2 ) then (Å®·ûË) y n = 

1 1 

1) (−1) n−1 { (n − 1) ! ⎯⎯⎯⎯ + ⎯⎯⎯⎯ } 

( x − a) n (x + a) n 

1 1 

2) (−1) n−1 { (n − 1) ! ⎯⎯⎯⎯ − ⎯⎯⎯⎯ } 

(x + a) n (x + a) n 


1 1 

3) (−1) n−1 { (n − 1) ! ⎯⎯⎯⎯ − ⎯⎯⎯⎯ } 

(x − a) n − 1 (x + a) n − 1 

1 

4) (−1) n−1 n! ⎯⎯⎯⎯⎯ 

(x 2 − a 2 ) n 



3 cos x + 2 sin x 

42. ∫ ⎯⎯⎯⎯⎯⎯ 

5 cos x + 4 sin x 

dx = 

23 2 

1) ⎯⎯ x − ⎯⎯ 

41 41 

log ⏐4 sin x + 5 cos x⏐ + c 

23x 2 

2) ⎯⎯+ ⎯ log ⏐5 cos x + 4 sin x⏐ + c 

41 41 

2x 23 

3) ⎯ + ⎯ log ⏐4 sin x + 5 cos x⏐ 

41 41 

+ c 

2 23 

4) ⎯ x + ⎯ log ⏐4 sin x + 5 cos x⏐ + c 

41 41 

43. ∫ (sin (logx) +cos (logx))dx is 

1) x cos (log x) +c 2) e x sin (log x) +c 

3) x sin (log x) +c 4) e x cos (log x) +c 

∫ 

sec xdx (sec x + tan x) 

44. If ⎯⎯⎯⎯⎯ = ⎯⎯⎯⎯⎯ n 

+ c, then (Å®·ûË) n = 

(sec x + tanx) 5 n 

1) − 6 2) − 5 3) 5 4) 4 

π / 2 

1 

45. ∫ ⎯⎯⎯⎯⎯⎯ dx = 

0 4cos2 x + 9sin 2 x 

1) ⎯ 

π 

2) ⎯ 

π 

3) ⎯ 

π 

4) ⎯ 

π 

4 8 16 12 

π / 2 

π / 2 I 1 


46. I 1 = ∫ f(sin2x) sin x dx and I 2 = ∫ f (sin2x) cos xdx, then (Å®·ûË) ⎯ = 

0 0 I 2 

1 

1) 1 2) 3) √ ⎯ 2 4) 2 

√ ⎯ 2 

47. The area in the first quadrant enclosed by the axes, the line x = y √ ⎯ 3 and the 

circle x 2 + y 2 = 4 (smaller area) is 

x = y √ ⎯ 3 , x2 + y 2 = 4 ©’ Åé~¬-©Â°j îËÊÆ Åûªu©p ¢Áj¨»©uç (¢Á·ü¿öÀ Åéπ~çapple) 

1) ⎯ 

π 

2) ⎯ 

π 

3) ⎯ 

π 

4) ⎯ 

π 

2 3 4 6 

48. The approximate value of ∫ 3 

x 4 dx using Trapezoidal rule and taking six equal 

interval is 

−3 


-võ„°œ--ñ«-®·-úø-¸ Ææ÷vû√Eo Ö°æ-ßÁ÷-TÆæ÷h, É*a† Åçûª-®√Eo Ç®Ω’ Ææ´÷† µ«í¬-©’í¬ BÆæ’-èπ◊çô÷ 

∫ 3 

−3 

x 4 dx ßÁ·éπ\ Öñ«b-®·ç°æ¤ N©’´ 

1) 11.5 2) 9 3) 115 4) 120 



49. Solution of the differential equation 

dy (x 2 y 2 ) dy 2 (xy) 3 dy 3 

x = 1+ [xy ⎯] + ⎯⎯⎯ [⎯] +⎯⎯[ ⎯] + .. is 

dx 2! dx 3! dx 

⎯] 

dy (x 2 y 2 ) dy 2 (xy) 3 dy 3 

x = 1+ [xy + ⎯⎯⎯ [⎯⎯] [ ⎯] +⎯⎯ + .. Å´-éπ-©† ÆæO’-éπ-®Ωù ≤ƒüµ¿† 

dx 2! dx 3! dx 

1) y = ln (x) +C 2) y = (ln x) 2 + C 

3) √ ⎯⎯⎯⎯⎯ 

y = ± (ln x) 2 + C 4) xy = x y + K 

50. The differential equation of the curve for which the normal at every point passes 

through a fixed point (h, k) is 

àüÁjØ√ Gçü¿’´¤ ´ü¿l UÆœ† ÅGµ-©ç• Í®ê (h, k) Gçü¿’´¤ -ü∆y®√ -¢Á-∞Ïh Ç ´véπç Å´-éπ-©† ÆæO’-éπ-®Ωùç 

dx 

dx 

1) y − k = ⎯ (h − x) 2) y − k = ⎯ (x − h) 

dy 

dy 

dy 

dy 

3) y − k = ⎯ (h − x) 4) y − k = ⎯ (x − h) 

dx 

dx 

dy xlogx 2 + x 

51. ⎯ = ⎯⎯⎯⎯⎯⎯ 

dx siny + y cosy 

1) y sin y = x 2 log x + c 2) y sin y = x 2 + c 

3) sin y = x 2 log x + c 4) y sin y = x log x + c 

52. The values of K for which the equation x 2 + y 2 + z 2 + 4x + 6y + 8z + K = 0 

represents a real sphere is 


x 2 + y 2 + z 2 + 4x + 6y + 8z + K = 0 ÆæO’-éπ-®Ωùç äéπ ¢√Ææh´ íÓ∞«Eo Ææ÷*ÊÆh 

1) K ≥ 19 2) K ≤ 29 3) K ≥ 39 4) K ≤ 39 

53. The pole of a straight line with respect to the circle x 2 + y 2 = a 2 lies on the 

circle x 2 + y 2 = 9a 2 . If the straight line touches the circle x 2 + y 2 = r 2 , then 

x 2 + y 2 = a 2 ü¿%≥ƒdu Ææ®Ω-∞¡-Í®ê vüµ¿’´ç x 2 + y 2 = 9a 2 ´%ûªhç O’ü¿ ÖçúÕ, Ç Í®ê 

x 2 + y 2 = r 2 ´%û√hEo Ææp %PÊÆh 

1) 9a 2 = r 2 2) 9r 2 = a 2 3) r 2 = a 2 4) 3r 2 = a 2 

54. If A and B are conjugate point w.r.t a circle with centre 'O' and radius 'r', then 

AB 2 = 


'O' Íéçvü¿çí¬, 'r' ¢√u≤ƒ®Ωl¥çí¬ Ö†o ´%û√hEéÀ A, B ©’ Ææçßª·í∫t Gçü¿’-´¤©’ Å®·ûË AB 2 = 

1) OA 2 + OB 2 2) OA 2 + OB 2 + 2r 2 

3) OA 2 + OB 2 + r 2 4) OA 2 + OB 2 − 2r 2 



55. If (1, 2), (4, 3) are limiting points of coaxial system then the equation of the circle 

in its conjugate system having minimum area is 

(1, 2), (4, 3) äéπ Ææ£æ…-éπ~´%ûªh Ææ®Ω-ùÀéÀ ÅĆµ Gçü¿’-´¤©’ Å®·ûË ü∆EéÀ ©ç•-Ææ-£æ…éπ~ ´%ûªh-Ææ-®Ω-ùÀapple 

ÅA ûªèπ◊\´ ¢Áj¨»©uç Ö†o ´%ûªh ÆæO’-éπ-®Ωùç 

1) x 2 + y 2 − 2x − 4y + 5 = 0 2) x 2 + y 2 − 8x − 6y + 25 = 0 

3) x 2 + y 2 − 5x − 5y + 10 = 0 4) x 2 + y 2 + 5x + 5y − 10 = 0 

56. The normal at 'P' cuts the axis of the parabola y 2 = 4ax in G and S is the focus 

of the parabola. If ∆ SPG is an equilateral then each side is of length 

y 2 = 4ax °æ®√-´-©-ßª÷-EéÀ 'P' Gçü¿’´¤ ´ü¿l UÆœ† ÅGµ-©ç-•-Í®ê -Åé~¬Eo G ü¿í∫_®Ω êçúÕ-Ææ’hçC. 

S Ø√Gµ, ∆ SPG Ææ´’-«£æ› vAµº’ïç Å®·ûË -Ç vA-µº’ï µº’ïç §Òúø´¤ 

1) a 2) 2a 3) 3a 4) 4a 

x 2 y 2 

57. The ends of minor axis and the Focii of ⎯ + ⎯ = 1 form a square, then its 

a 2 b 2 

eccentricity is 

x 2 y 2 

⎯ + ⎯ = 1 -D®Ω`-´%-ûªh Ø√µº’©’ v£æ«≤ƒyéπ~ç -ßÁ·éπ\ Åçû√u©ûÓ äéπ îªûª’-®Ω--vÆæç à®Ωp-úÕ-ûË 

a 2 b 2 

D®Ω`-´%ûªh ÖûË\ç-vü¿ûª 


1 1 √ ⎯ 3 

1) ⎯ 2) 3) ⎯⎯ 4) sin18° 

2 √ ⎯ 2 2 

x 2 y 2 

58. The equation ⎯⎯⎯ + ⎯⎯⎯ = 1 represents a hyperbola then 

7 − k 5 − k 

x 2 y 2 

⎯⎯⎯ + ⎯⎯⎯ = 1 ÅA °æ®√-´©ßª÷Eo Ææ÷*ÊÆh 

7 − k 5 − k 

1) 5 < k < 7 2) k < 5 (or) k > 7 

3) k < 5 4) k ≠ 5, k ≠ 7 

( 

π 

59. The equation of the line which passes through −1, ⎯⎯ ) and which is parallel to 

2 

r (2cosθ + √ ⎯ 3 sinθ) = 4 is 


π 

2 

ÆæO’-éπ-®Ωùç 

1) r (2 cosθ + √ ⎯ 3 sinθ) = √ ⎯ 3 2) r (2 cosθ + √ ⎯ 3 sinθ) = −√ ⎯ 3 

3) r (2 sinθ −√ ⎯ 3 cosθ) = 2 4) r (2 sinθ −√ ⎯ 3 cosθ) = −2 

r(2cosθ + √ ⎯ 3 sinθ) = 4 Í®êéÀ Ææ´÷ç-ûª-®Ωçí¬ Öçô÷ ( −1, ⎯⎯ ) Gçü¿’´¤ ü∆y®√ --¢Á-∞Ïx Í®-ë« 



60. If the roots of 3x 3 − 22x 2 + 48x − 32 = 0 are in H.P., then the roots are 

3x 3 − 22x 2 + 48x − 32 = 0 ÆæO’-éπ-®Ωù ´‚«©’ H.P. apple Öçõ‰ Ç ´‚«©’ 

1 1 3 4 

1) ⎯, ⎯, ⎯ 2) 4, 2, ⎯ 

4 2 4 3 

3) ⎯, 

1 

⎯, 

1 

⎯ 

2 

4) 3, 2, ⎯ 

3 

3 2 3 2 

61. For the equation ⏐x⏐ 2 + ⏐x⏐ −6 = 0, the roots are 

⏐x⏐ 2 + ⏐x⏐ −6 = 0 ÆæO’-éπ-®Ωù ´‚«©’ 

1) one and only one real number 2) real with sum one 

äÍé äéπ ¢√Ææh´ Ææçêu 

¢√Ææh´ç, ´‚«© ¢Á·ûªhç '1' 

3) real with sum zero 4) real with product zero 

¢√Ææh-¢√©’, ´‚«© ¢Á·ûªhç'0' 

62. If 20 3 − 2x2 = (40√ ⎯ 5) 3x2 − 2 , then (Å®·ûË) x = 

¢√Ææh-¢√©’, ´‚«© ©-•l¥ç '0' 

√ ⎯⎯ 13 

√ ⎯⎯ 12 

√ ⎯⎯ 4 

√ ⎯⎯ 5 

12 13 5 4 

1) ± ⎯ 2) ± ⎯ 3) ± ⎯ 4) ± ⎯ 


√ ⎯⎯⎯ 

√ ⎯⎯⎯ 

63. If x 3 , x 4 , x 5 , ... can be neglected, then x 2 + 16 − x 2 + 9 = 

√ ⎯⎯⎯ 

√ ⎯⎯⎯ 

x 3 , x 4 , x 5 ,... ©†’ NÆæt-JÊÆh x 2 + 16 − x 2 + 9 = 

x 2 x 2 x 2 x 2 

1) 1− ⎯ 2) 1 −⎯ 3) 1− ⎯ 4) 1 − ⎯ 

4 8 18 24 

64. In the expansion of (1 + x) n , if the 2 nd , 3 rd terms are respectively a, b then x = 

(1 + x) n NÆæh-®Ω-ùapple 2´, 3´ °æü∆©’ ´®Ω’-Ææí¬ a, b©’ Å®·ûË, x = 

2b a a 2 a 2 − 2b 

1) a − ⎯ 2) ⎯⎯⎯ 3) ⎯⎯⎯ 4) ⎯⎯⎯ 

a a 2 − 2b a 2 − 2b a 2 

x 4 + 3x + 1 C D E 

65. If ⎯⎯⎯⎯⎯⎯ = Ax + B + ⎯⎯ + ⎯⎯⎯ + ⎯⎯ then (Å®·ûË) A+ D = 

(x + 1) 2 (x − 1) x + 1 (x+1) 2 x − 1 

3 

1) 2 2) −2 3) ⎯ 4) 0 

2 

1 2 2 2 3 2 4 2 

66. ⎯ + ⎯ + ⎯ + ⎯ + ... ∞ = 

3! 4! 5! 6! 


1) 2e − 5 2) 2e − 4 3) 5e + 1 4) e − 1 


67. 

x x 2 x 3 

⎯ + ⎯ + ⎯ + ... 

1.2 2.3 3.4 

1 − x x − 1 

x 

x 

1 − x x − 1 

x 

x 

x + 1 x x 

1) 1 + ( ⎯⎯ ) log (1 − x) 2) 1 + ( ⎯⎯ ) log (1 − x) 

3) 1 + ( ⎯⎯ ) log (x − 1) 4) 1 + ( ⎯⎯ ) log (x − 1) 

68. If a ≠ 0 

⏐ x x + a x ⏐ x x x + a 2 


= 0 represents (Ñ ÆæO’-éπ-®Ωùç üËEo Ææ÷*-Ææ’hçC) 

1) a straight line parallel to X − axis 2) a straight line parallel to Y − axis 

X- Åé~¬-EéÀ Ææ´÷ç-ûª-®Ωçí¬ ÖçúË Í®ê Y- Åé~¬-EéÀ Ææ´÷ç-ûª-®Ωçí¬ ÖçúË Í®ê 

3) a parabola °æ®√-´-©ßª’ç 4) a circle ´%ûªhç 

69. Consider the following statements. éÀçC v°æ´-îª-Ø√-©†’ °æJ-Q-Lç-îªçúÕ. 

Statement - I: If det A = 0, then det (adj A) = 0. 

v°æ´-îª†ç – I: ⏐A⏐ = 0 Å®·ûË ⏐adj A⏐ = 0. 

Statement - II: If A is non-singular then det (A −1 ) = (det A) −1 . 

v°æ´-îª†ç – II: A ≤ƒ-üµ∆®Ω-ù --´÷-vAéπ -Å®·-ûË ⏐A −1 ⏐ = ⏐A⏐ −1 . 

Which of the above statements is/are correct? Â°j v°æ´-îªØ√applex ÆæÈ®j-†N àN? 

1) Both I and II I -´’-J-ßª· II 2) Neither I nor II àD- é¬ü¿’ 

3) I only I ´÷vûª¢Ë’ 4) II only II´÷vûª¢Ë’ 


70. If there is no solution for the system of equations x + y + z = 4, y + 2z = 5 

and x + y + pz = q 

Â°j ÆæO’-éπ-®Ωù ú´ÆænéÀ ≤ƒüµ¿† ‰éπ§ÚûË 

1) p = 1 and q = 4 2) p = 1 and q ≠ 4 3) p ≠ 1 and q = 4 4) p ≠ 1 and q ≠ 4 

71. Number of ways of arranging 3 boys and 4 girls so that no boy is in between any 

two girls 

-´·í∫’_®Ω’ «©’®Ω’, -†-©’í∫’®Ω’ «L-éπ-©†’ äéπ ´®Ω-Ææapple Å´’Ja†°æ¤púø’ à Éü¿l®Ω’ «L-éπ© ´’üµ¿u 

«©’®Ω’ ®√E Å´’-J-éπ© Ææçêu 

1) 576 2) 314 3) 144 4) 24 

72. In a shop there are 30 Thumsups, 20 Sprites, 40 Limcas. In how many ways a 

boy can purchase 10 cool drinks? 


äéπ ü¿’é¬-ùçapple 30 -ü∑¿-´’q°ˇ-©’, 20 -vÂÆjp-ö¸, 40 L-´÷\-©’ ÖØ√o®·. äéπ «©’úø’ 10 Qûª© 

§ƒFßª÷©-†’ éÌØ√-©-†’-èπ◊ç-õ‰ áEo Nüµ∆©’í¬ éÌ†-í∫-©úø’? 

-1) 66 2) 90 C 10 

3) 10 C 3 

4) 15 



73. The maximum number of points of intersection of 4 circles and 4 straight lines is 

4 ´%û√h©’, 4 Ææ®Ω-∞¡-Í®-ê©’ í∫J-≠æeçí¬ êçúÕç-îª’-èπ◊ØË Gçü¿’´¤©’ 

1) 25 2) 50 3) 56 4) 73 

74. If C(2n, 3) : C(n, 2) = 12 : 1 then (Å®·ûË) n = 

1) 4 2) 6 3) 5 4) 8 

75. A letter is known to have come from either 'LONDON' (or) 'CLIFTON' on the 

envelope just 2 consecutive letters 'ON' are visible. The probability that the 

letter comes from LONDON 

äéπ Öûªh®Ωç 'LONDON' (‰ü∆) 'CLIFTON' †’ç* ´*açC é¬F Ç éπ´-®Ω’Â°j È®çúø’ ´®Ω’Ææ 

°æü∆©’ 'ON' í¬ éπ-E°œÊÆh Ç Öûªh®Ωç LONDON †’ç* ®√´-ú≈-EéÀ Ö†o Ææçµ«-úûª 

12 5 3 2 

1) ⎯ 2) ⎯ 3) ⎯ 4) ⎯ 

17 17 17 5 

76. Four numbers are chosen at random from {1, 2, 3, ...40}. The probability that 

they are not consecutive is 

{1, 2, 3,... 40} †’ç* Ø√©’í∫’ Ææçêu-©†’ ßª÷-ü¿%*a¥éπçí¬ á†’oèπ◊çõ‰ ÅN ´®Ω’Ææ Ææçêu©’ 

é¬èπ◊çú≈ Öçúø--ö«-EéÀ Ææçµ«-úûª 


1 4 2469 7965 

1) ⎯⎯ 2) ⎯⎯⎯ 3) ⎯⎯⎯ 4) ⎯⎯⎯ 

2470 7969 2470 7969 

77. If x is a binomial variate with the range n = 6 and P(x = 2) = 4P (x = 4), then the 

parameter P of x is 

x ÅØËC Cy°æü¿ Nµ«-ïéπç Å®·u ü∆E ¢√u°œh n = 6, P(x = 2) = 4P(x = 4) Å®·ûË x °æ®√N’A 

P N©’´. 

1 1 2 3 

1) ⎯ 2) ⎯ 3) ⎯ 4) ⎯ 

3 2 3 4 

78. A random variable X has its range {0, 1, 2, 3, ...}. 

c(r + 1) 

If P(X = r) = ⎯⎯⎯⎯ for r = 0, 1, 2, ... then c = 

3 r 

x ÅØË ßª÷-ü¿%*a¥éπ îª©-®√P ¢√u°œh {0, 1, 2, 3, ...} 


c(r + 1) 

P(X = r) = ⎯⎯⎯⎯, r = 0, 1, 2... Å®·ûË c = 

3 r 

4 1 1 

1) ⎯ 2) ⎯ 3) 2 4) ⎯ 

9 2 4 



79. If a random variable X follows poision distribution and its variance (σ 2 ) = 4 then 

mean (µ) = 

ßª÷-ü¿%-*a¥éπ îª©-®√P X §ƒ®·-ïØ˛ Eßª’-´÷Eo §ƒöÀ-Ææ’hçC, ü∆E NÆæh %A (σ 2 ) = 4 Å®·ûË 

´’üµ¿u´’ç (µ) = 

1) 2 2) √ ⎯ 2 3) 4 4) 1 

1 

80. Suppose X follows a binomial distribution with parameters n = 100 and P = ⎯ . 

3 

Then P(X = r) is maximum when r = 

ßª÷-ü∑¿%-*a¥éπ îª©-®√P X Cy°æü¿ N-µ«-ï-Ø√Eo §ƒöÀ-Ææ’hçC. 

1 

n = 100, P = ⎯, P(X = r) í∫J≠æeç Å®·ûË r N©’´ 

3 

1) 65 2) 67 3) 33 4) 30 

PHYSICS 

81. The physical quantity having the dimensions [M −1 L −3 T +3 A 2 ] 

[M −1 L −3 T +3 A 2 ] N’ûª’©’ Ö†o µÃéπ ®√P 

1) resistance E®Óüµ¿ç 2) resistivity E®Óüµ¿éπûª 

3) electrical conductivity Nü¿’uû˝ ¢√£æ«-éπûª 4) electromotive force Nü¿’u-î√a¥-©éπ •©ç 

82. A swimmer crosses a river of width 'd' flowing at a velocity 'v'. While swimming, 

he keeps himself always at an angle of 120° with the river flow and on reaching 

the other point he finds a drift of d/2 in the direction of flow of river. The speed 

of swimmer with respect to river is 

d ¢Áúø©’p ÖçúÕ, 'v' ¢Ëí∫çûÓ v°æ´£œ«Ææ’h†o †CE äéπ úéÀh Ñü¿’ûª÷ ü∆ö«úø’. v°æ¢√£æ« C¨¡èπ◊ 

á©x°æ¤púø÷ 120° éÓùçapple ÑC† Åûªúø’, †CE ü∆öÀ† ûª®√yûª, †C C¨¡apple ûª† N≤ƒn-°æ†ç d/2 í¬ 

í∫’Jhç-î√úø’. Å®·ûË †C ü¿%≥ƒdu ÑC† úéÀh ¢Ëí∫ç? 


1) (2 − √ ⎯ 3)v 2) 2(2 − √ ⎯ 3)v 3) 4(2 − √ ⎯ 3)v 4) (2 + √ ⎯ 3)v 

83. A particle is projected from the ground with an initial speed of V at an angle θ 

with the horizontal. Average velocity of the particle between its point of 

projection and highest point of the trajectory is 

äéπ éπù«Eo V ûÌL ´úÕûÓ, éÀ~A-ïçûÓ θ éÓùç îËÊÆ« ØË© †’ç* v°æéÀ~°æhç îË¨»®Ω’. v°æéÀ~-°æh-Gçü¿’´¤, 

°æü∑¿çapple í∫J≠æe áûª’h ´’üµ¿u éπùç Ææí∫ô’ ¢Ëí∫ç 


V ⎯⎯⎯⎯⎯ V ⎯⎯⎯⎯⎯ 

1) ⎯ 

√ 1 + 2 cos2 θ 2) ⎯ 

√ 1 + cos2 θ 

2 2 

V ⎯⎯⎯⎯⎯ 

3) ⎯ 

√ 1 + 3cos2 θ 4) V cos θ 

2 


84. Two blocks of masses 5 kg and 2 kg are connected by a massless 

string as shown in the figure. A vertical force F is applied on the 

5 kg block. The value of F if tension in the string connecting the 

blocks is 40 N is (g = 10 ms −2 ) 

°æôçapple îª÷°œ†ô’x 5 kg, 2 kg vü¿ú-®√P Ö†o È®çúø’ C¢Á’t-©†’ vü¿ú-®√-P- 2 kg 

®Ω-£œ«ûª ü∆®ΩçûÓ éπL§ƒ®Ω’. 5 kg © C¢Á’tÂ°j Eôd-E-©’-´¤í¬ Â°jéÀ F •«Eo v°æßÁ÷-Tç-*-†-°æ¤púø’, C¢Á’t- 

©†’ éπ©’-°æ¤-ûª’†o ü∆®Ωçapple ûª†uûª 40 N Å®·ûË, F N©’´ 

1) 140 N 2) 70 N 3) 40 N 4) 100 N 

85. In inelastic collision of two bodies which of following do not change after the 

collision 

È®çúø’ ´Ææ’h-´¤© ÅÆœn-A-≤ƒn-°æéπ ÅGµ-°∂æ÷-ûªçapple, ÅGµ-°∂æ÷ûªç ûª®√yûª éÀçC-¢√-öÀapple àC ´÷®Ωü¿’? 

a) total kinetic energy b) total linear momentum 

¢Á·ûªhç í∫A-¨¡éÀh 

¢Á·ûªhç Í®&ßª’ vü¿ú-¢Ëí∫ç 

c) total energy d) total angular momentum 

¢Á·ûªhç ¨¡éÀh 


¢Á·ûªhç éÓùÃßª’ vü¿ú-¢Ëí∫ç 

1) a & b 2) b & c 3) b & d 4) a & d 

86. A force F acting on a body depends on its displacement S as F ∝ S −1/3 . The 

power delivered by F will depends on displacement as. 


´Ææ’h´¤ O’ü¿ °æE îËÆæ’h†o •©ç F, ≤ƒn†-vµºç¨¡ç S O’ü¿ F ∝ S −1/ 3 í¬ Çüµ∆-®Ω-°æ-úø’-ûª’çC. F ´©x 

Núø’-ü¿-„j† ≤ƒ´’®Ωnuç, ≤ƒn†-vµºç¨¡çO’ü¿ ÑN-üµ¿çí¬ Çüµ∆-®Ω-°æ-úø’-ûª’çC 

1) S 2/3 2) S −3/2 3) S 1/2 4) S 0 

87. From a circular disc of radius R, a square is cut out with a radius as its diagonal. 

The centre of mass of remainder is at a distance (from the centre) 

R ¢√u≤ƒ®Ωl¥ç Ö†o ´%û√h-é¬®Ω úÕÆæ’\ †’ç*, ¢√u≤ƒ®Ωl¥ç, éπ®Ωgçí¬ äéπ îªûª’-®Ω-v≤ƒEo éπAhJçî√®Ω’. 

N’TL† µ«í∫ç ßÁ·éπ\ vü¿ú-®√P Íéçvü¿ ü¿÷®Ωç (Íéçvü¿ç †’ç*) 

R R R R 

1) ⎯⎯⎯ 2) ⎯⎯ 3) ⎯⎯⎯ 4) ⎯⎯⎯ 

(4π − 2) 2π (π − 2) (2π − 2) 

88. A block is allowed to slide down an inclined plane of 45° which is smooth for 

first 9/25 of total length and it is rough for remaining part. Initially it starts from 

rest and comes to rest at the bottom of plane. Then coefficient of friction between 

the surfaces is 


45°¢√©’†o ¢√©’-ûª©ç Â°j†’ç* äéπ C¢Á’t ñ«®Ω’ûÓçC. ¢√©’-ûª©ç ¢Á·ûªhç §Òúø-´¤apple 9/25 

´çûª’ †’†’°æ¤ ûª©ç, N’í∫-û√C í∫®Ω’èπ◊ ûª©ç. ûÌLí¬ ÉC N®√-´’-ÆœnA †’ç* •ßª’-©’-üËJ, éÀçC 

µ«í¬-EéÀ îËÍ®Ææ-JéÀ N®√-´’-Æœn-AéÀ ´Ææ’hçC. ûª«© ´’üµ¿u °∂æ’®Ω{ù í∫’ùéπç 

25 16 9 25 

1) ⎯ 2) ⎯ 3) ⎯ 4) ⎯ 

16 25 25 9 


5 kg 

F


89. The energy required to shift a satellite from orbital radius 'r' to 2r radius is 'E'. 

What energy will be required to shift the satellite from orbital radius '2r' to orbital 

radius '3r'? 

äéπ Ö°æ-ví∫-£æ…Eo r ¢√u≤ƒ®Ωl¥ç †’ç* 2r ¢√u≤ƒ®√l¥EéÀ ≠œ°∂ˇd îËßª’ú≈-EéÀ é¬¢√Lq† ¨¡éÀh 'E'. '2r' 

¢√u≤ƒ®Ωl¥ç †’ç* 3r ¢√u≤ƒ®√l¥EéÀ ≠œ°∂ˇd îËßª’ú≈-EéÀ é¬¢√Lq† ¨¡éÀh 

E E E 

1) E 2) ⎯ 3) ⎯ 4) ⎯ 

2 3 4 

90. F−x and x−t graph of a particle in SHM are as shown in Fig. The maximum K.E. 

of particle is 

Ææ.£æ«.-îª.apple Ö†o éπùç ßÁ·éπ\ F − x, x − t ví¬°∂æ¤©†’ °æôçapple îª÷°œçî√®Ω’. éπùç í∫J≠æe 

í∫Aï¨¡éÀh 

-1 

F (N) 

10 

x (m) 


1) 16 mJ 2) 8 mJ 

3) 26 mJ 4) 0.8 mJ 

91. A wire of length 1 m and radius 1 mm is subjected to a load. The extension is 'x'. 

The wire is melted and then drawn into a wire of square cross−section of side 1 

mm. What is its extension under the same load? 

1 m §Òúø´¤, 1 mm ¢√u≤ƒ®Ωl¥ç Ö†o Bí∫èπ◊ µ«®√Eo Ææçüµ∆-Eç-î√®Ω’. ≤ƒí∫’-ü¿© 'x'. Bí∫†’ éπJ-Tç*, 

ûª®√yûª ü∆Eo 1 mm µº’ïç §Òúø´¤†o îªûª’-®ΩvÆæ ´’üµ¿u-îËa¥-ü¿çí¬ ´’Lî√®Ω’. ÅüË µ«®√-EéÀ ≤ƒí∫’-ü¿© 

1) π 2 x 2) πx 2 

3) πx 4) π/x 

4 

x (cm) 

92. Drops of liquid of density d are floating half immersed in a liquid of density ρ. 

If the surface tension of liquid is T then the radius of the drop will be 

(d = density of liquid drop) 

d ≤ƒçvü¿ûª Ö†o vü¿´-Gç-ü¿’-´¤©’, ρ ≤ƒçvü¿ûª Ö†o vü¿´çapple Ææí∫ç ´·EÍí« ûË©’ûª’-Ø√o®·. vü¿´ 


ûª©-ûª-†uûª T Å®·ûË, vü¿´ ¢√u≤ƒ®Ωl¥ç (d = vü¿´-Gç-ü¿’´¤ ≤ƒçvü¿ûª) 

⎯⎯⎯⎯ ⎯⎯⎯⎯ ⎯⎯⎯⎯ ⎯⎯⎯⎯ 

3T 6T 2T 3T 

1) ⎯⎯⎯⎯ 2) ⎯⎯⎯⎯ 3) ⎯⎯⎯⎯ 4) ⎯⎯⎯⎯ 

√ g(2d − ρ) √ g(2d − ρ) √ g(2d − ρ) √ g(4d − 3ρ) 


4 

5 

t(s)


93. A semicircular plate of mass 'm' has radius 'r' and centre 'C'. Its centre of mass is 

at a distance x from C. Its moment of inertia about an axis through its centre of 

mass and perpendicular to its plane is 

äéπ Å®Ωl¥ ´%û√h-é¬®Ω °æ∞Îx°æ¤ vü¿ú-®√P 'm', ¢√u≤ƒ®Ωl¥ç 'r', Íéçvü¿ç 'C'. Íéçvü¿ç 'C' †’ç* ü∆E vü¿ú- 

®√P Íéçvü¿ç x ü¿÷®Ωçapple ÖçC. Å®·ûË vü¿ú-®√P Íéçvü¿ç ü∆y®√ ¢Á∞¡⁄h ûª«-EéÀ ©ç•çí¬ ÖçúË 

Åéπ~-°æ-®Ωçí¬ ü∆E ïúøûªy vµ«´’éπç 

mr 2 mr 2 mr 2 mr 2 

1) ⎯ 2) ⎯ 3) ⎯ + mx 2 4) ⎯ − mx 2 

2 4 2 2 

94. A string is wrapped several times around a solid cylinder and the free end of 

string is held stationary while the horizontal cylinder is released from rest. The 

tension in the string will be 

°∂æ’†-Ææ÷h°æç îª’ô÷d, ûªçvAE î√« îª’ô’xí¬ îª’ö«d®Ω’. ûªçvA ÊÆyî√a¥ *´-®Ω†’ Æœn®Ωçí¬ Öçî√®Ω’. 

Ææ÷h§ƒEo N®√´’-ÆœnA †’ç* Núø’-ü¿© îËÊÆh, ûªçvAapple ûª†uûª 

mg mg mg 2mg 

1) ⎯ 2) ⎯ 3) ⎯ 4) ⎯ 

3 2 4 3 

95. There are two holes one each along the opposite sides of a wide rectangular tank. 

The cross section of each hole is 0.01 m 2 and the vertical distance between the 

holes is one meter. The tank is filled with water. The net force on the tank in 


newton when the water flows out of the holes is: (density of water is 1000 kg/m 3 ) 

¢Áúø„jp† D®Ω`-îª-ûª’-®Ω-v≤ƒ-é¬®Ω ö«uçèπ◊ úA-Í®éπ µº’ñ«© ¢Áç•úÕ È®çúø’ ®Ωçvüµ∆©’ îË¨»®Ω’. v°æA ®Ωçvüµ¿ç 

´’üµ¿u-îËa¥ü¿ç 0.01 m 2 , ®Ωçvüµ∆© ´’üµ¿u Eôd-E-©’´¤ ü¿÷®Ωç 1 m. ö«uçèπ◊†’ FöÀûÓ Eç§ƒ®Ω’. 

®Ωçvüµ∆© ü∆y®√ F®Ω’ •ßª’-ôèπ◊ ¢Á∞¡Ÿhçõ‰ ö«uçèπ◊ O’ü¿ °∂æL-ûª-•©ç (†÷uô-Ø˛-©apple) (FöÀ-≤ƒç-vü¿ûª 

1000 kg/m 3 ) 

1) 100 N 2) 200 N 

3) 300 N 4) 400 N 

96. A cylinder open at the top has a cross sectional area 10 sq.cm. A piston is allowed 

to fall freely from the top of a cylinder. If it travels 1/3 of the length of the 

cylinder at constant temperature, the mass of the piston is 


(g = 10 m/s 2 and 1 atm = 10 5 pa) 

Â°jµ«í∫ç ûÁJ* Ö†o Ææ÷h°æç ´’üµ¿uîËa¥ü¿ ¢Áj¨»©uç 10 cm 2 . Ææ÷h°æç Â°j†’ç* äéπ ´·≠æ-©-é¬Eo 

ÊÆyîªa¥í¬ éÀçCéÀ Ć«®Ω’. Æœn®Ω Ö≥Úg-ví∫ûª ´ü¿l ÅC Ææ÷h°æç §Òúø´¤apple 1/3 ´ ´çûª’ v°æßª÷-ùÀÊÆh, 

´·≠æ-©éπç vü¿ú-®√P (g = 10 m/s 2 , 1 atm = 10 5 pa) 

1) 2.5 kg 2) 15 kg 3) 7.5 kg 4) 10 kg 



97. A platinum resistance thermometer reads 0°C when its resistance is 80 Ω and 

100°C when its resistance is 90 Ω. Find the temperature at the platinum scale at 

which the resistance is 86 Ω. 

§ƒxöÀ†ç E®Óüµ¿ ü∑¿®√tO’-ô-®Ω’apple E®Óüµ¿ç 80 Ω Ö†o-°æ¤púø’ Ö≥Úg-ví∫ûª 0°C, 90 Ω Ö†o-°æ¤púø’ 

100°C. E®Óüµ¿ç 86 Ω Ö†o-°æ¤púø’, §ƒxöÀ†ç ÊÆ\©’ O’ü¿ Ö≥Úg-ví∫ûª 

1) 30°C 2) 60°C 

3) 20°C 4) 10°C 

98. A gas is compressed at a constant pressure of 50 N/m 2 from a volume of 10 m 3 

to a volume of 4 m 3 . Energy of 100 J is then added to the gas by heating. Its 

internal energy is 

Æœn®Ω-°‘-úø†ç 50 N/m 2 ´ü¿l äéπ ¢√ßª·´¤ 10 m 3 °∂æ’.°æ. †’ç* 4 m 3 °∂æ’.°æ.éÀ Ææç°‘úøuç îÁçCçC. 

¢ËúÕ îËßª’úøç ´©x 100 J ¨¡éÀhE ÅçCÊÆh, Åçûª-®Ω_ûª ¨¡éÀh 

1) increased by 400 J 2) increased by 200 J 

400 J Â°®Ω’-í∫’ûª’çC 200 J Â°®Ω’-í∫’-ûª’çC 

3) increased by 100 J 4) decreased by 200 J 

100 J Â°®Ω’-í∫’-ûª’çC 200 J ûªí∫’_-ûª’çC 

99. A substance of mass M kg requires a power input of P watt to remain in the molten 

state at its melting point. When the power source is turned off, the sample 


completely solidifies in time 't' seconds. The latent heat of fusion of the substance is 

M kg vü¿ú-®√P Ö†o °æü∆®Ωnç ü∆E vü¿O-µº-´-†-≤ƒn†ç ´ü¿l vü¿´-Æœn-Aapple Öçúøö«-EéÀ P watt ÉØ˛°æ¤ö¸ 

≤ƒ´’®Ωnuç Å´-Ææ®Ωç. ≤ƒ´’®Ωnu ï†-é¬Eo BÆœ-¢Ë-Æœ-†-°æ¤púø’ †´‚Ø√ °æ‹Jhí¬ 't' é¬©çapple °∂æ’F-µº-´†ç 

îÁçü¿’-ûª’çC. °æü∆®Ωn í∫’§Úh≠ægç 

1) Pt 2) ⎯ Pt 3) PtM 4) ⎯ PM M t 

100. Which of the following qualities suit for a cooking utensil? 

éÀçC-¢√-öÀapple ´çô-§ƒ-vûª-©èπ◊ ÆæJ§ÚßË’C 

1) High specific heat and low thermal conductivity 

ÅCµéπ NP-≥Úd≠ægç, Å©p Ö≠æg-¢√-£æ«-éπûª 

2) High specific heat and high thermal conductivity 

ÅCµéπ NP-≥Úd≠ægç, ÅCµéπ Ö≠æg-¢√-£æ«-éπûª 


3) Low specific heat and low thermal conductivity 

Å©p NP≥Úd≠ægç, Å©p Ö≠æg-¢√-£æ«-éπûª 

4) Low specific heat and high thermal conductivity 

Å©p NP≥Úd≠ægç, ÅCµéπ Ö≠æg-¢√-£æ«-éπûª 



101. Assertion (A): All particles between two consecutive nodes vibrate in the same 

phase. 

¢√uêu (A): È®çúø’ ´®Ω’Ææ v°æÆæpç-ü¿-Ø√© ´’üµ¿u Ö†o ÅEo éπù«©’ äÍé ü¿¨¡ûÓ éπç°œ-≤ƒh®·. 

Reason (R): Particles on two sides of a node vibrate mutually in opposite phase. 

é¬®Ωùç (R): v°æÆæpç-ü¿-Ø√©èπ◊ É®Ω’-¢Áj-°æ¤-« éπù«©’ °æ®Ω-Ææp®Ωç úA-Í®-éπ-ü¿-¨¡ûÓ éπç°œ≤ƒh®·. 

1) Both A and R are true and R is the correct explanation of A. 

A, R ÆæÈ®j-†N. R ÅØËC A èπ◊ ÆæÈ®j† N´-®Ωù. 

2) Both A and R are true and R is not the correct explanation of A. 

A, R ÆæÈ®j-†N. R ÅØËC Aèπ◊ ÆæÈ®j† N´-®Ωù é¬ü¿’. 

3) A is true, But R is false. 4) A is false, but R is true. 

A ÆæÈ®jçC, é¬F R ÆæÈ®jçC é¬ü¿’. 

A ÆæÈ®jçC é¬ü¿’, é¬F R ÆæÈ®jçC. 

102. A source of sound is moving along a circular orbit of radius 3 m with an angular 

velocity of 10 rad/s. A sound detector located far away from the source is 

executing linear simple harmonic motion along the line BD with amplitude 

BC = CD = 6 m. The frequency of oscillation of the detector is (5/π) per sec. The 

source is at the point A when the detector is at the point B. If the source emits a 

continuous sound wave of frequency 340 Hz, find the maximum and the 


minimum frequencies recorded by the detector (velocity of sound = 330 m/s.) 

äéπ üµ¿yE ï†éπç, 3 m ¢√u≤ƒ®Ωl¥ç Ö†o ´%û√h-é¬®Ω éπéπ~u ¢Áç•úÕ 10 rad/s éÓùÃßª’ ´úÕûÓ 

éπü¿’©’ûÓçC. ï†éπç †’ç* î√« ü¿÷®Ωçí¬ Å´’-Ja† üµ¿yE úÕõ„-éπd®Ω’, BC = CD = 6m éπç°æ† 

°æJ-N’-AûÓ BD Í®ê ¢Áç•úÕ Ææ.£æ«.-îª.†’ E®ΩyJhÆæ’hçC. úÕõ„-éπd®Ω’ éπç°æ† °æJ-N’A ÂÆéπ-†’èπ◊ (5/π). 

úÕõ„-éπd®Ω’ B ´ü¿l Ö†o-°æ¤púø’, ï†éπç A ´ü¿l ÖçC. ï†éπç 340 Hz §˘†”-°æ¤-†uçûÓ ÅN-*a¥-†oçí¬ 

üµ¿yEE à®ΩpJÊÆh, úÕõ„-éπd®Ω’ Jé¬®Ω’f îËÆœ† í∫J≠æe, éπE-≠æe §˘†”-°æ¤-Ø√u©’ (üµ¿yE ¢Ëí∫ç = 330 m/s) 

3m 

N 

M 

ΑA 

B ← C 

→ 

D 

1) 255, 442 2) 442, 255 

3) 295, 482 4) 482, 295 

103. When a light incident on a medium at an angle of incidence 'i' and 

refracted into a second medium at angle of refraction 'r', the graph 

of sin 'i' and sin 'r' is shown in the figure, then the critical angle 

for the two media is 


'i' °æûª† éÓùç ´ü¿l ßª÷†éπç O’ü¿ é¬çA °æûª-†¢Á’i, È®çúÓ ßª÷†-éπç-appleéÀ 'r' ´véÃ-µº-´† éÓùç ´ü¿l 

´véÃ-µº-´†ç îÁçCçC. sin 'i', sin 'r' ví¬°∂æ¤ °æôçapple îª÷°œçî√®Ω’. È®çúø’ ßª÷†-é¬© ÆæçCí∫l¥ éÓùç 

1 1 1 

1) sin −1 (√ ⎯ 3 ) 2) sin −1 ( ⎯) 3) cos −1 ( ⎯) 4) tan −1 ( ⎯) 

√ ⎯ 3 √ ⎯ 3 2 


↑ 

sin r 

30° 

sin i →


104. The dispersive powers of the materials of convex lens and concave lens placed 

in contact are in the ratio 1:2. For the achromatic combination, the focal length 

of convex lens is 100 cm. Then what is the focal length of concave lens? 

èπ◊çµ«-é¬®Ω, °æ¤ô-é¬®Ω éπô-é¬-©†’ Ææp®Ωzapple Öç*-†-°æ¤púø’, ¢√öÀ °æü∆-®√n© NÍé~-°æù ≤ƒ´’-®√nu© E≠æpAh 1:2 

---Å´®Ωg ÆæçßÁ÷-í¬-EéÀ, èπ◊çµ«-é¬®Ω éπôéπ Ø√µºuç-ûª®Ωç 100 cm Å®·ûË °æ¤ö«-é¬®Ω éπôéπ Ø√µºuç-ûª®Ωç 

1) 50 cm 2) 75 cm 3) 100 cm 4) 200 cm 

105. The maximum number of possible interference maxima for slit-separation equal 

to twice the wavelength in Young's double = slit experiment, is 

ßª’çí˚ Cy


110. Current passing through 3 Ω resistance is 

3 Ω E®Óüµ¿ç ü∆y®√ ¢Á∞¡Ÿh†o éπÈ®çô’ 

1) 14 ⎯ 3 

A 2) 3 A 

3) 2 A 4) 12 ⎯ A 5 

111. Statement A: Thermistors are widely used in measuring the rate of energy flow 

in microwave beams. 

Statement A: ¢Á’ivéÓ ûª®Ωçí∫ °æ¤çï v°æ≤ƒ®Ω ¨¡éÀh Í®ô’†’ éÌ©´-ú≈-EéÀ ü∑¿JtÆæ d®Ωx†’ Ö°æ-ßÁ÷-T-≤ƒh®Ω’. 

Statement B: Parallel combination of cells is preferred when internal resistance 

is quite negligible compared to load resistance and large emf is required. 

Statement B: appleúø’ E®Ó-üµ¿çûÓ §ÚLa-†-°æ¤púø’, Åçûª-®Ω_ûª E®Ó-üµ∆Eo °æJ-í∫-ù-†-apple-EéÀ BÆæ’-éÓ-†-°æ¤púø’, 

ÅCµéπ N.-î√.•. é¬¢√-Lq-†-°æ¤púø’, °∂æ’ö«© Ææ´÷ç-ûª®Ω Ææçüµ∆-Ø√Eo áçîª’-èπ◊çö«ç. 

1) A is true, B is false A Ææûªuç, B ÅÆæûªuç 

2) A is false, B is true A ÅÆæûªuç, B Ææûªuç. 

3) Both A and B is false A, B È®ç-úø÷ -ÅÆæûªuç. 

4) Both A and B is true A, B È®ç-úø÷ Ææûªuç. 

112. A thermocouple of resistance 16 ohm is connected in series with a galvanometer 

of 80 ohm resistance. The thermocouple develops an emf of 10 µ V/°C. When 

one junction is kept at 0°C and other in a other liquid. If the emf varies linearly 

with temperature difference and the galvanometer reads 8 milli volt, then 


temperature of the liquid is 

80 Ω E®Óüµ¿ç Ö†o í¬©y-Ø√-O’-ô-®Ω’ûÓ, 16 Ω E®Óüµ¿ç Ö†o Ö≠æg-ßª·-í¬tEo v¨ÏùÀapple Ææçüµ∆-Eç-î√®Ω’. 

Ö≠æg-ßª·í∫tç 10µ V/°C N.-î√.-•.†’ à®Ωp®Ω’Ææ’hçC. äéπ ÆæçCµE 0°C ´ü¿l, È®çúÓ ÆæçCµE ¢Ë®Ìéπ 

vü¿´çapple Öçî√®Ω’. Ö≥Úg-ví∫û√ µ‰ü¿çûÓ N.-î√.•. Í®&-ßª’çí¬ ´÷®Ω’-ûª’çC. í¬©y-Ø√-O’-ô®Ω’ 8 milli 

volt KúÕç-í∫’†’ Ææ÷*ÊÆh, vü¿´ç Ö≥Úg-ví∫ûª 

1) 240°C 2) 480°C 3) 540°C 4) 960°C 

113. A straight horizontal conducting rod of length 0.5 m and mass 50 g is suspended by 

two vertical wires at its ends. A current of 5.0 A is set up in the rod through the wires. 

What magnetic field should be set up normal to the conductor in order that the 

tension in the wires is zero? (Ignore the mass of the wires and take g =10 ms −2 ) 

50 ví¬. vü¿ú-®√P, 0.5 m §Òúø´¤†o A†oöÀ éÀ~Aï Ææ´÷ç-ûª®Ω ¢√£æ«éπ éπúŒfE, È®çúø’ Eôd-E-©’´¤ 

Bí∫© Ææ£æ…-ßª’çûÓ ¢Ë«úøD¨»®Ω’. Bí∫© ü∆y®√ éπúŒfapple 5AéπÈ®çô’ à®Ωp-úø’-ûª’çC. Bí∫apple ûª†uûª 

¨¡⁄†u´’´ú≈-EéÀ ¢√£æ«-é¬-EéÀ ©ç•çí¬ áçûª Åßª’-≤ƒ\çûª Íé~vû√Eo à®Ωp-®Ωî√L? (g = 10 ms −2 ) 


10V 

1) 0.1 T 2) 0.2 T 3) 0.3 T 4) 0.4 T 

2Ω 

B 

A 

C 

3Ω 

4V 



114. A circular loop of radius r carrying a current i is held at the centre of another circular 

loop of radius R (>>r) carrying a current I. The plane of the smaller loop 

makes an angle of 30° with that of the larger loop. If the smaller loop is held fixed 

in this position by applying a single force at a point on its periphery, what would 

be the minimum magnitude of this force? 

i éπÈ®çô’ v°æ¢√£æ«ç, r ¢√u≤ƒ®Ωl¥ç Ö†o ´%û√h-é¬®Ω ©÷°æ¤†’, I éπÈ®çô’ v°æ¢√£æ«ç, R(>>r) ¢√u≤ƒ®Ωl¥ç 

Ö†o ¢Ë®Ìéπ ´%û√h-é¬®Ω ©÷°æ¤ Íéçvü¿ç ´ü¿l Öçî√®Ω’. Â°ü¿l ©÷°æ¤ûÓ, *†o ©÷°æ¤ ûª©ç 30° éÓùç 

îËÆæ’hçC. *†o ©÷°æ¤ ´%ûªh °æJ-Cµ-O’ü¿ •«Eo v°æßÁ÷Tçîªúøç ü∆y®√ ©÷°æ¤†’ ÅüË ≤ƒn†çapple 

Öçî√®Ω’. Ñ •©ç °æJ-´÷ùç 

µ 0 

π iIr 

1) ⎯⎯⎯ 

µ 0 

π iIr 

2) ⎯⎯⎯ 

µ 0 

π iIr 

3) ⎯⎯⎯ 

µ 0 

π iIr 

4) ⎯⎯⎯ 

4R 3R 2R R 

115. For a series L−C−R circuit R = X L − 2X c . The impedance of the circuit and phase 

difference between alternating voltage and current will be 

L−C−R v¨ÏùÀ ´©-ßª’çapple R = X L - 2X c . Å´-®Óüµ¿ç, §Òõ„-E{-ßª’¸, éπÈ®ç-ô’© ´’üµ¿u ü¿¨»-µ‰ü¿ç 

´®Ω’-Ææí¬ 


√ ⎯ 5R 

1) ⎯⎯, tan −1 (2) 2) √ ⎯ 5 R, tan −1 (2) 

2 

√ ⎯ 5R 1 1 

3) ⎯⎯, tan (⎯) −1 4) √ ⎯ 5 R, tan (⎯) 

−1 2 2 2 

116. If 5% of the energy supplied to a bulb is irradiated as visible light, how many 

quanta are emitted per second by a 100 watt lamp? Assume wavelength of 

visible light as 5.6 × 10 −5 cm 

•©’sèπ◊ Ææ®Ω-°∂æ®√ îËÆœ† 5% ¨¡éÀh ü¿%íÓ_-îª-®Ω-é¬çAí¬ NéÀ-®Ωùç îÁçCûË, 100 watt •©’sûÓ ÂÆéπ-†’èπ◊ 

Öü∆_-®Ω-¢Á’i† §∂Úö«-†’© Ææçêu (ü¿%íÓ_-îª®Ω é¬çA ûª®Ωç-í∫-üÁj®Ωùç 5.6 × 10 −5 cm) 

1) 1.4 × 10 19 2) 3 × 10 3 3) 1.4 × 10 −19 4) 3 × 10 4 

117. If ν Kα , ν Kβ and ν Lα represent the frequencies of K α , K β and L α X−ray lines 

of a given material, then 


X− éÀ®Ωù Í®ê-©èπ◊ ν Kα , ν Kβ , ν Lα ©’ K α , K β , L α Í®ê© §˘†”-°æ¤-Ø√u-„jûË 

√ ⎯⎯ 

1) ν Kβ = ν Kα + ν Lα 2) ν Kβ = ν Kα + ν Lα 

3) ν Lα = ν Kα + ν Kβ 4) ν Kβ = ν Kα − ν Lα 


118. Half-life of a radioactive substance A is two times the half-life of another 

radioactive substance B. Initially the number of nuclei of A and B are N A and N B 

respectively. After three half lives of A number of nuclei of both are equal. Then 

the ratio of N A / N B is 

Í®úÕßÁ÷üµ∆Jtéπ °æü∆®Ωnç A Å®Ωl¥-@-N-ûª-é¬©ç, -´’®Ó Í®úÕ-ßÁ÷-üµ∆-Jtéπ °æü∆®Ωnç B Å®Ωl¥-@-N-ûª-é¬-©çapple È®çúø’ 

È®ô’x. -¢Á·-ü¿-ô A, B Íéçvü¿-é¬© Ææçêu ´®Ω’-Ææí¬ N A , N B . A ´‚úø’ Å®Ωl¥-@-N-ûª- é¬-«© ûª®√yûª, 

È®ç-úÕçöÀ Íéçvü∆© Ææçêu Ææ´÷†ç -Å®·-ûË N A / N B = 

1 1 1 1 

1) ⎯ 2) ⎯ 3) ⎯ 4) ⎯ 

4 8 3 6 

119. Consider the following statements and identify the correct answer - 

éÀçC¢√-öÀapple ÆæÈ®jçC -à-C? 

a) In forward bias of p - n diode, the effective barrier potential is (V B − V) 

(V B is barrier potential and V is applied external voltage) 

p - n ÆæçCµ úøßÁ÷ú˛ °æ¤®Ó-¨¡-éπtçapple, °∂æLûª Å´-®Óüµ¿ §Òõ„E{-ßª’¸ (V B − V) 

(V B Å´-®Óüµ¿ §Òõ„-E{-ßª’¸, V v°æßÁ÷-Tç-*† «£æ«u ã‰d-@) 

b) In reverse bias of p - n diode, the effective barrier potential is (V B + V) 

p - n ÆæçCµ úøßÁ÷ú˛ A®Ó-¨¡-éπtçapple, °∂æLûª Å´-®Óüµ¿ §Òõ„-E{-ßª’¸ (V B + V) 

c) In forward bias, an ideal p - n diode offers zero resistance 

°æ¤®Ó-¨¡-éπtçapple, Çü¿®Ωz p - n ÆæçCµ úøßÁ÷ú˛ E®Óüµ¿ç ¨¡⁄†uç 


d) In reverse bias, an ideal p - n diode offers infinite resistance 

A®Ó-¨¡-éπtçapple, Çü¿®Ωz p - n ÆæçCµ úøßÁ÷ú˛ E®Óüµ¿ç Å†çûªç 

1) a, b only are true a, b ´÷vûª¢Ë’ Ææûªuç 

2) a, b, c only are true a, b, c ´÷vûª¢Ë’ Ææûªuç 

3) a, b, c, d are true a, b, c, d Ææûªuç 4) All are false ÅFo ÅÆæûªuç 

120. In Amplitude Modulation éπç°æ† °æJ-N’A (AM) ´÷úø’u-‰-≠æ-Ø˛apple 

1) The amplitude of the carrier wave varies in accordance with the amplitude of 

the modulating signal. 

¢√£æ«éπ ûª®Ωçí∫ éπç°æ† °æJ-N’A, ´÷úø’u-‰-öÀçí˚ ÆæçÍéûªç ßÁ·éπ\ éπç°æ† °æJ-N’-AûÓ ´÷®Ω’-ûª’çC. 

2) The amplitude of carrier wave remains constant, frequency changes in 

accordance with the modulating signal. 

¢√£æ«éπ ûª®Ωçí∫ éπç°æ† °æJ-N’A Æœn®Ωç, §˘†”-°æ¤†uç, ´÷úø’u-‰-öÀçí˚ ÆæçÍé-ûªçûÓ ´÷®Ω’-ûª’çC. 

3) The amplitude of carrier wave varies in accordance with the frequency of the 


modulating signal 


¢√£æ«éπ ûª®Ωçí∫ éπç°æ† °æJ-N’A ´÷úø’u-‰-öÀçí˚ ÆæçÍéûª §˘†”-°æ¤-†uçûÓ ´÷®Ω’-ûª’çC. 

4) The amplitude changes in accordance with wavelength of the modulating 

signal. 

éπç°æ† °æJ-N’A, ´÷úø’u-‰-öÀçí˚ ÆæçÍéûª ûª®Ωç-í∫-üÁj-®ΩùçûÓ ´÷®Ω’-ûª’çC. 



CHEMISTRY 

121. The correct order of pH values of 0.1 M NH 4 Cl, 0.1 M KCN and 0.1 M KNO 3 

solutions is 

0.1 M NH 4 Cl, 0.1 M KCN, 0.1 M KNO 3 vü∆´-ù«© pH N©’-´© ÆæÈ®j† véπ´’ç 

1) NH 4 Cl < KNO 3 < KCN 2) KNO 3 < KCN < NH 4 Cl 

3) NH 4 Cl < KCN < KNO 3 4) KCN < KNO 3 < NH 4 Cl 

122. Which one of the following pairs represents the extensive properties? 

éÀçC¢√-öÀapple àN í∫£æ«† üµ¿®√t©’? 

1) Heat capacity, Pressure Ö≠æg-üµ∆-®Ωù, °‘úø†ç 

2) Specific heat, Temperature NP-≥Úd≠ægç, Ö≥Úg-ví∫ûª 

3) Heat capacity, Volume Ö≠æg-üµ∆-®Ωù, °∂æ’†-°æ-J-´÷ùç 

4) Enthalpy, Temperature áçü∑∆---Mp, Ö≥Úg-ví∫ûª 

123. The Langmuir adsorption isotherm equation is 

x ap 

⎯ = ⎯⎯⎯ . At high pressure, the equation transforms to 

m 1 + bp 

«çí˚-´‚®˝ ÅCµ-äpple-≠æù Ææ¢Á÷-≥Úg-ví∫û√ ÆæO’-éπ-®Ωùç 


x ap 

⎯ = ⎯⎯⎯ . ÅCµéπ °‘úø†ç ´ü¿l Ñ ÆæO’-éπ-®Ωùç éÀçC Nüµ¿çí¬ ´÷®Ω’-ûª’çC. 

m 1 + bp 

x x 1 x a x 

1) ⎯ = ap 2) ⎯ = ⎯⎯⎯ 3) ⎯ = ⎯ 4) ⎯ = b 

m m 1 + bp m b m 

124. Berilium carbide is hydrolysed using heavy water. The products formed are 

„K-Lßª’ç é¬È®js-ú˛†’ µ«®Ω-ï-©çûÓ ï©-N-¨Ïx-≠æùç îÁçCÊÆh à®ΩpúË ÖûªoØ√o©’ 

1) BeO, CH 4 2) Be(OD) 2 , CD 4 3) Be(OD) 2 , C 2 D 2 4) BeO, CD 4 

125. The stability order of hydrides of alkalimetals is é~¬®Ω-apple-£æ«°æ¤ Â£j«wúÁj-ú˛© Æœn®Ωûªy véπ´’ç 

1) LiH > NaH > KH > RbH > CsH 

2) CsH > RbH > KH > NaH > LiH 

3) LiOH > NaOH > KOH > RbOH > CsOH 

4) CsOH > RbOH > KOH > NaOH > LiOH 


126. The order of melting points of III A group elements is 

III A ví∫÷°æ¤ ´‚©-é¬© vü¿O-µº-´† ≤ƒnØ√© véπ´’ç 

1) B > Al > Tl > In > Ga 2) B > Tl > Al > In > Ga 

3) B > Al > In > Tl > Ga 4) B > In > Tl > Al > Ga 



127. List (°æöÀdéπ)- I List (°æöÀdéπ)- II 

Type of silicate 

(ÆœL-Íéö¸ ®Ωéπç) 

Empirical Formula 

(Åù’-µ«-Néπ §∂ƒ®Ω’t«) 

A) Sheet silicate °æ©éπ ÆœL-Íéö¸ I) Si 2 

O 7 

−6 

B) Cyclic silicate îªvéÃßª’ ÆœL-Íéö¸ II) (SiO 3 

) n 

2n− 

C) Sorosilicate ≤Ú®ÓÆœL-Íéö¸ III) SiO 4 

− 4 

D) Nesosilicate F≤ÚÆœL-Íéö¸ IV) (Si 2 

O 5 

) 

2n− 

n 

The correct match is ÆæÈ®j† ïûª†’ í∫’Jhç-îªçúÕ 

A B C D A B C D 

1) IV II I III 2) IV I II III 

3) II IV I III 4) II I IV III 

128. An oxide of Nitrogen 'X' is formed during thermal decomposition of ammonium 

nitrate. Regarding 'X' the incorrect statement is 

Å¢Á÷-tEßª’ç ØÁjvõ‰ö¸-†’ Ö≠æg N°∂æ’-ô†ç îÁçCÊÆh 'X' ÅØË ØÁjvöapple-ïØ˛ Ææ¢Ë’t-∞¡†ç à®Ωp-úÕçC. 'X' 

í∫’Jç* ÆæJ-é¬E ¢√uêu 

1) It is neutral and colourless gas ÉC ®Ωçí∫’ ‰E ûªôÆæn Ææyµ«-´ç- -Ö-†o ¢√ßª·´¤ 


2) It is neutral and paramagnetic 

ÉC ûªôÆænç, §ƒ®√ Åßª’-≤ƒ\çûª Ææyµ«-¢√Eo éπLT Öçô’çC 

3) It has linear shape DEéÀ Í®&ßª’ Çéπ%A Öçô’çC 

4) It has anaesthetic action DEéÀ Evü¿-°æ¤îËa í∫’ùç Öçô’çC 

129. Among the following statements how many are correct? 

éÀçü¿ É*a† ¢√uêuapplex áEo ÆæÈ®j-†N? 

I) Sulphur can form fluorides like S 2 F 2 , S 2 F 4 , S 2 F 10 

Ææ©p¥®˝ S 2 F 2 , S 2 F 4 , S 2 F 10 ÅØË §∂ÚxÈ®j-ú˛-©†’ à®Ωp®Ω’Ææ’hçC 

II) S − O − S link is present in H 2 S 2 O 8 

H 2 S 2 O 8 apple S − O − S •çüµ¿ç Öçô’çC 

III) SeCl 4 is sublimative and TeCl 4 is hygroscopic solid 


SeCl 4 Öûªp-ûª† °æü∆®Ωnç, TeCl 4 Â£j«víÓ-≤Ú\-°œé˙ °æü∆®Ωnç 

IV) SCl 2 is a dark red liquid with foul smell 

SCl 2 ´·ü¿’®Ω’ á®Ω’°æ¤ ®Ωçí∫’, ü¿’®√y-Ææ† Ö†o vü¿´ç 

1) I 2) II 3) III 4) IV 



130. The incorrect order among the following is 

éÀçC¢√-öÀapple ÆæJ-é¬E véπ´’ç 

1) Oxidising power: F 2 > Cl 2 > Br > I 2 

ÇéÃq-éπ-®Ωù ≤ƒ´’®Ωnuç: F 2 > Cl 2 > Br > I 2 

2) Electron affinity: Cl > F > Br > I 

á©-é¬ZØ˛ á°∂œ-EöÀ:Cl > F > Br > I 

3) Bond energy: Cl 2 > I 2 > Br 2 > F 2 

•çüµ¿ ¨¡éÀh: Cl 2 > I 2 > Br 2 > F 2 

4) Electronegativity: F > Cl > Br > I 

®Ω’ùN-ü¿’u-ü∆-ûªt-éπûª: F > Cl > Br > I 

131. At a given temperature the noble gas with lowest vapour pressure is 

EKgûª Ö≥Úg-ví∫ûª ´ü¿l Åûªu©p «≠æp°‘-úø†ç Ö†o ïúø-¢√-ßª·´¤ 

1) Ne 2) Ar 3) Kr 4) Xe 

132. To detect ammonium ion in the laboratory the reagent used is 

v°æßÁ÷í∫¨»©apple Å¢Á÷t-Eßª’ç Åßª÷-Ø˛†’ í∫’Jhçîªú≈-EéÀ Ö°æ-ßÁ÷TçîË é¬®Ωéπç 


1) HgI 2 2) HgCl 2 

3) K 2 [HgI 4 ] 4) K 2 {HgI 4 }+ KOH 

133. The process of percolating an acid or an aqueous solution over a finally 

powdered mineral is called 

Ææ÷éπ~ t Nµ«->ûª êEïç O’-ü¿’í¬ äéπ Ç´÷xEo ‰ü∆ ï©-vü∆-´-ù«Eo °æç°œ êE-ñ«Eo éπJ-TçîË 

°æü¿l¥AE à´’ç-ö«®Ω’? 

1) Smelting í∫©†ç 2) Leaching Eé~¬-∞¡† 

3) Poling §ÚLçí˚ 4) Zone refining ñappleØ˛ JÂ°∂j-Eçí˚ 

134. Phosphorous present in an organic compound is detected by using X in the form 

of 'Y'. Where X and Y respectively 

éπ®Ωs† Ææ¢Ë’t-∞¡-†çapple Ö†o §∂ƒÆæp¥®ΩÆˇ-†’ X ÅØË é¬®Ω-éπçûÓ 'Y' ÅØË °æü∆-®Ωnçí¬ í∫’Jh-≤ƒh®Ω’. Ééπ\úø 

X, Y©’ ´®Ω’-Ææí¬ 


1) (NH 4 ) 3 MoO 4 , (NH 4 ) 3 PO 4 .12 MoO 3 

2) (NH 4 ) 2 MoO 3 , (NH 4 ) 3 PO 4 .MoO 3 

3) (NH 4 ) 2 MoO 4 , (NH 4 ) 3 PO 4 .12 MoO 3 

4) (NH 4 ) 2 MoO 3 , (NH 4 ) 3 PO 4 .12 MoO 3 



135. An alkene on ozonolysis gives only ethanal. The ozonolysis products for its chain 

isomer are 

äéπ ÇM\Ø˛†’ ãñapple-F-éπ-®Ωùç îÁçCÊÆh Éü∑¿-Ø√¸ ´÷vûª¢Ë’ à®Ωp-úÕçC. Å®·ûË Ç ÇM\Ø˛ -ßÁ·éπ\ 

¨¡%çê© ≤ƒü¿%¨»uEéÀ ã-ñapple-Ø√-©-ÆœÆˇ Öûªp-Ø√o©’ 

1) Propanal, ethanal v§Ò°æ-Ø√¸, Éü∑¿-Ø√¸ 2) Propanal, methanal v§Ò°æ-Ø√¸, N’ü∑¿-Ø√¸ 

3) Propanone, methanal v§Ò°æ-ØÓØ˛, N’ü∑¿-Ø√¸ 4) Propanone, ethanal v§Ò°æ-ØÓØ˛, Éü∑¿-Ø√¸ 

136. Which of the following is not a green house gas? 

éÀçC¢√-öÀapple £æ«Jûª í∫%£æ« ¢√ßª·´¤ é¬EC? 

1) CCl 2 F 2 2) H 2 O (g) 3) O 3(g) 4) O 2(g) 

137. Which of the following reacts with Tollens reagent and liberates 22.4 lit of a gas 

per mole at S.T.P. with CH 3 MgBr? 

éÀçC¢√öÀapple àC CH 3 MgBr ûÓ îª®Ωu-ØÌç-C S.T.P. ´ü¿l 22.4 Mô®˝/¢Á÷¸ ¢√ßª·-´¤†’ 

Öü∆_JÆæ’hçC? 

1) CH 3 − C ≡ C − CH 3 2) CH 3 − C ≡ CH 

3) CH ≡ CH 4) CH 3 − CHO 

138. The number of stereoisomers possible for 4 − chloro − 2 − pentene are 


4 − éÓx®Ó − 2 − Â°çöÃØ˛éÀ ≤ƒüµ¿u´’ßË’u v§ƒüË-Péπ ≤ƒü¿%-¨»u© Ææçêu 

1) 4 2) 2 3) 3 4) 8 

PCl 5 

KNO 2 

139. C 2 H 5 OH ⎯→ X ⎯→ Y. The bond which is absent in 'Y' is 

PCl 5 

KNO 2 

C 2 H 5 OH ⎯→ X ⎯→ Y. Ééπ\úø 'Y' apple ‰E •çüµ¿ç 

1) C − C 2) C − O 3) C − N 4) N − O 

140. Oedema in legs is caused by the deficiency of 

éÀçC¢√-öÀapple à Nô-N’Ø˛ apple°æç ´©x é¬∞¡xapple ÅCµ-éπçí¬ F®Ω’ îË®Ω’-ûª’çC? 

1) B 1 2) B 2 3) B 5 4) B 7 

141. Which one of the following can be used as antioxidant for foods? 

éÀçC¢√-öÀapple üËEo Ç£æ…®Ω °æü∆-®√n©éÀ v°æA-Ç-éÃq-éπ-®Ω-ùÀí¬ Ö°æ-ßÁ÷-T-≤ƒh®Ω’? 


COONa 

OH 

OH 

C(CH 3 ) 3 

CH 3 

CH 3 

CH 3 

1) 2) 3) 

4) 

OCH 3 


Cl 

HO CH 3 

CH 3


142. The number of radial nodes for an orbital of potassium containing differentiating 

electron are 

§Òö«-≠œßª’çapple -µ‰-ü¿°æ-JîË á©-é¬ZØ˛ Ö†o ÇJs-ö«¸éÀ Í®úÕ-ßª’¸ ØÓú˛© Ææçêu 

1) 4 2) 3 3) 2 4) zero 

143. The uncertainties in finding position of proton and α −particle are same. The 

ratio of uncertainties in finding their velocities is 

v§Úö«Ø˛, α – éπù«© ≤ƒnØ√Eo éπ†’-éÓ\-´-úøçapple ÅE-Pa-ûª-û√y©’ Ææ´÷-†-¢Á’i-ûË ¢√öÀ ¢Ëí¬Eo éπ†’-éÓ\-´úøçapple 

ÅE-Paûªû√y© E≠æpAh 

1) 1 : 2 2) 2 : 1 3) 1 : 4 4) 4 : 1 

144. The covalent radius of chlorine is 0.99 A°. It's Vanderwaal's radius is 

approximately 

éÓxJØ˛ Ææ´’-ßÁ÷-ï-Fßª’ ¢√u≤ƒ®Ωl¥ç 0.99 A°. Å®·ûË -ü∆-E ¢√çúø®˝ ¢√¸ ¢√u≤ƒ®Ωl¥ç Ææ’´÷-®Ω’í¬ 

1) 3.6 A° 2) 1.8 A° 3) 1.98 A° 4) 3.0 A° 

145. Among the following bond angle is highest in 

éÀçC¢√-öÀapple •çüµ¿-éÓùç Åûªu-Cµ-éπçí¬ Ö†oC 

⊕ ⊕ ⊕ ⊕ 

1) NO 2 2) NH 4 3) H 3 O 4) CH 3 

146. I) Na 

1 1 

(s) +⎯Cl 2(g) ⎯→ NaCl (s) II) Na (s) 

+⎯Cl 

2 2 2 (g) ⎯→ NaCl (g) 

1 

III) ⎯ Cl 2 (g) ⎯→ Cl− (g) 

IV) Na + 2 

(g) + Cl− (g) ⎯→ NaCl (s) 


The number of endothermic and exothermic reactions in the above list 

respectively are 

Â°j ¢√öÀapple Ö≠æg-ví¬-£æ«éπ, Ö≠æg-¢Á÷-îªéπ îª®Ωu© Ææçêu ´®Ω’-Ææí¬ 

1) 2, 2 2) 1, 3 3) 3, 1 4) 0, 4 

147. A metal nitride has 72% metal by weight. The molecular formula of the nitride is 

M 3 N 2 . The equivalent weight of the metal is 

äéπ apple£æ«°æ¤ ØÁjwõ„j-ú˛apple 72% apple£æ«ç ÖçC. Ç apple£æ«°æ¤ ØÁjwõ„jú˛ §∂ƒ®Ω’t« M 3 N 2 Å®·ûË, Ç 

apple£æ«°æ¤ ûª’«uçéπ µ«®Ωç 


1) 12 2) 24 3) 72 4) 48 

148. With increase in temperature the fraction of total number of molecular of gas 

having following velocity decreases? 

Ö≥Úg-ví∫ûª Â°JÍí éÌDl ¢Á·ûªhç Åù’´¤applex éÀçC à ¢Ëí∫ç Ö†o Åù’´¤© µ«í∫ç ûªí∫’_-ûª’çC? 

1) C p 2) ⎯ C 3) C 4) All 



149. The ratio of volumes of 0.1 M H 2 O 2 required to reduce 100 ml of 0.1 M KMnO 4 

in acidic and dilute alkaline medium respectively 

Ç´’x, NM† é~¬®Ω ßª÷†é¬applex 100 N’Mx--M-ô®Ωx 0.1 M H 2 O 2 vü∆´-ùçûÓ îª®Ωuapple 0.1 M KMnO 4 

vü∆´ù °∂æ’†-°æ-J´÷ù«© E≠æpAh 

1) 2 : 3 2) 5 : 3 3) 3 : 5 4) 3 : 2 

150. 5 gm of an electrolyte A 3 B 2 (MW = 100) in 250 gm water freezes at 

− 0.74° C. If K f of water is 1.85 Km −1 , the percentage ionisation of the electrolyte 

is 

5 ví¬´·© A 3 B 2 Nü¿’u-Cy-¨Ïx≠æuç (Å.µ«. = 100)†’ 250 ví¬´·© FöÀapple éπJ-Tç-î√®Ω’. Ç 

vü∆´ù °∂æ’F-µº-´† Ö≥Úg-ví∫ûª − 0.74°C Å®·ûË Ç Nü¿’u-Cy-¨Ïx≠æuç Åßª’F-éπ-®Ωù ¨»ûªç 

(FöÀ K f N©’´ = 1.85 Km −1 ) 

1) 25% 2) 50% 3) 75% 4) 100% 

151. For an electrochemical cell M⏐M + ⏐⏐X − ⏐X, E 0 M + /M = − 0.56 V and E0 X/X − = 

0.26 V. The correct statement regarding the cell is 

= − 0.56 -V, - 

äéπ Nü¿’uû˝ ®Ω≤ƒ-ßª’† °∂æ’ôç M⏐M + ⏐⏐X − ⏐Xapple E 0 M + /M 

E 0 X/X − = 0.26 V ÖØ√o®·. éÀçC¢√-öÀapple ÆæÈ®j† ¢√uêu 

1) M can oxidise X − X − E M ÇéÃq-éπ-J-Ææ’hçC 

2) X can reduce M + M + E X éπ~®‚-éπ-J-Ææ’hçC 


3) M + X → M + + X − is spontaneous reaction 

M + X → M + + X − ÅØËC Ææyîªa¥çü¿ îª®Ωu 

4) M + X − → M + + X has standard e.m.f. of 0.82 V 

M + X − → M + + X ßÁ·éπ\ v°æ´÷ù e.m.f. N©’´ 0.82 V 

152. In electrochemical corrosion the metal undergoing corrosion 

'Nü¿’uû˝ ®Ω≤ƒ-ßª’† éπ~ßª’ç— v°ævéÀßª’apple éπ~ßª’ç îÁçüË apple£æ«ç 

1) Acts as anode ÇØÓ-ú˛í¬ °æEîËÆæ’hç-C 

2) Undergoes oxidation ÇéÃq-éπ-®Ωùç îÁçü¿’--ûª’ç-C 

3) Undergoes reduction éπ~ßª’-éπ-®Ωùç îÁçü¿’--ûª’ç-C 

4) Both 1 and 2 1, 2 È®ç-úø÷ 


153. A metal is crystallised in B.C.C. lattice. It's unit cell length is √ ⎯ 3 A°. The 

distance between nearest neighbours of metal atoms is 

äéπ apple£æ«ç B.C.C. E®√tùç éπLT ÖçC. ü∆E ßª‚Eö¸ ÂÆ¸ §Òúø´¤ √ ⎯ 3 A° Å®·ûË Ç 

apple£æ«çapple ÅA-Ææ-O’-°æçí¬ Ö†o È®çúø’ °æ®Ω-´÷-ù’-´¤© ´’üµ¿u ü¿÷®Ωç 

1) √ ⎯ 3 A° 2) 1.5 A° 3) 0.75 A° 4) √ ⎯ 2 A° 



154. Choose the correct statement from the following 

éÀçC¢√-öÀapple ÆæÈ®j† ¢√uêu†’ í∫’JhçîªçúÕ. 

1) The molecularity can't be defined for a complex reaction 

äéπ ÆæçéÀx-≠æ d îª®ΩuéÀ Åù’-ûª†’ E®Ωy-*ç-îª‰ç 

2) Molecularity may be zero (or) fractional 

Åù’ûª Ææ’Ø√o (‰ü∆) GµØ√oûªtéπ N©’-´-©†’ éπLT Öçúø-´îª’a 

3) Order of a reaction can be known from reaction mechanism 

îª®Ωu ßÁ·éπ\ véπ´÷çé¬-Eo îª®√u Nüµ∆†ç †’ç* éπ†’éÓ\-´îª’a 

4) Order and molecularity are never same for elementary reactions 

v§ƒü∑¿-N’éπ îª®Ωuapple Åù’ûª, véπ´÷çéπç äÍé Nüµ¿çí¬ á°æ¤púø÷ Öçúø´¤. 

155. In a reaction 2 SO 2 + O 2 2 SO 3 , the partial pressures of SO 2 and SO 3 are 

same at equilibrium. If the equilibrium constant of the reaction is 10 atm -1 , the 

equilibrium pressure of oxygen gas is 

2 SO 2 + O 2 2 SO 3 Å-ØË îª®Ωuapple SO 2 , SO 3 ´’üµ¿u Ææ´’-û√-ÆœnA °‘úøØ√©’ Ææ´÷-†çí¬ 

ÖØ√o®·. Ç îª®Ωu ßÁ·éπ\ Ææ´’-û√-ÆœnA Æœn®√çéπç N©’´ 10 Åö«t-Æœp¥-ßª’®˝-1 Öçõ‰, ÇéÀq-ïØ˛ ßÁ·éπ\ 

Ææ´’-û√-ÆœnA °‘úø†ç N©’´ 


1) 76 mm of Hg 2) 760 mm of Hg 3) 38 mm of Hg 4) 380 mm of Hg 

156. Assertion (A): H 2 O boils at higher temperature than H 2 S 

ü¿%úµø-¢√uêu (A): H 2 O ´’-JÍí Ö≥Úg-ví∫ûª H 2 S éπçõ‰ ÅCµéπç 

Reason (R) : H 2 O is thermally stable than H 2 S. 

é¬®Ωùç (R): H 2 O Ö≠æg Æœn®Ωûªyç H 2 S éπçõ‰ ÅCµéπç. 

1) A and R are true, R is the correct explanation of A. 

A, R ÆæÈ®j-†N, A éÀ R ÆæÈ®j† N´-®Ωù. 

2) A and R true, R is not the correct explanation of A. 

A, R ÆæÈ®j-†N, A éÀ R ÆæÈ®j† N´-®Ωù é¬ü¿’. 

3) A is true, R is false. A ÆæÈ®jçC, R ÆæÈ®jçC é¬ü¿’. 

4) A is false, R is true. A ÆæÈ®jçC é¬ü¿’, R ÆæÈ®jçC. 

moist ûªúÕ 

Moist ûªúÕ 

157. C 2 H 5 OH ⎯→ X + Y CH 3 COCH 3 ⎯→ X + Z 

CaOCl 2 CaOCl 2 

The functional isomer of the product formed by the distillation of 'Z' is 


'Z' E ÊÆyü¿†ç îÁçCÊÆh à®ΩpúË Öûªp-Ø√o-EéÀ v°æ¢Ë’ßª’ Ææ´‚£æ« ≤ƒü¿%¨¡uç 

1) Propanal v§Ò°æ-Ø√¸ 2) Propanol v§Ò°æ-ØÓ¸ 

3) Propane v§Ò°æ-ØÓØ˛ 4) Ethenol ÉC∑-ØÓ¸ 



NH 3 

158. H 3 CCO 2 H ⎯→ X, where 'X' is 

NH 3 

H 3 CCO 2 H ⎯→ X, Ééπ\úø 'X'ÅØËC 

1) H 3 CCONH 2 2) H 3 CCO 2 NH 4 

3) CH 3 − CH = NOH 4) CH 3 CH 2 NC 

159. Diazotization test is used to detect which one of the following compound? 

úøßª’-ñapple-õ„j-ñ‰-≠æØ˛ °æKéπ~†’ Ö°æ-ßÁ÷-Tç* éÀçC¢√-öÀapple üËEo í∫’Jh-≤ƒh®Ω’? 

OH 

NH 2 CHO COOH 

1) 2) 3) 4) 

160. Nucleic acids are †÷uéÀx-é˙˝ Ç´÷x©’ 

1) Polysaacharides §ƒM-¨»-ê-È®j-ú˛©’ 2) Polynucleotides §ƒM†÷uéÀx-ßÁ÷-õ„j-ú˛©’ 

3) Polypeptides §ƒM-Â°-Â°kd-ú˛©’ 4) Triglycerides wõ„jTx-ï-È®j-ú˛-©’ 

KEY 

MATHEMATICS 

1) 1 2) 2 3) 1 4) 3 5) 1 6) 3 7) 1 8) 1 9) 2 10) 4 11) 4 12) 3 13) 1 14) 1 15) 2 16) 3 

17) 4 18) 2 19) 4 20) 3 21) 3 22) 3 23) 2 24) 2 25) 4 26) 3 27) 4 28) 3 29) 1 30) 1 

31) 3 32) 3 33) 3 34) 2 35) 2 36) 3 37) 1 38) 4 39) 2 40) 2 41) 1 42) 2 43) 3 44) 2 

45) 4 46) 1 47) 2 48) 3 49) 3 50) 1 51) 1 52) 2 53) 2 54) 4 55) 3 56) 4 57) 2 58) 1 

59) 2 60) 2 61) 3 62) 2 63) 4 64) 1 65) 3 66) 1 67) 1 68) 2 69) 1 70) 2 71) 1 72) 1 

73) 2 74) 3 75) 1 76) 3 77) 1 78) 1 79) 3 80) 3 

PHYSICS 

81) 3 82) 2 83) 3 84) 1 85) 2 86) 4 87) 1 88) 1 89) 3 90) 2 91) 1 92) 1 93) 4 94) 1 

95) 2 96) 2 97) 2 98) 1 99) 2 100) 4 101) 2 102) 2 103) 2 104) 4 105) 2 106) 3 

107) 1 108) 3 109) 4 110) 3 111) 1 112) 4 113) 2 114) 1 115) 3 116) 1 117) 1 

118) 2 119) 3 120) 1 

CHEMISTRY 

121) 1 122) 3 123) 3 124) 2 125) 1 126) 1 127) 1 128) 2 129) 3 130) 3 131) 4 

132) 4 133) 2 134) 3 135) 3 136) 4 137) 2 138) 1 139) 2 140) 1 141) 2 142) 2 

143) 4 144) 2 145) 1 146) 2 147) 1 148) 4 149) 2 150) 1 151) 3 152) 4 153) 2 

154) 1 155) 1 156) 2 157) 1 158) 2 159) 2 160) 2. 



(-Ñ -v°æ-¨¡o°æ-vû√-Eo -N-ï-ßª’-¢√-úø-apple-E -X-îÁj-ûª-†u -N-ü∆uÆæçÆæn-© -E°æ¤-ù’-©’ ®Ω÷-§Òç-Cç-î√®Ω’.)

R - eenadu pratibha

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