part-1 : physics · iitian’s tapasya, pushpanjali place, boring road crossing, patna-1, mob....

IITian’s TAPASYA, Pushpanjali Place, Boring Road Crossing, Patna-1, Mob. 8102926610 www.iitianstapasya.com

PART-1 : PHYSICS

1. The motorized drum turns clockwise at constant speed causing the vertical cable to have a constant downward velocity 5 m/s. The pulley connecting the 81 kg block is not fixed, if the tension in the cable

is T (in newton) then T

185 at the instant shown is. (Neglect the diameter and mass of the small

pulleys)

(A) 5 (B) 4 (C) 6 (D) None of these

2. A particle is projected with speed 30m/s at angle 22.5° with horizontal from ground as shown. AB and CD are parallel to y-axis and B is highest point of trajectory of particle. CD/AB is

(A) 3 (B) 3/2 (C) 2 (D) 4

3. Two cars A and B moving on two straight tracks inclined at an angle 60° heading towards the

crossing initially their positions are as shown in the figure. Both cars have same speed. Minimum

seperation between them during their motion will be.

(A) 10 km (B) 5 3 km (C) 5 km. (D) 20 km3


4. The wedge is moved towards right with acceleration a, which is slowly increased from zero. The

tension in the string just when the small block of mass m breaks contact with the surface of wedge is

(Assume all surfaces smooth, the string inextensible and neglect rotational effect’s.)

(A) mg sin (B) mg cosec (C) mg tan (D) mg cot

5. The maximum angle to the horizontal at which a stone can be thrown so that it always moves away from the thrower will be :

(A) 1 2sin3

(B) 1 2 2sin3

(C) 1 1sin3

(D) 1 2sin3

6. A man starts walking on a circular track of radius R. First half of the distance he walks with speed V1 ,

half of the remaining distance with speed V2, then half of the remaining time with V1 and rest with V2

and completes the circle. Average speed of the man during entire motion in which he completes the

circle is.

(A) 1 2 1 22 22 1 1 2

2V V (V V )V 2V 2V V

(B) 1 2 1 2

2 21 2 1 2

4V V (V V )V 2V 5V V

(C) 1 2 1 2

2 21 2 1 2

V V (V 2V )V V 4V V

(D)

21 2

2 21 2 1 2

(V 2V )V V 2V V

7. Two blocks of masses 8kg and 6kg are connected with a string & placed on a rough horizontal

surface. Surface itself is accelerating up with constant acceleration 2 m/s2. Two forces 60 N each are

acting on the two blocks as shown. Friction coefficient for 8kg is 0.5 & that for 6 kg is 0.6. Tension in

the string is : (g = 10 m/s2).

(A) 60 N (B) 12 N (C) 43.2 N (D) 16.8 N

8. Block A of weight 500 N and block B of weight 700 N are connected by rope pulley system as shown.

The largest weight C that can be suspended without moving block A and B is W. The coefficient of

friction for all plane surfaces of contact is 0.3. The pulleys are ideal. Find W90

(A)12 (B) 22 (C) 9 (D) 18


9. O is a point at the bottom of a rough plane inclined at an angle to the horizontal. Coefficient of

friction between AB is tan2 and between BO is 3 tan

2 . B is the mid–point of AO. A block is

released from rest at A. Then identify which graphs are correct during motion of block from point A to

O taking direction down the incline plane as positive (sin = 1/5) :

(A) (B) (C) (D)

10. A block B of mass 10 kg is placed on smooth horizontal surface over it another block A of same mass

is placed. A horizontal force F is applied on block B.

S1 : No block will move unless F > 10 N. S2 : Block A will move towards left.

S3 : Acceleration of block B will never be less than that of A.

S4 : The relative motion between A and B will start when F exceeds 10 N.

(A)FFFF (B)TTTT (C) FFTF (D) TTFF

11. Block A of mass m is placed on a plank B. A light support S is fixed on plank B and is attached with

the block A with a spring of spring constant K. Consider that initially spring is in its natural length. If

the plank B is given an acceleration a, then maximum compression in the spring is xmak

. Find the

value of x. (All the surfaces are smooth)

(A) ma2k

(B) 2mak

(C) mak

(D) 4mak


12. Mass m shown in figure is in equilibrium. If it is displaced further by x and released find its

acceleration just after it is released. Take pulleys to be light & smooth and strings light.

(A) 4kx5m

(B) 2kx5m

(C) 4kxm

(D) none of these

13. In the figure shown find out the maximum height reached by the particle. (g = 10 m/s2)

(A) 0.5 m (B) 0.75 m (C) 1 m (D) none of these

14. Power of the only force acting on a particle of mass m = 1 kg moving in straight line depends on its

velocity as P = v2 where v is in m/s and P is in watt. If initial velocity of the particle is 1 m/s, then the

displacement of the particle in n2 second will be :

(A) ( n2 – 1)m (B) ( n2)2 m (C) 1 m (D) 2 m 15. A particle is moving along an elliptical path with constant speed. As it moves from A to B, magnitude

of its acceleration

(A) continuously increases

(B) continuously decreases

(C) Remains constant

(D) first increases and then decreases

16. A small bead of mass m = 1 kg is free to move on a circular hoop. The circular hoop has centre at C

and radius r = 1 m and it rotates about a fixed vertical axis. The coefficient of friction between bead

and hoop is μ = 0.5. The maximum angular speed of the hoop for which the bead does not have

relative motion with respect to hoop, at the position shown in figure is : (Take g = 10 m/s2)

(A) 1/25 2 (B) 1/2

10 2 (C) 1/215 2 (D) 1/2

30 2


17. Two blocks of mass m1 and m2 (m1 < m2) are connected with an ideal spring on a smooth horizontal

surface as shown in figure. At t = 0 m1 is at rest and m2 is given a velocity v towards right. At this

moment, spring is in its natural length. Then choose the correct alternative :

(A) Block of mass m2 will be finally at rest after some time.

(B) Block of mass m2 will never come to rest.

(C) Both the blocks will be finally at rest.

(D) None of these

18. Three point masses are attached by light inextensible strings of various lengths to a point O on the

ceiling. All of the masses swing round in horizontal circles of various radii with the same angular

frequency (one such circle is drawn in the shown figure.) Then pick up the correct statement.

(A) The vertical depth of each mass below point of suspension from ceiling is different.

(B) The radius of horizontal circular path of each mass is same.

(C) All masses revolve in the same horizontal plane.

(D) All the particles must have same mass.

19. One end of a light rod of length 1 m is attached with a string of length 1m. Other end of the rod is

attached at point O such that rod can move in a vertical circle. Other end of the string is attached with

a block of mass 2kg. The minimum velocity that must be given to the block in horizontal direction so

that it can complete the vertical circle is (g = 10 m/s2).

(A) 4 5 (B) 5 5 (C) 10 (D) 3 5


20. A block of mass m and length is kept at rest on a rough horizontal ground of friction coefficient k.

A man of mass m is standing at the right end. Now the man starts walking towards left and reaches

the left end within time ‘t’. During this time, the displacement of the block is : (Assume the pressing

force between the block and the ground remains constant and its value is same as it was initially.

Also assume that the block slides during the entire time (t)) :

(A) 2

kgt2

(B)

2kgt

2

(C) 2

kgt2

(D)

2

21. A particle moving with velocity ˆ ˆ(2i 3j) m/s collides with a surface at rest in xz–plane as shown in

figure and moves with velocity ˆ ˆ(2i 2j) m/s after collision. Then coefficient of restitution is

(A) 23

(B) 1 (C) 8

13 (D) 4

5

22. A ball is suspended from the top of a cart by a light string of length 1.0 m. The cart and the ball are

initially moving to the right at constant speed V, as shown in figure I. The cart comes to rest after

colliding and sticking to a fixed bumper, as in figure II. The suspended ball swings through a

maximum angle 60°. The initial speed V is (take g = 10 m/s2) (neglect friction)


(A) 10 m/s (B) 2 5 m/s (C) 5 2 m/s (D) 4 m/s

23. Two blocks each of mass m are joined together using an ideal spring of force constant K and natural

length 0 . The blocks are touching each other when the system is released from rest on a rough

horizontal surface. Both the blocks come to rest simultaneously when the extension in the spring is

04 . The coefficient of friction between each block and the surface (assuming it to be same between

any of the blocks and the surface) is :

(A) 0K40mg

(B) 0K8mg

(C) 03K8mg

(D) 0K1720 mg

24. Two spherical bodies of masses m and 5m and radii R and 2R respectively, are released in free

space with initial separation between their centres equal to 12 R. If they attract each other due to

gravitational force only, the distance covered by smaller sphere just before collision is

(A) 15R2

(B) 13R2

(C) 10 R (D) 17R2

25. In the figure shown a semicircular area is removed from a uniform square plate of side ' ' and mass

‘m’ (before removing). The x-coordinate of centre of mass of remaining portion is (The origin is at the

centre of square)

(A) ( 2)

2 (8 )

(B)

( 2)2 (8 )

(C) ( 2)8

(D)

4( )3

2(8 )

26. A car of mass ‘m’ is driven with acceleration ‘a’ along a straight level road against a constant external

resistive force ‘R’. When the velocity of the car is ‘V’, the rate at which the engine of the car is doing

work will be

(A) RV (B) maV (C) (R + ma)V (D) (ma – R)V

27. A particle moves with a velocity ˆ ˆ ˆv (5i 3 j 6k)

m/s under the influence of a constant force

ˆ ˆ ˆF (10i 10 j 20k)

+N. The instantaneous power applied to the particle is :


(A) 200 J/s (B) 40 J/s (C) 140 J/s (D) 170 J/s

28. A skater of mass m standing on ice throws a stone of mass M with a velocity of v m/s in a horizontal

direction. The distance over which the skater will move back (the coefficient of friction between the

skater and the ice is ) :

(A) 2 2M v

2m g (B)

2

2Mv

2m g (C)

2 2

2M v

2m g (D)

2 2

2 2M v

2m g

29. Two blocks of masses m and M are moving with speeds v1 and v2 (v1 > v2) in the same direction on

the frictionless surface respectively, M being ahead of m. An ideal spring of force constant k is

attached to the backside of M (as shown). The maximum compression of the spring when the block

collides is :

(A) 1mvk

(B) 2Mvk

(C) 1 2mM(v v )

(M m)K

(D) None of above is correct.

30. There are hundred identical sliders equally spaced on a frictionless track as shown in the figure.

Initially all the sliders are at rest. Slider 1 is pushed with velocity v towards slider 2. In a collision the

sliders stick together. The final velocity of the set of hundred stucked sliders will be :

(A) v/99 (B) v/100 (C) zero (D) v


OHCH3

CH2 C

OH

CH2

COOH

C OH

COOH O

PART-2 : CHEMISTRY

31. IUPAC name of the following compouund is :

(A) 2-methyl-3-cyclohexenol

(B) 3-methyl-1-cyclohexen-4-ol

(C) 4-hydroxy-3-methyl-1-cyclohexene

(D) 2-hydroxy-1-methylcyclohexene

32. Common name of CH2 = CH — CN is :-

(a) acrylonitrile (b) vinyl cyanide (c) allyl cyanide (d) allyl nitrile

(A) a, b and d (B) a and b (C) only b (D) a, b and c

33. The correct systematic IUPAC name of the given compound is :

(A) 3–Carboxy–3–hydroxy butane dioic acid

(B) 2–Hydroxy propane–1,2,3–tricarboxylic acid

(C) 3–Hydroxy butane dioic acid

(D) 2–Bis(carboxymethyl)–2–hydroxy ethanoic acid

34. The third line in Balmer series corresponds to an electronic transition between which Bohr's orbits in

hydrogen :-

(A) 5 3 (B) 5 2 (C) 4 3 (D) 4 2 35. An electron in a hydrogen atom in its ground state absorbs energy equal to ionisation energy of Li+2.

The wavelength of the emitted electron is :-

(A) 3.32 × 10–10 m (B) 1.17 Å (C) 2.32 × 10–9 nm (D) 3.33 pm

36. Given DH for the process Li (g) Li+3 (g) + 3e– is 19800 kJ/mole & IE1 for Li is 520 then IE2 & IE1 of

Li+ are respectively (approx value) :-

(A) 11775, 7505 (B) 19280, 520 (C) 11775, 19280 (D) Data insufficient

37. Which of the following statement is INCORRECT.

(A) em

ratio for canal rays is maximum for hydrogen ion.

(B) em

ratio for cathode rays is independent of the gas taken.

(C) The nature of canal rays is dependent on the electrode material.

(D) The em

ratio for electron is expressed as 2

2E

2B V, when the cathode rays go undeflected under the

influence of electric field (E), magnetic field (B) and V is potential difference applied across electrodes

38. If in Bohr's model, for unielectronic atom, time period of revolution is represented as Tn,z where n

represents shell no. and z represents atomic number then the value of T1,2 : T2,1 will be :-

(A) 8 : 1 (B) 1 : 8 (C) 1 : 1 (D) None of these


39. Consider the following statements :

The coefficient B in the virile equation on state PVm = RT 2

m m

B C1 ..........V V

a : is independent of temperature

b : is equal to zero at boyle temperature

c : has the dimension of molar volume Which of the above statements are correct. (A) a and b (B) a and c (C) b and c (D) a, b and c

40. At low pressures, the vander Waal's equation is written as :

2ap

V

V = RT

The compressibility factor is then equal to :

(A) a1

RTV

(B) RTV1

a

(C) a1

RTV

(D)RTV1

a

41. The density of a gas at 27°C and 1 atm is d. Pressure remaining constant at which of the following

temperatures will its density become 0.75 d?

(A) 20°C (B) 30°C (C) 400 K (D) 300 K 42. A certain volume of argon gas (Mol Wt. 40) requires 45 s to effuse through a hole at a certain

pressure and temperature. The same volume of another gas of unknown molecular weight requires

60 s to pass through the same hole under the same conditions of temperature and pressure. The

molecular weight of the gas is :

(A) 53 (B) 35 (C) 71 (D) 120

43. Following graph shows variation of I.P. with atomic number in second period (Li – Ne). Value of I.P. of

Na (11) will be :-

(A) Above Ne

(B) Below Ne but above O

(C) Below Li (D) Between N and O 44. Lanthanoid contraction is caused due to :

(A) the same effective nuclear charge from Ce to Lu

(B) the imperfect shielding on outer electrons by 4f electrons from the nuclear charge

(C) the appreciable shielding on outer electrons by 4f electrons from the nuclear charge

(D) the appreciable shielding on outer electrons by 5d electrons from the nuclear charge 45. The ground state electronic configurations of the elements, U, V, W, X and Y (these symbols do not

have any chemical significance) are as follows :

U 1s2 2s2 2p3 V 1s2 2s2 2p6 3s1


W 1s2 2s2 2p6 3s2 3p2 X 1s2 2s22p6 3s2 3p6 3d5 4s2

Y 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p6

Determine which sequence of elements satisfy the following statements : (i) Element forms a carbonate which is not decomposed by heating

(ii) Element is most likely to form coloured ionic compounds

(iii) Element has largest atomic radius

(iv) Element forms only acidic oxide

(A) V W Y U (B) V X Y W (C) V W Y X (D) V X W U

46. Match List I with List II and select the correct answer using the codes given below :

List I List II

A. 1s2, 2s2 2p6, 3s2 3p6, 4s2 1. In

B. 1s2, 2s2 2p6, 3s2 3p6 3p6 3d10, 4s1 2. Pd

C. 1s2, 2s2 2p6, 3s2 3p6 3d10, 4s2 4p6 4d10 3. Ca D. 1s2, 2s2 2p6, 3d10, 4s2 4p6 4d10, 5s2 5p1 4. Cu

Code : A B C D

(A) 1 2 3 4

(B) 1 3 2 4

(C) 3 4 2 1

(D) 1 4 3 2

47. Which of the following have same value of optical rotation ?

(A) I, IV (B) I, II (C) III, IV (D) I, III

48. The following compound can exhibit

(A) Geometrical isomerism only.

(B) Optical isomerism & geometrical isomerism only.

(C) Optical isomerism, geometrical isomerism & metamerism.

(D) Optical isomerism, geometrical isomerism & tautomerism.

3

23

CH|

CHOCHCHCHCHCH


49. is diastereomers of

(A) (B) (C) (D) 50. Tetracyline is called a broad spectrum antibiotic because it active against a wide variety of bacteria.

How many chirality center does tetracyline have?

(A) 3 (B) 4 (C) 5 (D) 6

51. How many stereoisomer may have this natural occuring compound.

(A) 8

(B) 16

(C) 64

(D) 128

52. Which will not show geometrical isomerism.

(A) (B) (C) (D)

53. 200 ml of a gaseous mixture containing CO, CO2 and N2 on complete combustion in just sufficient

amount of O2 showed contraction of 40 ml when the resulting gases were passed through KOH

solution it reduces by 50 % then calculate the volume ratio of 2 2CO CO NV : V : V in original mixture.

(A) 4 : 1 : 5 (B) 2 : 3 : 5 (C) 1 : 4 : 5 (D) 1 : 3 : 5


54. Number A container fitted with frictionless massless piston consist of five valves–I, II, III, IV and V.

These valves open automatically if pressure exceed over 1.5, 2.2, 2.5, 4.4 and 4.8 atm respectively.

Under the given initial conditions (mentioned in given diagram) system is in state of equilibrium.

Piston is now pressed in downward direction very slowly.

[Note: Consider the diameter of valve tube negligible and temperature remain constant.]

Select the correct option(s):

(A) Valve –II will be opened first

(B) As the piston crosses the valve which will be opened first, the remaining number of moles in

container are 5/3 .

(C) Valve–III will be the second valve which open

(D) Number of moles will zero as piston crosses Valve–V

55. Following represents the Maxwell distribution curve for an ideal gas at two temperatures T1 & T2.

Which of the following option is incorrect ?

(A) Total area under the two curves is independent of moles of gas

(B) If dU1= f Umps1 & dU2 = f Umps2 then A1 = A2

(C) T1 > T2 and hence higher the temperature, sharper the curve.

(D) The fraction of molecules having speed = Umps decreases as temperature increases.


56. 500 mL of a 0.05 M Mohr salt solution required the same volume of permanganate solution for

complete oxidation. Which of the followings is (are) true regarding the above redox reaction?

(1) The molarity of KMnO4 must be 0.01 M if the medium is acidic.

(2) The molarity of KMnO4 must be 0.0167 M if the medium is basic.

(3) The medium has no role to play in redox reaction.

(4) In the above reaction Fe(II) is oxidized to Fe(III) irrespective of medium.

(A) 1,2,3,4 (B) 1,2,4 (C) 1,3,4 (D) 1,2,3

57. A solution is prepared by dissolving a solid mixture of K2C2O4 and KHC2O4. A 10 mL portion of this

solution required 10 mL of 0.05 M KOH solution. In a separate analysis, 10 mL of the same stock

solution required 25 mL of a 0.10 M HCl solution. Which of the following is (are) correct statement(s)?

(1) The mixture has K2C2O4 and KHC2O4 is 2 : 1 molar ratio.

(2) The mixture has equimolar amounts of the two salts.

(3) 5 mL of the same stock solution would require 15 mL of a 0.02 M acidified dichromate solution.

(4) 8 mL of the same stock solution would require 24 mL of a 0.02 M acidified permanganate solution.

(A) 1, 3 (B) 1,4 (C) 1,3,4 (D) 1,2,3

58. 20 mL of a solution containing equal moles of Na2CO3 and NaHCO3 required 16 mL of a 0.16 M HCl

solution to reach the phenolphthalein end point. What volume of a 0.10 M H2SO4 solution would have

been required had methyl orange been used as indicator?

(A) 38.40 mL (B) 24.60 mL (C) 19.20 mL (D) 12.30 mL

59. 0.45 g pure crystal of Na2C2O4.xH2O was dissolved in water and diluted to 100 mL A 25 mL portion of

this solution required 10 mL of a 0.05 M H2SO4 solution to reach the end point. The value of x in the

salt is

(A) 2 (B) 3 (C) 4 (D) 5

60. Which of the following percentage strength is not possible for a sample of oleum?

(A) 104 % (B) 108 % (C) 122 % (D) 130 %


PART-3 : MATHS

61. If b > a, then the equation (x–a) (x–b) – 1 = 0 has

(A) both roots in (a,b) (B) both roots in (– ,a )

(C) both roots in (b, ) (D) one root in , a and other in (b,)

62. If 2x a 3 x a 0 has at least one positive root, then a

(A) , 0 7,9 (B) ( , 0] [7, ) (C) ( , 0] [9, ) (D) , 2 8,

63. If a, b, c are three distinct real numbers in G.P. and if a + b + c = xb, then

(A) x –1 or x 3 (B) x 1 or x 3 (C) x 3 or x 2 (D) x 4 or x 3

64. If the roots of the equation 2ax bx c 0 be and and those of the equation

2Ax Bx C 0 be k and k, then 2

2

b 4acB 4AC

is

(A) 2

2

aA

(B) 1 (C) aA

(D) Aa

65. If 2p x ax bx c and 2Q x ax dx c, ac 0 then the equation p x .Q x 0 has

(A) Two real roots (B) More than two real roots

(C) at least two real roots (D) No real root

66. If a, b and c are distinct positive real numbers and 2 2 2a b c 1, then ab bc ca is

(A) less than 1 (B) equal to 1 (C) greater than 1 (D) any real number

67. If axlog x, logbx x cxlog x are in H.P. where a, b, c, x belong to (1, ), then a, b, c are in

(A) A.P. (B) G.P. (C) H.P. (D) A.G.P.

68. If a, b, c are in H.P., then which of following incorrect

(A) a b c, ,

b c c a a b will be in A.P. (B)

a b c, ,b c a c a b a b c

are in H.P.

(C) 1 1 1 1 1 1, ,a b c b c a c a b

are in H.P. (D) bc ca ab, ,

b c c a a b are in A.P.

69. Let f(x) be a polynomial having all coefficient real, if 2 + 3i is a root of f(x) = 0 then

(A) 2 –3i is its other root (B) f(x) is not divisible by x2 – 4x + 13

(C) 2 –3i may not be its other root

(D) the sum of the roots of f(x) = 0 may not be a real number.


70. If 2b 4ac for the equation 4 2ax bx c 0, then all roots of the equation will be non zero real if

(A) b 0, a 0, c 0 (B) b 0,a 0, c 0 (C) b 0, a 0, c 0 (D) None of these

71. If is one root of the equation 24x 2x 1 0 , then its other root is given by

(A) 34 2 (B) 34 3 (C) 12

(D) 12

72. If a, b, c Q then which of the following equations does not have rational roots

(A) 2ax bx c 0 where if a + b + c = 0 (B) 2a c b x 2cx b c a 0

(C) 2 2 2 2 2 2abc x 3a cx b cx 6a 4ab 2b 0 (D) 2a b c x a c b x b c a 0

73. Which of the following statement is not true

(A) If 2 2 2a , b , c are in A.P. then b+c, c+a and a + b are in H.P.

(B) If th th th thp ,q , r ,s terms of an A.P. are in G.P. then p-q, q-r, r-s are in G.P.

(C) If b is HM of a & c then 1 1 1 1

b a b c a c

(D) If b is HM of a & c then 1 1 1 1

b a b c a c

74. The real values of for which the equation 3 2x 3x 9x 0 has three distinct real roots, if

(A) (–2,0) (B) [0,1] (C) [1, 2] (D) None of these

75. If cos x tan y , cos y tan z , cos z tan x then the value of sin x is

(A) 0sin36 (B) ocos36 (C) o2 sin18 (D) 02cos18

76. The number of pairs x,y satisfying the equations sin x sin y sin x y and x y 1 is

(A) 0 (B) 2 (C) 4 (D) 6

77. Let tan cot tan cot0 01 2 3 40 45 , t tan , t tan , t cot , t cot

then

(A) 1 2 3 4t t t t (B) 4 3 1 2t t t t (C) 4 1 2 3t t t t (D) None of these

78. The number of solutions of the equation cos x sin x , 0 x 4 is

(A) 2 (B) 4 (C) 6 (D) 8

79. If 3 15and 2 , sin

2 2 17 and 12tan , then sin

5 is

(A) 21

221 (B)

21221

(C) 7

221 (D)

71221

80. If and tan .tan .tan 14 4 4

then the value of

cos cos cos is

(A) 0 (B) 1 (C) –1 (D) 2


81. If A B C , then minimum value of 2 2 2cot A cot B cot C is

(A) 0 (B) 1 (C) 2 (D) 3

82. If 1 2 3 4x , x , x , x are roots of the equation 4 3 2 1x x sin 2 x cos 2 x cos sin 0,& sin2

then 1 1 1 11 2 3 4T an x Tan x Tan x Tan x can be equal to

(A) (B) 2 (C) (D)

83. If 1 1sin x cos x 0, where ‘x’ is a non-negative real number and . denotes the greatest

integer function, then complete set of values of x is

(A) cos1,1 (B) 1, cos1 (C) sin1,1 (D) cos1,sin1

84. The equation 1 1 13x 4xsin sin sin x,5 5

has

(A) 3 roots whose sum is zero (B) 2 roots

(C) 3 roots which are in G.P. (D) 3 roots which are in H.P.

85. The value of 1 1 1sin cos cos cos x sin sin x , where x ,2

, is

(A) 2

(B) (C) 2

(D) 34

86. Let f : R R and g : R R be two one–one and onto functions such that they are the mirror images

of each other about the line y = a. If h(x) = f(x) + g(x), then h(x) is (A) one-one onto (B) one–one into (C) many one-one (D) many one into

87. The set of values of so that f(x) = 2x 1

x 1

does not take any value in the interval

11,3

is

(A) 1,4

(B) [2, ) (C)

1 , 24

(D) 1,4

[2, )

88. Period of the function f(x) = cos2 {2x} + sin2 {2x} is (where {} denotes the fractional part of x).

(A) 1 (B) /2 (C) 1/2 (D)

89. Let f : R 0,2

defined by f(x) = tan–1 (x2 + x +), then the set of values of for which f is onto, is

(A) [0, ) (B) [-2, 1] (C) 1 ,4

(D) none of these

90. If f(x) is a polynomial function satisfying the condition f(x).f(1/x) = f(x) + f(1/x), xR-{0} and f(2) = 9

then

(A) 2 f(4) = 3 f(6) (B) 7 f(1) = f(3) (C) 9 f(3) = 2 f(5) (D) f(10) = f(11)

part-1 : physics · iitian’s tapasya, pushpanjali place, boring road crossing, patna-1, mob....

Documents