Pitampura, Delhi - 110034 Phone: 011-45221191-93...

Vidyamandir Classes

VMC/JEE-2014 1 Final JEE Mains/ACEG

Aggarwal Corporate Heights, 3rd Floor, Plot No. A - 7, Netaji Subhash Place,

Pitampura, Delhi - 110034 Phone: 011-45221191-93

Final JEE Mains/JEE-2014

29/03/2014

TEST CODE : ACEG M.M. : 360

03:00 PM - 06:00 PM TIME : 3.00 Hrs

Read the following Instructions very carefully before you proceed.

1. The question paper consists of 3 parts (Part I : Chemistry, Part II : Physics, Part III : Mathematics).

Each Part contains 30 Straight Objective Questions.

2. For each question you will be given 4 Marks if you have darkened only the bubble corresponding to the

correct answer. 1 Mark will be deducted for indicating incorrect response for any question.

No deduction from the total score will be made if no response is indicated.

3. There is only One Correct Response for each question. Filling up More than One response in each

question will be treated as Wrong Response and marks for Wrong response will be deducted.

4. Use Blue/Black Ball Point Pen only for writing particulars/marking responses on the Answer Sheet. Use of

pencil is strictly prohibited. However for rough work, use pencil on question paper itself.

5. No candidate is allowed to carry any textual material, printed or written, bits of papers, pager,

mobile phone, any electronic device, etc., except the Admit Card inside the examination hall/room.

6. Rough work is to be done on the space provided for this purpose in the Test Booklet only.

7. For answering a question, an ANSWER SHEET (OMR SHEET) is provided separately. Please fill your

Test Code, Roll No. and Group properly in the space given in the ANSWER SHEET.

8. Do not fold or make any stray marks on the Answer Sheet.

9. On completion of the test, the candidate must hand over the Answer Sheet to the Invigilator on duty in

the Room/Hall. However, the candidates are allowed to take away this Test Booklet with them.

10. No one will be permitted to leave the test room before the end of the test, i.e. 06.00 PM

Vidyamandir Classes


PART - I (CHEMISTRY) 120 MARKS

STRAIGHT OBJECTIVE TYPE

This Part contains 30 Multiple Choice Questions. Each Question has 4 choices A, B, C & D, out of which

Only One is Correct :

1. One liter of gas A at two atmospheric pressure and two liters of gas B at three atmospheric pressure are

mixed in a four liter flask to form an ideal gas mixture. What will be the final pressure of the gaseous

mixture if the gases initially and finally were at the same temperature?

(A) 1.0 atm (B) 1.5 atm (C) 2.0 atm (D) 2.5 atm

2. 3 mol of a mixture of FeSO4 and Fe2(SO4)3 required 100 mL of 2 M KMnO4 solution in acidic medium.

Hence, mole fraction of FeSO4 in the mixture is:

(A) 1

3 (B)

2

3 (C)

2

5 (D)

3

5

3. Which of the following are not correct statements?

I. Carbohydrates are the polyhydroxy alcohols and phenols

II. All amino acids have different isoelectric point

III. Sucrose reduces Tollen’s reagent

IV. Starch is known as invert sugar also

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

SPACE FOR ROUGH WORK

Vidyamandir Classes


4. A mixture of nitrogen and hydrogen in the ratio of 1 : 3 reach equilibrium with ammonia when 50% of the

mixture has reacted. If the total pressure is p, the partial pressure of ammonia in the equilibrium mixture

was.

(A) p

2 (B)

p

3 (C)

p

4 (D)

p

6

5. Which of the following compounds reacts most rapidly with the cold AgNO3 solution?

(A) CH3CH = CHCl (B) CH3CH2CH2Cl

(C) CH2 = CHCH2Cl (D) CH3CH2CH(Cl)2

6. In Cannizzaro reaction given below :

OH

2 22PhCHO PhCH OH PhCO−

−→ +

the slowest step is :

(A) The abstraction of proton from the carboxylic group

(B) The deprotonation of PhCH2OH

(C) The attack of OH− at the carbonyl group

(D) The transfer of hydride to the carbonyl group

7. Acetone (CH3COCH3) is the major product in:

I. H O3

2 2CH C CH⊕

= = →

II. H SO /HgSO /H O2 4 4 2

3CH C CH≡ →

III. 3BH THF.3

H O /OH2 2

CH C CH≡ →

(A) I (B) II (C) III (D) None of these


Vidyamandir Classes


8. How much amount of CaCl2 (i = 2.47) is dissolved in 2.5L of water so that its osmotic pressure become

0.75 atm at 27 C° ?

(A) 0.3 mol (B) 0.03 mol (C) 3 mol (D) 0.003 mol

9. The term anomers of glucose refers to :

(A) isomers of glucose that differ in configuration at carbon one (C 1)−

(B) isomers of glucose that differ in configuration at carbons one and four (C 1 and C 4)− −

(C) a mixture of (D)-glucose and (L)-glucose

(D) enantiomers of glucose

10. Which of the following is incorrect statement?

(A) Principal quantum number can not be negative

(B) Azimuthal quantum number can not be negative

(C) Magnetic quantum number can not be negative

(D) Spin quantum number can be negative

11. The product P in the reaction:

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


Vidyamandir Classes


12. The transition metals exhibit higher enthalpies of atomization due to :

(A) tendency of exhibiting variable oxidation states

(B) the presence of incompletely filled d-subshell

(C) their atoms existing in the solid state with unpaired electrons

(D) strong interatomic interaction arising because of having large number of impaired electrons in their

atoms

13. Which of the following ionic substances is most effective in coagulating aluminium hydroxide sol?

(A) Soldium chloride (B) Calcium chloride

(C) Ferric sulphate (D) Potassium phosphate

14. The boiling points of F2, Cl2, Br2 and I2 increase as we go down the group. This is best attributed to

difference in :

(A) Covalent bond strengths (B) dipole forces

(C) London dispersion forces (D) colligative forces

15. A gas is heated in such a way so that its pressure and volume both becomes double. Again by lowering

temperature, one fourth of initial number of moles of air has been taken in, to maintain the double volume

and pressure. By what fraction, the temperature must have been raised finally ?

(A) 1

5 times (B)

4

5 times (C)

16

5 times (D)

8

5 times


Vidyamandir Classes


16. In a cube structure of diamond which is made from X and Y, where X atoms are at the corners of the cube

and Y at the face centres of the cube. The molecular formula of the compound is :

(A) X2Y (B) X3Y (C) XY2 (D) XY3

17. The standard oxidation potentials of Zn, Cu, Ag and Ni electrodes are +0.76, 0.34, 0.80− − and +0.25 V

respectively. Which of the following reactions will provide maximum voltage ?

(A) 2Cu 2Ag (aq) Cu (aq) 2Ag+ ++ → +

(B) 2Zn 2Ag (aq) Zn (aq) 2Ag+ ++ → +

(C) 2 2Zn Cu (aq) Zn (aq) Cu+ ++ → +

(D) 2

2Zn 2H (aq) Zn (aq) H+ ++ → +

18. Molecules of a gas have ‘Z’ degree of freedom, where degree of freedom represents the number of

independent methods to express the energy of molecules. Determine the value of γ .

(A) Z

12

γ = + (B) 2

1Z

γ = + (C)

n2

1Z

γ = +

(D) 2

1Z

γ = −

19. What will be the value of Λ for a 0.001Maq. solution of 3NH ?

Given 5bK 1.6 10−= × , 1 2 1238ohm cm mol .− −Λ° =

(A) 1 2 131.58ohm cm mol− − (B)

1 2 142.78ohm cm mol− −

(C) 1 2 129.99ohm cm mol− − (D) 1 2 118.47ohm cm mol− −


Vidyamandir Classes


20. The isotherm obtained for CO is as follows :

The compressibility factor for the gas at point A will be :

(A) b

1V

− (B) b

1V

+ (C) b

1RT

+ (D) a

1RTV

+

21. Ionisation energy of He+ is 18 119.6 10 J atom− −× . The energy of the stationary state ( )n 1= of 2Li + is :

(A) 15 12.2 10 J atom− −− × (B)

17 18.82 10 J atom− −×

(C) 16 14.41 10 J atom− −× (D) 17 14.41 10 J atom− −− ×

22. If a reaction is non-spontaneous at its freezing point and becomes feasible at its boiling point, then :

(A) H∆ is ve− , S∆ is +ve (B) H∆ and S∆ both are +ve

(C) H∆ and S∆ both are ve− (D) H∆ is +ve, S∆ is ve−

23. A substance undergoes first order decomposition. The decomposition follows two parallel first order

reactions as

The percentage distribution of B and C are :

(A) 50% B and 50 % C (B) 76.83%B and 23.17%C

(C) 90%B and 10%C (D) 60%B and 40%C


Vidyamandir Classes


24. Which of the following statements is/are not correct?

(A) La(OH)3 is less basic than Lu(OH)3

(B) In lanthanide series, ionic radius decrease from La3+ ion

(C) La is actually an element of transition series rather than lanthanides

(D) Atomic radius of Zr and Hf are sane because of lanthanide contraction

25. The ONO angle is maximum in :

(A) 3NO− (B) 2NO− (C) 2NO (D) 2NO+

26. Name the type of structure of silicate in which one oxygen atom is shared between two [ ]44SiO−units.

(A) Linear chain silicate (B) Pyrosilicate

(C) Sheet silicate (D) Three-dimensional

27. Al and Ga have nearly the same covalent radii because of :

(A) Greatest shielding effect of s-electrons of Ga atoms

(B) Poor shielding effect of s-electrons of Ga atoms

(C) Poor shielding effect of d-electrons of Ga atoms

(D) Greatest shielding effect of d-electrons of Ga atoms


Vidyamandir Classes


28. The IUPAC name of the compound,

2

2

CH CH COOH is :| |OH NH

− −

(A) 2-Amino-3-hydroxypropanoic acid (B) 1-Hydroxy-2-aminopropan-3-ioc acid

(C) 1-Amino-2-hydroxypropanoic acid (D) 3-Hydroxy-2-aminopropanoic acid.

29. Aqueous solution of borax acts as a buffer because :

(A) It contains weak acid and its salt, with strong base

(B) It contains tribasic acid and strong base

(C) It contains number of natural water molecules

(D) None of these

30. In which reaction does the oxidation state of the group 14 element change?

(A) [ ] [ ]44 2Si 4 OH SiO 2H− −+ → + (B) [ ] [ ] [ ]4 4 4 62

GeCl 2 Et N Cl Et N GeCl+ →

(C) ( )4 3 2 4SiCl 4NH Si NH 4HCl+ → + (D) 4 2 2 2SiH O SiO 2H O+ → +


Vidyamandir Classes


PART - II (PHYSICS) 120 MARKS




31. In the figure the springs S1 S2 S3 and have spring constants

K1 = 50 N/m, K2 = 30 N/m, K3 = 30 N/m and K4 60 N/m

respectively. The mass of the block is 10 gm.

Find the period of small oscillations of the block.

(A) 20

secπ

(B) 30

secπ

(C) 40

secπ

(D) 50

secπ

32. For an EM wave traveling along positive x-axis, the electric field vector at a point is 720 j . Then magnetic

field vector at the same point is :

(A) 62 4 10−× ˆ. k (B) 62 4 10−− × ˆ. k (C) 52 16 10−× ˆ. k (D) 52 16 10−− × ˆ. k

33. In a region, steady and uniform electric and magnetic fields are present. These two fields are parallel to

each other. A charged particle is released from rest in this region. The path of the particle will be

(A) helix (B) straight line (C) ellipse (D) circle

34. A string is stretched between fixed points separated by 75.0 cm. It is observed to have resonant frequencies

of 420 Hz and 315 Hz. There are no other resonant frequencies between these two. Then, the lowest

resonant frequency for this string is.

(A) 105 Hz (B) 1.05 Hz (C) 1050 Hz (D) 10.5 Hz


m

S1

S2 S3 S4

Vidyamandir Classes


35. The circuit has two oppositely connected ideal diodes in

parallel. What is the current flow in the circuit?

(A) 1.71 A (B) 2.00 A

(C) 2.31 A (D) 1.33 A

36. If the binding energy per nucleon in 7 43 2andLi He nuclei are 5.60 MeV and 7.06 Mev respectively, then in

the reaction 7 43 22+ →p Li He energy of proton must be.

(A) 28.24 MeV (B) 17.28 MeV (C) 1.46 MeV (D) 39.2 MeV

37. The diagram shows the energy levels for an electron in a certain

atom. Which transition shown represents the emission of a photon

with the most energy?

(A) I (B) II

(C) III (D) IV

38. Suppose the gravitational force varies inversely as the nth power of distance. Then the time period of a

planet in circular orbit of radius R around the sun will be proportional to :

(A)

1

2

n

R

+

(B)

1

2

n

R

−

(C) Rn (D)

2

2

n

R

−


12V

4Ω

3Ω 2Ω

D2 D1

n = 4

n = 3

n = 2

n = 1 I II III IV

Vidyamandir Classes


39. A radiation of energy E falls normally on a perfectly reflecting surface. The momentum transferred to the

surface is :

(A) E/c (B) 2E/c (C) Ec (D) E/c2

40. The total current supplied to the circuit by the battery is :

(A) 1 A (B) 2 A

(C) 4 A (D) 6 A

41. The length of a magnet is large compared to its width and breadth. The time period of its oscillation in a

vibration magnetometer is 2 s. The magnet is cut along its length into three equal parts and three parts are

then placed on each other with their like poles together. The time period of this combination will be :

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

42. In an LCR series a.c. circuit, the voltage across each of the components, L, C and R is 50 V. the voltage

across the LC combination will be :

(A) 50 V (B) 50 2 V (C) 100 V (D) 0 V (zero)

43. A coil having n turns and resistance ΩR is connected with a galvanometer of resistance 4 ΩR .

This combination is moved in time t seconds from a magnetic flux W1 Weber to W2 Weber. The induced

current in the circuit is :

(A) 2 1

5

−W W

Rnt (B)

( )2 1

5

−−

n W W

Rt (C)

( )2 1−−

W W

Rnt (D)

( )2 1−−

n W W

Rt


2Ω6V

6Ω3Ω

1 5Ω.

Vidyamandir Classes


44. A block of mass 15 kg is resting on a rough inclined lane as shown in the figure. The minimum horizontal

force F of 50N is required to prevent down word slipping the coefficient of friction between the surfaces of

contact is.

(A) 1/2

(B) 2/3

(C) 3/4

(D) 1/4

45. A particle is projected form the ground with an initial speed of V at an angle θ with horizontal.

The average velocity of the particle between its point of projection and the highest point of trajectory is:

(A) 21 22

+V

cos θ (B) 21 22

−V

cos θ

(C) 21 32

+V

cos θ (D) v cosθ

46. The number of images formed by the lens as

shown in the figure is :

(A) 1 (B) 2

(C) 3 (D) 4

47. If the ratio of change in current in emitter and corresponding change in collector current is 1.013, then the

value of β is :

(A) 0.987 (B) 75.92 (C) 1.006 (D) 79.68


M

45

F

1µ 2µ

Vidyamandir Classes


48. The 3 physical quantities are related as3 2

=a b

xc

, if the age error in a, b, and c are 2 1 and 4± ± ±%, % % ,

respectively, then age error in x is :

(A) 8± % (B) 12± % (C) 14± % (D) 10± %

49. Two identical long, solid cylinders are used to conduct heat from temperature T1 to temperature T2.

Originally the cylinders are connected in series and the rate of heat transfer is H. If the cylinders are

connected in parallel, then the rate of heat transfer would be :

(A) H/4 (B) 2H (C) 4H (D) 8H

50. A disc of mass M and radius R is performing pure rolling motion in the

x-y plane as shown in the figure. The magnitude of angular momentum

of the disc about O is :

(A) 2

2

MR ω (B) 2MR ω

(C) 23

2MR ω (D)

22MR ω

51. 743 J of heat energy is added to raise the temperature of 5 mol of an ideal gas by 2k at constant pressure.

How much heat energy is required to raise the temperature of the same mass of the gas by 2 K at constant

volume?

(A) 826 J (B) 743 J (C) 660 J (D) 620 J

52. Three capacitors connected in series have an effective resistance of 2 Fµ . If one of the capacitors is

removed, the equivalent capacitance becomes 3 Fµ . The capacitance of the capacitor that is removed is:

(A) 6 Fµ (B) 1 Fµ (C) 3 2/ Fµ (D) 2 3/ Fµ


O

R R ω

x

y

Vidyamandir Classes


53. The angle of declination at any point on the surface of the earth

(A) is equal to 11 5. ° and same everywhere on the earth

(B) is equal to 8° and same everywhere on the earth

(C) has different values at different points on the surface of the earth

(D) is the angle between the axis of the magnetic dipole of the earth and the axis of rotation of the

earth

54. A shell at rest at the origin explodes into three fragments of mass 1 kg, 2 kg and m kilograms. The 1 kg and

2 kg pieces fly off with speeds of 12 m/s along the x-axis and 8m/s along the y-axis, respectively. If the

m kilogram piece files off with a speed of 40 m/s, the total mass of the shell would be :

(A) 0.5 kg (B) 5 kg (C) 3.5 kg (D) 4.5 kg

55. A point charge q is placed at the centre of one of the face of cuboid as

shown in figure. Find the electric flux crossing through the upper surface.

(A) 06

q

ε (B)

024

q

ε

(C) 012

q

ε (D) Zero

56. If length of a potentiometer wire is 300 cm and in its primary circuit a standard cell of emf 2 V and a

rheostat having resistance setting at 4Ω is connected, the resistance per unit length of potentiometer wire

is 2Ω/ .m If a battery of emf 1V and internal resistance 0 5Ω. is connected in secondary, then null point will

be obtained at:

(A) 250 cm (B) 200 cm (C) 150 cm (D) 100 cm


Vidyamandir Classes


57. A block of mass m is gently placed over a massive plank moving horizontally over a smooth surface with

velocity 6 m/s. The coefficient of friction between the block and plank is 0.2. The distance travelled by the

block till it slides on the plank is (take g = 10 m/s2)

(A) 4 m (B) 6 m (C) 9 m (D) 12 m

58. The refractive index of a 60° prism is ( )7 3/ . The minimum angle of incidence of a ray of light that can

be transmitted through the prism is:

(A) 30° (B) 40° (C) 50° (D) 60°

59. A current I flows through a thin wire shaped as regular polygon of n sides which can be inscribed in a

circle of radius R. The magnetic field induction at the centre of polygon due to one side of the polygon is:

(A) 0

Itan

R n

µ π

π (B)

0

4

Itan

R n

µ π

π (C)

0

2

Itan

R n

µ π

π (D)

0

2

Icos

R n

µ π

π

60. With reference to the following figure, which of

the following is possible?

(A) A = 0, B = 0, X = 1

(B) A = 0, B = 1, X = 0

(C) A = 1, B = 0, X = 0

(D) A = 1, B = 1, X = 0


Vidyamandir Classes


PART - III (MATHEMATICS) 120 MARKS




61. The sum of the series 2 3 4 5 6 7

2 1 2 1 2 1 21

3 3 3 3 3 3 3.............+ + + + + + + + upto infinite terms is equal to :

(A) 15

8 (B)

8

15 (C)

27

8 (D)

21

8

62. If f is a positive function such ( ) ( )f x T f x+ = where 0T x R> , ∀ ∈ then :

( ) ( ) ( )( ) ( ) ( )2 2

2 2

4 4n

f x T f x T .............. nf x nTlim n

f x T f x T .......... n f x n T→∞

+ + + + + + + + + + + +

is :

(A) 2 (B) 2

3 (C)

3

2 (D) None of these

63. The arithmetic mean of a set of observations is X . If each observation is divided by α and then is

increased by 10, then the mean of the new series is :

(A) X

α (B)

10X

α+

(C) 10X αα+

(D) 10Xα +

64. Let f and g be twice differentiable function on R and ( ) ( )5 8 5 2f " , g"= = ,

then ( ) ( ) ( ) ( )( ) ( ) ( ) ( )5

5 5 5

5 5 5x

f x f x f 'im

g x g x g'→

− − − − − −

is equal to :

(A) 0 (B) 1 (C) 2 (D) 4


Vidyamandir Classes


65. If 2sin x . cos y = 1, then 2

2at

4 4

d y

dx

π π ,

is :

(A) 4− (B) 2− (C) 6− (D) 0

66. If x1 and x2 are roots of the quadratic equation 22 3 4 0x x+ − = , then the quadratic equation whose roots

are ( ) 212 3x

−+ and ( ) 222 3x

−+ , is equal to :

(A) 264 25 1 0x x+ + = (B)

264 25 1 0x x− + =

(C) 264 25 1 0x x+ − = (D)

264 25 1 0x x− − =

67. In parallelogram PQRS (taken in order), P is ( )1 1− , − , Q is (8, 0) and R is (7, 5). Then point S has

co-ordinates :

(A) ( )1,4− (B) ( )2 2− , (C) 7

22

− ,

(D) ( )2 4− ,

68. Consider the function ( )

1 0 1

2 1 2

x x xf x

x x

+ ; ≤ < =

− ; ≤ ≤ where . denotes the fractional part function. Which

of the following statement is Incorrect ?

(A) ( )1x

lim f x→

exists

(B) ( ) ( )0 2f f≠

(C) ( )f x is continuous in [0, 2]

(D) ( )f x takes all intermediate values between ( ) ( )0 to 2f f


Vidyamandir Classes


69. If 1

3 3 4

2 3 4 then

0 1 1

A A−−

= − ; −

is equal to :

(A) A (B) A2 (C) A

3 (D) A

4

70. If2 1

2

xa tan

a

x a

alim

x e

π

→

− =

, then a is equal to :

(A) π− (B) π (C) 2

π (D)

2

π−

71. The roots of the equation 2 6 2x x x− − = +| | are given by :

(A) 2 2 4− , , (B) 0, 1, 4 (C) 2 1 4− , , (D) 0, 2, 4

72. Number of 7 digit telephone numbers that can be created if the first three digits must be 426,427or 428 and

right most digit is divisible by 3, is k thousand then k is equal to :

(A) 12 (B) 9 (C) 6 (D) 3

73. Let ( )3 2 4 2= + + ; = +ˆˆ ˆa i j k b i k and 4 2 3c i j k= + + . Sum of distinct values of α for which the

equation ( )xa yb zc xi y j zkα+ + = + + has non trivial solution is :

(A) 1− (B) 4 (C) 7 (D) 8


Vidyamandir Classes


74. If the maximum number of distinct elements in a symmetric matrix of order n is 45, then the value of n is :

(A) 9 (B) 10 (C) 15 (D) None of these

75. A line passes through origin and is perpendicular to two parallel lines 2 6 0x y+ + = and 4 2 9 0x y+ − = ,

then the ratio in which the origin divides this line segment is :

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

76. Let R be the set of real numbers. Consider the following subsets of R R.×

( ) ( ) 1 and 0 2 is an integerS x y y x x T x y x y= , : = + < < , = , : − .

Which one of the following is true?

(A) Neither S nor T is an equivalence relation on R

(B) Both S and T are equivalence relations on R

(C) S is an equivalence relation on R but T is not

(D) T is an equivalence relation on R but S is not

77. Let ( )1 1 0

1 0

tan xf x x

x

− ; ≠

= ; =

Then which of the following statement is Correct ?

(A) f has a non removable discontinuity of finite type at x = 0

(B) f has a non-removable discontinuity of oscillatory type at x = 0

(C) f has a non-removable discontinuity of infinite type at x = 0

(D) f is continuous on ( ) ( )0 0−∞, ∪ , ∞


Vidyamandir Classes


78. If point A lies on line 1 2 3

2 3 4

x y z− − −= = and point B lies on line

2 4 6

3 7 6

x y z− − −= = then AB can

be parallel to :

(A) 2i j k+ + (B) i j k+ + (C) 3i j k+ + (D) 4i j k+ +

79. The range of the function ( ) 1 1f x cos x tan x− −= + is :

(A) 3

4 4

π π , (B)

3

2 2

π π , (C)

5

3 4

π π , (D)

5

4 4

π π ,

80. The integral

( )21

ln xdx

ln x+∫ is equal to :

(A) ( )3

1

1c

ln x+

+ (B)

( )21

1c

ln x+

+ (C)

( )21

xc

ln x+

+ (D)

( )1

xc

ln x+

+

81. If anda b c, are vectors such that andb c are perpendicular, but anda b are not. Let m be a real

number. If x . a m x b c= , × = then :

(A) ( )

( )mb a c

xc . b

+ ×= (B)

( )( )

mb a cx

a . b

− ×=

(C) ( )

( )mb a . c

xa . b

+= (D)

( )( )

mb a cx

a . b

+ ×=


Vidyamandir Classes


82. The shelf life, in days for bottles of a certain prescribed medicine is a random variable having the density

function ( ) ( )320 000

0100

0 elsewhere

xf x x

, ; > = + ;

, the probability that a bottle of this medicine will have a shelf

life of at least 10 days is :

(A) 1

121 (B)

21

121 (C)

1

11 (D)

100

121

83. If A is a skew-symmetric matrix and n is odd positive integer, then An is :

(A) A symmetric matrix (B) A skew-symmetric matrix

(C) A diagonal matrix (D) None of these

84. The smallest natural number c for which the equation ex = cx2 has exactly three distinct solutions, is :

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

85. The approximate percentage of the interval [ ]5 15− , for which the inequality 7

44

xx

> −+

is satisfied, is :

(A) 55% (B) 65% (C) 60% (D) 45%

86. If x1, x2,…….., x18 are observations such that ( )18

1

8 9j

j

x

=

− =∑ and ( )18

2

1

8 45j

j

x

=

− =∑ , then the standard

deviation of these observations is :

(A) 18

34 (B) 5 (C) 5 (D)

3

2


Vidyamandir Classes


87. The value of ( )20

11

x

xx

lim ln t dtx→

−

+∫ is equal to :

(A) 0 (B) 1 (C) 1− (D) 2

For Questions 88 - 89

Consider the function ( ) 1

2

2

1

xf x sin x R

x

− = ∀ ∈ +

.

88. Number of points where ( )f x is not differentiable, is :

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

89. The value of ( )0f ′ is :

(A) 2 (B) 2− (C) 1 (D) Non existent

90. The integral ( )1

0

f x dx∫ is equal to :

(A) 1

22 2

lnπ− (B) 2

2ln

π− (C)

12

4 2ln

π− (D) None of these


Pitampura, Delhi - 110034 Phone: 011-45221191-93...

Documents

Transcript of Pitampura, Delhi - 110034 Phone: 011-45221191-93...