Func+Lim+Cont+Diffe,Electro+Current,Sol+Alkyl Paper 2

7/31/2019 Func+Lim+Cont+Diffe,Electro+Current,Sol+Alkyl Paper 2

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APEX INSTITUTE TEST PAPER-2

APEX INSTITUTE FOR IIT-JEE / PMT ; 9910817866 , 9990495952 Page 2

MATHEMATICS

Section - I

This section contains 8 multiple choice questions. Each question has 4 choices.(a),

(b),(c) and (d), out of which ONLY ONE is correct.

1. Period of sin 2 cos8 x x+ is

(a) / 2π (b) / 8π (c) /16π (d) . . N O T

2. For what value of ‘a’ f(x) = a x³ - 9x² + 9x + 11 is one-one.

(a) 2 (b) 3 (c) 4 (d) N.O.T

3. If f(x) = sin [ ]a x, (where [.] denotes the denotes the greatest integer function), has π as it’s

fundamental period, then

(a) a = 1 (b) a∈[1, 2) (c) a = 9 (d) a∈[4, 5)

4. f :[-20, 20] → R, defined by

2

( ) x

f xa

=

sin x + cos x ([.] denotes the greatest integer

function) is an even function, then set of values of ‘a’ is given by

(a) R (b) [0, 400] (c) (400, ∞ ) (d) null set

Space for rough work





5. If f(x) = sin x + cos x , g(x) =2

x -1 then g(f(x)) in invertible in the domain

(a) 0,2

π

(b) ,4 4

π π −

(c) ,2 2

π π −

(d) [ ]0,π

6. Period of the function f(x) = [ ]( )1

sin 3 sin 3 sin 33

x x x+ + where [.] denotes the greatest

integer function

(a)3

π (b)

2

3

π (c)

4

3

π (d) π

7. If domain of f(x) is [-1,2] then domain of f ( )24 x x− + where [.] denotes the greatest integer

function is

(a) 1, 7 − (b) 3, 1 3, 7 − − ∪ −

(c) ( 1, 7 − (d) 3, 1 3, 7 − ∪

8. If 5 x+ ( )

2

2 3 13 x

x≥ the solution set for x is

(a) [ )2,∞ (b) { }2 (c) ( ], 2−∞ (d) [ ]0,2






Section – II

(Multiple Correct Answer (s) Type)

This section contains 5 multiple choice questions. Each question has four choices (a), (b),(c),

and (d) out of which ONE or MORE may be correct.

9. f ( x) =2

3

4 – x+ log10( x

3– x) is defined for x belongs to

(a) (–1, 0) (b) (2, 3) (c) (1, 2) (d) (2, ∞)

10. f ( x) =( 1)( – 3)

– 2

x x

x

+is defined for x belongs to

(a) [–1, 3] (b) [–1, 2) (c) (2, 3) (d) [3, ∞)

11. For each real x, let f ( x) = max{ x, x2}. Then f ( x) is equal to

(a) x2

for x ≤ 0 (b) x for all x in [0, 1]

(c) f ( x) = x for all x ∈ [0, 1] (d) f ( x) = x2

for all x ≥ 1

12. The period of the function f ( x) = sin3 xcos[3 x] – cos3 xsin[3 x], where [.]

denotes the greatest integer function is

(a) 6 (b) 3 (c) 1/3 (d) 1/6

13. For each real x, let f ( x) = max{ x, x2}. Then f ( x) is equal to

(a) x2

for x ≤ 0 (b) x for all x in [0, 1]

(c) f ( x) = x for all x ∈ [0, 1] (d) f ( x) = x2

for all x ≥ 1






Section – III

( Assertion Reason Type)

Directions : Question number 14 to 17 are Assertion Reason type questions. Each of these

Questions contains two statements : Statement-1(Assertion) and Statement-2 (Reason). You

have four alternative choices, only one of which is correct answer. Select the correct choice.

(a) Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation for

Statement-1.

(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for

Statement-1.

(c) Statement-1 is true, Statement-2 is false. (d)Statement-1 is false, Statement-2 is true.

14. Statement-1 : f ( x) = [sin x] – [cos x] is discontinuous at

2

xπ

= where [.] represents the

greatest integer function.

Statement-2 : If f ( x) and g( x) are discontinuous at x = a then f ( x) + g( x) is discontinuous at x

= a.

15. Statement-1 : If

2

3

3 – , 1( )

1 , 1

x x f x

x x

>=

+ ≤then f ( x) is differentiable at x = 1.

Statement-2 : A function y = f ( x) is said to have a derivative if 0

( ) – ( )limh

f x h f x

h+→

+=

–0

( – ) – ( )lim–h

f x h f xh→

.

16. Let f : [0, 2π] → [–1, 1] be given by f ( x) = sin x

Statement–1 : f is periodic.

Statement–2 : A function g with domain of definition X = D(g) is said to be periodic if there

is a non zero number T such that for any x ∈ X both x + T ∈ X and x – T ∈ X

and the relation g( x) = g( x + T )

17. Let f : A → A be a one–one function where A is a finite set.

Statement–1 : f is objective.Statement–2 : A one–one function defined on a finite set is onto also.






Section – IV

(Integer Answer Type)

This section contains 6 questions. The answer to each of the questions is a single-digit

integer, ranging from 0 to 9. The bubble corresponding to the correct answer is to be

darkened in the Answer sheet.

18. Period of the function f(x) = [x] + [2x] + [3x] + …… + [nx] -nx, when n∈ N is______

19. The no. of points of non differentiability of ( )( ) min 1 , , 1 f x x x x= + − is______

20. The number of points of discontinuity of the function f ( x) =6 3

cos x x

π π

, (where [ y]

denotes the largest integer less than or equal to y in the interval)11

,10 10

π π , is

21. The number of positive integers in the range of the function f ( x) =

2

2

tan 4 tan 9

1 tan

x x

x

+ +

+

22. Let f (a) = g(a) = k and their nth derivatives f n(a), gn(a) exist and are not equal for some n.

Further, if x

( ) ( ) – ( ) – ( ) ( ) ( )lim

( ) ( )a

f a g x f a g a f x g a

g x f x→

+

−= 4, then the value of k is equal to

23. The period of [ ]4 2

cos – cos x x x xe

π π + +is [.] denotes the greatest integer function.




APEX INSTITUTE

APEX INSTITUTE FOR IIT- EE

This section contains 8

(b),(c) and (d), out of w

1. The potential drop across the

a)4V

2. Kirchoff’s first law is based o

(a) Law of conservation of energ

(c) Law of conservation charge

3. A capacitor P having capacita

capacitance of P farad is require

would bea) 1

4) Which of the following state

a) When electric field enters into

b) When electric field enters into

normal.

c) When electric field enters into

d) The component of electric fiel


/ PMT ; 9910817866 , 9990495952

PHYSICS

Section – I

ultiple choice questions. Each question has 4 c

hich ONLY ONE is correct.

0 ohm resistor is equal to

B)6V C)8V

y. (b) Law of conservation

(d) Law of conservation

nce of P farad can withstand a maximum voltage

around a battery of Emf 10V.Then the total nu

b) 5 c) 15

ent is true?

a medium of higher dielectric constant it bents t

a medium of higher dielectric constant it bents

a medium of higher dielectric constant then its

ld along the tangential surface to the dielectric is

TEST PAPER-2

Page 7

oices.(a),

D)10V

of volume

of current.

of 2 V .A net

ber of P needed

d)25

owards the normal.

way from the

agnitude decreases.

equal to zero.





5.The work done in bringing a 5 coulomb charge from the surface of a uniformly charged thin

spherical shell of potential 20V ,to its center is equal to

a)5 units b)0 units c)10 units d)20 units

6. Whenever two charged bodies are connected using a metallic wire

a) Charge flows through them till the charges on both of them are equal .

b) Charge flows through them till the potential of both are equal.

c) Charge flows through them till the force exerted by one on the other is equal to zero.

d) Charge will not flow through them.

7. Which of the following is true regarding a battery

a) Its Emf and Tpd may have different values

b) The internal resistance of a battery is due to the area of the plates

c) A battery is a source of constant potential difference

d) A battery is a source of constant charge.

8) A capacitor C was connected to a battery and then withdrawn. It was then connected to a capacitor

of equal magnitude which was initially uncharged.

a) The magnitude of charge on C will decrease

b) The energy stored in C would increase.

c) The energy supplied by the battery will get dissipated

d) The electric field intensity between the plates of C would increase.






Section – II




9. Four equal charges are kept at the four corners of a square.

a) The electric field at the intersection of diagonal will be zero.

b) There would be a total of 5 points where electric field would be zero.

c) A positive charge at the intersection of diagonal will be in equilibrium.

d) A negative charge at the intersection of diagonal will be in stable equilibrium.

10. On which of the following factors do the resistance of a wire depend

a) Temperature b) Pressure c) Length d) Luminous intensity

11. A capacitance is connected to a battery of constant potential difference V.And the absolute

permittivity of the free space started to decrease suddenly .Then which of the following is true

a) A positive work will be done by the battery.

b) Charge on the capacitor would decrease.

c) Charge on the capacitor will increase.

d) Battery will do a negative work.

12.If the potential in space is given by V=xy , where x and y are the x and y coordinates of any point

in space with respect to a fixed reference origin then which of the following is true

a) V (3,4)=12V b)x axis and y axis is the reference point

c) |E(1,2)|= 2i+j d) |E|= constant

13.Select the incorrect statement.

a)Coulomb law can be used to find the attraction between Na ion and Cl ion in NaCl molecule.

b)The net charge enclosed in a Gaussian surface is zero ,then the electric field is equal to zero.

c)The single plate containing charge can store energy.

d)An isolated sphere containing charge can store energy.






Section – III






Statement-1.


Statement-1.


14. Statement-1 A capacitor stores the total energy in form of electric field intensity.

Statement II: If a capacitor has charge on its plates then there always exists some electric field

between the plates.

15. Statement-1 If positive charge q is brought outside a closed volume then the net electric flux

through the volume will increase.

Statement II: According to gauss law net flux through a closed volume is directly proportional to

the charge enclosed.

16. Statement-1 The electric field due to a continuous charge distribution is found by taking a small

element at some general point and then integrating it over the entire distribution.

Statement II: Finding the electric field using the distance of the point where the electric field is to

be found out from the center of the charge distribution would serve the same purpose,

17. Statement-1 If four charge of equal positive magnitude are kept at the vertices of a cube and a

negative charge is placed at the body center of the cube, then the negative charge

would be in a state of stable equilibrium.

Statement II: At the body center of the cube , the electric field due to the charges at vertex would

be zero.






Section – IV





18.A battery of emf E and internal resistance r is connected to an external resistance R .The

maximum power in the external circuit is 9 W .The current flowing in the circuit under the conditions

is 3 ampere .What is the value of E. (Power=i2R)

19. If a charge of q is placed at the vertex of a cube of side a .Then the flux through the cube is equal

toq

k ο

ε

.Then the value of k is equal to.

20. Two charges one of magnitude 4C and other of magnitude -8C are kept at 10 m apart. The

distance of point P from 4C charge (in terms of nearest integer),Where the electric field would be zero

is?

21. A dipole is kept inside a cube of side a. The dipole has a charge of +4C as one of its charge.

If the net magnitude of flux through the cube is equal to k .Then the value of k is?

22. The ratio of the potential at the center and surface of a solid sphere is equal to k .Then 2k is equal

to?

23.Between two points A and B battery of potential difference 3V is connected to similar battery in

sense of regular polarity such that negative of one battery faces the positive of second. Then the

potential difference between A and B is equal to?




APEX INSTITUTE

APEX INSTITUTE FOR IIT- EE

This section contains 8

(b),(c) and (d), out of w

1. Which of the following has

a. 0.03 M AlCl3

b. 0.075 M CuSO4

c. 0.14 M sucrose

d. 0.04 M BaCl2

2. 2-Relative decrease in va

mol H2Ois 0.50. on reacti

a. 1 mol Ag Cl

b. 0.25 mol AgCl

c. 2 mol AgCl

d. 0.40 mol AgCl

3. 3. PH of a 0.1 M monoba

temperature T K is give

a. 0.1RT

b. 0.11RT

c. 1.1 RT

d. 0.01 RT

4. If relative decrease in vap

percentage ionization of N

(a)60% (b)

5 Hydrogenation of the adjoi

(a) an optically active compo

(b) an optically inactive com

(c) a racemic mixture

(d) a diastereomeric mixture

/ PMT ; 9910817866 , 9990495952

CHEMISTRY

Section - I

ultiple choice questions. Each question has 4 c

hich ONLY ONE is correct.

minimum freezing point in water . assuming (e

our of an aqueous solution containing 2 mol [C

on with AgNO3, this solution will from

sic acid is found to be 2. Hence its osmotic press

R=0.821

ur pressure is 0.4 for a solution containing 1 mol

aCl

0% (c) 100% (d) 40%

ning compound in the presence of poisoned pall

nd

ound

TEST PAPER-2

Page 12

oices.(a),

imolal=eqimolar)

(NH3)3 Cl] Cl in 3

re at a given

l NaCl in 3 mol H2O,

adium catalyst gives





6 In which of the following lone pair indicated is not involved in resonance

7 Which of the following statement are correct ? Delocolisation of electron increase molecular

stability because

(a) electron nuclei attraction increases (b) electron electron repulsion increases

(c) potential energy of the molecule increases (d) potential energy of the molecule decreases

8

.






Section – II




9. The total vapour pressure of a binary solution is given by , P=(100XA+260XB) mmHg Where

XA and XB are the mole fractions of components A and B. This indicates that the:

(a) Vapour pressure of pure AandB are 260mmHg and 100 mmHg respectively

(b) Vapour pressure of solution is less than the pure B component

(c) Vapour pressure of solution is less than the pure A component

(d) Vapour pressure of pure A is 100mmHg and that of pure B is 260 mmHg

10. The following is correct for an ideal solution?

(a) △Hmix=0 and △Vmix=0 (b) △Vmix=0 and △Smix=0

(c) △H mix ⟩ 0 and △Smix ⟩ 0 (d) △Gmix=0 and △Smix ⟩ 0

11. Which of the following Rxn products are correct?

(a) CH3Cl +AgCN → CH3CN +AgCl (b) CH3Cl +NaCN → CH3NC +NaCl

(c) CH3Cl +AgNO2 → CH3NO2 +AgCl (d) CH3Cl +NaNO2 →CH3ONO +NaCl

12. For the depression of freezing point experiment .The correct statement (s) is/ are

(a) Vapour pressure of pure solvent is more than that of solution

(b) Vapour pressure of pure solvent is less than that of solution

(c) only solute molecules solidify at freezing point(d) only solvent molecules solidify at freezing point

13.Which of the following depends on temperature

a)molarity b)normality c)formality d)molality





Section – III






Statement-1.


Statement-1.


14. Statement-1.Resonating structure of oxalate ion is four

Statement II: there are two type of deloclisation of π electrons

15. Statement-1.The freezing point of 0.05M urea solution is different from that of 0.05 NaCl solution

Statement II: The depression in freezing point is directly proportional to the number of species

present in the solution.

16. Statement-1.RCl be converted in RF by using KF ether as solvent .

Statement II: The reaction follows SN1 mechanism.

17. Statement-1.If one component obeys Raoult’s law over a certain range of composition,the other

component will not obey Henry’s law in that range.

Statement II: Raoult’s law is special case of Henry law.






Section – IV





18.The number of resonating structure of Anilinium ion?

19)25.6g of sulphur in 100g benzene shows a depression in freezing point of 5.12 degree,Kf of

benzene is 5.12 degree kg/mol . If the molecular formula of sulphur is Sx.Then the value of x is equal

to.

20.How many chiral centres are present in 6-Bromo-8-chloro-2,4,5-triethyl-decan-3oloicacid.

21.Find the total number of product that would by obtained when 2,2-Dimethylhexane react with Cl2 in

presence of sunglight?

22.At 10 degree celcius the osmotic pressure of urea solution is 500 mm.The solution is diluted and the

temperature is raised to 25 degree Celcius ,when the osmotic pressure is found to be 105.3 mm. Then

ratio of final volume to initial volume would be.

23.Number of optical isomers of tartaric acid is equal to?





Answers

Section-I(Only one Option is correct)

1. d 2.a 3.d 4.c 5. 6. 7. 8.

Section – II (Multiple Correct Answer (s) Type) 9. a,c,d 10.b,d 11.a,b 12.c 13.a,b

Section – III


14.c 15.d 16.d 17.

Section – IV


18. ( 1) 19. (5) 20. (4) 21. (9) 22. () 23. (1)

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Func+Lim+Cont+Diffe,Electro+Current,Sol+Alkyl Paper 2

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