Sec: XII-IIT Assignment-06 Date: 10-03-2021 Physics

Narayana IIT Academy XII–IIT–ASSIGNMENT-PCM

NARAYANA IIT/NEET ACADEMY

1

Sec: XII-IIT Assignment-06 Date: 10-03-2021

Physics : Current Electricity

Single Correct 1. The Charge on a capacitor of capacitance 10 F connected as shown in the figure:-

(A) 20 C (B) 14 C (C)10 C (D) zero

2. The temperature of a metal wire rises when a electric current passes through it because :

(A) Collision of a metal atoms with each other releases heat energy

(B) Collision of conduction electrons with each other release heat energy

(C) When the conduction electrons fall from higher energy level to a lower energy level heat energy

is released

(D) Collision of conduction electrons with the atoms of the metal gives them energy which appears

as heat.

3. The metallic block has no potential difference applied across it,then the mean velocity of free

electrons :

(A)Proportion to T (B) Proportional to T

(C)Zero (D) Finite but independent of temperature

4. All bulbs in the circuit shown in the figure are identical. Which bulb glows most brightly?

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

5. The drift velocity of free electrons in a conductor is v, when a current i is flowing in it. If both the

radius and current are doubled, then the drift velocity will be :

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

6. In the circuit shown in the figure when the switch is closed, the initial current through the 1 resister

just after closing the switch is



2

(A) 2A (B) 4A (C) 3A (D) 6A

7. In the shown network charges in capacitors are same, then 1

2

C

Cis

(A) 5

3 (B) 1:1 (C) 1:3 (D) 1:5

8. A capacitor is charged up to V volts. The space between two plates of capacitor is filled with

dielectric medium of constant K and conductivity . The time after which charge on capacitor

becomes 1

etimes its initial charge is

(A) 0K

(B) 0

K

(C)

2k

(D) 0

2

k A

d

9. AB is a wire of uniform resistance. The galvanometer G shows no current when the length AC = 20

cm and CB = 80 cm. The resistance R is equal to

(A) 2 (B) 8 (C) 20

(D) 40

10. An electric bulb rated 220 V, 100 W is connected in series with another bulb rated 200 V, the power

consumed by the 100 W bulb will about

(A)25 W (B) 14 W (C) 60 W (D) 100 W

11. A group of N cells whose emf varies directly with the internal resistance as per the equation

1.5N NE r are connected as shown in the figure below. The current I in the circuit is



3

(A) 0.51 A (B) 5.1 A (C) 0.15 A (D) 1.5 A

12. The total current supplied to the circuit by the battery is

(A) 1 A (B) 2 A (C) 4 A (D) 6 A

13. What is equivalent time constant of RC circuit shown in figure

(A) 1.5 RC (B) 3 RC (C) 2 RC (D) 2

RC

14. Find the ratio of currents as measured by ammeter in two cases when the key is open and when the

key is closed

(A) 9/8 (B) 10/11 (C) 8/9 (D) None of the above

15. Two resistances are connected in two gaps of a metre bridge. The balance point is 20 cm from the

zero end. A resistance of 15 is connected in series with the smaller of the two. The null point

shifts to 40 cm. Then the value of the smaller resistance is :

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

16. Two batteries one of the emf 3V, internal resistance 1 and the other of emf 15 V, internal

resistance 2 are connected in series with a resistance R as shown in figure. If the potential

difference between a and b is zero, the resistance R is :



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(A) 5 (B) 7 (C) 3 (D) 1

17. The deflection in a galvanometer falls from 50 divisions to 20 divisions, when a 12 shunt is

applied the galvanometer resistance is

(A) 18 (B) 24 (C) 30 (D) 36

18. A 1 F capacitor is connected in the circuit shown below. The EMF of the cell is 3V and internal

resistance is 0.5 .The resistors 1R and

2R have values 4 and 1 respectively .The charge on the

capacitor in steady state is

(A)1 C (B) 2 C (C)1.33 C (D) Zero

19. A Charged capacitor is allow to discharge through a resistor by closing the key at the instant t=0. At

the instant t=ln (4) s , the reading of the ammeter falls half the initial value. The resistance of the

ammeter is equal to

(A) 0.5 (B) 1 (C) 2 (D) 4

20. The potential difference A BV V between points A and B for the circuit segment shown in figure at

the given instant is

(A) 12 V (B) -12V (C) 6V (D) -6V

21. A battery of internal resistance 4 is connected to the network of resistances as shown. In order to

give the maximum power to the network, the value of R (in ) should be



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(A) 4/9 (B) 8/9 (C) 2 (D) 18

22. The charge flowing through a resistor R varies as Q 2Q t t t .The total heat produced is R is:

(A)3R

(B)

3

2

R

(C)

3

3

R

(D)

3

6

R

23. The cell of internal resistance r is connected to a load of resistance R. Energy is dissipated in the

load, but some thermal energy is also wasted in the cell. The efficiency of such an arrangement is

found from the expression

in

in

Energy dissipated theload

Energy dissipated thecompletecircuit

Which of the following gives the efficiency in this case?

(A)r

R (B)

R

r (C)

r

R r (D)

R

R r

24. Figure shows a network of three resistances. When some potential difference is applied across the

network, thermal powers dissipated by A,B and C are in the ratio

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

25. The energy stored in the capacitor in the steady state is

(A) 338 J (B) 196 J (C) 98 J (D) 8 J

26. What is the charge stored on each capacitor 1C and 2C in the circuit shown in figure?

(A) 6 C , 6 C (B) 6 C , 3 C (C)3 C , 6 C (D)3 C ,3 C

27. An infinite ladder network is arranged with resistances R and 2 R as shown. The effective resistance

between terminals A and B is



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(A) (B) R (C) 2 R (D) 3 R

28. The effective resistance between points P and Q of the electrical circuit shown in the figure is

(A) 2Rr/(R+r) (B) 8R(R+r)/ (3R+r) (C) 2r+4R (D) 5R/2+2r

29. In the given circuit, with steady current, the potential drop across the capacitor must be

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

30. Find out the value of current through 2 resistance for the given circuit

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

31. Find the effective resistance between the points A and B in figure.

32. In the circuit shown in figure, find the value of unknown resistor R.

33. When two identical batteries of internal resistance 1 each are connected in series across a resistor

R, the rate of heat produced in R is 1J .When the same batteries are connected in parallel across R,

the rate is 2J .If 1 2.25J 2J then the value of R in is.



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34. The ammeter current in the circuit shown in figure is 1

x.Find the value of x.

35. Compute the value of battery current in the circuit shown in figure. All the resistances are in ohm.

36. In the meter bridge circuit shown in figure . Find the length AC (in cm) at null deflection in

galvanometer.

37. Find the current in 5 resistance in circuit shown in figure:-

38. Find the velocity of charge carriers in 1A current in copper conductor of cross –section 21cm and

length 10 km. Free electron density of copper is 288.5 10 per 3m . How long (in years) will it take the

charge to travel from one end of the conductor to the other?

39. For what value of battery voltage E the potential of A is equal to the potential of B?

40. What shunt resistance is required to make the 1.00 mA, 20 galvanometer into an ammeter with a

range of 0 to 50.0 mA?



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CHEMISTRY : ElectroChemistry

1. The standard oxidation potentials, oE for the half- reaction are as

2 2Zn Zn e ; 0.76oE V

2 2Fe Fe e ; 0.41oE V the

o

cellE is :

2 2Fe Zn Zn Fe is :

(A) – 0.35 V (B) + 0.35 V (C) + 1.17 V (D) – 1.17 V

2. oE for some half cell reactions are given below

4 22 ; 0.151oSn e Sn E V

2 2

22 2 ; 0.92oHg e Hg E V

2

2 24 2 2 ; 1.45oPbO H e Pb H O E V

based on the given data which statement is correct

(A) 4Sn

is a stronger oxidizing agent than 4Pb (B)

2Sn is a stronger reducing agent than

2

2Hg

(C) 2Hg is strong oxidizing agent than 4Pb (D) 2Pb is a stronger reducing agent than 2Sn

3. The standard reduction potentials at 25 oC for the following half reactions are given against each –

2 ( ) 2 ,Zn aq e Zn s –0.762 V

3 3 ,Cr aq e Cr s –0.740 V

22 2 ,H e H g 0.00 V

3 2Fe e Fe 0.77 V

Which is the strongest reducing agent -

(A) Zn (B) Cr (C) 2H g (D) 3Fe aq

4. The standard reduction potential for and electrodes are and V

respectively. For the cell reaction, , the standard e.m.f. is:

(A) + 0.30 V (B) 0.58 V (C) + 0.58 V (D) 0.30 V

5. The standard potential of 2Cu

/Cu and 2 /Cu Cu

are 0.337 and 0.153 respectively. The standard electrode

potential of /Cu Cuhalf- cell is -

(A) 0.184 V (B) 0.827 V (C) 0.521 V (D) 0.490 V

6. The standard electrode potential for the reactions,

Ag aq e Ag s

2 2Sn aq e Sn s

at 25 oC are 0.80 volt and –0.14 volt, respectively. The emf of the cell

2| 1 || 1 |Sn Sn M Ag M Ag is -

(A)0.66 Volt (B) 0.80 Volt (C)1.08 Volt (D) 0.94 Volt



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7. A very thin copper plate is electro – plated with gold using gold chloride in HCl. The current was

passed 20 minutes and the increase in the weight of the plate was found to be 2g.[Au = 197]. The

current passed was

(A) 0.816 amp (B) 1.632 amp (C) 2.448 amp (D) 3.264 amp

8. In the electrolysis of an aqueous 2SnCl

solution ,4.48 L of chlorine at STP were liberated at the

anode. The mass of tin deposited at the cathode was (M of Sn = 118.5).

(A)119 g (B) 79.3 g (C) 47.4 g (D)23.7 g

9. Electrolytic reduction of 6.15 g of nitrobenzene using a current efficiency of 40 % will require

which of following quantity of electricity.[C= 12, H = 1, N=14, O= 16]

(A) 0.75 F (B) 0.15 F (C) 0.75 C (D) 0.125 C

10. Two aqueous solution A and B containing solute 4CuSO and NaBr respectively were electrolysed

using platinum electrodes. The pH of the resulting solutions will show a/an

(A) Increase in both the solutions (B) Decrease in both the solutions

(C) Increase in A and decrease in B (D) Decrease in A and increase in B

11. The EMF of the cell,

Zn | Zn2+ (0.01M) | | Fe2+ (0.001M) | Fe

at 298 K is 0.2905 then the value of equilibrium constant of the cell reaction is

(A) 0.32

0.0295e (B) 0.32

0.029510 (C) 0.26

0.029510 (D) 0.32

0.059110

12. Resistance of 0.2 M solution of an electrolyte is 50 . The specific conductance of the solution is 1.4

S m–1. The resistance of 0.5 M solution of the same electrolyte is 280 . The molar conductivity of

0.5 M solution of the electrolyte in S m2 mol–1 is

(A) 5 × 102 (B) 5 × 10–4 (C) 5 × 10–3 (D) 5 × 103

13. Four alkali metals and are having respectively standard electrode potential as

Which one will be the most reactive?

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

14. The highest electrical conductivity of the following aqueous solution is of

(A) 0.1 M acetic acid (B) 0.1 M chloroacetic acid

(C) 0.1 M fluoroacetic acid (D) 0.1 M difluoroacetic acid

15. A student made the following observations in the laboratory:

(i) Clean copper metal did not react with 1 molar Pb(NO3)2 solution

(ii) Clean lead metal dissolved in a 1 molar AgNO3 solution and crystals of Ag metal appeared

(iii) Clean silver metal did not react with 1 molar Cu(NO3)2 solution.

The order of decreasing reducing character of the three metals is:

(A) Cu, Pb, Ag (B) Cu, Ag, Pb (C) Pb, Cu, Ag (D) Pb, Ag, Cu

16. The time required to coat a metal surface of 80 cm2 with 5 10-3 cm thick layer of silver (density

1.05 g cm-3) with the passage of 3A current through a silver nitrate solution is:

(A) 115 sec (B) 125 sec (C) 135 sec (D) 145 sec



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17. The variation of equivalent conductance of weak electrolyte with concentration is correctly shown in fig

(A)

Y

X C

(B)

Y

X C

(C)

Y

X C

(D)

Y

X C

18. One ampere of current is passed for 9650 second through molten AlCl3. What is the weight in grams of Al

deposited at cathode? (Atomic weight of Al = 27)

(A) 0.9 (B) 9.0 (C) 0.18 (D) 18.0

19. What is the standard reduction potential (E°) for 3Fe Fe ?

Given that :

2

3 2

2 0

Fe /Fe3 2 0

Fe /Fe

Fe 2e Fe;E 0.47V

Fe e Fe ;E 0.77V

(A) + 0.057V (B) + 0.30 V (C) – 0.30 V (D) – 0.057V

20. Which of the following expression is correct?

(A) (B)

(C) (D)

21. The potential of a hydrogen electrode at pH = 10 is

(A) 0.59 V (B) 0.00 V (C) –0.59 V (D) –0.059 V

22. Which of the following statements about a salt bridge in a voltaic cell is TRUE ?

(A) Free electrons flow through the salt bridge to maintain electrical neutrality in the two half cells.

(B) The salt bridge allows the ions present in the two half- cells to mix extensively

(C) The wire must be connected directly to the salt bridge, in order to maintain electrical neutrality

in the two half cells.

(D) Ions from the electrolyte in the salt bridge flow into each half-cell to maintain electrical

neutrality

23. In acidic medium is converted to . The quantity of electricity in faraday required to

reduce 0.5 mole of to would be

(A) 2.5 (B) 5 (C)1 (D) 0.5

24. Each of the three metals and were put in turn into aqueous solution of the other two.

+ Salt of (or + Salt of Which observation is probably incorrect?

(A) No action observed (B) Nothing can be decided



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(C) (D) No action observed

25. The molar conductivities of KCl, NaCl and are 152, 128 and 111 S respectively.

What is the molar conductivity of ?

(A) 101 S (B) 87 S (C) -101 S (D) -391 S

26. The number of coulombs required to reduce 12.3 g of nitrobenzene to aniline is

(A) 115800 C (B) 5790 C (C) 28950 C (D) 57900 C

27. A solution of sodium sulphate in water is electrolysed using inert electrodes. The products at the

cathode and anode are respectively

(A) 2 2,H O (B) 2 2,O H (C) 2 ,O Na (D) 2 2,O SO

28. Which of the following reactions is correct for a given electrochemical cell at 25 ℃?

(A)

(B)

(C)

(D)

29. What is the effect of dilution on the equivalent conductance of strong electrolyte?

(A) Decreases on dilution (B) Remains unchanged

(C) Increases on dilution (D) None of these

30. The corrosion of iron object is favoured by :

(A) Presence of ion

(B) Presence of moisture in air

(C) Presence of impurities in iron object

(D) All of the above

31. Equivalent conductance of 0.2M (aq.) solution of a weak monobasic acid HA, is 2 110S cm eq and

that at infinite dilution is 2 1200S cm eq . What is the pH of the solution ?

32. How many faradays of electricity is required for electrolysis of 72 gm of acidified water.

33. If an aq. NaCl solution is electrolyzed using a current of 5A for 200 min, volume of 2Cl gas in L

produced under STP conditions is ____ (F= 96500 C)

34. How many faradays are needed to reduce 1 mole of 4MnO to

2+Mn ?

35. A cell is to be constructed to a redox change : 3 22 3Cr Cr Cr .The number of cells with

different oE and ‘n’ but same value of

oG can be made (Given,

3 2 3/ /0.40 , 0.74o o

Cr Cr Cr CrE V E V and 2 /

0.91o

Cr CrE V )

36. Calculate the EMF of a Daniel cell when the concentration of 4ZnSO and 4CuSO are 0.001 M and

0.1M respectively. The standard potential of the cell is 1.1 V.



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37. How long (in sec.) a current of 2A has to be passed through a solution of 3AgNO to coat a metal

surface of 280cm with 5 m thick layer ? Density of silver = 310.8 /g cm

38. The temperature coefficient of a given cell P

E

T

is 4 11.5 10 VK at 300 K. The change in entropy

(in J/K) of cell during the course of reaction,

2 2Pb s HgCl aq PbCl aq Hg l

39. A current of 0.2 A is passed for 10 minutes through 30.05dm of 0.1 M NaCl. If only Chlorine is

produced at anode and water is reduced to 2H at cathode , What is the OH concentration in the

solution after electrolysis.

40 The resistance of a10

NKCl solution is 250calculate the specific conductance and the equivalent

conductance of the solution if the electrodes in the cell are 7cm apart and each has an area of 7 sq.

cm..



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MATHS : Vector & 3D

1. A vector of magnitude 3, bisecting the angle between the vectors a = 2i + j – k and b = i – 2j + k and m

aking an obtuse angle with b is

(A) 6

j–i3 (B)

14

k2–j3i (C)

14

)k2–j3i(3 (D)

10

j–i3

2. In a triangle ABC, I is the in centre. If BC = , CA = , AB = , then

IA +

IB +

IC is equal to

(A) zero vector (B) ()

IA (C) ()

IB (D) ()

IC

3. If vectors

AB= – 3i + 4

k and

AC =5i – 2

j + 4

k are the sides of a ABC, then the length of

the median through A is

(A) 14 (B) 18 (C) 29 (D) 5

4. When a right handed rectangular Cartesian system oxyz is rotated about the z-axis through an angle

4

in the counter-clockwise direction it is found that a vector

a has the components 22 , 23 and 4.

The components of a in the oxyz coordinate system are

(A) 5, –1, 4 (B) 5, –1, 4 2 (C) –1, –5, 4 2 (D) None of these

5. For any four points P, Q, R, S,

QSRPPSQR–RSPQ is equal to 4 times the area of the triangle

(A) PQR (B) QRS (C) PRS (D) PQS

6. For any vectorp , the vector

2

3{|

p ×

i |2 + |

p ×

j |2 + |

p ×

k |2} is

(A) (p )2 (B) 2(

p )2 (C) 3(

p )2 (D) 4(

p )2

7. If three non-zero vectors

a ,

b ,

c are such that

a ×

b = 2

a ×

c , |

a | = |

c | = 1, |

b | = 4 and the angle

between

b and

c is cos–1

4

1 then

b – 2

c =

a , where is equal to :

(A) ± 2 (B) ± 4 (C) 2

1 (D)

4

1

8. a

, b

, c

are three non-coplanar vector such that ]cba2cbacba[

= k ]cba[

then k is

(A) 3 (B) –3 (C) 2 (D) 6

9. If a ,

b ,

c are three non-coplanar vector

r,q,p and are reciprocal vectors, then

ncmba .

nrmqp is equal to

(A) 2 + m2 + n2 (B) m + mn + n

(C) 0 (D) None of these

10. If a

, b

, c

represents adjacent edges of parallelopiped then its volume is

(A) 3

22 (B)

3

22 (C) 4 2 (D)

3

2



14

11. If a

, b

, c

represents adjacent edges of tetrahedron such that | a

| = | b

| = | c

| = 2 and angle between

a

and b

is /3, b

and c

is /3 and a

and c

is /3 then its volume is

(A) 4 2 (B) 3

2 (C)

3

22 (D)

3

22

12. Vector perpendicular to i – j – k and in the plane of i + j + k and – i + j + k is

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

13. If a = (5

î –

^j +

^k );

b = 2

î – 3

^j –

^k ; c =–3

î +

^j +

^k and d = 2

^j +

^k , then the value of

d . [a × (

b × c × d )] is equal to

(A) 100 (B) 99 (C) 98 (D) 96

14. If

x and

y are two non-collinear vectors and ABC is a triangle with sides a, b, c satisfying

(20a – 15b)

x + (15b – 12c)

y + (12c – 20a) (

x ×

y ) = 0. Then ABC is

(A) an acute angled (B) an obtuse angled (C) a right angled (D) isosceles

15. Let

r be a unit vector satisfying

r ×

a =

b , where |

a | = 3 and |

b | = 2 , Then

(A)

r = 3

2(

a +

a ×

b ) (B)

r = 3

1(

a ×

b ±

a )

(C)

r = (

a ×

b ± a ) (D)

r = (

b ±

a ×

b )

16. Let a

and b

are two perpendicular unit vectors. If c

is another unit vector equally inclined at angle

to the vectors a

and b

, then the set of exhaustive values of in

[0, 2] is

(A)

2,0 (B)

4,0 (C)

4

3,

2 (D)

4

3,

4

17. Let the unit vector a &

b are perpendicular and the moduli vector

c inclined at an angle to

a &

b . If

c =

a + m

b + n(

a +

b ) then

(A) =n (B) n2 = 1 – 22 (C) n2 = cos 2 (D) m2 = 1 cos 2

4

18. If a =

î + 2

^j + 4

^k ,

b = 2

î – 3

^j +

^k ,

c =

î + 4

^j – 4

^k , then the vector

a × (

b ×

c ) is orthogonal to -

(A) a (B)

b (C)

c (D)None of these

19. If a

, b

, c

are non-coplanar vectors and r

be any vector in the space then

[ b

c

r

] a

+ [ c

a

r

] b

+ [ a

b

r

] c

=

(A) [ c

a

b

] r

(B) 2[ a

b

c

] r

(C) 2[ a

b

c

] r

(D) [ b

c

a

] r



15

20. A parallelogram is constructed on vectors a

= 3

–

, b

=

+ 3

if |

| = |

| = 2, and angle

between

and

is 3

, then length of a diagonal of parallelogram is

(A) 54 (B) 2 3 (C) 74 (D) None of these

21. If a

and b

are unequal unit vectors such that ba)]ba2()ab[()ba(

then smaller angle

between a

and b

is

(A) 2

(B) 0 (C) /3 (D) /4

22. The lines r

= i – j + (2i + k) and r

= (2i – j) + (i + j – k) intersect for

(A) = 1, = 1 (B) = 2, = 3 (C) all values of and (D) no value of and

23. The shortest distance between a diagonal of a cube of edge-length one unit and the edge not meeting

it, is

(A) 3

1

(B)

2

1 (C) 2 (D) None of these

24. Angle between one diagonal of a cube and a diagonal of one face is-

(A) cos–1

6

2 (B) cos–1

6

4 (C) cos–1

2

1 (D) Not defined

25. ABC is a triangle A = (2, 3, 5), B = (–1, 3, 2) and C = (, 5, ). If the median through A is equally

inclined to the axes, then

(A) = = 5 (B) = 5, = 7 (C) = 7, = 10 (D) = 0, = 0

26. The direction cosines of two lines are related by + m + n = 0 and a2 + bm2 + cn2 = 0. The lines

are parallel if a–1 + b–1 + c–1 equals

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

27. The direction cosines of a line satisfy the relation ( + m) = n, mn + n + m = 0.

The value of , for which the two lines are perpendicular to each other is-

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

28. If the lines 1

2–x=

1

3–y=

4–z and

1–x =

2

4–y =

1

5–z intersect at a point (), then

(A) = –1 (B) = 2 (C) = –3 (D) None of these

29. The co-ordinates of a point on the line 2

1x =

3

1y

= z at a distance 4 14 from the point (1, –1, 0)

are

(A) (–9, –13, 4) (B) (8 14 + 1, –12 14 – 1, 4 14 )

(C) (–7, 11, –4) (D) (–8 14 + 1, 12 14 – 1, – 4 14 )

30. Let PN be perpendicular from point P(1, 2, 3) to xy plane if OP makes an angle with positive

direction of z- axis and ON makes an angle with positive direction of x- axis, where O is origin

( are acute angles), then



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(A) sin sin = 1

14 (B) cos cos =

14

1

(C) tan = 3

5 (D) None of these

Integer Type Questions

31. A horizontal plane 4x – 3y + 7z = 0 is given. A line of greatest slope passes through the point

(2, 1, 1) in the plane 2x + y –5z = 0. Find the greatest integral value of x + y + z if P (x, y, z) lies on

line as well as on first plane.

32. The plane ax + by = 0 is rotated through an angle about its line of intersection with the plane

z = 0. If the equation of plane in new position is ax + by ± z 22 ba tan + c = 0. Find c.

33. If equation of the plane through the straight line 5

z

3

2y

2

1x

and perpendicular to the plane x – y

+ z + 2 = 0 is ax – by + cz + 4 = 0, then find the value of 342

c10b10a10 23 .

34. If the reflection of the point P(1, 0, 0) in the line 8

10z

3

1y

2

1x

is (). Find – ( + + )

35. If the planes x – cy – bz = 0, cx – y + az = 0 and bx + ay – z = 0 pass through a straight line, then

find the value of a2 + b2 + c2 + 2abc

Numerical Based Questions

36. Let OA= a

, OB= 2 a

+ 10 b

, OC = b

where O, A, C are non collinear points. Let denote the area of

the quadrilateral OABC. Let m denotes the area of parallelogram with OA and OC as adjacent sides.

If = 2m then find the value of .

37. A plane passes through the point (1,1,1) cuts the coordinate axes at A,B & C respectively such that

OA = OB = OC, where O is the origin and volume of tetrahedron OABC is then value of is equal

to

38. Let A(1, 1, 1), B(2, 3, 5), C(–1, 0, 2) be three points, then equation of a plane parallel to the plane

ABC which is at a distance 2 is 2x – 3y + z + 2 = 0 , then equals

39. If the locus of a point, the sum of squares of whose distances from the planes:

x –z = 0, x –2y + z = 0 and x + y + z = 0 is 36 is x2 + y2 + z2 = 2k , then k equals

40. The tangent of the angle between a diagonal of a cube and the diagonal of a face (which meets the

former) is

Documents

Sec: XII-IIT Assignment-06 Date: 10-03-2021 Physics