Comp 2017 Btest-7 Set A

YOUR STRATEGIC MOVE

Date: 20th DEC 2015 Bakliwal Tutorials-IIT Comprehensive 2017 B-Test 7 Total Time: - 3.00 hrs Sub: -Physics, Math, Chemistry Max. Marks: - 270

Name of Student:- ___________________ SET NO : A

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PHYSICS SECTION - I Single Correct Answer Type

This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Marking (+4, -1) Q1. A uniform rod is kept vertically on a horizontal smooth surface at a point O. If it is rotated slightly and

released, it falls down on the horizontal surface. The lower end will remain (A) At O (B) at a distance less than 2l from O (C) at a distance 2l from O (D) at a distance larger than 2l from O

Q2. The moment of inertia of a uniform semicircular wire of mass M and radius r about a line perpendicular

to the plane of the wire through the center is:

(A) 2Mr (B) 21 Mr2

(C) 21 Mr4

(D) 22 Mr5

Q3. A mass m is moving with a constant velocity along a line parallel to the x-axis, away from the origin. Its

angular momentum with respect to the origin: (A) is zero (B) remains constant (C) goes on increasing (D) goes on decreasing Q4. Two uniform rods of equal length but different masses are rigidly joined to

form an L-shaped body, which is then pivoted about O as shown. If in

equilibrium the body is in the shown configuration, ratio Mm

will be:

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

Q5. Two moving particles P and Q are 10 m apart at a certain instant. The

velocity of P is 8 m s making an angle of 30with the line joining P and that of Q is m s making an angle 30with PQ as shown in the figure. Then angular velocity of P with respect to Q is:

(A) 0 rad s (B) 0.1 rad s (C) 0.4 rad s (D) 0.7 rad s

Q6. Let I be the moment of inertia of a uniform square plate about an axis AB that passes through its center

and is parallel to two of its sides. CD is a line in the plane of the plate and it passes through the center of the plate, making an angle with AB. The moment of inertia of the plate about the axis CD is equal to:

(A) I (B) 2I sin (C) 2I cos (D) 2I cos2

BT Tests Bakliwal Tutorials - IIT


Q7. A particle of mass ‘m’ and velocity ‘V0’ moving on a straight line 0ax by c . Then angular momentum of the particle about origin

(A) 0mV C (B)

0

2 2

mV C

a b (C) 2 2

0mV a b (D) None

Q8. A force of Fk acts on O, the origin of the coordinate system. The torque about

the point (1, -1) is: (A) F i j (B) F i j

(C) F i j (D) F i j

SECTION – II One or More than one Correct Answer(s) Type) This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE OR MORE may be correct. Marking Scheme (+5, -1) Q9. The moment of inertia of a uniform circular disc of mass M and radius R about its centre and normal to

its plane is 21 MR2

.Then

(A) its radius of gyration about the centre is R.

(B) the moment of inertia of the disc about its diameter is 21 MR4

(C) the moment of inertia of the disc about an axis passing through a point on its edge and normal to the

disc is 23 MR2

(D) the moment of inertia of the disc about a tangent in the plane of the disc is 25 MR4

.

Q10. Three forces act on a wheel of radius 20 cm as shown in fig.

(A) The torque produced by the force of 8N is 0.8 Nm clockwise about ‘O’

(B) The torque produced by the force of 4N is 0.8 Nm anticlockwise about ‘O’

(C) The torque produced by the force of 9N is zero about ‘O’

(D) The net torque produced by the forces is 1.8 Nm clockwise. about ‘O’ Q.11 The moment of inertia of a uniform disc about its diameter is I. Then the moment of inertia about an axis (A) passing through its centre and perpendicular to its plane is 2I. (B) tangential to its plane is 5I. (C) tangential and perpendicular to its plane is 6I. (D) all of the above choices are correct.

Q12. A wire of mass M, length L and density is bent to form a circular ring of radius R. Then, the moment

of inertia of the ring about its diameter is



(A) 21 MR2

(B) 4R L (C) 2

2

ML8

(D) 2 3R L

8

Q13. Which of the following statements is/are correct about a particle moving in a circle with a constant

speed? (A) The linear velocity and acceleration vectors are perpendicular to each other (B) The linear velocity vector is always perpendicular to the angular velocity vector. (C) The force acting on the particle is radial. (D) The force does no work on the particles. Q14. The position vector of a particle with respect to origin O is r

. IF the torque acting on the particle is zero,

then (A) the linear momentum of the particle remains constant (B) the angular momentum of the particle about O remains constant (C) the force applied to the particle is perpendicular to r

(D) the force applied to the particle is parallel to r

. Q.15. The moment of inertia of a thin square plate ABCD, of uniform thickness about

an axis passing through the centre O and perpendicular to the plane of the plate is

(A) 1 2I I (B) 3 4I I (C) 1 3I I (D) 1 2 3 4I I I I Where I1, I2, I3 and I4 are respectively moments of inertia about axes 1, 2, 3, and 4 which are in the plane of the place.

Q16. The axis of rotation of a purely rotating body (A) Must pass through the centre of mass (B) May pass through the centre of mass (C) Must pass through the body (D) May pass through the body

SECTION - III Integer Type This section contains 4 integer type questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Marking (+5, 0) Q17. A disc in YZ plane, of mass 20 kg and radius 10 cm can rotate about a fixed horizontal axis (X axis)

passing through its centre of mass if the disc is pulled downwards with a tangential force of 5N then its angular acceleration is

Q18. A thin uniform circular disc has a radius R. A square portion of diagonal equal to

R is cut out from it. The distance between the centre of mass of the remaining

portion of the disc from the centre of the complete disc is

Rn 2 1

.

Then n is ………….



Q19. Two circular loops A and B of radii R and 2R respectively are made of the same wire. Their moments of inertia about the axis passing through the centre and perpendicular to their plane are AI and BI

respectively. Then ratio B

A

II

is ………….

Q.20 A mass is whiled in a circular path with constant angular velocity and its angular momentum is L. If the

string is now halved keeping the angular velocity the same, the angular momentum is Ln

. Then n is …

MATHEMATICS SECTION - I Single Correct Answer Type

This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Marking (+4, -1) Q 1. If is a complex root of z3 = 1, then |1 + 2 + 32| = (A) 1 (B) 2 (C) 3 (D) 13 Q 2. The rat io of the areas of two circles at the centre of which two arcs of the same lengths

subtends angle of 45º and 60º is: (A) 4/3 (B) 3/4 (C) 16/9 (D) 9/16 Q 3. If the circle 2 2 2 2 0x y gx fy c bisects the circumference of the circle

2 2 2 2 0,x y g x f y c then (A) 2 ( ) 2 ( )g g g f f f c c (B) 2 ( ) 2 ( )g g g f f f c c (C) 2 ( ) 2 ( )g g g f f f c c (D) 2 ( ) 2 ( ) .g g g f f f c c

Q 4. 5

6 62 , ,i ii

e e e

form a (A) scalene triangle (B)right angle triangle

(C) equilateral triangle (D) right angle isosceles Q 5. z1, z2 represents any two points A, B in the Argand plane such that OA = OB = 2, where O is the origin

and Arg (z1/z2) = /3, Then in the triangle OAB the distance of any vertex, from the orthocentre of the triangle is

(A) 23

(B) 32

(C) 13

(D) 3

Q 6. If w is an imaginary cube root of unity, then the value of

2 2 2cos[{(1 )(1 ) (2 )(2 ) .......(10 )(10 )} ]900

w w w w w w

(A) 0 (B) 1 (C) –1 (D) 12

Q 7. Consider the following three statements (A) If z is any complex number then |z| = zz (B) If z is any complex number which is purely real then |z| = max {–z, z }.



(C) If z represents any point in the Argand plane and z1, z2 are any two fixed points such that

1

2

z zz z

, then locus z is always circle

(A) (a) is true but (b), (c) are false (B) (b) is true but (a), (c) are false (C) (a), (b) are true but (c) is false (D) (a), (b), (c) are true. Q 8. If ax2 + bx + 6 = 0 (aR+ – {0} & bR) does not have two distinct real roots, then the least value of 3a +

b is (A) 4 (B) – 1 (C) 1 (D) – 2

SECTION – II One or More than one Correct Answer(s) Type)

This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE OR MORE may be correct. Marking Scheme (+5, -1)

Q 9. If z is a complex number such that Re z 1z 1

= 0, then

(A)

11 i tan Arg z2z

11 i tan A r g z2

(B) |z| = 1

(C) z lies on the circle x2 + y2 = 1 (D) none of these

Q 10.The value of 6

1

2 2sin cos7 7k

k ki

is

(A) – 1 (B) 0 (C) – i (D) i Q 11. The solution of inequality

2 2sin x cos x(81) (81) 18 is (A) n + /3 (nz) (B) n + /4 (nz) (C) n – /4 (nz) (D) n + /8 (nz) Q 12. If the equation ax2 + bx + c = 0 (a > 0) has two real roots and such that < 2 and

> 2, then (A) b2 – 4ac < 0 (B) c < 0, b2 – 4ac > 0 (C) a – |b| + c < 0 (D) 4a – 2 |b| + c < 0 Q 13. If the length of transverse common tangent of the circle x2 + y2 = 1 and (x – )2 + y2 = 1 is 2 3 , then the

can be (A) –2 (B) 2 (C) –4 (D) 4 Q 14. The inequality |z – 4| < | z – 2| represents: (A) Re(z) > 0 (B) Re(z) < 0 (C) Re (z) > 4 (D) Re(z) > 3 Q 15. If z sat isfies the inequality |z – 1 – 2i| ≤ 1, then (A) min (arg (z)) = tan–1 (3/4) (B) max (arg(z)) = π/2 (C) min (|z|) = 5 – 1 (D) max (|z|) = 5 + 1



Q 16. If 1Z lies on 1Z and 2Z lies on 2Z , then

(A) 1 23 2 5Z Z (B) 1 21 3Z Z (C) 1 23 5Z Z (D) 1 2 1Z Z

SECTION – III- Integer Type This section contains 4 integer type questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Marking (+5, 0) Q 17. LET A1, A2, A3, …. , A51 are fifty one arithmetic means inserted between the numbers a and b. If value

of 51 1

51 1

b A A ab A A a

is M, then remainder when M is divided by 10 is

Q 18. Find the radius of the circle (2 3 ) (2 3 ) 4 0zz i z i z . Q 19. Find the number of integral values of k for which x2 – 2(4k – 1)x + 15k2 – 2k – 7 0 holds for all x. Q 20. Let a, b, c, d are four distinct real numbers and they are consecutive terms of an arithmetic progression. If

2(a –b) + x(b – c)2 + (c – a)3 = 2 (a – d) + (b – d)2 + (c – d)3, then if the least positive integral value of x is M. Find the sum of digits of M.

CHEMISTRY SECTION - I Single Correct Answer Type

This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Marking (+4, -1) Q1. Light can be used to excite electrons enough to remove an electron from a molecule. When light of an

appropriate frequency is shined on oxygen, the O O bond becomes stronger despite the loss of an electron. This is because: (A) Losing an electron always result in an increase in bond strength because the positively charged ion

produced holds the electrons it has more strongly. (B) The light removes an electron from a bonding orbital, increasing the bond order and bond strength. (C) The light removes an electron from an antibonding orbital, increasing the bond order and bond

strength. (D) None of these.

Q2. Correct IUPAC name of the following compound is:

a) 3-(Hepta-2, 4,6-trienyl)-4-bromo cyclopenta-2,4,-dien-1-ol b) 7-(2-Bromo-4-hydroxy cyclopenta-1, 4-dienyl) hepta-1,3,5-triene c) 7-(5-Bromo-3-hydroxycyclopenta-1,4-dienyl) hepta-1,3,5-triene d) 3-Bromo-4-(hepta-2,4,6-trienyl) cyclopenta-2,4-dien-1-ol

Q3. Which of the following statements is correct? (A) Noble gases are insoluble in water (B) The solubility of noble gases in water is fairly high due to London dispersion force (C) The solubility of noble gases increases with the decrease in size of the noble gas atom (D) The solubility of noble gases in water is fairly high due to dipole-induced dipole interaction.



Q4. The correct IUPAC name of the compound is:

2 3

2 2 2 3

Me|

Et C CH CH CH CH|

Et CH CH CH CH CH

(A) 5,6 Diethyl 3 methyldec 4 ene (B) 5,6 Diethyl 8 methyldec 6 ene (C) 6 Butyl 5 ethyl 3 methyloct 4 ene (D) 2,4,5 Triethyl 3 nonene

Q5. It was observed that when a gas was heated from 300K to 600K, the molar specific heat of the gas at any

temperature ‘T’ was found to be 2 .600T JC mol K

. Then find the change in Entropy (in J/K) for the

process.

(A) 1.82 (B) 1.89 (C) 2.4 (D) 2.8

Q6. Consider the following P vs T graph for a reversible process performed on a fixed amount of ideal gas.

Then find the point at which the volume of the gas would be maximum.

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

Q7. Consider the following concentration vs time graph for the equilibrium:

A nB . Then, find the value of the equilibrium constant Kc for the

reaction.

(A) 74

(B) 1 (C) 274

(D) None of these

Q8. The equilibrium constant Kp for the reversible reaction 2 2s g gS O SO is 4. Then find the moles of

solid Sulphur that would precipitate in a constant volume container, if initially it was filled with SO2 gas at a pressure of 10 atm.

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

SECTION - II Multiple Correct Answer Type

This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Marking (+5, -1)



Q9. Select the correct statement(s): (A) Mn Od in 4MnO is less than that in 2

4MnO (B) O Od in 2 2O F is almost same with that in 2O molecule (C) P Fd is greater than P Cld in 2 3PF Cl (D) All Cl Fd in 3ClF are equal. Q10. Which of the following structure/s are not the correct structure of 3-Ethyl-5,5-diisopropyl-7-methylnonane

Q11. Select the correct statement (A) Alcohols are insoluble in water (B) 2KHCl exist but 2KHF does not. (C) Hydrogen bond is merely an electrostatic force rather than a chemical bond (D) Density of water is less than ice. Q12. Select the incorrect statement(s):

is 2 2 Methylbutyl cyclohexan 1 ol (A) IUPAC name of (B) IUPAC name of 1 cyclopropylbutane

is 2 Amino 3 cyclopent 2 enyl propan 1 ol (C) IUPAC name of



(D) IUPAC name of

2 2

COOH|

HOOC CH C CH COOH|

OH

is 3 Carboxy 3 hydroxypentane 1,5 dioic acid

Q13. For a reversible reaction 0 200 calH mol , it was observed that at 100K the value of the equilibrium

constant was 10. Then which of the following values can be the possible values for K at any other temperature ?

(A) 2 (B) 20 (C) 200 (D) 2000

Q14. Which of the following statements is true?

(A) Absolute Enthalpy of elements in their most stable state is zero.

(B) If KP = KC for all temperatures for an equilibrium reaction then changing pressure does not affect the equilibrium composition.

(C) At equilibrium, the rate constant of the forward reaction is equal to the rate constant of the backward reaction.

(D) If ambient pressure is changed at a constant temperature, then the vapour pressure of the liquid also changes.

Q15. Consider the reversible process

20 calH mol 22 2 44 2g g g gCO H CO H O .

What should be the conditions of pressure and temperature for which maximum methane would be produced?

(A) high P (B) high T (C) low T (D) low P

Q.16 In presence of a catalyst, what happens to an equilibrium reaction.

(A) Energy of activation changes for both forward and backward reactions

(B) The equilibrium composition remains unchanged due to the addition of catalyst.

(C) Catalyst can change the rate of forward as well as backward reactions

(D) Catalyst cannot change the time required for the equilibrium to be achieved.



SECTION - III Integer Type This section contains 4 integer type questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Marking (+5, 0)

Q17. The sum of total no of 2 and 3 H atoms in 2,5,6 Trimethyloctane is ____. Q18. The sum of the number of d orbitals whose lobes are available along the axis and are involved in the

hybridization of central atoms of 5XeF and 5XeF is _____. Q19. For the reaction 2( ) 2( ) ( ) 2 ( )g g g gCO H CO H O , K is 0.63, at 700o C and 1.66 at 1000o C. The

average oH for the temperature range considered is:

Q20. Ammonium carbamate, when heated, gives a mixure of vapours as 2 4 3 22NH COONH NH CO .

The vapour density of the mixture was 17.7. If ‘x’ is the degree of dissociation, then the integer closest to 10x is:

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Comp 2017 Btest-7 Set A