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Signs of hope in Pakistan

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6 signs of hope in Pakistan
Any pessimistic view of Pakistan, however, while endemic in the West, differs considerably from the perspective of Pakistani analysts who cautiously point to more optimistic scenarios. They cite six hopeful developments.
1.  No military coup d’etat
Despite a weak coalition civilian government, there has been no coup d’état. Shuja Nawaz of the Atlantic Council notes the military has “held back over the last four years, [and is] now gradually stepping back” from the day-to-day political arena.
2.  Resurgent judiciary
A resurgent judiciary in Pakistan has emerged as a potent force. In 2007, 2008, and 2009 it played a critical role in driving Gen. Pervez Musharraf, the military dictator, from office. In a country where millions are serfs and villeins and humans are occasionally sold like chattel, the Supreme Court increasingly offers a venue for redress of grievances.
3.  A more moderate Islam
There is even a budding moderating trend on Pakistan’s religious landscape. Hassan Abbas, another
Pakistani analyst, recently commented that “there is a renewed effort across Pakistan among … [Muslim] clerics to challenge Al Qaeda and the Taliban.” It manifests itself in a reassertion of a more moderate Islam that preaches that suicide bombings are un-Islamic.
4.  Normalization with India
Pakistan’s generals, who have thrived for decades by promoting a perceived threat from India, now seem to realize the greater threat is internal terrorism, not to mention the violent secessionist movement in the province of Baluchistan. 
Professor Abbas observed, “Even the military has signed on to the reality of normalization with India because [if] you normalize with India then the Army can deal with the internal militancy.”
5.  Growth of news and social media outlets
The proliferation of broadcast media outlets coupled with an explosion of social media like Facebook are further reshaping the landscape. Now everyone is becoming part of the political process, challenging politicians and government institutions, including the Army.
6.  A push for ‘good governance’
The entry of Imran Khan, the national cricket hero, into the political election melee could well meet a genuine public craving for change. Ultimately Mr. Khan’s new political movement could even challenge the stagnant two-party system. 

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Energetics Of Chemical Reaction

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Thermodynamics

Definition

It is branch of chemistry which deals with the heat energy change during a chemical reaction.


Types of Thermochemical Reactions

Thermo-chemical reactions are of two types.

1. Exothermic Reactions

2. Endothermic Reactions


1. Exothermic Reaction

A chemical reaction in which heat energy is evolved with the formation of product is known as Exothermic Reaction.

An exothermic process is generally represented as

Reactants ----> Products + Heat


2. Endothermic Reaction

A chemical reaction in which heat energy is absorbed during the formation of product is known as endothermic reaction.

Endothermic reaction is generally represented as

Reactants + Heat ----> Products


Thermodynamic Terms

1. System

Any real or imaginary portion of the universe which is under consideration is called system.


2. Surroundings

All the remaining portion of the universe which is present around a system is called surroundings.


3. State

The state of a system is described by the properties such as temperature, pressure and volume when a system undergoes a change of state, it means that the final description of the system is different from the initial description of temperature, pressure or volume.


Properties of System

The properties of a system may be divided into two main types.

1. Intensive Properties

Those properties which are independent of the quantity of matter are called intensive properties.

e.g. melting point, boiling point, density, viscosity, surface, tension, refractive index etc.


2. Extensive Properties

Those properties which depends upon the quantity of matter are called extensive properties.

e.g. mass, volume, enthalpy, entropy etc.

First Law of Thermodynamics

This law was given by Helmheltz in 1847. According to this law

Energy can neither be created nor destroyed but it can be changed from one form to another.

In other words the total energy of a system and surroundings must remain constant.


Mathematical Derivation of First Law of Thermodynamics

Consider a gas is present in a cylinder which contain a frictionless piston as shown.
Diagram Coming Soon


Let a quantity of heat q is provided to the system from the surrounding. Suppose the internal energy of the system is E1 and after absorption of q amount of heat it changes to E2. Due to the increase of this internal energy the collisions offered by the molecules also increases or in other words the internal pressure of the system is increased after the addition of q amount of heat. With the increase of internal pressure the piston of the cylinder moves in the upward direction to maintain the pressure constant so a work is also done by the system.

Therefore if we apply first law of thermodynamics on this system we can write

q = E2 - E1 + W

OR

q = ?E + W

OR

?E = q - W

This is the mathematical representation of first law of thermodynamics.


Pressure - Volume Work

Consider a cylinder of a gas which contain a frictionless and weightless piston, as shown above. Let the area of cross-section of the piston = a

Pressure on the piston = P

The initial volume of the gases = V1

And the final volume of the gases = V2

The distance through which piston moves = 1

So the change in volume = ?V = V2 - V1

OR ?V = a x 1

The word done by the system W = force x distance

W = Pressure x area x distance

W = P x a x 1

W = P ? V

By substituting the value of work the first law of thermodynamics may be written as

q = ?E + P ?V

The absorption or evolution of heat during chemical reaction may take place in two ways.


1. Process at Constant Volume

Let qv be the amount of heat absorbed at constant volume.

According to first law qv = ?E + P ?V

But for constant volume ?V = O

Therefore,

P ?V = P x O = O

So,

qv = ?E + 0

Or

qv = ?E

Thus in the process carried at constant volume the heat absorbed or evolved is equal to the energy ?E.


2. Process at Constant Pressure

Let qp is the amount of heat energy provided to a system at constant pressure. Due to this addition of heat the internal energy of the gas is increased from E1 to E2 and volume is changed from V1 to V2, so according to first law.

qp = E2 - E1 + P(V2 - V1)

Or

qp = E2 - E1 + PV2 - PV1

Or

qp = E2 + PV2- E1 - PV1

Or

qp = (E2 + PV2) - (E1 - PV1)

But we known that

H = E + PV

So

E1 + PV1 = H1

And

E2 + PV2 = H2

Therefore the above equation may be written as

qp = H2 - H1

Or

qp = ? H

This relation indicates that the amount of heat absorbed at constant pressure is used in the enthalpy change.


Sign of ?H

?H represent the change of enthalpy. It is a characteristic property of a system which depends upon the initial and final state of the system.

For all exothermic processes ?H is negative and for all endothermic reactions ?H is positive.


Thermochemistry

It is a branch of chemistry which deals with the measurement of heat evolved or absorbed during a chemical reaction.

The unit of heat energy which are generally used are Calorie and kilo Calorie or Joules and kilo Joules.

1 Cal = 4.184 J

OR

1 Joule = 0.239 Cal


Hess's Law of Constant Heat Summation

Statement

If a chemical reaction is completed in a single step or in several steps the total enthalpy change for the reaction is always constant.

OR

The amount of heat absorbed or evolved during a chemical reaction must be independent of the particular manner in which the reaction takes place.


Explanation

Suppose in a chemical reactant A changes to the product D in a single step with the enthalpy change ?H
Diagram Coming Soon

This reaction may proceed through different intermediate stages i.e., A first changes to B with enthalpy change ?H1 then B changes to C with enthalpy change ?H2 and finally C changes to D with enthalpy ?H3.

According to Hess's law

?H = ?H1 + ?H2 + ?H3


Verification of Hess's Law

When CO2 reacts with excess of NaOH sodium carbonate is formed with the enthalpy change of 90 kJ/mole. This reaction may take place in two steps via sodium bicarbonate.

In the first step for the formation of NaHCO3 the enthalpy change is -49 kJ/mole and in the second step the enthalpy change is -41 kJ/mole.


According to Hess's Law

?H = ?H1 + ?H2

?H = -41 -49 = -90 kJ/mole


The total enthalpy change when the reaction is completed in a single step is -90 kJ/mole which is equal to the enthalpy change when the reaction is completed into two steps. Thus the Hess's law is verified from this example. 
__________________




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Mathematics I Definitions

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Mathematics Chapter 1 Definitions




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CHAPTER NO 2 SCALARS AND VECTORS

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CHAPTER NO  2            SCALARS AND VECTORS

 1. A vector is described by magnitude as well as:  a)   Angle     b)   Distance  c)   Direction     d)   Height
C

 2. Addition, subtraction and multiplication of scalars is done by:  a)     Algebraic principles    b)   Simple arithmetical rules  c)   Logical methods    d)   Vector algebra

 A

 3. The direction of a vector in a plane is measured with respect to two straight lines which are _______  to each other.  a)   Parallel     b)   Perpendicular  c)   At an angle of 60o    d)   Equal

 B

 4. A unit vector is obtained by dividing the given vector by:  a)   its magnitude     b)   its angle  c)   Another vector    d)   Ten

 A

 5. Unit vector along the three mutually perpendicular axes x, y and z are denoted by:  a)   â, b, ĉ     b)   î, ĵ,  ǩ  c)   ṕ, q, ȓ     d)   ẋ, ŷ, ẑ

 B

 6. Negative of a vector has direction _______ that of the original vector.  a)   Same as     b)   Perpendicular to  c)   Opposite to     d)   Inclined to

 C

 7. There are _______ methods of adding two or more vectors.  a)   Two      b)   Three  c)   Four      d)   Five

 A

 8. The vector obtained by adding two or more vectors is called:  a)   Product vector    b)   Sum vector  c)   Resultant vector    d)   Final vector

 C

 9. Vectors are added according to:  a)   Left hand rule     b)   Right hand rule  c)   Head to tail rule    d)   None of the above

 C

 10. In two-dimensional coordinate system, the components of the origin are taken as:  a)   (1, 1)     b)   (1, 0)  c)   (0, 1)     d)   (0, 0)

 D

 11. The resultant of two or more vectors is obtained by:  a)   Joining the tail of the first vector with the head of the last vector.  b)   Joining the head of the first vector with the tail of the last vector.  c)   
Joining the tail of the last vector with the head of the first vector.  d)   Joining the head of the last vector with the tail of the first vector.

 A

 12. The position vector of a point p is a vector that represents its position with respect to:  a)   Another vector    b)   Centre of the earth  c)   Any point in space    d)   Origin of the coordinate system

 D

 13. To subtract a given vector from another, its _______ vector is added to the other one.  a)   Double     b)   Half  c)   Negative     d)   Positive

 C

 15. The direction of a vector ℱ can be fond by the formula:  a)   ⊖ = tan-1 (Fy/Fx)    b)    ⊖= sin-1 (Fx/F)  c)   ⊖ = sin-1 (Fy/Fx)    d)   ⊖ = tan-1 (F/Fy)

 C

 16. The y-component of the resultant of ᶇ vectors can be obtained by the formula:  a)   Ay = ∑Ar cos ⊖r    b)   Ay = ∑Ar tan ⊖r  c)   Ay = ∑Ar tan-1 ⊖r    d)   Ay = ∑Ar sin ⊖r


 17. The sine of an angle is positive in _______ quadrants.  a)   First and Second    b)   Second and fourth  c)   First and third     d)   Third and fourth


 18. The cosine of an angle is negative in _______ quadrants.  a)   Second and fourth    b)   Second and third  c)   First and third     d)   None of the above


 19. The tangent of an angle is positive in _______ quadrants.  a)   First and last     b)   First only  c)   Second and fourth    d)   First and third


 20. If the x-component of the resultant of two vectors is positive and its y-component is negative, the  resultant subtends an angle of _______ on x-axes.  a)   360o -  ⊖     b)   180o +  ⊖  c)   180o +  ⊖     d)    ⊖



 21. Scalar product is obtained when:  a)   A scalar is multiplied by a scalar  b)   A scalar is multiplied by vector  c)   Two vectors are multiplied to give a scalar d)   Sum of two scalars is taken



 22. The scalar product of two vectors Ā and Ḃ is written as:  a)   Ā x Ḃ     b)   Ā.  Ḃ c)   ĀḂ     d)   AB


 23. The scalar product of two vectors F and V with magnitude of F and V is given by:  a)   FV sin⊖       b)   FV tan⊖  c)   F/V cos⊖       d)   FV cos⊖


 24.  The magnitude of product vector C i.e. AxB=C, is equal to the:  a)   Sum of the adjacent sides   b)   Area of the parallelogram  c)   Product of the four sides   d)   Parameter of the parallelogram


 26. The scalar product of a vector A is given by:  a)   A cos⊖       b)   A sin⊖    c)   A tan⊖       d)   None of the above

 D

 27. If two vectors are perpendicular to each other, their dot product is:  a)   Product of their magnitude   b)   Product of their x-components  c)   Zero      d)   One

 C

 28. If  i, j,  k are unit vectors along x, y and z-axes then i.j = j.k = k.i= ?  a)   1      b)   -1  c)   -1/2        d)   0

 D

 29. i.i = j.j = k.k =  _______  a)   0      b)   1  c)   -1      d)   1/2

 B

 30. If  dot product of two vectors which are not perpendicular to each other is zero, then either of the  vectors is:  a)   A unit vector     b)   Opposite to the other  c)   A null vector     d)   Position vector

 C


32. In the vector product of two vectors A & B the direction of the product vector is:  a)   Perpendicular to A      b)   Parallel to B   c)   Perpendicular to B    d)   Perpendicular to the plane joining both               A&B
D


34. The magnitude of vector product of two vectors A & B is given by:  a)   AB sin⊖       b)   AB  c)   AB cos⊖       d)    A/B tan⊖
A

 35. If  i, j,  k are unit vectors along x, y and z-axes then k. j = _______  a)   i      b)   j  c)   -k        d)   -i

 D

 36. i x i = j x j = k x k =  _______  a)   0      b)   1  c)   -1      d)   1/2

 A

 37. k x i =  _______  a)   j      b)   -j    c)   k      d)   -k

 A

 38. The torque is given by the formula:  a)   ζ = r . F     b)   ζ =  F x r  c)   ζ = r x F     d)   ζ =  -r x F

 C

 39. The force on a particle with charge q and velocity in a magnetic field B is given by:  a)   q (V x B)     b)   -q (V x B)  c)   1/q (V x B)     d)   1/q (B x V)

 A

 40. The scalar quantities are described by their magnitude and _______  a)   Direction     b)   Proper unit  c)   With graph     d)   None of these

 B

 46. We can write vector C as:  a)   C      b)   Ç  c)   a & b both are correct    d)   Ĉ

 C

 47. The module is another name of _______ of the vector.  a)   Magnitude     b)   Null   c)   Zero      d)   None of these

 A


49. The vector whose magnitude is equal to one is called _______.  a)   Unit vector     b)   Null vector  c)   Zero vector     d)   Positive vector
A

C
51. The formula of unit vector is defined as_______.  a)   Dividing the vector by its magnitude  b)   Dividing the magnitude by its vector  c)   Draw a cap on it    d)   None of these
A


53. In negative of a vector, a vector has same magnitude but _______ direction.  a)   Positive     b)   Negative  c)   Opposite     d)     None of these
C


55. The null-vector has _______ magnitude.  a)   Four      b)   Five  c)   Zero      d)   Six
C




60. Symbol “∑” is known as _______.  a)   Pi      b)   Resultant  c)   Power     d)   Summation
D

A
62. Let we have two vectors A and B, then according to subtraction of vector, we can write _______.  a)   A+B = A-B     b)   A-B = A+ (-B)  c)   A+B = A+ (-B)    d)   None of these
B

 63. The process of replacing one vector by two or more parts is called_______  a)   Addition of two vectors   b)   Subtraction of vectors  c)   Resolution of vectors    d)   None of these

 C

 64. If we replace vector F into two components Fx and Fy then Fx and Fy are  called_______ respectively.  a)   Horizontal and vertical components  b)   Vertical and horizontal components  c)   Positive and negative components  d)   None of these

 A

 65. If Fx and Fy are the components of vector F, then we can write as _______.  a)   F= Fx-Fy       b)   F= Fx+Fy    c)   a & b both are correct    d)   None of these

 B


71. If the x-component of the resultant is negative and its y-component is positive, the result is true  for.  a)   An angle of (180o-ᶿ) with x-axis  b)   An angle of (180o-ᶿ) with y-axis  c)   An angle of 90o    
d)   An angle of 180o
A

 72. The x-component of the resultant is positive and its y-component is negative, then the result is true  for.  a)   An angle of (180o-ᶿ) with y-axis  b)   An angle of (90o-ᶿ) with x-axis  c)   An angle of (360o-ᶿ) with x-axis  d)   None of these

 C

 73. The product of two vector is called scalar or dot product when they give _______.  a)   Vector quantity    b)   Scalar quantity  c)   Negative quantity    d)   Positive quantity

 B

 74. When the multiplication of two vectors result into a vector quantity, then the product is called  _______.  a)   Cross product     b)   Dot product  c)   Magnitude of two vectors   d)   None of these

 A

 75. The scalar product of two vectors L and M is defined as _______  a)   L x M= L.M cosᶿ    b)   L.B= L.M cosᶿ  c)   L.M= L.M sinᶿ    d)   L x M= L.M sinᶿ

 B

 76. “Sin ᶿ” is _______ in second quadrant and first quadrant.  a)   Negative     b)   Null  c)   Positive     d)   None of these

 C

 77. “Cos ᶿ” is positive in first and _______ quadrant.  a)   Fourth     b)   Second  c)   Third     d)   None of these

 A

 78. The tangent of an angle is positive in first and _______ quadrant.  a)   Fourth     b)   Third  c)   Second      d)   Fifth

 B

 79. The cosine of an angle is negative in _______ quadrants.  a)   Second and third    b)   First and second  c)   Third and fourth    d)   None of these

 A

 80. If L.M= M.L, then we can say:  a)   Scalar product is commutative   b)   Scalar product is positive  c)   Scalar product is negative   d)   None of these

 A





88. A scalar is a physical quantity which is completely specified by:  a)   Direction only    b)   Magnitude only  c)   Both magnitude & direction     d)   None of these
D

 89. A vector is a physical quantity which is completely specified by:  a)   Both magnitude & direction   b)   Magnitude only  c)   Direction only      d)   None of these

 A

 90. Which of the following is a scalar quantity?  a)   Density     b)   Displacement  c)   Torque       d)   Weight

 A

 91. Which of the following is the only vector quantity?  a)   Temperature     b)   Energy  c)   Power       d)   Momentum

 D

 92. Which of the following lists of physical quantities consists only of vectors?  a)   Time, temperature, velocity   b)   Force, volume, momentum  c)   Velocity, acceleration, mass     d)   Force, acceleration, velocity

 D

 93. A vector having magnitude as one, is known as:  a)   A position vector    b)   A null vector  c)   A unit vector       d)   A negative vector

 C

 94. A vector having zero magnitude is called:  a)   A unit vector     b)   A position vector  c)   A negative vector      d)   A null vector

 D

 95. A vector which specifies the direction is called:  a)   A null vector     b)   A unit vector  c)   A position vector      d)   A resultant vector

 B

 96. If a vector is divided by its magnitude, we get  a)   A resultant vector    b)   A null vector  c)   A unit vector       d)   A position vector

 C

 97. The rectangular components of a vector have angle between them  a)   0o      b)   60o  c)   90o        d)   120o

 C

 98. A force of 10N is acting along y-axis. Its component along x-axis is  a)   10 N      b)   20 N  c)   100 N       d)   Zero N

 D

 99. Two forces are acting together on an object. The magnitude of their resultant is minimum when the  angle between force is  a)   0o      b)   60o  c)   120o        d)   180o

 D

 100. Two forces of 10N and 15N are acting simultaneously on an object in the same direction. Their  resultant is  a)   Zero      b)   5 N  c)   25 N        d)   150 N

 C

 101. Geometrical method of addition of vectors is  a)   Head-to-tail rule method   b)   Rectangular components method  c)   Right hand rule method     d)   Hit and trial method

 A

 102. A force F of magnitude 20N is acting on an object making an angle of 300 with the X-axis. Its Fy  component is  a)   0      b)   10 N  c)   20 N        d)   60 N

 B

 103. The resultant of two forces each of magnitude F is 2F, then the angle between them will be  a)   120o      b)   30o  c)   60o        d)   0o

 D

 104. Two equal forces F and F make an angle of 180o with each other, the magnitude of their resultant  is  a)   Zero      b)   F  c)   2F        d)   3F
A

 105. If two forces of 10N and 20N are acting on a body in the same direction, then their resultant is   a)   10N      b)   20N  c)   30N        d)   200N

 C


A
108. The scalar product of two vectors is zero, when   a)   They are parallel    b)   They are anti-parallel  c)   They are equal vectors      d)   They are perpendicular to each other
D

A
110. If the dot product of two non-zero vectors vanishes, the vectors will be   a)   In the same direction    b)   Opposite to each other  c)   Perpendicular to each other     d)   Zero
C

112. The dot product of two vectors is negative when  a)   They are parallel vectors   b)   They are anti-parallel vectors  c)   They are perpendicular vectors     d)   None of the above is correct
B

 113. The vector product of two vectors is zero, when  a)   They are parallel to each other   b)   They are perpendicular to each other  c)   They are equal vectors      d)   They are inclined at angle of 60o

 A

 114. If () points along positive z-axis, then the vectors and must lie in  a)   zx-plane     b)   yz-plane  c)   xy-plane       d)   None of the above
C

 115. If = A1+ and = B1+ B2 are non-parallel vectors, then the direction is  a)   Along      b)   Along x-axis  c)   Along y-axis       d)   Along z-axis

 D


124.  When we take scalar product of a vector by itself (self product) the result gives the:  a)   Magnitude of the vector   b)   Square root of the magnitude of the vector  c)   Square of the magnitude of the vector  d)   Same vector
C

 126. A vector in space has  a)   One component    b)   Two components  c)   Three components    d)   No component

 C

 127. x- and y-components of the velocity of a body are 3 ms-1 and 4 ms-1 respectively. The magnitude of  velocity is  a)   7 ms-1     b)   1 ms-1  c)   5 ms-1     d)   2.64 ms-1

 C



130. A force of 30 N acts on a body and moves it 2m in the direction of force. The work done is  a)   60 J      b)   15 N  c)   0.06 J     d)   Zero
A

 131. A horse is pulling a cart exerting a force of 100 N at an angle of 30 to one side of motion of the cart.  Work done by the horse as it moved 20m is  a)   173.2 J     b)   1732 J  c)   86.6 J     d)   1000 J

 B

 132. Identify the vector quantity  a)   Time     b)   Work  c)   Heat      d)   Angular momentum

 D

 133. Identify the scalar quantity  a)   Force     b)   Acceleration  c)   Displacement     d)   Work

 D

 134. Which of the following is a scalar quantity  a)   Electric Current    b)   Electric field  c)   Acceleration     d)   Linear Momentum

 A

 135. Which of the following is not a vector quantity  a)   Density     b)   Displacement  c)   Electric field intensity    d)   Angular momentum

 C

 136. Vectors are the physical quantity which are completely represented by their magnitude as well as in  proper __________________ .  a)   Unit and Direction    b)   Unit  c)   Direction     d)   Number with proper Unit

 C

 137. Which one of the following is the scalar quantity  a)   Force     b)   Work  c)   Momentum     d)   Velocity

 B

 138. Which one of the following is the vector quantity  a)   Acceleration     b)   Power  c)   Density     d)   Volume

 A

 139. Which of the following is the example of scalar quantity  a)   Momentum     b)   Force  c)   Acceleration     d)   Mass

 D

 140. Which of the following is the example of vector quantity  a)   Volume     b)   Temperature  c)   Velocity     d)   Speed

 C

 141. A vector whose magnitude is same as that of A, but opposite in direction is known as  a)   Null vector     b)   Negative vector  c)   Addition vector    d)   Subtraction vector

 B

 142.  Let us take i, j, k be three unit vectors such that:  a)   i . j = 0     b)   i . j = 1  c)   i . j = k     d)   i . j = j

 A

 143. Physical quantities represented by magnitude are called  a)   Scalar     b)   Vector  c)   Functions     d)   None of the above

 A

 144. Physical resultant of two or more vectors is a single vector whose effect is same as the combine  effect of all the vectors to be added is called.  a)   Unit vector     b)   Product vector  c)   Component of vector    d)   Resultant of vector

 D

 145. Vectors are added graphically using  a)   Right hand rule    b)   Left hand rule  c)   Head to tail rule    d)   Hit and trial rule

 C

 146. The angle between rectangular components of vector is  a)   45o      b)   60o  c)   90o      d)   180o

 C

 147. Two forces 3N and 4N are acting on a body, if the angle between them is 90 then magnitude of  resultant force is  a)   2 Newton     b)   5 Newton  c)   7 Newton     d)   10 Newton

 B

 148. Which of the following quantity is scalar  a)   Electric field     b)   Electrostatic potential  c)   Angular momentum    d)   Velocity

 B

 149. Two vectors having different magnitudes  a)   Have their direction opposite   b)   May have their resultant zero  c)   Cannot have their resultant zero   d)   None of the above

 C

 150. If A and B are two vectors, then the correct statement is   a)   A + B = B + A    b)   A - B = B - A  c)   Ax B = Bx A    d)   None of the above

 A

 151. When three forces acting at a point are in equilibrium:   a)   Each force is numerically equal to the sum of the other two  b)   Each force is numerically greater than the sum of the other two  c)   Each force is numerically greater than the difference of the other two  d)   None of the above

 A

 152.  If two vectors are anti-parallel, scalar product is equal to the:  a)   Product of their magnitudes   b)   Negative of the product of their magnitude  c)   Equal to zero     d)   None of the above

 B

 153. Angular momentum is   a)   Scalar     b)   A polar vector  c)   An axial vector    d)   Linear momentum

 C

 154. The scalar product of two vectors is negative when they are   a)   Anti-parallel vectors    b)   Parallel vectors  c)   Perpendicular vectors    d)   Parallel with some magnitude

 A

 155. Scalar product is also called   a)   Cross product     b)   Vector product  c)   Base vector     d)   Dot product

 D

 156.  Scalar product is also known as:  a)   Dot product     b)   Cosine product  c)   Cross product     d)   None of the above

 A

 157. If a vector α makes an angleᶿ with the x-axis its x-component is given as   a)   a cosᶿ     b)   a sinᶿ    c)   a tanᶿ     d)   a sinα

 A

 158. Cross product of two vectors is zero when they are   a)   Of different magnitude and perpendicular to each other  b)   At an angle of 60o  c)   Parallel to each other    d)   At an angle of 90o

 C

 159. A vector is multiplied by positive number then   a)   Its magnitude changes    b)  Its direction changes but magnitude              remains the same  c)   Its magnitude as well as direction changes d)   Neither its magnitude nor direction               changes

 A

 160. If two forces act together on an object then the magnitude of the resultant is least when the angle  between the forces is   a)   60o      b)   90o  c)   180o      d)   360o

 C

 161. If A.B = 0, we conclude that   a)   Either of two vectors is a null   vector  b)   Both of the vectors are null vectors  c)   The vectors are mutually perpendicular  d)   All of the above

 D

 162. Two forces each of magnitude F act perpendicular to each other. The angle made by the resultant  force with the horizontal will be   a)   30o      b)   45o  c)   60o      d)   90o

 B

 163. If a charged particle of mass m and charge q is projected across uniform magnetic field B with a  velocity V, it experience magnitudes force given by   a)   F = q (Vx B)     b)   F = (V. B)  c)   F =  VxB/q     d)   F = qxB/V

 A

 164. If Ax B points along positive z-axis then the vectors A and B must lie in   a)   YZ-plane     b)   ZX-plane  c)   XY-plane     d)   None of the above

 C

 165. If the resultant of two vectors each of magnitude F is also of magnitude F, the angle between them  will be   a)   90o      b)   60o  c)   30o      d)   120o

 D


167. A vector which has magnitude ‘One’ is called   a)   A resultant vector    b)   A unit vector  c)   A null vector     d)   A positive vector
B

 168. The Fx component of a force vector ‘F’ of magnitude 30N make an angle of 60o with X-axis is   a)   7N      b)   15N  c)   5N      d)   10N

 B

 169. When a certain vector is multiplied by -1, the direction changes by  a)   90o      b)   180o  c)   120o      d)   60o

 B

 170. The minimum number of unequal forces whose vector sum can be zero is   a)   1      b)   2  c)   3      d)   4

 C

 171. If a force of 10N makes an angle of 30o with x-axis, its x-component is given by   a)   0.866N     b)   0.886N  c)   89.2N     d)   8.66N

 D

 172. Two forces each of 10N magnitude act on a body. If the forces are inclined at 30o and 60o with x- axis, then the x-component of their resultant is   a)   10N      b)   1.366N  c)   13.66N     d)   136.6N

 C

 173. When two equal forces F and F make an angle of 180o with each other, the magnitude of their  resultant is   a)   F      b)   2F  c)   0      d)   3F

 C

 174. The scalar or dot product of  A with itself i.e. A.A is equal to   a)   2A      b)   A2  c)   A/2      d)   None of the above

 B

 175. If the vectors A and B are of magnitude 4 and 3 cm making of 30o and 90o respectively with X- axis, their scalar product will be   a)   0 cm2     b)   18 cm2  c)   6.0 cm2     d)   21 cm2

 C

 176. If the dot product of two non-zero vectors vanishes, the vectors will be   a)   Parallel to each other    b)   Anti-parallel to each other  c)   Perpendicular to each other   d)   None of the above

 C

 177. Dot product of two non-zero vectors is zero (a.b = 0) when angle between them is be   a)   30o      b)   45o  c)   60o      d)   90o

 D



180. The scalar product of two vectors is negative when   a)   They are parallel vectors   b)   They a anti-parallel vectors  c)   They are perpendicular vectors   d)   They are parallel with some magnitude
B

 181. The cross-product of two vectors is a negative vector when   a)   They are parallel vectors   b)   They are anti-parallel vectors  c)   They are perpendicular vectors   d)   They are rotated through 270o

             D




186. The y-component of a vector 100N force, making an angle of 30o with the x-axis is  a)   50N      b)   20N  c)   10N      d)   80N
A



194. Dot or scalar product obeys  a)   Associative law    b)   Commutative law  c)   Distributive law    d)   All these
D




198. If displacement of a body is d= 3i, its only significance is  a)   The displacement of 3 units is not along any axis b)   The displacement of 3 units along z-axis  c)   The displacement of 3 units along y-axis  d)   The displacement of 3 units along x-axis
D

 199. The magnitude of a vector A=Axi+Ayj+Azk is  a)   Ax2 + Ay2 + Az2    b)   (Ax + Ay + Az)2  c)   (Ax2 + Ay2 + Az2)1/2   d)   A /√3
C




203. A force of 10N is acting on a body making an angle of 45o with x-axis. its x and y components are  a)   7.07 N and 7.07 N    b)   7.07 N and 5 N  c)   5 N and 7.07 N    d)   8.66 N and 5 N
A




206. The magnitude of resultant of three vectors is 3. Its x-component is 2, y-component is 1 then its z- component will be  a)   4      b)   1  c)   2      d)   0
C

 207. If two equal unit vectors are inclined at an angle of 900, then magnitude of their resultant will be  a)   2      b)   √2  c)   1      d)   0

 B

 208. Unit vector is used to specify  a)   Magnitude of a vector    b)   Dimension of a vector  c)   Direction of a vector    d)   Position of a vector

 C

 209. The unit vector of a vector A of magnitude 2 is  a)   2A      b)   A2  c)   A/2      d)   A2/2

 A

 210.  When the product of two vectors is a scalar quantity, it is called:  a)   Vector product    b)   Multiplication of vectors  c)   Dot product     d)   Cross product

 C

 211. The angle of a vector A = Axi - Ayj with the x-axis will be in between  a)   0 o to 90 o     b)   90 o to 180 o  c)   180 o to 270 o     d)   270 o to 360o

 C

 212. A vector having magnitude equal to given vector but in opposite direction is called  a)   Unit vector     b)   Positive vector  c)   Negative vector    d)   Position vector

 C


214. When two equal and opposite vectors are added, then their resultant will have  a)   Same magnitude    b)   Double magnitude  c)   Zero magnitude    d)   Half magnitude
C

 215. A force of 20N is acting along x-axis, Its component along x-axis is  a)   20N      b)   10N  c)   5N      d)   Zero

 A

 216. Two forces of same magnitude are acting on an object, the magnitude of their resultant is minimum  if the angle between them is  a)   45o      b)   60o  c)   90o      d)   180o

 D

 217. If two forces each of magnitude 5N act along the same line on a body, then the magnitude of their  resultant will be  a)   5 N      b)   10 N  c)   20 N      d)   30 N

 B

 218. If A = Axi + Ayj and B = Bxi + Byj then A.B will be equal to  a)   AxBx + AyBy     b)   AxBy + AyBx  c)   Ax2By2 + Ay2Bx2    d)   Ax2Bx2 + Ay2By2

 A

 219. If cross product between two non zero vectors A and B is zero then their dot product is  a)   AB sinᶿ         b)   AB cosᶿ      c)   0      d)   AB

 D

 220. The cross product of a vector A with itself is  a)   A2      b)   2A  c)   0      d)   1
C

 221. If A = Ai and B = Bj then A . B is equal to  a)   AB      b)   Zero  c)   1      d)   AB k

 B

 222. The product i xj is equal to  a)   Zero      b)   1  c)   k      d)   -k

 C

 223. The magnitude of i. (i xk) is  a)   i      b)   0  c)   -1      d)   j

 B

 224. If x-component of a vector is 3 N and y-component is -3 N, then angle of the resultant vector with x- axis will be  a)   45o      b)   315o  c)   135o      d)   225o

 B

 225. If A = 3i + 4j, then the magnitude of A will be  a)   7      b)   5  c)   25      d)   1

 B

 226. When a force of 10 N is acting on a body making an angle of 60o with x-axis and displaces this body  through 10 m, then scalar product of force and displacement is  a)   100 J     b)   50 J  c)   8.66 J     d)   50 N

 B

 227. If A = 2i + 2j and B = -2i + 2j then A . B will be equal to  a)   -4      b)   0  c)   2      d)   8

 B

 228. Two vectors of magnitude 20 N and 2m are acting on opposite direction. Their scalar product will be  a)   40 Nm     b)   40 N  c)   -40 Nm     d)   40 m

 C

 229. If A = 3i + 6j, B = xi + k and A.B = 12, then x will be equal to  a)   2      b)   4  c)   12      d)   3

 B

 230. A physical quantity which is completely described by a number with proper units is called  a)   Scalar     b)   Vector  c)   Null vector     d)   None of the above

 A

 231. A physical quantity which requires magnitude in proper units as well as direction is called  a)   Scalar     b)   Vector  c)   Null vector     d)   None of the above

 B

 232. A vector whose magnitude or modulus is one and it points in the direction of a given vector is called  _______  a)   A unit vector     b)   A null vector  c)   Negative of a vector    d)   Zero vector

 A

 233. A vector having an arbitrary direction and zero magnitude is called _______  a)   A unit vector     b)   A null vector  c)   Inverse of a vector    d)   None of the above

 B

B
235. For a force F, Fx = 6 N Fy = 6 N. What is the angle between F and x-axis   a)   Less than 30o     b)   60o  c)   45o      d)   Greater than 60o
C

A
237. A simple example of a dot product is the_______  a)   Force     b)   Energy  c)   Work     d)   Momentum
C

 238. If the vectors A.B = 0, either the vectors are mutually perpendicular to each other or one or both  vectors are  a)   Unit vectors     b)   Null vector  c)   Base vectors     d)   None of the above

 B

 239. The scalar product of a vector Awith itself i.e. A.A is called   a)   A null vector     b)   Square of the vector  c)   Unit vector     d)   Magnitude of 

 B

 240. The scalr product of Aand B in the form of the components Ax, Ay, Az, and Bx, By, Bz, is defined as  a)   Ax By + Ax Bx + Az Bz    b)   Ax Bb + Bz Bz + Az Bz  c)   Ax Bx+ Ay By + Az Bz    d)   Az By + Ax Bx + Ay Bz

 C


243. The vector product of a vector by itself is  a)   1      b)   -1  c)   0      d)   None of the above
C
B
245. In contrast of a scalar a vector must have a   a)   Direction     b)   Weight  c)   Quantity     d)   None of the above
A

 246. Electric intensity is a  a)   Ratio     b)   Scalar  c)   Vector     d)   Pure number

 C

 247. The acceleration vector for a particle in uniform circular motion in  a)   Tangential to the orbit    b)   Directed toward the centre of the orbit  c)   Directed in the same direction as the force vector d)   b and c
D

 248. Which of the following group of quantities represent the vectors  a)   Acceleration, Force, Mass   b)   Mass, Displacement, Velocity  c)   Acceleration, Electric flux, Force  d)   Velocity, Electric field, Momentum

 D

 249. The following physical quantities are called vectors  a)   Time and mass    b)   Temperature and density  c)   Force and displacement   d)   Length and volume

 C

 250. Scalar quantities have  a)   Only magnitudes    b)   Only directions   c)   Both magnitude and direction   d)   None of these

 A

 251. The vector quantity which is defined as the displacement of the particle during a time interval  divided by that time interval is called  a)   Speed     b)   Average speed  c)   Average velocity    d)   None of these

 C

 252. For the addition of any number of vectors in a given coordinate system the first step is to  a)   Find out the algebraic sum of all the individual x-components  b)   Find out the algebraic sum of all the individual y-components   c)   Resolve each given vector into its rectangular components (x and y components)   d)   Find out the magnitude of the sum of all the vectors

 C

 253. When a vector is multiplied by a negative number, its direction  a)   Is reversed     b)   Remains unchanged  c)   Make an angle of 60o    d)   May be changed or not

 A

 254. A vector which can be displaced parallel to itself and applied at any point is known as  a)   Parallel vector    b)   Null vector  c)   Free vector     d)   Position vector

 C

 255. A vector in any given direction whose magnitude is unity is called  a)   Normal vector    b)   Parallel vector  c)   Free vector     d)   Unit vector

 D

 256. The position vector of a point p is a vector that represents its position with respect to  a)   Another vector    b)   Centre of the earth  c)   Any point in space    d)   Origin of the coordinate system

 D

 257. Negative of a vector has a direction _______ that of the original vector  a)   Same as     b)   Perpendicular to  c)   Opposite to     d)   Inclined to

 C

 258. The sum and difference of two vectors are equal in magnitude. The angle between the vectors is  a)   0o      b)   90o  c)   120o      d)   180o

 B

 259. In graphical addition of vectors  a)   The position of vectors is unimportant  b)   The order of vectors is not to be altered  c)   The direction of resultant is unknown  d)   The position of vectors is important

 B

 260. The dot product of i and j is  a)   More     b)   1  c)   0     d)   Any value

 C

 261. The magnitude of product vector C i.e. A x B=C, is equal to the  a)   Sum of the adjacent sides   b)   Area of the parallelogram  c)   Product of the four sides   d)   Parameter of the parallelogram

 B

 262. If two vectors lie in xy-plane, their cross product lies  a)       In the same plane    b)   Adjacent plane  c)   Along perpendicular to that plane  d)   Parallel to the plane

 C

 263. Two forces of 8N and 6N are acting simultaneously at right angle, the resultant force will be  a)   14N      b)   2N  c)       10N      d)   12N

 C

 264.  The scalar product of two vectors is zero, when:  a)   They are equal vectors    b)   They are in the same direction  c)   They are at right angle to each other  d)   They are opposite to each other

 C

 265. Two forces of magnitude 20N each are acting 30o & 60owith the x-axis, the y-component of the  resultant fore is approx.  a)   20 N      b)   40 N  c)   27.32 N     d)   17.32 N

 C


267. (6i+4j-k) . (4i+2j-2k) = ?  a)   24i+8j+2k     b)   30  c)   34      d)   40
C

 268. The projection of A = 2i-3j+6k onto the direction of vector A= i+2j+2k is  a)   8      b)   3  c)   8/3      d)   6

 C

 269. The quantities which can be added, subtracted and multiplied by simple algebraic rules are:  a)   Scalars     b)   Vectors  c)   Physical     d)   Positive

 A

 270. Choose the vector  a)   Weight and mass    b)   Velocity and speed  c)   Force and acceleration    d)   Velocity and energy

 C

 271. The length of the arrow represents the _______ of a vector  a)   Direction     b)   Magnitude  c)   Direction and magnitude both   d)   Resultant of the vector

 B

 272. Vector A has the same magnitude as B but opposite in direction, then A is said to be  a)   Normal vector    b)   Negative vector  c)   Null vector     d)   Unit vector

 B

 273. The sum of two vectors equal in magnitude but opposite in direction is  a)   Less than the individual vectors   b)   Greater than the individual vectors  c)   Equal to the individual vector   d)   Zero

 D

 274. To add all vectors we add their representative lines by  a)   Right hand rule    b)   Head-to-tail rule  c)   Left hand rule     d)   Hit and trial principle

 B

 275. Vector addition is  a)   Associative     b)   Commutative  c)   Distributive     d)   Both a) and b)

 D

 276. A vector whose tail lies at the origin of the coordinates and whose head lies at the position of point  ‘P’ in space, known as  a)   Free vector     b)   Fixed vector  c)   Position vector    d)   Parallel vector

 C

 277. If the magnitudes and directions of two vectors are same then these two vectors are  a)   Equal     b)   Same  c)   Equivalent     d)   Opposite

 A

 278. A vector lying along x-axis has  a)   Its x and z components zero   b)   Its y-component equal to zero  c)   Its x and y components equal to zero  d)   None of these

 D

 279. The resultant vector of two vectors will be zero if  a)   the magnitude of the vector is zero    b)   The magnitude of both vectors is same and angle b/w their direction is 90o  c)   The magnitude of both vectors is same and angle b/w their direction is 180o  d)   The magnitude of both vectors is different and angle b/w their direction is 45o

 C

 280. The magnitude of resultant of two vectors acting at right angle is _______ than the individual  vectors  a)   More     b)   Less  c)   Equal     d)   Thrice

 A

 281. The angle between the rectangular components of a vector is always  a)   Less than 90o     b)   Greater than 90o  c)   Equal to 180o     d)   Equal to 90o

 D

 282. If a vector  A lies in xy-plane and it makes an angle ‘ᶿ’ with the side of y-axis. Then its y-component  is:  a)   Ay = A Cosᶿ        b)   Ay = A Secᶿ      c)   Ay = A Sinᶿ         d)   Ay = A Tanᶿ

 A

 283. The components of a vector behave like:  a)   Vector quantities    b)   Scalar quantities  c)   Magnitudes     d)   Directions

 A

 284. A vector B in 4th quadrant than:   a)   Its x-component is -ve and its y-component is +ve  b)   Its x-component is +ve and its y-component is +ve  c)   Its x-component is +ve and its     y-component is -ve  d)   Its x-component is -ve and its y-component is -ve
C

 285. The process by which a vector can be reconstituted from its components is known as:  a)   Principle of parallelogram   b)   Division of vectors  c)   Composition of vectors   d)   Factorization of vectors

 C


D

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