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৪৯তম বিসিএস ⎯ ফলিত গণিত [৫৬১]

পরীক্ষা৪৯তম বিসিএস ⎯ ফলিত গণিত [৫৬১]তারিখতারিখ অনির্ধারিতসময়30 minutes২৮ বৈধ · ১ অসম্পূর্ণ
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সিলেবাস
Exam - 01 Topics: Statics (a) Forces acting in a plane, parallel forces, moments and couples. (b) Equilibrium of coplanar forces. Astatic, stable and unstable equilibrium [Source: Class - 01 and Relevant Books]
প্রশ্ন দেখুনঅনুশীলন
ঘনত্ব
উত্তর
উত্তরিতবর্তমানপুনরায় দেখুনঅসম্পূর্ণ

৪৯তম বিসিএস ⎯ ফলিত গণিত [৫৬১]

৪৯তম বিসিএস ⎯ ফলিত গণিত [৫৬১] · তারিখ অনির্ধারিত · ২৯ প্রশ্ন

১.
The distance between the forces acting in the couple is ____________
  1. ক
    Infinity
  2. খ
    Zero
  3. গ
    A finite distance
  4. ঘ
    A circular loop
সঠিক উত্তর: গ
A finite distance
উত্তর
সঠিক উত্তর: গ
A finite distance
গ
ব্যাখ্যা
The distance between the forces acting in the couple is having a finite distance. Couple is the combination of two forces which are acting in the same sense of rotation. That is they are acting in the opposite direction to provide the same direction rotation.
২.
Which one is astatic equilibrium?
  1. ক
    A ball in a bowl
  2. খ
    A pendulum at its lowest point.
  3. গ
    A pencil balanced vertically on its tip
  4. ঘ
    None of this
সঠিক উত্তর: ঘ
None of this
উত্তর
সঠিক উত্তর: ঘ
None of this
ঘ
ব্যাখ্যা
a ball in a bow and a pendulum at its lowest point are stable equilibrium.
A pencil balanced vertically on its tip is unstable equilibrium.
৩.
What is/are the conditions for equilibrium?
  1. ক
    Net Force is Zero
  2. খ
    Net Torque is Zero
  3. গ
    One of these is Sufficient
  4. ঘ
    Both of them.
সঠিক উত্তর: ঘ
Both of them.
উত্তর
সঠিক উত্তর: ঘ
Both of them.
ঘ
ব্যাখ্যা
conditions for equilibrium are 
1.Net Force is Zero
2.Net Torque is Zero
৪.
The resultant of two equal forces is equal to either of these forces. The angle between them is
  1. ক
    45°
  2. খ
    60°
  3. গ
    90°
  4. ঘ
    120°
সঠিক উত্তর: ঘ
120°
উত্তর
সঠিক উত্তর: ঘ
120°
ঘ
ব্যাখ্যা
p2 = p2+p2+2P.P Cosα
2p2 Cosα = -p2
Cosα = -1/2
α = 120
৫.
Among the given pair of forces, the resultant of two vectors can never be 3 units. The forces are
  1. ক
    1 unit and 2 units
  2. খ
    4 units and 8 units
  3. গ
    12 units and 15 units 
  4. ঘ
    23 units and 23 units
সঠিক উত্তর: খ
4 units and 8 units
উত্তর
সঠিক উত্তর: খ
4 units and 8 units
খ
ব্যাখ্যা
The smallest possible resultant is when the two vectors are in opposite directions, which gives:
R = |A - B|
The largest possible resultant is when the vectors are in the same direction:
R = A + B

4 units and 8 units
The smallest resultant is |4 - 8| = 4 units.
The largest resultant is 4 + 8 = 12 units.
৬.
  
The value of theta for the given figure is
  1. ক
    90°
  2. খ
    60°
  3. গ
    45°
  4. ঘ
    30°
সঠিক উত্তর: ক
90°
উত্তর
সঠিক উত্তর: ক
90°
ক
ব্যাখ্যা
৭.
A rigid ball of weight 10 N is suspended with the help of a string. The ball is pulled by a horizontal force F such that the string makes an angle of 60° with the vertical. The magnitude of force F is
  1. ক
    10√3
  2. খ
    10/√3
  3. গ
    10√2
  4. ঘ
    10/√2
সঠিক উত্তর: ক
10√3
উত্তর
সঠিক উত্তর: ক
10√3
ক
ব্যাখ্যা

Lami's Theorem

T/sin90=F/sin120=10/sin150
F=10 Sin120/Sin150
F=10√3
৮.

If point A is in equilibrium under the action of the applied forces, the values of tension. Tension through AB=?
  1. ক
    400√3 N
  2. খ
    400/√3 N
  3. গ
    400 N
  4. ঘ
    None of these
সঠিক উত্তর: ক
400√3 N
উত্তর
সঠিক উত্তর: ক
400√3 N
ক
ব্যাখ্যা

Lami's theorem
We have angle BAC = 180° - (30° + 60°) = 90°
800/Sin90 = T/Sin120
T = 400√3 N

৯.
The moment of a given system of forces about three points (2,0), (0,2) and (2,2) are 3,4,10 units respectively. Find The componets of the resultant force alonog X axis.
  1. ক
    3
  2. খ
    -3
  3. গ
    3.5
  4. ঘ
    -3.5
সঠিক উত্তর: গ
3.5
উত্তর
সঠিক উত্তর: গ
3.5
গ
ব্যাখ্যা


Source:  Mechanics, Science View Publications

১০.
Lami's theorem states that
  1. ক
    three forces acting at a point are always in equilibrium
  2. খ
    if three forces acting on a point can be represented in magnitude and direction by the sides of a triangle, the point will be in a state of equilibrium
  3. গ
    three coplanar forces acting at a point will be in equilibrium if each force is proportional to the sine of the angle between the other two
  4. ঘ
    three coplanar forces acting at a point will be in equilibrium if each force is inversely proportional to the sine of the angle between the other two
সঠিক উত্তর: গ
three coplanar forces acting at a point will be in equilibrium if each force is proportional to the sine of the angle between the other two
উত্তর
সঠিক উত্তর: গ
three coplanar forces acting at a point will be in equilibrium if each force is proportional to the sine of the angle between the other two
গ
ব্যাখ্যা
১১.
Which one is not true about couple?
  1. ক
    The net force of a couple is always zero
  2. খ
    The net moment (or torque) is non-zero
  3. গ
    Forces are at the same direction
  4. ঘ
    None of these
সঠিক উত্তর: গ
Forces are at the same direction
উত্তর
সঠিক উত্তর: গ
Forces are at the same direction
গ
ব্যাখ্যা

A couple is defined as a pair of forces that are equal in magnitude, opposite in direction, and not collinear. The net force of a couple is always zero, while the net moment (or torque) is non-zero and depends on the perpendicular distance between the forces. 

১২.
Which one is not a force?
  1. ক
    Thrust
  2. খ
    Friction
  3. গ
    Weight
  4. ঘ
    All of these are forces.
সঠিক উত্তর: ঘ
All of these are forces.
উত্তর
সঠিক উত্তর: ঘ
All of these are forces.
ঘ
ব্যাখ্যা
In physics, force is an interaction that can cause a change in an object's motion or shape. It's essentially a push or a pull that, when applied, can either accelerate a body, change its direction, or deform its shape. Force is a vector quantity, meaning it has both magnitude (strength) and direction.
১৩.

ABCDEF is a regular hexagon. Calculate the resultant force along OC.
  1. ক
    -3
  2. খ
    -4
  3. গ
    4
  4. ঘ
    6
সঠিক উত্তর: ক
-3
উত্তর
সঠিক উত্তর: ক
-3
ক
ব্যাখ্যা

X=1cos0+2Cos(-120)+3Cos120+4Cos0+5Cos(-120)+6Cos(120)  
   =-3

১৪.
Two force s of magnitude s 5N and 12N are acting at an angle of 90° to each other. The resultant force is: 
  1. ক
    7N
  2. খ
    17N
  3. গ
    13N
  4. ঘ
    None of these
সঠিক উত্তর: গ
13N
উত্তর
সঠিক উত্তর: গ
13N
গ
ব্যাখ্যা

১৫.
The equations of equilibrium for a non-concurrent force system are:
  1. ক
    ∑Fy = 0
  2. খ
    ∑Fx​ = 0, ∑Fy​ = 0
  3. গ
    ∑Fx​ = 0
  4. ঘ
    ∑Fx​ = 0, ∑Fy = 0 and ∑M = 0
সঠিক উত্তর: ঘ
∑Fx​ = 0, ∑Fy = 0 and ∑M = 0
উত্তর
সঠিক উত্তর: ঘ
∑Fx​ = 0, ∑Fy = 0 and ∑M = 0
ঘ
ব্যাখ্যা

Equations of equilibrium for Non-concurrent force System: A non-concurrent force system will be in equilibrium if the resultant of all forces and moments is zero.
ΣFx = 0, ΣFy = 0 and ΣM = 0

১৬.
Two forces F and √3F act on a particle in directions inclined at an angle of 120° to each other. Find the magnitude of the resultant.
  1. ক
    F
  2. খ
    √7F
  3. গ
    7F
  4. ঘ
    √3F
অনির্ধারিত
ব্যাখ্যা

সঠিক উত্তর: √(4-√3)F
​অপশনে সঠিক উত্তর না থাকায় প্রশ্নটি বাতিল করা হলো। 
​--------------- 
​
​

১৭.
If three forces acting in one plane upon a rigid body keep it in equilibrium, then____
  1. ক
    they must meet in a point
  2. খ
    they must be parallel.
  3. গ
    they must either meet in a point or be parallel.
  4. ঘ
    None of these.
সঠিক উত্তর: গ
they must either meet in a point or be parallel.
উত্তর
সঠিক উত্তর: গ
they must either meet in a point or be parallel.
গ
ব্যাখ্যা

If three forces acting in one plane upon a rigid body keep it in equilibrium, they must either meet in a point or be parallel.

১৮.

The forces along OA,OB,OC are in equlibrium. Which one is correct?
  1. ঘ
    All of these
সঠিক উত্তর: ঘ
All of these
উত্তর
সঠিক উত্তর: ঘ
All of these
ঘ
ব্যাখ্যা

১৯.
According to the Parallelogram Law of Forces, the resultant of two forces acting at an angle to each other is represented by:
  1. ক
    the difference of their magnitudes 
  2. খ
    the perpendicular bisector of the two forces
  3. গ
    the sum of their magnitudes 
  4. ঘ
    the diagonal of the parallelogram formed by the two forces
সঠিক উত্তর: ঘ
the diagonal of the parallelogram formed by the two forces
উত্তর
সঠিক উত্তর: ঘ
the diagonal of the parallelogram formed by the two forces
ঘ
ব্যাখ্যা

Parallelogram Law of Forces
It states that if two forces acting at a point are represented in magnitude and direction by the adjacent sides of a parallelogram, then the diagonal of the parallelogram represents their resultant force.

২০.
Three forces 3N, 4N & 5N acts along AB, BC & CA respectively of a triangle ABC and the forces are in equilibrium. The length of CA 7cm. What is the value of AB.
  1. ক
    12cm
  2. খ
    0.8cm
  3. গ
    5.6cm
  4. ঘ
    4.2cm
সঠিক উত্তর: ঘ
4.2cm
উত্তর
সঠিক উত্তর: ঘ
4.2cm
ঘ
ব্যাখ্যা

২১.

What is the component of the resultant force S along X axis?
  1. ক
    3
  2. খ
    0.5
  3. গ
    1.5
  4. ঘ
    0
সঠিক উত্তর: খ
0.5
উত্তর
সঠিক উত্তর: খ
0.5
খ
ব্যাখ্যা

২২.
Two unlike parallel forces of 15N and 10N act at the two ends of a light rod of length 8m . At what distance from the greater force will their resultant act?
  1. ক
    16/5
  2. খ
    16
  3. গ
    24
  4. ঘ
    24/5
সঠিক উত্তর: খ
16
উত্তর
সঠিক উত্তর: খ
16
খ
ব্যাখ্যা

২৩.
Two like parallel forces of 20N and 10N act at the two ends of a light rod of length 60m. If the forces exchange their point of act, then how much will their resultant shift?
  1. ক
    40m
  2. খ
    20m
  3. গ
    30m
  4. ঘ
    45m
সঠিক উত্তর: খ
20m
উত্তর
সঠিক উত্তর: খ
20m
খ
ব্যাখ্যা

২৪.
Two like parallel forces of 10N and 5N act at the two ends of a light rod of length 20m. If we add 5N force on both end with same direction, then how much will their resultant shift?
  1. ক
    6.67
  2. খ
    8
  3. গ
    1.23
  4. ঘ
    1.33
সঠিক উত্তর: ঘ
1.33
উত্তর
সঠিক উত্তর: ঘ
1.33
ঘ
ব্যাখ্যা

২৫.
Which one is the example of neutral equilibrium?
  1. ক
    A marble at the bottom of a bowl
  2. খ
    A pendulam hanging Vertically down.
  3. গ
    a marble on a flat, horizontal surface.
  4. ঘ
    All of these
সঠিক উত্তর: গ
a marble on a flat, horizontal surface.
উত্তর
সঠিক উত্তর: গ
a marble on a flat, horizontal surface.
গ
ব্যাখ্যা

In physics, neutral equilibrium describes a state where a body, when slightly displaced, neither returns to its original position nor moves further away.

২৬.
Which one is an example of unstable equilibrium?
  1. ক
    A book lying flat on a table
  2. খ
    An inflated ballon floating at a neutral height in water.
  3. গ
    A pencil blanced perfectly on its tip.
  4. ঘ
    None of these
সঠিক উত্তর: গ
A pencil blanced perfectly on its tip.
উত্তর
সঠিক উত্তর: গ
A pencil blanced perfectly on its tip.
গ
ব্যাখ্যা

Unstable equilibrium refers to a state where a system is in balance, but any small disturbance will cause it to move away from that balance.

২৭.
Which one is an example of stable equilibrium?
  1. ক
    a marble on a flat, horizontal surface.
  2. খ
    A marble at the bottom of a bowl.
  3. গ
    None of these.
  4. ঘ
    Both a & b.
সঠিক উত্তর: খ
A marble at the bottom of a bowl.
উত্তর
সঠিক উত্তর: খ
A marble at the bottom of a bowl.
খ
ব্যাখ্যা

a state in which a body tends to return to its original position after being disturbed.

২৮.
What is the type of force applied while pushing a car?
  1. ক
    Frictional Force
  2. খ
    Gravitational Force
  3. গ
    Tension Force
  4. ঘ
    Muscular Force
সঠিক উত্তর: ঘ
Muscular Force
উত্তর
সঠিক উত্তর: ঘ
Muscular Force
ঘ
ব্যাখ্যা

The force applied while pushing a car is muscular force, which is generated by the muscles in the body.
When a person pushes a car, their muscles exert force on the car in the direction they want to move it. This force is transmitted through the body to the car.Unlike other forces, such as friction or gravitational force, muscular force is a voluntary force, controlled by the action of muscles and bones

২৯.
 In which direction should the force be applied to balance a force in the direction of North-East direction?
  1. ক
    South
  2. খ
    West
  3. গ
    South-West
  4. ঘ
    North-East
সঠিক উত্তর: গ
South-West
উত্তর
সঠিক উত্তর: গ
South-West
গ
ব্যাখ্যা

A force will ballance if we applied a equal force in opposite direction.