MP Police SI (Technical) Mock Test - 5 - MP Police SI MCQ

Given,

The average weight of the students in a group = 75.4 kg

Let the total number of students be .

As we know,

Average

Total weight of all students

Next, we have that four students added to the class weighing 72.9 kg, 73.8 kg, 79.5 kg and 87.4 kg 313.6 kg

The total number of students will be .

The average weight is increased by

So the new average weight kg

Now,

Total weight of all students

Initially, the number of students in the group was 46.

The particle is said to move at a constant speed only change in direction affects the acceleration.

To calculate the average acceleration, we recall the formula given by:

where is the average acceleration, is the final velocity, is the initial velocity and is the time taken.

Now, after a half cycle, the direction of the velocity changes direction to opposite the direction before the half cycle, hence, we can say that initial velocity and final velocity  

Hence, by substitution, we have that

Now, we also know that

so

Substituting into

We have

Since it is a half revolution of a circle, the total distance covered is given by:

So,

Given:

A can do of a work in 10 days.

B can do of the some work in 10 days.

Calculation:

Let, the total work be 100 units.

So, units

A can do 40 units in 10 days.

Also, units

can do 50 units in 10 days.

Efficiency of units/day

Efficiency of units/day

Efficiency of units/day

They both work together for 5 days.

Work done in 5 days units day days units

Remaining work = Total work - Work done units

Time taken to complete the work alone days

The dimensional formula is used to express any physical quantity in terms of fundamental quantities.

• Dimensional Analysis: It is a technique adopted to derive a relationship between various physical quantities using their dimensions and units of measurement. The two basic rules followed in the dimensional analysis are:
• Only those quantities that have the same dimensions can be added and subtracted from each other.
• Two physical quantities are equal if they have the same dimensions.​

Dimensional unit of mass = [M]

Dimensional unit of acceleration (unit:

We know that,

Force

Therefore, the dimensional formula of force

The terms a is subtracted from bt. Thus, they will have the same dimensions.

On the LHS is a force whose dimensional formula is .

Therefore, the dimensional formula of and bt will be

On equating,

The units for length , mass and time are meter , kilogram and second respectively.

Substituting the units for dimensions and ,

and

Nylon is a polymer which contains nitrogen. It contains amide linkage as shown below.

Nylon is used in making bristles for brushes, in the manufacture of cords, sheets, ropes etc.

Given:

Radius cm

Distance of from the centre is cm.

We know that:

If from one external point, two tangents are drawn to a circle then they have equal tangent segments.

So,

In the given figure,

cm

In :

cm

In the horizontal direction, the stone is thrown horizontally, so there is no acceleration acting on it. Therefore, the horizontal velocity remains constant throughout the motion. The horizontal distance traveled by the stone is given by:

horizontal velocity time

In the vertical direction, the stone experiences free fall motion with constant acceleration due to gravity. The time taken for the stone to hit the ground can be found using the equation:

where is the height of the building and is the acceleration due to gravity .

Using the given values, we can calculate the time taken for the stone to hit the ground:

Simplifying this equation gives:

seconds

Now we can substitute the value of t into the equation for the horizontal distance traveled to find R:

horizontal velocity t

Therefore, the stone hits the ground at a distance of 24 meters from the building.

On dropping a sheet of paper and a stone from the same height on the earth together, the paper will reach the ground after the stone. This is due to the resistance of the air. Air exerts resistance on falling moving objects due to friction. The resistance of air on paper is greater than that on stone.

Kepler’s laws of planetary motion:

The law of Orbits: Every planet moves around the sun in an elliptical orbit with the sun at one of the foci.

The law of Area: The line joining the sun to the planet sweeps out equal areas in equal intervals of time. i.e., areal velocity is constant.

According to this law, the planet will move slowly when it is farthest from the sun and more rapidly when it is nearest to the sun. It is similar to the law of conservation of angular momentum.

The law of periods: The square of the period of revolution (T) of any planet around the sun is directly proportional to the cube of the semi-major axis of the orbit i.e., T² ∝ r³

According to the law of periods:

⇒ T² ∝ r³

Let the speed of train be .

Distance length of

Speed of first person be , Speed of second person be

Relative speed, person moving opposite direction,

First person passes

Second person passes

Substitute the value of in equation (1)

The length of the train is .

A quantity which can be measured and by which various physical phenomenon can be explained in the form of laws is called a physical quantity. For example length, mass, time, force etc.

Measurement is necessary to determine the magnitude of a physical quantity, to compare two similar physical quantities and to prove physical laws or equations.

Physical quantity Magnitude Unit

Where represents the numerical value and u represents the unit.

constant

constant

Given,

Radius

As we know,

Area of the circle

Area of circle

cm

8 woodcutters cut 15000 cft timber in 1 week

So 4 woodcutters cut in 1 week

In four weeks they will cut 7500 × 4 = 30000 cft

∴ Correct answer is 30000

Taking all person of same nationality as one person, then we will have only three people.

These three person can be arranged themselves in 3! Ways.

8 Indians can be arranged themselves in 8! Way.

4 American can be arranged themselves in 4! Ways.

4 Englishman can be arranged themselves in 4! Ways.

Hence, required number of ways = 3! 8! 4! 4! Ways.

On the Kelvin scale, the boiling point of the water or steam point is considered to be and its freezing point is . Whereas it was assumed that at when there is no relative motion of particles. The change in temperature of corresponds to a change of less than on the Celsius scale.

In

(radii of circles)

In

(radii of circles)

Hence, the correct option is (B).

Given:

The average price of mobile phones is Rs.

The highest and lowest price mobile phones are sold out then the average price of the remaining mobile phones is Rs.

The cost of the highest mobile phone Rs.

We know that,

Average

Average price of mobile phones is

Sum of price of mobile phones is Rs.

Sum of price of mobile phones is Rs.

Sum of highest and lowest price of phones Rs.

Cost of lowest mobile phone Rs.

I.

II.

Then,

So, when for

And when for

So, we can observe that .

According to the question, sin θ and cos θ are the roots of the equation ax² + bx + c = 0,

sin θ + cos θ = ----(i)

sin θ . cos θ = ----(ii)

(sinθ + cos θ)² = sin²θ + cos²θ + 2 sin θ cos θ ----(iii)

Form (i), (ii) and (iii), we get

⇒ b² = a² + 2ac

⇒ a² - b² + 2ac = 0

As we know,

Efficiency ratio is inversely proportional to time

Efficiency ratio of and

Efficiency of

Efficiency ratio of to

Total work units

Work done by in days units

∴ Remaining work units

∴ Time taken by and to complete units days

Force: The interaction which after applying on a body changes or try to change the state of rest or state of motion is called force.

Force, F = m × a

Where m is the mass of the object and a is the acceleration of the object.

The net force is defined as the vector sum of the forces acting on an object.

Given that,

Mass of the block, m = 12 kg

Net force = 50 - 20 = 30 N

Net force, F = m × a

30 = 12 × a

Acceleration, a = 2.5 m/s²

As we know that the average is the middle number of the series.So in the first 13 numbers, 7th number = x. 13th number = x+6. So in the next 19 numbers, the first number will be (x+7) and the last one will be (x+25).

Average of the next 19 numbers

According to the question,

A train of length m takes seconds to cross another train ‘’ m long from the opposite direction,

Total distance

Relative speed m/s

Formula:

m

So, the value of is m

Given:

is the centre of circle.

and are the radii of circle.

The parallel chords of the circle have values equal of cm and cm respectively.

Distance between parallel chords () cm

Concepts:

The line drawn from the centre of the chord of a circle is perpendicular to the chord and bisects the chord of the circle.

In right – angled triangle, Hypotenuse Perpendicular Base

Calculation:

Let and be the parallel chords of length cm and cm respectively.

Distance between parallel chords cm

In , line (length “”) drawn from centre meets chord at .

In

.....(i)

In , line (length “”) drawn from centre meets chord at .

cm cm

In ,

.....(ii)

Equating (i) and (ii)

cm

Distance between small chord and centre of the circle is equal to cm.

Gravitational force is responsible of objects falling back on Earth, revolution of Earth around Sun and Moon around Earth. It allows everything in the Universe to be in controlled motion.

Gravity is not a dissipative force since no energy is lost from a system when motion takes place. Further it is also very weak force.

I.

II.

Comparison between x and y (via Tabulation):

∴ Relation between x and y cannot be established.

A cricket ball has maximum inertia because inertia is the quantity that depends solely on the mass of the body. The more mass, the more inertia.

Given:

x² + bx + c = 0

The roots of the equation are two consecutive integers.

As we know,

Quadratic equation = x² - (sum of roots)x + product of roots

x² + bx + c = 0 ---(1)

Let the roots are n, n + 1.

So, a quadratic equation will be,

x² - (n + n + 1)x + n(n + 1) = 0

⇒ x² - (2n + 1)x + n(n + 1) = 0

So,

⇒ b² - 4ac = (2n + 1)² - 4n(n+ 1)

∵ (a + b)² = a² + 2ab + b²

⇒ b² - 4ac = 4n² + 4n + 1 - 4n² - 4n

⇒ b² - 4ac = 1