Indian Navy MR Mock Test - 1 - Airforce X Y / Indian Navy SSR MCQ

Let the cost price of the article be Rs. x, then
According to the question,
180 – x = x – 120
⇒ x + x = 180 + 120
⇒ 2x = 300
⇒ x = (300/2) = 150
Cost Price of the article = Rs. 150
Profit = 180 – 150 = 30
Profit percentage = (30/150) x 100 = 20%

The given details are:
Working 8 hours a day, Ashu can complete work in = 18 days
Working 1 hour a day, Ashu can complete the work in = 18×8 = 144 days
∴ Number of hours Ashu should work to complete the work in 12 days:
= 144/12 = 12 hours/day

Given:
f(x) = 4x3+2x2+5x−a
and x = 3
When we put the value of root in the polynomial, then the value of the polynomial is equal to zero.
F(3) = 4(3)³ + 2(3)² + 5(3) − a
⇒ 0 = 108 + 18 + 15 − a
⇒ 0 = 141 − a
⇒ a = 141
∴ Value of a is 141.

Given:
x⁴ - 3x³ + 4x² - 3x + 5 and x = 3
(3)⁴ - 3(3)³ + 4(3)² - 3(3) + 5
⇒ 81 - 81 + 36 - 9 + 5
⇒ 27 + 5
⇒ 32

Sodi­um is an el­e­ment in the 1 group of the 3 pe­ri­od of the Pe­ri­od­ic Ta­ble. It is a sil­very-white met­al. It is quite mal­leable and soft (metal­lic sodi­um can eas­i­ly be cut with a knife or scalpel, and a fresh cut shines in the air). It has high ­con­duc­tiv­i­ty.
It has a low melting point and reacts vigorously with water.
Chemical reaction:
2Na(s) + 2H₂O → 2NaOH(aq) + H₂(g)

Let, 'n' be the number of cylinders that can be formed;
∴ Volume of spherical ball = n × Volume of one cylinder

⇒ n = 2700.

Let rate is R%
According to the question,

So, R = 5%

Let AB be the chord and O be the center of the circle.
Also OP perpendicular to AB
In ΔOPB,
OB² = PB² + OP²
⇒ OB² = 12² + 5²
⇒ OB² = 169
⇒ OB = 13
Diameter = 2 × OB = 26

Given:
Ratio of A, B, C and D = 3 : 7 : 11 : 13
Let, share of A = Rs. 3x
Share of B = Rs. 7x
Share of C = Rs. 11x
Share of D = Rs. 13x
According to question,
⇒ 3x + 7x + 11x + 13x = 3162
⇒ 34x = 3162
⇒ x = 93
∴ Share of D = 13 × 93 = Rs. 1209

Dry ice is the common name for the solid form of carbon dioxide.

• It's called dry ice because it doesn't melt into a wet liquid.
• Dry ice sublimates, which means it goes from its solid form directly to its gaseous form.

The substances in which heat is transmitted easily and rapidly through the conduction method are called good conductors. The thermal conductivity of an ideal conductor is infinite and the thermal resistance is zero. For example, gold, silver, copper, aluminum, etc. Silver has the highest thermal conductivity.

Distance covered by the first train in 2 hrs = 40 × 2 = 80 km
Let the speed of the second train be x km/hr
According to the question
Speed = Distance/Time
⇒ (x – 40) = 80/4
⇒ x – 40 = 20
⇒ x = 20 + 40
∴ x = 60 km/hr.

Given:
(999)² - 2²
We know that,
a² – b² = (a + b) × (a – b)
According to the formula used,
(999)² - 2²
= (999 + 2) × (999 – 2)
= (1001) × (997)
= (1000 + 1) × (997)
= (1000 × 997) + (1 × 997)
= 997000 + 997
= 997997
∴ The value of (999)² – 2² is 997997.

Given:
The distance of chord MN from the center is 15 cm
The length of chord MN is 40 cm
Concept:
Chord length using perpendicular distance from the centre = 2 × √ (r² – d²) [∵ r = radius, d = perpendicular distance]
Calculation:

Length of Chord = 2 × √ (r² – d²)
40 =  2 × √ (r² – 15²) = 25 cm
∴ Option 4 is the correct answer.

Given:
20% of P = 30% of Q = 1/6 of R
Calculation:
20% of P = 30% of Q = 1/6 of R

Similarity, 

∴ P : Q : R = 15 : 10 : 18

• Kinetic energy (K.E): The energy possessed by a body by the virtue of its motion is called kinetic energy.

The expression for kinetic energy is given by:
KE = (1/2)mv²
Where m = mass of the body and v = velocity of the body

• Momentum (p): The product of mass and velocity is called momentum.

Momentum (p) = mass (m) × velocity (v)

Given:
25 ÷ 5 of 12 × 2 − 9 ÷ 27 of 3 × 5 − 14 ÷ 28 × 4 
Concept used:
Bodmas 

Calculation:
Here, using the rule of bodmas , we have 
25 ÷ 5 of 12 × 2 - 9 ÷ 27 of 3 × 5 - 14 ÷ 28 × 4 
⇒ 25 ÷ 60 × 2 - 9 ÷ 81 × 5 - 14 ÷ 28 × 4 
⇒ 25/60 × 2 - 9 /81` × 5 - 14/28 × 4
⇒ 5/12 × 2 - 1/9 × 5 - 1/2 × 4 
⇒ 5/6 - 5/9 - 2 
⇒ (15−46)/18  = -31/18 
Hence, the required value is -31/18.

Given:
2m + 8w = 5 days
3m + 4w = 6 days
Formula used:
Total work = Efficiency × days 
Calculations:
⇒ (2m + 8w)5 = (3m + 4w)6
⇒ 10m + 40w = 18m + 24w
⇒ 16w = 8m
⇒ m/w = 2/1
⇒ Total work = (2 × 2 + 8 × 1) × 5
⇒ Total work = 12 × 5 = 60
Time taken by 1m and 2 w = 60/(1 × 2 + 2 × 1)
⇒ 15 days
∴ Time taken by 1 man and 2 woman is 15 days.

Pooja sells an article to Shweta at a% profit and then Shweta sells the same article to Barkha for b% profit. If Barkha buys the article at Rs. x,
The price at which Pooja buys the same article = y
Then,
⇒ x = (100% + a%) × (100% + b%) × y
According to the question,
⇒ 660 = (100% + 10%) × (100% + 20%) × y
⇒ 660 = 110% × 120% × y
⇒ 660 = 1.1 × 1.2 × y
⇒ 660 = 1.32 × y
⇒ y = Rs. 500
Therefore, 'Rs. 500' is the required answer.

• Given mass of body (m) = 50 kg
• h = 41×15 = 615 cm = 6.15 m
• t = 10 s, g = 10 ms^–2
• Potential energy = mgh
  • = 50 × 10 × 6.15
  • = 3075
• Power = Workdone/time
  • = (3075/10) 
  • = 307.5 W

Given:
Diagonal of the square = 16 cm

Concept used:
Diagonal of a square = a√2
Area of a square = a²
where a is the length of its side.
Calculation:
Side of the square = 16 ÷ √2 = 8√2
Area of the square = (8√2)² = 128 cm²
∴ The area of a square inscribed in a circle, whose diagonal is 16 cm, is 128 cm².

Given:
(sin⁴ 45°+ cos⁴ 60°) + (tan⁴ 45°+ cot⁴ 45°) 
Concept Used:

Calculation:
⇒ According to the question,
⇒ (sin⁴ 45°+ cos⁴ 60°) + (tan⁴ 45°+ cot⁴ 45°) 
⇒ Putting the values of the angles in the above equation we get,

Therefore, the value of (sin⁴ 45°+ cos⁴ 60°) + (tan4 45°+ cot4 45°) is 37/16. 

• Glass is optically denser than water.
• Refractive indices of materials in ascending order are Air, Water, and Glass.
• The Refractive index is the ratio of the speed of mild in a vacuum to its velocity in a specific medium.
• Air has the bottom refractive index. Diamond has the best refractive index.
• A medium is more uncommon when the speed of light increments when the light goes through that medium.
• The speed of light in air is more than the speed of light in the glass, and that implies air is optically more uncommon than glass.

• Energy can neither be created nor destroyed, but it can be converted into one another. It is called the Law of conservation of energy.
• The law of conservation of energy states that “In a closed system, i.e., a system that is isolated from its surroundings, the total energy of the system is conserved.”

• The carbon atom is tetravalent even though it has unpaired electrons.
• It is determined that the floor kingdom of a neutral carbon atom does indeed contain two unpaired electrons.
• The Co²⁺ ion in an aqueous answer is octahedrally coordinated and paramagnetic, with 3 unpaired electrons.

J. B. Dunlop invented the Pneumatic rubber tyre.
John Boyd (J.B.) Dunlop (5 February 1840 – 23 October 1921) was a Scottish inventor and veterinary surgeon who spent most of his career in Ireland. Familiar with making rubber devices, he re-invented pneumatic tyres for his child's tricycle and developed them for use in cycle racing. 

The correct pair of the country - capital are: Cuba - Havana

• Cuba officially the Republic of Cuba is a country comprising the island of Cuba, as well as Isla de la Juventud and several minor archipelagos. Cuba is located where the northern Caribbean Sea, Gulf of Mexico, and Atlantic Ocean meet.
• Havana is the capital and largest city of Cuba. The heart of the La Habana province, Havana is the country's main port and leading commercial center. The city has a population of 2.1 million inhabitants, and it spans a total of 781.58 km2 (301.77 sq mi) – making it the largest city by area, the most populous city, and the fourth largest metropolitan area in the Caribbean region.

The correct match is A - 1, B - 4, C - 2, D - 3.

Dandi March or Salt Satyagraha, major nonviolent protest action in India led by Mahatma Gandhi in March–April 1930.
The Poorna Swaraj declaration was promulgated by the Indian National Congress on 26 January 1930, resolving the Congress and Indian nationalists to fight for Poorna Swaraj, or complete self-rule independent of the British Empire. The flag of India was hoisted by Jawaharlal Nehru on 31 December 1929 on the banks of Ravi river, in Lahore.
Red Shirt movement was started by Abdul Ghaffar Khan of the North-West Frontier Province of India in 1930. His followers were pledged to nonviolence, and they derived their popular title from the red colour of their shirts.
The Bardoli Satyagraha, 1928 was a movement in the independence struggle led by Sardar Vallabhai Patel for the farmers of Bardoli against the unjust raising of taxes.

Dadabhai Naoroji is known as Grand Old man of India.
Dadabhai Naoroji was born on 4 September 1825 in a poor Parsi family in Bombay. He was an Indian political leader, merchant, scholar and writer. He is also called the 'unofficial ambassador of India' and has played a huge role in India gaining independence from the British.

Lavani is the traditional dance form of Maharashtra.

• It is a combination of traditional song and dance that has performed especially with the Dholki beats which is a percussion instrument.
• It has made a significant contribution to the growth of Marathi folk theatre.
• This dance form began in the 17th Century.
• The songs are sung at a fast tempo.