Search Previous Year Questions

1. In a row, Kishore is at 11^th place from the left and Pratik is at 13^th place from the right.

2. They interchange their positions, Kishore becomes 15^th from the left.

=> The total number of persons = Kishore position from left + Kishore position from right - 1

=> The total number of persons = 15 + 13 - 1 = 28 - 1 = 27

Hence, “27” person were seated in the row.

The Correct answer is F × s

Key Points

• The formula for work done is: W = F × s, where W is the work done, F is the constant force applied, and s is the distance through which the force is applied.
• In this scenario, the girl pushes the trolley with a constant force of F over a distance s. The work done is the product of the force applied and the distance moved in the direction of the force.
• Work is a scalar quantity, and its unit in the SI system is Joule (J), where 1 Joule = 1 Newton meter (N·m). The formula reflects this relationship.

The correct answer is Damoh.

In News

• Child marriages in Madhya Pradesh have risen by 47% since 2020, with Damoh district emerging as the worst hotspot in 2025.

Key Points

• Child marriage cases in Madhya Pradesh increased from 366 in 2020 to 538 in 2025, marking a 47% rise.
• Damoh district alone accounted for 21% of all child marriages in 2025, with cases rising sharply from 33 in 2024 to 115 in 2025.
• The rise in child marriages is notably concentrated in Bundelkhand, central MP, Gwalior–Chambal, and tribal areas, indicating socio-economic vulnerabilities.
• Despite ongoing awareness campaigns, child marriages continue to be a persistent issue in certain districts of Madhya Pradesh.

Additional Information

• District-Level Statistics
• Damoh: 115 cases of child marriage in 2025 (21% of MP's total cases).
• Increase from 33 cases in 2024 to 115 in 2025 highlights a severe surge.
• Statewide Data
• Rise from 366 cases in 2020 to 538 cases in 2025, despite efforts to raise awareness and reduce child marriages.
• Key Vulnerable Regions
• Bundelkhand, central MP, Gwalior–Chambal, and tribal belts are the worst affected areas.
• Socio-economic factors like poverty, illiteracy, and entrenched cultural practices contribute to the problem.
• Impact of Awareness Campaigns
• Although campaigns are ongoing, child marriage rates remain alarmingly high in specific districts.
• Greater efforts are required to address the root causes and ensure effective implementation of the law.

Given:

sin A = 6/7

Concept:

sin²A + cos²A = 1 and

sec A = 1/cos A

Calculation:

⇒ cos A = √(1 - sin² A)

⇒ √(1 - (6/7)²) = √(1 - 36/49)

⇒ √(13/49) = √(13)/7

⇒ sec A = 1/cos A = 7/√(13)

Hence, the value of sec A is 7/√(13).

The logic is:

Hence, ‘GRQ’ is the correct answer.

Given:

The perimeter of an isosceles triangle = 91 cm.

One of the equal sides measures 28 cm.

Concept used:

An isosceles triangle two angles will also be the same in front of the equal sides.

Formula used:

P = (2a + b)

Where, p = perimeter

a = side and b = another side

Calculation:

Let the length of the equal sides be x

P = (2a + b)

⇒ 91 = 2 × 28 + b

⇒ (91 – 56) = b

⇒ 35 = b

∴ The length of the non-equal side is 35 cm.

∴ Option 4 is the correct answer.

The correct answer is m g h.

Key Points

• Gravitational potential energy is the energy possessed by an object due to its position in a gravitational field.
• The formula for gravitational potential energy is given by U = mgh, where 'm' is mass, 'g' is the acceleration due to gravity, and 'h' is the height.
• This formula assumes that the height 'h' is small compared to the radius of the Earth, so the gravitational force can be considered constant.
• The unit of gravitational potential energy in the International System of Units (SI) is the Joule (J).

Additional Information

• Gravity
• Gravity is a force that attracts two bodies towards each other, depending on their masses and the distance between them.
• The acceleration due to gravity on Earth is approximately 9.8 m/s².
• Potential Energy
• Potential energy is the stored energy of an object due to its position or state.
• It can be converted into other forms of energy, such as kinetic energy.
• Kinetic Energy
• Kinetic energy is the energy that an object possesses due to its motion.
• The formula for kinetic energy is given by KE = 0.5 * m * v², where 'm' is mass and 'v' is velocity.
• Conservation of Energy
• The law of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another.
• In a closed system, the total energy remains constant.

The correct answer is option 1.

Key Points

Dry Ports in Madhya Pradesh:

• First Dry Port:
• Established in 1994 at Pithampur in Dhar district by Container Corporation of India Limited (CONCOR), a Central Government undertaking. Hence, option 1 is correct.
• Second Dry Port:
• The second dry port was established at Mandideep in Raisen district.
• Dry Port at Mangliya:
• A dry port was established in 2017-18 at Mangliya, located on the Indore-Dewas border.
• Largest Dry Port in South Asia:
• In 2019-20, the second largest dry port of South Asia is being built at Tihi, 5 km away from Pithampur, Dhar district.
• The dry port at Tihi is being developed over 40 hectares.
• ICD Tughlakabad:
• South Asia's first and largest dry port is located at Tughlakabad, Delhi, and spans 44 hectares. It is also known as ICD (Inland Container Depot) Tughlakabad.

Given:

The radius of a circle = 50 cm

Distance of chord AB from the center of the circle = 14 cm

Formula used:

In a circle, the perpendicular bisector of a chord passes through the center of the circle.

If a perpendicular is drawn from the center of a circle to a chord, it bisects the chord.

In a right triangle, the square of the hypotenuse (longest side) is equal to the sum of the squares of the other two sides.

Calculation:

Let's solve the question:

First, let's draw a rough diagram of the circle and chord AB:

Let O be the center of the circle, and let M be the midpoint of the chord AB. Draw OM, which is the perpendicular bisector of AB.

By the property of perpendicular bisectors, OM passes through the center O of the circle.

Since OM is perpendicular to AB, we can use the Pythagorean theorem to find the length of AM (or BM), which is half of the chord AB:

\(AM^2 + OM^2 = OA^2\ AM^2 + 14^2 = 50^2\ AM^2 = 50^2 - 14^2\ AM = BM = √(50^2 - 14^2)\ AM = BM = √(2500 - 196)\ AM = BM = √2304\ AM = BM = 48\)

Therefore, the length of the chord AB is:

AB = 2 × AM

= 2 × 48

= 96 cm

The diameter of the circle is twice the radius, so it is:

diameter = 2 × radius

= 2 × 50

= 100 cm

Therefore, the sum of the chord AB and the diameter of the circle is:

AB + diameter = 96 + 100

= 196 cm

Hence, the sum of chord AB and the diameter of this circle is 196 cm.

(Left) 2 @ 1 ϕ $ λ £ 5 3 & 9 # * 2 @ 6 7 & % 3 £ 2 & 1 5 (Right)

Logic: symbol ⇔ number ⇔ number

Numbers are there, each of which is immediately preceded by a symbol and also immediately followed by a number

2 @ 1 ϕ $ λ £ 5 3 & 9 # * 2 @ 6 7 & % 3 £ 2 & 1 5

In the above series, only 3 numbers follow this sequence 

Hence, the correct answer is "3".