Search Previous Year Questions

The correct answer is Lining of lung alveoli, for gas exchange.

Key Points

• The tissue described is the Simple Squamous Epithelium, which is characterized by a single layer of extremely thin, flat, and scale-like cells.
• These cells form a delicate lining that facilitates the transport of substances across a semi-permeable membrane through the process of diffusion.
• In the Lung Alveoli, this thinness is critical for the efficient exchange of Oxygen and Carbon Dioxide between the air sacs and the surrounding capillaries.
• Due to its minimal thickness, it provides the shortest possible distance for gas molecules to travel, ensuring rapid respiratory exchange.

 Additional Information

• Stratified Squamous Epithelium:
• Found in the Skin, where epithelial cells are arranged in many layers to prevent wear and tear and provide protection to the body.
• Cuboidal Epithelium:
• Found in the Lining of Kidney Tubules and ducts of salivary glands.
• Consists of cube-shaped cells that provide mechanical support and assist in secretion and absorption.
• Columnar Epithelium:
• Found in the Inner Lining of the Intestine, where tall, pillar-like cells facilitate absorption and secretion.
• In parts like the respiratory tract, these may have Cilia (hair-like projections) to move mucus forward.

The correct answer is An oxidising agent.

Key Points

• Bleaching powder, chemically identified as Calcium Hypochlorite, has the molecular formula CaOCl₂. It is widely recognized as a powerful oxidising agent in various industrial chemical processes.
• Its oxidative capability stems from its ability to release nascent oxygen. When bleaching powder reacts with moisture or dilute acids, it liberates Chlorine gas, which subsequently forms Hypochlorous acid (HClO) in the presence of water.
• The Hypochlorous acid further decomposes to yield Nascent Oxygen ([O]). This nascent oxygen is highly reactive and facilitates the oxidation of colored organic compounds, turning them into colorless substances, which is the fundamental mechanism of bleaching.
• In the Textile Industry, it is used for bleaching cotton and linen, while in the Paper Industry, it is utilized to whiten wood pulp.
• Beyond bleaching, its role as an oxidising agent makes it essential for disinfecting drinking water supplies by destroying bacteria and other harmful microorganisms through cellular oxidation.

 Additional Information

• Chemical Preparation:
• Bleaching powder is manufactured by the action of Chlorine gas on dry slaked lime (Calcium Hydroxide, Ca(OH)₂).
• The industrial production typically occurs in a Hasenclever plant or a Bachmann plant.
• Conceptual Distinctions:
• Reducing Agent: These substances donate electrons and undergo oxidation themselves. Bleaching powder acts as an electron acceptor, making it the opposite of a reducing agent.
• Neutralising Agent: These are used to balance pH levels in acid-base reactions. Although bleaching powder is slightly basic, its primary industrial utility is its redox potential rather than its acidity-correcting properties.
• Catalyst: A substance that speeds up a reaction without being consumed. Bleaching powder is a reactant that is chemically transformed during the bleaching and disinfection process.
• Chloroform Production: It is also used as a key reagent in the synthesis of Chloroform (CHCl₃) through its reaction with ethanol or acetone.

The correct answer is 3000.

Key Points

• Frequency is defined as the number of complete cycles, vibrations, or oscillations that occur per unit of time. The standard SI unit for frequency is the Hertz (Hz).
• One Hertz corresponds to one vibration per second. Therefore, a sound source with a frequency of 50 Hz completes exactly 50 vibrations every second.
• The time duration provided in the problem is one minute. To calculate the total number of vibrations using the standard formula, the time must be converted into seconds.
• Since 1 minute is equal to 60 seconds, the total time interval for the observation is 60 seconds.
• The total number of vibrations is calculated by multiplying the frequency by the total time (Total Vibrations = Frequency × Time).
• Substituting the values: 50 vibrations/second × 60 seconds = 3000 vibrations. Thus, the source completes 3000 full cycles in one minute.

 Additional Information

• Time Period (T): It is the time required for one complete vibration. It is the inverse of frequency (T = 1/f). For a frequency of 50 Hz, the time period is 1/50 = 0.02 seconds.
• Audible Range: The range of frequencies that the average human ear can perceive is between 20 Hz and 20,000 Hz. A 50 Hz sound is within the audible spectrum and is perceived as a very low-pitched sound.
• Pitch and Frequency: The pitch of a sound depends on the frequency of the vibration. Higher frequency results in a high-pitched or shrill sound, whereas lower frequency results in a deep or bass sound.
• Infrasonic and Ultrasonic:
• Frequencies below 20 Hz are known as infrasonic sounds, which are often produced by earthquakes or large animals like elephants.
• Frequencies above 20,000 Hz are known as ultrasonic sounds, used in medical imaging (Ultrasound) and by animals like bats for navigation.
• Wave Equation: The relationship between the speed of sound (v), frequency (f), and wavelength (λ) is given by v = f × λ.

The correct answer is Hydra.

Key Points

• Hydra is a multicellular freshwater organism belonging to the phylum Cnidaria. It is primarily known for reproducing through budding, an asexual process where a small outgrowth or bud forms on the parent body due to repeated mitotic cell divisions at a specific site.
• Once the bud matures and develops tiny tentacles and a mouth, it constricts at the base and detaches to become a new independent organism. This is distinct from fission, which involves the splitting of a single parent cell.
• Amoeba, Leishmania, and Paramecium are all unicellular protozoans that reproduce through various forms of fission, where the parent cell divides into two or more daughter cells.
• Fission is the simplest method of asexual reproduction in single-celled organisms, while Hydra utilizes more complex cellular differentiation and regenerative cells for its reproductive processes.

 Additional Information

• Amoeba:
• Reproduces via simple binary fission, where the division of the nucleus and cytoplasm can occur along any plane or axis.
• Leishmania:
• The causative parasite of Kala-azar (Visceral Leishmaniasis).
• It exhibits binary fission in a definite longitudinal orientation in relation to its whip-like flagellum.
• Paramecium:
• A ciliated protozoan that typically undergoes transverse binary fission.
• It possesses two types of nuclei, a macronucleus and a micronucleus, both of which participate in the division process to ensure genetic continuity.

Shortcut Trick

The total difference in percentage = Gain % − (Loss %) = 19% − (−6%) = 25%.

This 25% change is equal to the increase in Selling Price of ₹960.

25% of Cost Price = ₹960

⇒ 100% of Cost Price = 960 × 4 = ₹3840.

∴ The correct answer is ₹3840.

Alternate Method

Given:

Initial Loss = 6%

Final Gain = 19%

Increase in Selling Price (SP) = ₹960

Formula Used:

SP = CP × (100 ± Profit or Loss %)/100

Let the Cost Price (CP) be ₹x.

⇒ Initial Selling Price (SP₁) = x × (100 − 6)/100 = 0.94x

⇒ New Selling Price (SP₂) = x × (100 + 19)/100 = 1.19x

⇒ According to the question: SP₂ − SP₁ = 960

⇒ 1.19x − 0.94x = 960

⇒ 0.25x = 960

⇒ x = 960 ÷ 0.25

⇒ x = 960 × 4 = 3840

∴ The correct answer is ₹3840.

Additional Information

Profit and Loss Percentage

Profit % = (Profit ÷ CP) × 100 and Loss % = (Loss ÷ CP) × 100. Both are always calculated on the Cost Price unless stated otherwise.

Selling Price Calculation

When Profit % is P, SP = CP × (100 + P)/100. When Loss % is L, SP = CP × (100 − L)/100.

Marked Price and Discount

Discount is always calculated on the Marked Price (MP). SP = MP − Discount. Discount % = (Discount ÷ MP) × 100.

Shortcut Trick

Total Work = LCM(10, 15, 20) = 60 units.

Efficiencies: A = 6, B = 4, C = 3; Combined (A+B+C) = 13 units/hr.

Work done by A and B in 2 hr = (6 + 4) × 2 = 20 units.

Remaining work = 60 − 20 = 40 units.

Time for remaining work (t) = 40 ÷ 13 ≈ 3 hr

∴ The correct answer is 3 hr.

Alternate Method

Given: Time taken by A = 10 hr, B = 15 hr, and C = 20 hr.

Formula: Efficiency = Total Work ÷ Time Taken

⇒ Efficiency of A and B working together = 6 + 4 = 10 units/hr

⇒ Work done by A and B in the first 2 hr = 10 × 2 = 20 units

⇒ Remaining work to be completed = 60 − 20 = 40 units

⇒ Combined efficiency of A, B, and C = 6 + 4 + 3 = 13 units/hr

⇒ Time taken to finish remaining work (t) = 40 ÷ 13 ≈ 3.08 hr

⇒ So, the value of t = 3 hr

∴ The correct answer is 3 hr.

Additional Information

Total Work using LCM

Taking the Least Common Multiple (LCM) of individual time periods is the most efficient way to assign a value to total work.

Efficiency Relation

Efficiency is inversely proportional to the time taken to complete the work (E ∝ 1/T).

Combined Work Formula

If multiple people work together, their individual efficiencies are added to find the total rate of work per unit time.

Shortcut Trick

Total Area printed = Number of revolutions × Curved Surface Area (CSA)

4158 = 350 × 2 × (22/7) × r × 2.1

4158 = 44 × 350 × 0.3 × r

4158 = 4620 × r ⇒ r = 4158 ÷ 4620 = 0.9 m

r = 0.9 × 100 cm = 90 cm

∴ The correct answer is 90 cm.

Alternate Method

Given:

Length of the cylindrical drum (h) = 2.1 m

Number of revolutions (n) = 350

Total printed area = 4158 m²

Formula Used:

Curved Surface Area of Cylinder = 2 × π × r × h

Total Area = n × Curved Surface Area

Calculations:

⇒ Total Area = n × (2 × π × r × h)

⇒ 4158 = 350 × 2 × (22/7) × r × 2.1

⇒ 4158 = 350 × 2 × 22 × r × 0.3

⇒ 4158 = 4620 × r

⇒ r = 4158 ÷ 4620

⇒ r = 0.9 m

⇒ r = 0.9 × 100 cm

⇒ r = 90 cm

∴ The correct answer is 90 cm.

Additional Information

Volume of a Cylinder

The capacity of a cylindrical container is given by the formula V = πr²h.

Total Surface Area of a Cylinder

It includes the curved area and the areas of the two circular bases: TSA = 2πr(r + h).

Unit Conversion

Always ensure units are consistent. 1 meter (m) = 100 centimeters (cm) and 1 m² = 10,000 cm².

Shortcut Trick

Test the standard trigonometric values for θ within the range 0° ≤ θ ≤ 90°.

If we put θ = 90°, then cos 90° = 0 and sin 90° = 1.

LHS: 10(0)² + 7(1)² = 0 + 7 = 7. Since LHS = RHS, θ = 90° is correct.

Value required: sin 90° + cos 90° = 1 + 0 = 1.

∴ The correct answer is 1.

Alternate Method

Given: 10 cos² θ + 7 sin² θ = 7 and 0° ≤ θ ≤ 90°

Formula Used: sin² θ + cos² θ = 1

⇒ 10 cos² θ + 7 sin² θ = 7

⇒ 3 cos² θ + 7 cos² θ + 7 sin² θ = 7

⇒ 3 cos² θ + 7(cos² θ + sin² θ) = 7

⇒ 3 cos² θ + 7(1) = 7

⇒ 3 cos² θ = 7 − 7

⇒ 3 cos² θ = 0

⇒ cos θ = 0

⇒ Since 0° ≤ θ ≤ 90°, θ = 90°

⇒ Now, sin θ + cos θ = sin 90° + cos 90°

⇒ 1 + 0 = 1

∴ The correct answer is 1.

Additional Information

Trigonometric Identities

Fundamental identities include sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, and 1 + cot²θ = cosec²θ.

Specific Values for Sine and Cosine

sin 0° = 0, sin 90° = 1 | cos 0° = 1, cos 90° = 0.

Quadratic Form in Trig

Equations of the form a cos²θ + b sin²θ = c can be solved by converting all terms to either sin²θ or cos²θ using basic identities.

Shortcut Trick

Value of one-third of the number = Final Result − Increase

⇒ 51 − 37 = 14

Original number = 14 × 3 = 42

Sum of the digits = 4 + 2 = 6

∴ The correct answer is 6.

Alternate Method

Given:

Let the original number be x.

According to the question, one-third of x increased by 37 equals 51.

Calculations:

⇒ (x/3) + 37 = 51

⇒ x/3 = 51 − 37

⇒ x/3 = 14

⇒ x = 14 × 3

⇒ x = 42

Now, calculate the sum of the digits of 42:

⇒ Sum = 4 + 2 = 6

∴ The correct answer is 6.

Additional Information

Linear Equation in One Variable

An equation of the form ax + b = c, where x is the unknown variable and a, b, c are constants.

Digit Sum Concept

The digit sum is the sum of all individual digits of a number. For example, for 123, the sum is 1 + 2 + 3 = 6.

Divisibility by 3 and 9

A number is divisible by 3 (or 9) if the sum of its digits is divisible by 3 (or 9).