Given:

Logic: (2nd row - 1st row)²= 3rd row

For, 1st row

(25 - 11)²= 14²= 196

For, 2nd row

(28 - 18)²= 10²= 100

Similarly,

For, 3rd row

(23 - ?)²= ?²= 81

81​ = 9

23 - 9 = 14

So, the missing term is 14.

Thus, correct option is (c).

Logic: In option a, b and d shapes are diagonally.

Given:

PQRS is a cyclic quadrilateral inscribed in a circle with centre O.

∠PQR : ∠PSR = 11 : 7

PQ = QR (i.e., triangle PQR is isosceles)

Concept Used:

Opposite angles in a cyclic quadrilateral are supplementary:
∠PQR + ∠PSR = 180°

In an isosceles triangle (PQ = QR), base angles are equal:
∠QPR = ∠PRQ

In any triangle, the sum of all angles is 180°.

The angle subtended by a chord at the centre is twice the angle subtended at the circumference.

Formula Used:

Opposite angles in cyclic quad: ∠PQR + ∠PSR = 180°

Base angles in isosceles triangle: ∠QPR = ∠PRQ

Central angle theorem: ∠POQ = 2 × ∠PRQ

Let ∠PQR = 11x and ∠PSR = 7x

=> 11x + 7x = 180°

=> 18x = 180°

=> x = 10°

Thus, ∠PQR = 110°, ∠PSR = 70°

In triangle PQR:

PQ = QR => ∠QPR = ∠PRQ = y (say)

∠PQR = 110°, so

y + y + 110° = 180°

=> 2y = 70°

=> y = 35°

Then, ∠POQ = 2 × ∠PRQ = 2 × 35° = 70°

Now in triangle OPQ:

OP = OQ => triangle is isosceles

∠POQ = 70°, so remaining 2 angles are equal and each is:

Given:

Height of the tent = 14 units

Radius of the tent = 7 units

We need to find the area of canvas required to make the tent.

Formula Used:

The surface area of a cone (representing the tent) is given by:

Surface Area = πr l), where

r = radius of the base, l = slant height of the cone

Solution:

r = 7 units, h = 14 units

To calculate the slant height (l), we use the Pythagorean theorem:

l = √(r² + h²)

l = √(7² + 14²)

l = √(49 + 196)

l = √245

l ≈ 7√5 units

Now, using the surface area formula:

Surface Area = π × 7 × 7√5

Surface Area = π × 7 × 7√5

Surface Area ≈ 49√5π

Given:

​PARENT → PWRANT, SING → SENG

TERMINATE → ?

Logic: Shifting vowels by -4 and leaving consonants unchanged.

​​PARENT → PWRANT

So, TERMINATE becomes TARMENWTA.

Thus, the correct option is: (d)

Given:

46 → 414

52 → 468

Logic: Number × 9 = Result

Identifying the Pattern

46 → 414 = 46 × 9 = 414

52 → 468 = 52 × 9 = 468

Applying the Pattern to 67

67 × 9 = 603

Thus, the correct option (C) 603.

The correct answer is (c) lower than the pH value of milk

Explanation:

Curd vs Milk pH:

• The pH value of curd is lower than the pH value of milk. Milk generally has a pH around 6.5 to 7 (slightly acidic), while curd (or yogurt) is more acidic due to the fermentation process.
• During fermentation, lactic acid bacteria convert lactose (milk sugar) into lactic acid, which lowers the pH. As a result, the pH of curd typically ranges from 4.5 to 5.5, making it lower than the pH of milk.

Information Booster:

Fermentation process: The process of making curd involves the fermentation of lactose by lactic acid bacteria (such as Lactobacillus). The bacteria produce lactic acid, which decreases the pH, making the curd acidic.

pH Scale:

Definition: The pH scale measures the concentration of hydrogen ions (H⁺) in a solution. It ranges from 0 to 14.

• 0-6: Acidic solution (stronger as the number decreases)
• 7: Neutral (pure water)
• 8-14: Basic (stronger as the number increases)

pH and Hydrogen Ion Concentration:

• Lower pH = higher H⁺ concentration (acidic).
• Higher pH = higher OH⁻ concentration (basic).

Universal Indicators:

Used to measure pH, showing different colors based on H⁺ ion concentration.

Acids & Bases:

• Strong acids: Higher H⁺ concentration (lower pH).
• Weak acids: Lower H⁺ concentration (higher pH).
• Bases: As pH increases from 7 to 14, the OH⁻ concentration rises, indicating stronger bases.
• Key Term: "pH" stands for 'potenz' (German for "power"), referring to the power of hydrogen ion concentration.

Given:

​Statement:

Use ‘Calvin Klein’ jeans. Nothing comes between me and my Calvins. — An advertisement.

According to the given information:

Conclusions:

I. Catchy slogans do not attract people.

The statement itself is an advertisement using a catchy slogan, implying that it is designed to attract people. This conclusion directly contradicts the purpose of the advertisement. This conclusion does not follow.

II. People like dark shades of jeans.​​​

The statement makes no reference to the color of the jeans. It focuses on the emotional connection to the brand rather than any specific physical attributes like color. This conclusion does not follow.

Thus, the correct option is (d) Neither conclusion I nor II follows.

The correct answer is (d) Instantaneous Dipole Moment

Explanation:

Non-polar molecules do not have a permanent dipole moment because their electrons are symmetrically distributed.

However, due to temporary fluctuations in electron density, they can develop instantaneous dipole moments.

These temporary dipoles can induce dipoles in neighboring molecules, leading to weak attractive forces known as London Dispersion Forces (Van der Waals forces).

• Instantaneous dipole moments arise when electrons in a molecule momentarily cluster on one side, creating a temporary partial charge difference.
• These dipoles quickly disappear as electrons redistribute, making them temporary rather than permanent.
• This phenomenon is most significant in noble gases (e.g., He, Ne, Ar) and non-polar molecules (e.g., O₂, N₂, CH₄, CO₂, CCl₄).
• It is the primary force holding non-polar molecules together in the liquid and solid states.

Information Booster:

London Dispersion Forces (LDFs):

• A type of Van der Waals force that arises due to temporary dipoles.
• Strength increases with molecular size and surface area (larger molecules have stronger LDFs).
• Responsible for the existence of liquid and solid phases of noble gases like argon and krypton.

Examples of Non-Polar Molecules with Instantaneous Dipoles:

• Noble Gases → He, Ne, Ar, Kr
• Diatomic molecules → O₂, N₂, Cl₂, H₂
• Hydrocarbons → CH₄ (Methane), C₂H₆ (Ethane), CCl₄ (Carbon tetrachloride)

The correct answer is:(B) Progesterone

Explanation:

• Progesterone is the hormone commonly used in oral contraceptives (birth control pills).

• It works by preventing ovulation, thickening the cervical mucus, and altering the uterine lining, making it difficult for a fertilized egg to implant.

Information Booster:

• Progesterone is often used in combination with estrogen in oral contraceptives to enhance their effectiveness.

• Progestin, a synthetic form of progesterone, is also used in many hormonal birth control methods, including pills, IUDs, and implants.

• Oral contraceptives are a popular and reliable method of birth control when used correctly.

• Progesterone can also be prescribed for hormonal replacement therapy in postmenopausal women.

Additional Information:

• Cortisone: A steroid hormone used to treat inflammation, not related to contraception.

• Testosterone: The primary male sex hormone, not used in contraceptives.

• Aldosterone: A hormone involved in salt and water balance, not related to contraception.