Mathematics and Science PYQs

The correct answer is Ligament.

• A Ligament is a fibrous connective tissue, which connects bone to another bone.

Important Points

Key Points

• There are 3 types of bone tissue:
• Compact tissue: The harder, outer tissue of bones.
• Cancellous tissue: The sponge-like tissue inside bones.
• Subchondral tissue: The smooth tissue at the ends of bones, which is covered with another type of tissue called cartilage.

The correct answer is Rhizophora.

• Many mangrove species show some form of vivipary. Rhizophora is an example.
• The ovum is fertilized while still on the parent tree and grows by a combination of photosynthesis and acquisition of nutrients from the parent.

Important Points

• In viviparous germination, the seeds germinate while still attached to the parent plant.
• The growth of the embryo continues until it pierces the seed coat, while still attached to the mother plant, without cessation of activity.

Key Points

• Difference between germination and vivipary:

The correct answer is water.

• Photosynthesis uses carbon dioxide and water to assemble carbohydrate molecules (usually glucose) and releases oxygen into the air.
• Carbon dioxide is the byproduct of respiration.
• In this process, water and carbon dioxide react in the presence of sunlight to give off oxygen and form glucose molecules.
• Photolysis of water is the source of oxygen liberated in photosynthesis.
• The process is explained through the following equation:
• 6 CO2 + 6 H2O + light → C6H12O6 + 6 O2

Where, CO2 is Carbon Dioxide

H2O is Water

C6H12O6 is Sugar 

O2 is Oxygen

Important Points

• With the help of chlorophyll, plants obtain their nutrients and water from the soil, and sunlight provides solar energy for photosynthesis.
• The proportion of carbon in their chemical makeup can rise on a particularly sunny day because more photosynthesis occurs.

Key Points

• The fungus receives sugar from the plant—made by photosynthesis in the leaves and transported to the roots via the plant’s sap.
• In places where there is no sunlight, organisms producing their food are called chemotrophs.
• Those in the deep ocean, organisms get the energy from chemicals released by hydrothermal vents.
• Bacteria can do photosynthesis.

The correct answer is heparin.

• Heparin is an anticoagulant (blood thinner) that prevents the formation of blood clots.
• It is also used before surgery to reduce the risk of blood clots.

Important Points

The correct answer is pancreas.

• Islets of Langerhans are islands of endocrine cells scattered throughout the pancreas.
• The islets of Langerhans are a cluster of cells within the pancreas that are responsible for the production and release of hormones that regulate glucose levels.
• These cells discovered by Dr. Paul Langerhans.
• Pancreatic islets house three major cell types:
• Alpha cells (A cells) secrete the hormone glucagon.
• Beta cells (B cells) produce insulin.
• Delta cells (D cells) secrete the hormone somatostatin, which is also produced by a number of other endocrine cells in the body.

Important Points

• The stomach is the widest part of the digestive system. It not only digests food, it also stores it.
• The stomach is a bean-shaped sack located behind the lower ribs.
• The stomach secretes hydrochloric acids and enzymes that break down the food so that it can continue on its journey through the digestive system.
• This process called peristalsis (mix the food with the acid and enzymes).
• The human liver is the largest glandular organ of the human body and the second largest organ besides our skin.
• Some of these important functions include supplying glucose to the brain, combating infections, and storing nutrients.
• the liver detoxifies the harmful things we take in like alcohol and drugs.
• The liver creates the blood that circulates in bodies. The liver starts producing blood before born.
• The liver has the amazing ability to regenerate itself, making liver transplant possible.
• Heart is a part of circulatory system and responsible for pumping oxygen-rich blood throughout our body.
• An electrical system controls the rhythm of your heart. It’s called the cardiac conduction system.
• Cardiac muscle is a special type of muscle tissue that's only found in your heart.
• Coordinated contractions of cardiac muscle, which are controlled by special cells called pacemaker cells, allow for your heart to pump blood as a single functional unit.

Key Points

• The first open-heart surgery occurred in 1893. It was performed by Daniel Hale Williams, who was one of the few black cardiologists in the United States at the time.
• The first implantable pacemaker was used in 1958. Arne Larsson, who received the pacemaker, lived longer than the surgeon who implanted it.

The correct answer is protein.

• Enzymes are proteins.
• They are high molecular weight compounds made up principally of chains of amino acids linked together by peptide bonds.
• Enzymes can be denatured and precipitated with salts, solvents, and other reagents.
• Enzymes function as organic catalysts. A catalyst is a chemical involved in, but not changed by a chemical reaction.
• The enzyme speeds up the reaction by lowering the activation energy needed for the reaction to start.

Important Points

The correct answer is Ascorbic acid.

• Vitamin C, also known as ascorbic acid or L-ascorbic acid.
• The richest sources of ascorbic acid including Indian gooseberry, citrus fruits such as limes, oranges, and lemons, tomatoes, potatoes, papaya, green and red peppers, kiwifruit, strawberries, etc.
• Deficiency of Vitamin C and iron often occur in anemia.

Important Points

• Formic acid is also known as methanoic acid (HCOOH).
• It is naturally found in ants.
• It is made by the action of sulphuric acid upon sodium formate, which is produced from carbon monoxide and sodium hydroxide.
• Maleic acid is a butanediol acid in which the double bond has a cis- (Z)-configuration.
• It found in many fruits, including apricots, blackberries, blueberries, cherries, grapes, mirabelles, peaches, pears, plums, and quince
• Maleic acid is present in the apple.
• Palmitic Acid is a saturated long-chain fatty acid with a 16-carbon backbone.
• It found naturally in palm oil and palm kernel oil, as well as in butter, cheese, milk, and meat.
• The palmitic acid is attached to the alcohol form of vitamin A, called retinol, to make vitamin A stable in milk.

Given Data:

a, a + 2, a + 4 are prime numbers.

Concept Used:

3, 5, 7 are the only set of three prime numbers which are in arithmetic progression with common difference = 2

Calculation:

a, a + 2, a + 4, these three terms are in Arithmetic progression with common difference = 2.

Comparing a, a + 2, a + 4 with 3, 5, 7, we will get the value of a as 3

⇒ Number of possible values of a is 1 i.e. 3

∴ The number of values of a is 1.

Mistake Points There is a difference between the value of 'a' and the number of values of 'a'

Here the value of a = 3 but the number of values that 'a' can have is 1 because only 1 value satisfies for a i.e 3

Concept Used:

2-digit number × 2-digit number = 4-digit number.

To find the biggest 4-digit number which is a perfect square, we have to take the square of biggest 2-digit number.

Calculation:

2-digit biggest number = 99

99² = 9801

∴ The biggest 4-digit number which is a perfect square = 9801.

Concept Used:

To find the remainder of f(x), we have to put the value of x from x – a = 0

Calculation:

x – 1 = 0 ⇒ x = 1

f(x) = x¹³ + 1

putting x = 1,

f(1) = 1¹³ + 1 = 2

Remainder = 2

∴ When x¹³ + 1 is divided by x - 1, the remainder is 2.

Calculation:

According to the question,

A is a non-empty subset = A ⊆ C

B is a non-empty subset = B ⊆ C

By Distributive property,

 A ∪ (A ∩ B)  = (A ⋃ A) ∩ (A ⋃ B) = A

Given Data:

Rate = r = 5% per annum

Present population = 4410

Calculation:

Let population of village 2 years ago be x

After the first year, the population = x × (100 + 5)/100 = 21x/20

After second year, the population (Present population) = (21x/20) × (100 + 5)/100 = (21x/20) × (21/20) = 441x/400 = 4410(Given)

⇒ x = 4410 × 400/441 = 4000

∴ The population before 2 years = 4000.

 

5% = 1/20

For the first year,              20 → 21

For the Second Year,         20 → 21

                                    ----------------------

                                         400 → 441

441 → 4410    (Given)

⇒ 400 → 4000

∴ The population before 2 years = 4000.

Given:

The total price of shares = Rs. 2500000

Price of one share = Rs. 100

Concept used:

Number of shares = Total price of shares/Price of one share

Calculation:

The total price of shares = Rs. 2500000

Price of one share = Rs. 100

Number of shares = Total price of shares/Price of one share

⇒ Number of shares = 2500000/100 = Rs. 25000

∴ The number of shares circulated by the company is 25000.

Given:

Total number of cards = 52

Formula used:

Probability = Number of favorable outcome/ Total number of outcome

Calculation:

Total number of the spade in a standard deck of card = 13

Total number of aces in a standard deck of card = 4

Number of an ace in spade = 1

Number of favorable outcome = 13 + 4 – 1 = 16

Total number of outcome = 52

Probability = Number of favorable outcome/ total number of outcome

⇒ Probability = 16/52 = 4/13

∴ The probability that the card is a spade or an ace is 4/13.

Given:

ABCD is a cyclic quadrilateral

∠ADC = 4y + 20°

∠ABC = 4x°

∠BAD = 3y – 5°

∠BCD = 7x + 5°

Concept used:

Sum of the opposite angle of a cyclic quadrilateral is 180°.

Calculation:

ABCD is a cyclic quadrilateral

∴ ∠ADC + ∠ABC = 180°

⇒ 4y + 20° + 4x° = 180°

⇒ x + y + 5° = 45°

⇒ x + y = 40°        ……(1)

And,

∠BAD + ∠BCD = 180°

⇒ 3y – 5° + 7x + 5° = 180°

⇒ 7x + 3y = 180°     …….(2)

Multiply 3 in equation (1) and subtract it in equation (2).

7x + 3y – 3x – 3y = 180° - 120°

⇒ 4x = 60°

⇒ x = 15°

Put value of x in equation (1)

x + y = 40°

⇒ 15° + y = 40°

⇒ y = 25°

∴ The ordered pair (x, y) is (15°, 25°).

Given:

25, 26, 27, 23, 27, 26, 24, x, 27, 26, 25, 25

Concept used:

The mode is the value that appears most often in a set of data values.

Calculation:

Following data is arranged in ascending order:

23, 24, 25, 25, 25, 26, 26, 26, 27, 27, 27, x.

The number of repetitions in data.

23 and 24 - 1 time

25 and 26 - 3 times

27 - 3 times

If Mode = 27

i.e., 27 appears most often (4 times) in given sets of data values.

∴ x = 27

Given:

x = 2, y = 1, z = -3

Formula used:

x3 + y3 + z3 – 3xyz = (x + y + z)(x2 + y2 + z2 – xy – yz – zx)

Calculation:

x + y + z = 2 + 1 + (-3) = 3 – 3 = 0

If x + y + z = 0,

Then x3 + y3 + z3 – 3xyz = 0

∴ x3 + y3 + z3 – 3xyz = 0.

Given:

Ladies ∶ Gents = 3 ∶ 2

Concept used:

x/y = a/b

⇒ bx = ay

Calculation:

Let, the number of Ladies and Gents in the gathering be 3x and 2x respectively.

According to question,

3x/(2x + 20) = 2/3

⇒ 9x = 2 × (2x + 20)

⇒ 9x = 4x + 40

⇒ 5x = 40

⇒ x = 8

The number of ladies in gathering = 3x = 3 × 8 = 24

∴ The number of ladies was 24.

Given:

\(\frac{{\rm{a}}}{2} = {\rm{;}}\frac{{\rm{b}}}{3} = {\rm{;}}\frac{{\rm{c}}}{4} = \frac{{2{\rm{a;}} - {\rm{;}}3{\rm{b;}} + {\rm{;}}5{\rm{c}}}}{{\rm{k}}}\)

Calculation:

Let, \(\frac{{\rm{a}}}{2} = {\rm{;}}\frac{{\rm{b}}}{3} = {\rm{;}}\frac{{\rm{c}}}{4} = \frac{{2{\rm{a;}} - {\rm{;}}3{\rm{b;}} + {\rm{;}}5{\rm{c}}}}{{\rm{k}}} = {\rm{x}}\)

a/2 = x

⇒ a = 2x       .……(1)

b/3 = x

⇒ b = 3x          .…….(2)

c/4 = x

⇒ c = 4x           ……..(3)

\(\frac{{2{\rm{a;}} - {\rm{;}}3{\rm{b;}} + {\rm{;}}5{\rm{c}}}}{{\rm{k}}} = {\rm{x}}\)

⇒ 2a – 3b + 5c = kx

Using equation (1), (2) and (3)

⇒ (2 × 2x) – (3 × 3x) + (5 × 4x) = kx

⇒ 4x – 9x + 20x = kx

⇒ 15x = kx

⇒ k = 15

∴ The value of k is 15.

Given:

A Δ B = A

Concept:

The Δ in set theory is the symmetric difference of two sets.

A Δ B = (A – B) ∪ (B – A)

Calculation:

A Δ B = A

\( \Rightarrow \left( {{\rm{A}} - {\rm{B}}} \right) \cup \left( {{\rm{B}} - {\rm{A}}} \right) = {\rm{A}}\)

\( \Rightarrow \left( {{\rm{A}} \cap {\rm{B'}}} \right) \cup \left( {{\rm{B}} \cap {\rm{A'}}} \right) = {\rm{A}}\)

\( \Rightarrow \left( {{\rm{A}} \cup {\rm{B}} \cap {\rm{A'}}} \right) \cap \left( {{\rm{B'}} \cup {\rm{B}} \cap {\rm{A'}}} \right) = {\rm{A}}\)

\( \Rightarrow \left[ {\left( {{\rm{A}} \cap {\rm{A'}}} \right) \cup {\rm{B}}} \right] \cap \left[ {\left( {{\rm{B'}} \cup {\rm{B}}} \right) \cap {\rm{A'}}} \right] = {\rm{A}}\)

\( \Rightarrow \left[ {\emptyset \cup {\rm{B}}} \right] \cap \left[ {{\rm{U}} \cap {\rm{A'}}} \right] = {\rm{A}}\)

\( \Rightarrow {\rm{B}} \cap {\rm{A'}} = {\rm{A}}\)

\( \Rightarrow {\rm{B}} - {\rm{A}} = {\rm{A}}\)

\( \Rightarrow {\rm{A}} \cap {\rm{B}} = \emptyset \)

\(\therefore {\bf{A}} \cap {\bf{B}} = \emptyset \)