We’ve developed the first-ever complete set of worked solutions for the IMAT 2023 exam, carefully designed to support students aiming to succeed in the IMAT 2025. These solutions follow the official 2023 exam structure, offering detailed, step-by-step explanations for every question. The IMAT 2023 included 9 questions in logical reasoning, problem-solving, and reading comprehension, 23 in biology, 15 in chemistry, and 13 in mathematics and physics. Whether you’re reviewing past papers or building confidence for your upcoming exam, this resource is your ultimate guide to mastering the IMAT.
Correct Answer: A) The June temperature this year is consistent with an observed trend.
This question tests reading comprehension. For best results, first read the passage to get an overview, then examine the options and locate the relevant information in the text.
Option A Explanation:
A) The June temperature this year is consistent with an observed trend.
The text mentions "a pattern of strengthening global heating" caused by fossil fuel burning, and the June temperature aligns with this observed warming trend. Thus, this option is true.
Option B Explanation:
B) June 1979 was the hottest month to date.
False. The text does not state that June 1979 was the hottest; rather, it indicates that temperatures this June are nearly 1°C above the average levels since 1979.
Option C Explanation:
C) Temperatures in June are not related to the El Niño phenomenon.
False. The text explicitly mentions El Niño as a contributing factor, stating it "typically causes temperatures to spike across the world."
Option D Explanation:
D) The El Niño phenomenon limits the effects of burning fossil fuels.
False. El Niño adds to the warming effects caused by fossil fuels, giving "a further pulse of heat" rather than limiting it.
Option E Explanation:
E) This year, June will be the hottest month on record since 1979.
False. The text says June is not yet complete and may not set a new record, although it is following a warming trend.
Correct Answer: D) Elizabeth Bennet - Little Women
According to the given options, the wrong pair is the option D) Elizabeth Bennet - Little Women.
Elizabeth Bennet is a character from Pride and Prejudice, written by Jane Austen.
The main characters of Little Women (written by Louisa May Alcott) are the March sisters, such as Jo and Meg.
Correct Answer: C) Julius Caesar's account of the Gallic war.
The work known as De Bello Gallico is a series of commentaries written by Julius Caesar, chronicling his military campaigns during the Gallic Wars.
Thus, the correct option is C) Julius Caesar's account of the Gallic war.
Analysis of Other Options
A) A painting by Eugène Delacroix.
• Incorrect. While Eugène Delacroix was a famous Romantic painter, De Bello Gallico is not one of his works. His notable paintings include Liberty Leading the People.
B) An opera by Richard Wagner.
• Incorrect. Richard Wagner, a German composer, wrote operas such as The Ring Cycle and Tristan und Isolde. De Bello Gallico is not an opera.
D) A sculpture by Auguste Rodin.
• Incorrect. Auguste Rodin, a renowned French sculptor, created works like The Thinker and The Kiss. He did not create a sculpture called De Bello Gallico.
E) A collection of poems on the Gallic war by Horace.
• Incorrect. Horace, a Roman poet, wrote works such as Odes and Satires, but he did not write a collection of poems specifically about the Gallic War.
Correct Answer: A) Head of State but not Head of Government.
In a parliamentary system of government, the President of the Republic typically serves as the Head of State, a largely ceremonial position. Their role in judiciary matters is often symbolic or limited to appointments, depending on the country's constitution.
The Head of Government is the Prime Minister, and holds executive powers and runs the government.
Thus, the correct option is option A.
Correct Answer: C) 36
Given : 1 pair of new born rabbits (needs one month to mature)
3 pairs of mature rabbit (can breed every month)
After one month,
- 3 pairs of mature rabbit will produce new 3 pairs of offsprings and the previously born pair of rabbits matures now.
- So, pair of mature rabbits = 4, pair of newborn rabbits = 3
After next one month,
- Pair of mature rabbits = 7 (4 + 3), pair of new born rabbits = 4
After next one month,
- Pair of mature rabbits = 11 (7 + 4), pair of new born rabbits = 7
Thus, total number of rabbits at the end of the 3rd month = 18 × 2 = 36
Correct Answer: E) 4:1
Given: Half-life of X = 2 years, half-life of Y = 3 years
To calculate the remaining mass of an element after n half-lives, follow this formula:
Remaining mass = Initial mass × (½)n
Initial ratio X:Y = 8 : 1
Let initial masses be 8m for X and m for Y.
After 6 years:
- X has undergone 3 half-lives
- Y has undergone 2 half-lives
New mass of X = 8m × (½)3 = 8m × 1/8 = m
New mass of Y = m × (½)2 = m × 1/4 = m/4
So, new mass ratio after 6 years:
m : m⁄4 = 4 : 1
Correct Answer: E) €6.80
Let's solve this step by step by checking each requirement against the given options.
Protein content ≥ 20g
This eliminates Tuna, Vegetables, and Ham sandwiches.
Fat content < 10g
This eliminates the Salmon sandwich.
Energy ≥ 1,300 kJ
This eliminates the Turkey sandwich.
Only two options remain: Chicken and Beef.
Since we need the minimum price, we choose the Chicken sandwich at €6.80.
Therefore, option E is correct.
Correct Answer: C) The economic benefits derived from the Copernicus programme outweigh its costs.
To solve this question, we must first identify the passage's main conclusion. Then, we can eliminate options that weaken this conclusion and compare the remaining choices to find which one most strengthens the argument.
The passage discusses the Copernicus European Earth Observation Programme. It first describes Copernicus' various functions, then concludes that due to its significant benefits, the program should continue to receive funding. Therefore, the main argument is that Copernicus provides valuable services and deserves ongoing financial support.
Options A and E weaken the argument by suggesting alternative programs or methods could provide similar benefits.
Option B discusses the relative importance of social and scientific advances, which is not directly relevant to the passage's main argument.
Option D supports the argument but focuses on international cooperation rather than funding.
Option C most effectively strengthens the argument by demonstrating that the Copernicus programme's financial benefits exceed its costs, making it the correct answer.
Correct Answer: A) Early promise does not guarantee high achievement in the long term..
To find the conclusion in this passage, let’s first break it down into its key components.
The passage starts with the Matthew effect – a belief that students with early academic success tend to make less progress over time compared to their peers.
The subsequent statements will help determine if they support this initial premise and lead us to the conclusion.
Research findings are provided as evidences:
- High achievers in year 3 made less progress to year 9 than expected.
- Students with below-average scores made more progress than high achievers.
- Compensatory growth (more progress by initially low achievers) was significant in reading and numeracy, especially reading.
The evidence supports the Matthew effect. Therefore, we need to find a conclusion in the options that aligns with this initial premise.
Analysis of Other Options
A) Early promise does not guarantee high achievement in the long-term.
Correct. This directly aligns with the study’s finding and Matthew effect.
B) It is easier to teach brighter students than those who are below average.
Incorrect. The passage does not discuss the difficulty of teaching students based on ability.
C) Rates of improvement from a low base will always be more rapid than progress from a higher base.
Incorrect. While the study highlights a compensatory growth pattern in this specific dataset, it does not generalize to “always” or all contexts. And it does not mention about the rate.
D) Numerical skills are harder to improve than language skills.
Incorrect. Although compensatory growth was more significant in reading, the passage does not claim numeracy is harder to improve—just that differences were observed.
E) The ‘Matthew effect’ is the result of low expectations by teachers.
Incorrect. The passage does not discuss about teacher expectations.
Correct Answer: A) 3-4-2-1
Let’s analyse each reaction first:
1. Ethyl alcohol fermentation of four molecules of glucose
Fermentation is a metabolic process that extends glycolysis to allow continuous ATP production without oxygen.
It has two main steps: glycolysis, which breaks down glucose into pyruvate and generates a net gain of 2 ATP per glucose molecule through substrate-level phosphorylation,
and NAD+ regeneration, which restores NAD+ from NADH but produces no ATP. Without NAD+ regeneration, glycolysis would stop.
Since each glucose yields 2 ATP, fermenting 4 glucose molecules produces a total of 8 ATP.
Although fermentation types like lactic acid and alcohol fermentation differ in end products, the ATP yield remains the same because it is entirely dependent on glycolysis.
2. Lactic acid fermentation of six molecules of glucose
This is also one of the fermentation processes, differing in the end products formed from pyruvate.
Thus, this reaction also produces 2 ATP per 1 molecule of glucose and for 6 glucose, it yields 12 ATP molecules.
3. The electron transport chain stage of cellular respiration
The electron transport chain (ETC) is the final stage of cellular respiration, following glycolysis and the citric acid cycle,
and is the most efficient catabolic pathway for glucose metabolism.
In this aerobic process, oxygen acts as the final electron acceptor, allowing the transfer of electrons through a series of protein complexes embedded in the inner mitochondrial membrane.
This transfer drives the production of ATP through oxidative phosphorylation.
As a result, the complete oxidation of one glucose molecule typically yields about 30 to 32 ATP, making it the major source of ATP in cellular respiration.
4. Glycolysis of seven glucose molecules
The net energy yield from glycolysis, per glucose molecule, is 2 ATP plus 2 NADH.
Thus, glycolysis of 7 glucose molecules yields 14 ATP molecules.
To rank the reactions in order of the total number of net ATP molecules produced from largest to smallest:
3 > 4 > 2 > 1
Correct Answer: C) Women are more likely to suffer from DMD than men.
Since it is mentioned in the paragraph that DMD is an X-linked recessive genetic disease, and X chromosome is one of the two sex chromosomes,
it can be derived that DMD is a sex-linked inherited disease.
Option A Explanation:
Since the mutated allele is present on the X chromosome, the spread of the mutated allele is influenced by how quickly the associated X chromosome proliferates within the population.
Thus, this statement is right.
Option B Explanation:
DMD is a sex-linked inherited disease. Thus, this statement is right.
Option C Explanation:
Because males have only one X chromosome, presence of one recessive allele is enough to develop the condition,
in other words, any male receiving the recessive allele from his mother will express the trait.
As a result, far more males than females have X-linked recessive disorders.
Thus, this statement is wrong.
Option D Explanation:
Because males have only one X chromosome, presence of one recessive allele is enough to develop the condition,
in other words, any male receiving the recessive allele from his mother will express the trait.
Thus, this statement is right.
Option E Explanation:
If an X-linked trait is due to a recessive allele, a female will express the phenotype only if she is homozygous for that allele.
Thus, this statement is right.
Correct Answer: D) Y and W
Option A Explanation:
pH range for enzyme X = 6.4 – 8.2
pH range for enzyme Z = 4 – 8.5
There is an overlapping pH range where both enzymes can function together.
Option B Explanation:
pH range for enzyme X = 6.4 – 8.2
pH range for enzyme Y = 3.9 – 7.2
There is an overlapping pH range where both enzymes can function together.
Option C Explanation:
pH range for enzyme W = 8 – 12.1
pH range for enzyme Q = 1.3 – 9.5
There is an overlapping pH range where both enzymes can function together.
Option D Explanation:
pH range for enzyme Y = 3.9 – 7.2
pH range for enzyme W = 8 – 12.1
There is no overlapping pH range where both enzymes can function together.
If the pH is adjusted to suit one enzyme, the other enzyme will not function at all.
Thus, this is the correct answer for the pairs of enzymes listed below that cannot function together in the same environment.
Option E Explanation:
pH range for enzyme Y = 3.9 – 7.2
pH range for enzyme Z = 4 – 8.5
There is an overlapping pH range where both enzymes can function together.
Correct Answer: C) Uracil
It is given that the virus has DNA as its primary molecule.
DNA is composed of three main components: a deoxyribose pentose sugar, a phosphate group, and a nitrogenous base. The nitrogenous bases in DNA are either purines (adenine and guanine) or pyrimidines (thymine and cytosine). Importantly, uracil is not found in DNA; it is present only in RNA.
Correct Answer: B) 3 only
Pancreas produces 2 hormones: insulin and glucagon.
In the adrenal gland, adrenal medulla produces epinephrine and norepinephrine and adrenal cortex produces mineralocorticoids, glucocorticoids, and sex hormones.
Analysis of the given statements
1. Balancing the amount of calcium in the bone and blood:
The main hormones involved in calcium regulation are parathyroid hormone (PTH), vitamin D (calcitriol), and calcitonin.
PTH increases blood calcium levels by stimulating bone resorption, enhancing calcium reabsorption in the kidneys,
and activating vitamin D, which promotes calcium absorption in the intestines.
Calcitonin, produced by the thyroid gland, lowers blood calcium levels by inhibiting bone resorption.
Therefore, the adrenal glands and pancreas do not play a primary role in regulating calcium levels in bone and blood.
2. Accelerating sodium absorption in the renal tubules:
Mineralocorticoids, primarily aldosterone, play a key role in salt and water retention by promoting sodium reabsorption and potassium excretion in the kidneys.
Other important hormones involved in regulating salt and water balance include renin, angiotensin I, angiotensin II, and antidiuretic hormone (ADH),
which help maintain blood pressure and fluid homeostasis.
In contrast, pancreatic hormones do not have a direct role in salt and water regulation.
3. Balancing the glucose level in the blood:
Both pancreatic hormones, insulin and glucagon, are essential for regulating blood glucose levels.
Insulin lowers blood glucose by promoting glucose uptake and storage, while glucagon raises it by stimulating glycogen breakdown and gluconeogenesis.
Additionally, several adrenal gland hormones, including epinephrine, norepinephrine, and glucocorticoids (e.g., cortisol),
can increase blood glucose levels during stress or fasting by enhancing gluconeogenesis, glycogenolysis, and reducing glucose uptake by tissues.
Thus, functions seen by the adrenal gland and pancreas are only relevant in the 3rd event.
The correct option is option B) 3 only.
Correct Answer: B) 1, 2 and 3
Many animals exhibit homeostasis for a range of physical and chemical properties through a control system.
-
Blood glucose concentration is regulated by both negative and positive feedback mechanisms involving hormones such as
insulin and glucagon.
Insulin lowers blood glucose levels by promoting cellular uptake and storage of glucose,
while glucagon raises blood glucose levels by stimulating glycogen breakdown and glucose production in the liver, maintaining glucose homeostasis. - Body temperature is regulated through mechanisms like sweating and shivering to maintain a stable temperature inside the body for proper functioning.
- Water level is also controlled through hormones and thirst mechanism to maintain a stable osmolarity value in the extracellular and intracellular space.
- Body weight is not a tightly controlled variable by homeostatic mechanisms and is influenced by factors like genetics, diet, metabolism, and lifestyle.
Thus, only the 1, 2 and 3 are regulated by homeostasis in the body.
Correct Answer: E) Plastid, Mitochondria, Nucleus
In cellular organelles,
- Organelles without membrane are ribosome, microtubules, centrosomes, centrioles, nucleolus.
- Organelles with single membrane are vacuoles, lysosome, rough ER, smooth ER, golgi body, peroxisomes.
- Organelles with double membrane are nucleus, mitochondria, plastids and chloroplasts (specialized plastids).
Thus, the correct option is option E.
Correct Answer: B) 3
If an X-linked trait is due to a recessive allele, a female will express the phenotype only if she is homozygous for that allele. Thus, to pass the disorder to daughter, both parents must carry at least one copy of the color blindness gene on their X chromosome.
Among the three families given, only Family 3 has both mother and father carrying the colorblindness gene, making it the only family where the daughter can inherit the disorder.
Thus, the correct option is option B.
Correct Answer: E) Occurrence in germ cells
Option A Explanation:
Having recessive mutation will not play a role in the process of evolution if it occurs in the body cells because the mutated gene will not be inherited by the offspring and as a result, it does not contribute to the evolution process.
Option B Explanation:
For a mutation to play a role in the process of evolution, it must be passed through from generation to generation which means it must occur in the germ cells, not in the body cells.
Option C Explanation:
Having a dominant mutation will not play a role in the process of evolution if it occurs in the body cells because the mutated gene will not be inherited by the offspring and as a result, it does not contribute to the evolution process.
Option D Explanation:
Mutation formed by X-Ray will not play a role in the process of evolution if it occurs in the body cells because the mutated gene will not be inherited by the offspring and as a result, it does not contribute to the evolution process.
Option E Explanation:
For a mutation to play a role in the process of evolution, it must be passed through from generation to generation which means it must occur in the germ cells.
Correct Answer: C) Redox reactions involve the transfer of electrons, where the molecule that gains electrons is reduced, and the molecule that loses electrons is oxidized
In many chemical reactions, there is a transfer of one or more electrons (e-) from one reactant to another. These electron transfers are called oxidation-reduction reactions, or redox reactions for short. In a redox reaction, the loss of electrons from one substance is called oxidation, and the addition of electrons to another substance is known as reduction. Thus, option C) best describes redox reactions in living things.
Correct Answer: C) 0.6
frequency of A =
Thus, the correct option is option C.
Correct Answer: C) Pineal gland
The circadian rhythm is the natural, internal process that regulates the sleep–wake cycle and repeats roughly every 24 hours. Key hormones involved include melatonin, produced by the pineal gland, which promotes sleep, and cortisol, which peaks in the morning to promote wakefulness. Circadian rhythms influence not only sleep but also other physiological processes like hormone release, body temperature, and metabolism.
Option A Explanation:
The amygdala is involved in processing emotions, memory, and fear responses. It does not regulate circadian rhythms.
Option B Explanation:
The corpus callosum is a bundle of nerve fibers that connects the two hemispheres of the brain and facilitates
communication between them. It is unrelated to circadian rhythm regulation.
Option C Explanation:
For pineal gland, it plays a crucial role in regulating the circadian rhythm by producing and releasing
melatonin, a hormone that signals the body when it is time to sleep. Thus, this option is true.
Option D Explanation:
The thalamus acts as a relay center for sensory information to the cerebral cortex. While it plays a role in sleep
and wakefulness, it is not the primary regulator of circadian rhythms.
Option E Explanation:
The hippocampus is primarily involved in memory formation and spatial navigation. It does not regulate circadian rhythms.
Correct Answer: E
We can summarize the complex series of chemical reactions in photosynthesis with this chemical equation:
6CO₂ + 12H₂O + light energy → C₆H₁₂O₆ + 6CO₂ + 6O₂
Water appears on both sides of the equation because 12 molecules are consumed and 6 molecules are newly formed during
photosynthesis. We can simplify the equation by indicating only the net consumption of water:
6CO₂ + 6H₂O + energy → C₆H₁₂O₆ + 6O₂
Thus, Option E represents the balanced equation for the overall reaction of photosynthesis.
Correct Answer: A) 2 - 1 - 3
Immediately after acetylcholine binds to postsynaptic receptors of a muscle fibre, it opens ligand-gated ion channels, cause depolarization and action potential generation.
The action potential propagates along the sarcolemma and into the T-tubules. This causes calcium ions (Ca²⁺) to be released from the Sarcoplasmic reticulum into the sarcoplasm.
Calcium binds to troponin C causing a conformational change in troponin and tropomyosin, exposing myosin-binding sites on actin.
Myosin heads bind to the exposed binding sites on actin, forming cross-bridges.
Then, muscle fiber contracts according to the sliding filament mechanism.
Thus, the correct order of the given event would be 2-1-3
Correct Answer: B) 4.7%
64 codons can be made from 3 bases and among these 64 codons, 3 codons (UAA, UAG, UGA) are stop codons and do not code for any amino acid.
Percentage of stop codons =
3⁄64
× 100 = 4.7%
Thus, the correct answer is option B) 4.7%
Correct Answer: A) Prokaryotic DNA consists of circular chromosomes located within the cytoplasm
In a prokaryotic cell, the DNA is concentrated in a region that is not membrane-enclosed, called the nucleoid. Most genes are carried on a single bacterial chromosome that consists of a circular DNA molecule and associated proteins.
Option A Explanation:
This option accurately describes prokaryotic DNA.
Option B Explanation:
This option is wrong because prokaryotic DNA is not organized into chromatin fibers.
Option C Explanation:
This option is wrong because prokaryotic genes are carried only on a single chromosome not multiple.
Option D Explanation:
This option is wrong because prokaryotic DNA is not associated with histone proteins and prokaryotes do not carry out either mitosis or meiosis. They undergo a type of reproduction called binary fission.
Option E Explanation:
This option is incorrect because prokaryotic DNA is typically continuous, lacking introns, unlike eukaryotic DNA which contains introns within its coding regions.
Correct Answer: A) 6, 12, 16
It is given that the fragment of double-stranded DNA contains 12 phosphates. Each nucleotide is composed of deoxyribose sugar, phosphate group and nitrogenous base. Thus, if there is 12 phosphate in the DNA, there must be 12 deoxyribose sugar. Since it is a double-stranded DNA, there must be 6 base pairs.In double-stranded DNA, the number of purines (adenine and guanine) is always equal to the number of pyrimidines (thymine and cytosine) due to base pairing rules. Adenine pairs with thymine and guanine pairs with cytosine, maintaining a strict 1:1 ratio between purines and pyrimidines. This balance, described by Chargaff’s rules, ensures the stability and uniform width of the DNA double helix.
Each base pair has 1 purine (either A or G) and 1 pyrimidine (either T or C). Since there are 6 base pairs in total, Total purines = 6.
The fragment contains 2 adenines (A), which pair with 2 thymines (T). Each A-T pair contributes 2 hydrogen bonds: and thus, this gives 4 hydrogen bonds. The remaining base pairs are 4 G-C pairs (since 6 base pairs - 2 A-T pairs = 4 G-C pairs). Each G-C pair contributes 3 hydrogen bonds and thus, this gives 12 hydrogen bonds. Total hydrogen bonds = 4 + 12 = 16
Thus, total number of purine bases = 6
total number of deoxyribose sugar = 12
total number of hydrogen bonds = 16
The correct option is option A) 6, 12, 16
Correct Answer: E) The surface area-to-volume ratio decreases as the cell grows larger
As a cell increases in size, its surface area grows at a slower rate compared to its volume because surface area scales with the square of the linear dimension, while volume scales with the cube of the linear dimension. As a result, smaller cells have a larger surface area-to-volume ratio, which facilitates more efficient exchange of materials with their environment, whereas in larger cells, this ratio decreases, making transport of substances less efficient as size increases.
Only the option E) accurately describes the surface area-to-volume ratio and cell growth.
Correct Answer: E) The Golgi apparatus processes and packages proteins to be exported from the cell
We can think of the Golgi as a warehouse for receiving, sorting, shipping, and even some manufacturing. It consists of stacks of associated, flattened sacs, or cisternae which are not physically connected to each other and is especially extensive in cells specialised for secretion.
Functions of golgi apparatus
- products of the ER, such as proteins, are modified and stored and then sent to other destinations
- membrane phospholipids may also be altered in the Golgi
- manufactures some macromolecules
- add molecular identifying tags to the products
Option A Explanation:
This option is wrong because in neuronal cells, neurotransmitters need to be released and Golgi apparatus is specialized to handle the packaging and sorting of these molecules. Thus, golgi is an essential organelle in neuronal cells.
Option B Explanation:
This option is incorrect because, although the Golgi apparatus processes lipids, it does not handle lipid molecules entering the cell. Instead, it processes lipids synthesized in the smooth endoplasmic reticulum.
Option C Explanation:
The statement is incorrect because lysosomes are responsible for breaking down macromolecules, damaged organelles, and cellular waste, not for digesting vesicles released from the Golgi apparatus. Proteins processed and packaged by the Golgi are transported in secretory vesicles to the plasma membrane, where they are released into the extracellular space through exocytosis. Lysosomes function in degradation rather than secretion, so they do not play a role in releasing proteins from the cell.
Option D Explanation:
This option is wrong because once proteins are synthesized on ribosomes (in the cytoplasm as free ribosomes or rough ER as bound ribosomes), they are not sent back to the nucleus for “translation verification.” Proteins are modified, sorted, and packaged in the Golgi before being sent to their final destinations.
Option E Explanation:
This option correctly describes about the primary function of the golgi apparatus.
Correct Answer: E) When glucose-6-phosphate is changed to fructose-6-phosphate
Glycolysis is a ten-step metabolic pathway that breaks down glucose into pyruvate. Isomerase enzymes play a crucial role at specific stages of this process. One key step involves the conversion of glucose-6-phosphate to fructose-6-phosphate by phosphoglucose isomerase. Another important isomerase-catalyzed reaction is the interconversion between dihydroxyacetone phosphate (DHAP) and glyceraldehyde-3-phosphate (G3P), catalyzed by triose phosphate isomerase. These isomerase steps are essential for ensuring that glycolysis proceeds efficiently by rearranging molecules into forms that can continue through subsequent reactions.
Option A Explanation:
This option is wrong because for phosphorylation, kinase enzyme would be used. In glycolysis, kinase enzymes play a crucial role by catalyzing the transfer of phosphate groups from ATP to specific substrates, a process known as phosphorylation. Key kinases involved include hexokinase, which phosphorylates glucose to form glucose-6-phosphate in the first step, and phosphofructokinase-1 (PFK-1), which catalyzes the conversion of fructose-6-phosphate to fructose-1,6-bisphosphate — a major regulatory step. Later, phosphoglycerate kinase and pyruvate kinase facilitate substrate-level phosphorylation steps that generate ATP. Overall, kinase enzymes are essential for both the energy investment and energy payoff phases of glycolysis.
Option B Explanation:
This option is wrong because isomerase enzyme are not the same enzyme as dehydrogenase enzymes. In glycolysis, the key dehydrogenase enzyme is glyceraldehyde-3-phosphate dehydrogenase (G3PDH). This enzyme catalyzes the sixth step of glycolysis, where glyceraldehyde-3-phosphate (G3P) is oxidized and phosphorylated to form 1,3-bisphosphoglycerate (1,3-BPG). During this reaction, NAD+ is reduced to NADH, capturing energy in the form of high-energy electrons. This step is crucial because it links the oxidation of glucose-derived molecules to the generation of NADH, which will later feed electrons into the electron transport chain under aerobic conditions. Thus, dehydrogenase enzymes in glycolysis are essential for energy transfer and the continuation of the metabolic pathway.
Option C Explanation:
This option is wrong because aldolase enzyme is used in the mentioned reaction instead of isomerase enzyme. In glycolysis, the aldolase enzyme catalyzes the cleavage of fructose-1,6-bisphosphate into two three-carbon molecules: dihydroxyacetone-phosphate (DHAP) and glyceraldehyde-3-phosphate (G3P).
Option D Explanation:
This option is wrong because in the mentioned reaction, isomerase enzyme does not take part.
Option E Explanation:
This option correctly describes one of two reactions where isomerase enzyme is used in glycolysis pathway.
Correct Answer: A) No, unless you know the position of the phosphate group, you cannot differentiate the 3' end from the 5' end.
A polynucleotide has a built-in directionality along its sugar-phosphate backbone, running from the 5′ end to the 3′ end, much like a one-way street. The 5′ end is characterized by a phosphate group attached to the 5′ carbon of the sugar, while the 3′ end has a hydroxyl group on the 3′ carbon. This structural arrangement establishes the molecule’s direction. Therefore, to determine the orientation of a polynucleotide, it is necessary and sufficient to identify the positions of the phosphate group and the hydroxyl group.
Thus, the correct option is option A.
Correct Answer: C) 2
The pathway of electron transport
- NADH donates electrons to complex I (NADH dehydrogenase), while FADH2 donates electrons to complex II (succinate dehydrogenase).
- CoQ shuttles electrons from complexes I and II to complex III.
- Complex III passes electrons to another mobile carrier, cytochrome c.
- Cytochrome c carries electrons from complex III to complex IV.
- The final step in the chain, complex IV transfers electrons to oxygen, the terminal electron acceptor.
- Oxygen combines with electrons and protons (H+) to form water.
- As electrons move through complexes I, III, and IV, protons (H+) are pumped from the mitochondrial matrix into the intermembrane space.
- This creates a proton gradient (electrochemical gradient) across the inner mitochondrial membrane which is used by ATP synthase to catalyze the conversion of ADP to ATP.
Analysis of the given statements
- Statement 1 is wrong because Complex I of the electron transport chain transfers electrons from NADH to coenzyme Q, not from FADH2.
- Statement 2 correctly describes a step in oxidative phosphorylation.
- Statement 3 is wrong because oxygen accepts electrons from complex IV and there is no oxygen in complex III.
- Statement 4 is wrong because complex IV receives electrons from complex III, not from NADH.
Thus, the correct option is option C) 2
Correct Answer: C) 1, 2, 3, and 4
Mendel deduced two fundamental principles of heredity, now called the law of segregation and the law of independent assortment.
4 concepts of the Mendel’s model
- Alternative versions of genes account for variations in inherited characters.
- For each character, an organism inherits two copies (that is, two alleles) of a gene, one from each parent.
- If the two alleles at a locus differ, then one, the dominant allele, determines the organism’s appearance; the other, the recessive allele, has no noticeable effect on the organism’s appearance.
- The two alleles for a heritable character segregate (separate from each other) during gamete formation and end up in different gametes. (Law of segregation)
Law of independent assortment
- Two or more genes assort independently—that is, each pair of alleles segregates independently of any other pair of alleles—during gamete formation.
These are the main inheritance patterns that Mendel observed and developed through his experiments.
Among 5 points mentioned in the question, it can be seen that point 1 to 4 accurately reflect Mendel’s law. The last point “individuals with heritable traits more suited to the environment will have an increased chance of survival” reflects the concept of natural selection from Darwin’s theory of evolution, not Mendel’s laws of inheritance.
Thus, the correct option is option C) 1, 2, 3 and 4
Correct Answer: D) x-2
According to the given information,
mass number (A) = 2x+2, number of protons (Z) = x
As the ion has a positive charge of 2+, there are two less electrons than protons:
Thus, number of electrons = x - 2
Correct Answer: C) 2P
This is a question about the ideal gas law equation.
Given: The gas has fixed volume.
Solution :
T₁ = 27 + 273 = 300 K
P₁ = P Pa
T₂ = 327 + 273 = 600 K
P₂ = ?
According to Gay-Lussac's law,
P₁ / T₁ = P₂ / T₂
P₂ = P₁ × T₂ / T₁ = (P × 600 K) / 300 K = 2P Pa
Correct Answer: A) 3, 5, 1, 2, 4
To solve this question, we have to compare the acidity of each solution and the most acidic solution will have the lowest pH and the least acidic solution will have the highest pH.
CH₃COOH is a weak acid and it will dissociate into less than 0.1 mole of hydrogen ion.
NaCl is a neutral salt and thus, pH would be around 7.
H₂SO₄ is a strong diprotic acid and it will dissociate into 0.2 moles of hydrogen ion. This solution seems to be the most acidic one among others and thus will have the lowest pH.
Ba(OH)₂ is a strong base and thus, it will have the highest pH among others.
HNO₃ is a monoprotic strong acid and it will dissociate into 0.1 mole of hydrogen ion.
Thus, in comparison, solutions in order of increasing pH would be H₂SO₄, HNO₃, CH₃COOH, NaCl, Ba(OH)₂. In number, it would be 3, 5, 1, 2, 4.
Correct Answer: D) 1, 2 and 3
Structural isomers (or constitutional isomers) are compounds that have the same molecular formula but different structural arrangements of atoms (in the amounts of branching in their chains, or in the positions or the nature of functional groups).
Thus, we have to find the molecular formula for each compound first.
In the compound number 1, there are 6 carbon atoms, 12 hydrogen atoms and 2 oxygen atoms. Thus, the molecular formula is C6H12O2.
In the compound number 2, there are 6 carbon atoms, 12 hydrogen atoms and 2 oxygen atoms. Thus, the molecular formula is C6H12O2.
In the compound number 3, there are 6 carbon atoms, 12 hydrogen atoms and 2 oxygen atoms. Thus, the molecular formula is C6H12O2.
The molecular formula of hexanoic acid is CH3(CH2)4COOH, which can be converted to C6H12O2.
It can be seen that all 3 compounds have the same molecular formula with hexanoic acid but different structural arrangements of atoms. Thus, all 3 compounds are the structural isomers of hexanoic acid.
Correct Answer: B) A base
From the Oxidation-Reduction point of view, Since the oxidation states of sulfur and nitrogen do not change, no redox reaction occurs. Thus, options D and E can be excluded.
For HNO₃ to be a catalyst, it must stay unchanged at the end of the process. Thus, option C can be excluded.
From acid-base point of view, Since H₂SO₄ transfer a proton to HNO₃, H₂SO₄ is an acid and HNO₃ is a base. Thus, nitric acid is considered as a base in this equation.
Correct Answer: A) Carbon dioxide
At first, we can exclude the molecules that do not have linear structures.
In nitrogen dioxide (NO₂), the nitrogen atom is bonded to one oxygen atom through a double bond and to another oxygen atom through a single bond. Additionally, there is a lone unpaired electron (a radical) on the nitrogen atom. This arrangement results in three electron domains (two bonding regions and one unpaired electron) around the nitrogen. According to the VSEPR theory, the electron domain geometry is trigonal planar. However, due to the presence of the lone unpaired electron, the molecular geometry is bent and the molecule is not perfectly planar.
In sulfur trioxide, each oxygen atom forms a double bond with the sulfur atom, resulting in three bonding pairs around the sulfur atom. This arrangement leads to a trigonal planar electron domain geometry.
In sulfur dioxide, sulfur is bonded to two oxygen atoms via double bonds and there is one lone pair on sulfur. Since there are 3 electron domains on sulphur atom, its electron domain geometry is trigonal planar.
Thus, we can exclude these 3 options.
If we compare carbon dioxide and silicon dioxide, both molecules have linear shape. However, silicon dioxide is insoluble in water. Therefore, it cannot react with water to form acidic solution. Silicon dioxide (SiO₂) is insoluble in water because it has a giant covalent network structure, where each silicon atom is strongly bonded to four oxygen atoms in a three-dimensional lattice. These covalent bonds are extremely strong and require a large amount of energy to break. Water, being a polar solvent, dissolves substances by surrounding and separating individual ions or molecules, but it cannot disrupt the extensive covalent bonds in SiO₂. As a result, silicon dioxide remains insoluble in water.
Thus, the only correct option is A) Carbon dioxide.
A document has been prepared to include the images and diagrams related to the questions, placed directly below the worked solutions for clarity and reference.
Correct Answer: B) Ice has a greater volume than liquid water as the particles are further apart.
Option A Explanation:
Ice have greater volume than liquid water due to maximum hydrogen bonding which keeps the molecules at a fixed distance. The particles in ice state has less kinetic energy than those in the liquid state. Thus, this option is false.
Option B Explanation:
Ice have greater volume than liquid water due to maximum hydrogen bonding which keeps the molecules at a fixed distance and further apart. Thus, this option is true.
Option C Explanation:
In fact, ice has a greater volume than liquid water because the water molecules in ice are arranged in a rigid, open hexagonal lattice held together by hydrogen bonds. This structure keeps the molecules further apart compared to the more disordered, closer-packed arrangement in liquid water. As a result, ice is less dense and occupies more volume than the same mass of liquid water.
Option D Explanation:
While it is true that liquid water molecules have more kinetic energy than those in ice (because temperature and molecular motion are higher in liquids), kinetic energy does not directly determine volume. The volume is smaller in liquid water because the increased movement allows the molecules to break some hydrogen bonds and pack closer together, reducing the volume compared to the rigid open structure of ice.
Option E Explanation:
Liquid water and ice do not have the same volume. Ice occupies more volume than the same mass of liquid water because of its expanded hydrogen-bonded structure. This is why ice is less dense than water, causing it to float, not because their volumes are equal. Floating occurs due to the lower density of ice, not due to equal volumes.
Correct Answer: D) At a lower temperature the value of Kc will increase.
Given : It is a gaseous exothermic reaction and the Kc value is very small.
From its very small Kc value, it can be deduced that there are proportionately less products with respect to reactants, so the equilibrium mixture lies to the left and there are more moles on the left-hand side of the reaction. This excludes the option A and option C.
Addition of a catalyst effects only the rate of the reaction by increasing its speed.. It does not effect the yield. This excludes the option B.
Since the reaction is an exothermic reaction, if the temperature is decreased, the reaction will shift to the right and more products will be formed. This increases the Kc value. Thus, option D is true.
For option E, we cannot conclude anything without the information about the mole ratios of the reactants and products.
Correct Answer: E) Amide
Paracetamol is an aromatic compound with hydroxyl group and amide group as functional groups. Hydroxyl group can be found on the provided structure as an OH group attached to the benzene ring and amide group as -CONH group attached to the benzene ring.
Thus, the correct option is option E.
Correct Answer: A) Elements = 3, molecules = 4
Both elements and molecules are under the category of pure substances.
An element is composed of only one type of atoms. Elements cannot be broken down into simpler substances via a chemical reaction.
A molecule is a group of two or more atoms (either the same element or different elements) held together by chemical bonds.
In the five given substances, N₂, O₂, and Ar are elements because they consist of only one type of atom. N₂, O₂, CO₂, and H₂O are molecules because they are a group of two or more atoms held together by chemical bonds.
Thus, 3 of given substances are elements and 4 of given substances are molecules. The correct option is option A.
Correct Answer: C) Neon (Z = 10)
Ionization energy : the energy required to remove one mole of electrons from one mole
of gaseous atoms in their ground state.
Ionization energy trend : increase across a period and decrease down a group.
Alkali metals such as Sodium, Potassium and Lithium tend to have lower ionization energy because they are group 1 elements and they have only 1 electron on the highest principle energy level and it does not need much energy to remove that electron. Thus, we can exclude option A, D and E.
Noble gases such as Neon and Argon have the fully filled electrons shells and thus, a lot of energy is required to remove an electron from the stable octet. In comparison, the removed electrons are much further from nucleus in Argon than in Neon. Thus, attraction between the removed electrons and nucleus is stronger in Neon and has higher ionization energy.
Therefore, among the given elements, Neon has the highest first ionization energy.
Correct Answer: B) PF₃
Option A Explanation:
In BeF2 molecule, molecular geometry is linear shape and dipoles cancel out. Thus, it does not have an overall dipole moment.
Option B Explanation:
In PF3 molecule, molecular geometry is trigonal pyramidal shape and dipoles do not cancel out. Thus, it has overall dipole moment.
Option C Explanation:
In CF4 molecule, molecular geometry is tetrahedral shape and dipoles cancel out. Thus, it does not have an overall dipole moment.
Option D Explanation:
In SF6 molecule, molecular geometry is octahedral shape and dipoles cancel out. Thus, it does not have an overall dipole moment.
Option E Explanation:
In PF5 molecule, molecular geometry is trigonal bipyramidal geometry shape and dipoles cancel out. Thus, it does not have an overall dipole moment.
A document has been prepared to include the images and diagrams related to the questions, placed directly below the worked solutions for clarity and reference.
Correct Answer: E) C
Reaction:
TiO2 + 2Cl2 + 2C → TiCl4 + 2CO
In this reaction, Cl is reduced because its oxidation state decreases from 0 to -1.
C is oxidized because its oxidation state increases from 0 to +2.
In a redox equation, the substance that is reduced is the oxidizing agent, the substance that is oxidized is the reducing agent.
Thus, in this reaction, C is the reducing agent.
Correct Answer: A) 50⁄56 × 100
To solve this question, we need to find the theoretical yield from the reaction first.
Given:
Experimental yield = 50g
m(Fe2O3) = 80g
M(Fe2O3) = 2Fe + 3O = 2(56) + 3(16) = 112 + 48 = 160g/mol
In moles, n(Fe2O3) = m / M = 80⁄160 g/mol = 0.5 mol
According to the balanced reaction given,
1 mole of Fe2O3 can yield 2 moles of Fe.
Thus, 0.5 mole of Fe2O3 will yield 1 mole of Fe, which is 56g in mass.
Now, we can calculate the percentage yield using the formula:
Percentage yield = experimental yield / theoretical yield × 100%
= 50⁄56 × 100
Thus, the correct option is option A.
Correct Answer: A
A diprotic acid is an acid that can donate two protons per molecule when dissolved in water. These protons are usually attached to highly electronegative atoms (e.g., oxygen).
Option A Explanation:
The mentioned molecule is ethane dioic acid. It has 2 carboxyl groups each of which contains 2 dissociable hydrogen atoms and this is a weak acid. Thus, this option is true.
Option B Explanation:
The mentioned molecule is sulfuric acid. Even though it has 2 dissociable protons, it is a strong acid. Thus, this option is false.
Option C Explanation:
The mentioned molecule is formic acid. It has only one dissociable proton. Thus, this option is false.
Option D Explanation:
The mentioned molecule is acetylenediol. Since its 2 hydrogen atoms are not bonded to highly electronegative atom, they cannot dissociate into protons. Thus, this option is false.
Option E Explanation:
The mentioned molecule is ethylene diol. It has 2 hydroxyl groups as functional groups and it is not an acid. Thus, this option is false.
Let's re-simplify the function first and then find the inverse.
Given: f(x) = 2 ln(x) − 2 ln(x − 1)
⇒ f(x) = 2[ln(x) − ln(x − 1)]
⇒ f(x) = 2 ln( x ⁄ (x − 1) )
Let y = f(x)
y = 2 ln( x ⁄ (x − 1) )
⇒ y ⁄ 2 = ln( x ⁄ (x − 1) )
To eliminate the logarithm, exponentiate both sides using the natural base e:
ey ⁄ 2 = x ⁄ (x − 1)
Now, solve for x:
ey ⁄ 2·x − x = ey ⁄ 2
x( ey ⁄ 2 − 1 ) = ey ⁄ 2
⇒ x = ey ⁄ 2 ⁄ ( ey ⁄ 2 − 1 )
The function f(x) is defined for x > 1, meaning x is always greater than 1.
This ensures the logarithms are defined and the values inside the logarithms are positive.
The inverse function f⁻¹(y) is:
x = ey ⁄ 2 ⁄ ( ey ⁄ 2 − 1 )
For the inverse function, we need to ensure the expression ey ⁄ 2 ⁄ ( ey ⁄ 2 − 1 ) is valid.
Specifically, we need to avoid division by zero, which occurs if:
ey ⁄ 2 − 1 = 0
⇒ ey ⁄ 2 = 1 ⇒ y ⁄ 2 = 0 ⇒ y = 0
To avoid division by zero, y must be such that ey ⁄ 2 > 1, which is true when y ⁄ 2 > 0,
or equivalently, y > 0.
So, the expression for its inverse function is:
x = ey ⁄ 2 ⁄ ( ey ⁄ 2 − 1 ), y > 0
First solve the quadratic equation:
Using the quadratic formula:
Interpretation:
As there is a negative number inside the root, the solutions of this quadratic equation are complex numbers.
Since the quadratic equation 2x² − 6x + 5 = 0 has complex roots, it means the graph does not cross the x-axis and is always positive for all real values of x.
Therefore, the inequality 2x² − 6x + 5 > 0 is true for all real numbers x.
Final Answer:
Let’s assume that it is x kg of sugar and 5x kg of flour.
After adding 1 kg of sugar and 2 kg of flour:
New sugar quantity = x + 1
New flour quantity = 5x + 2
Given the new ratio is 2:5:
(x + 1) / (5x + 2) = 2 / 5
Solving for x:
5(x + 1) = 2(5x + 2)
5x + 5 = 10x + 4
5x = 1 → x = 1/5
So the initial quantities are 1/5 kg of sugar and 1 kg of flour.
After adding 1 kg of sugar and 2 kg of flour:
New sugar quantity = 1/5 + 1 + 1 = 11/5
New flour quantity = 1 + 2 + 2 = 5
So, the new ratio is:
(11/5) ÷ 5 = 11/25
When rolling two standard six-sided dice, each die can land on one of six faces numbered from 1 to 6.
To list all possible outcomes in correct order, fix the first die's result and vary the second die’s result.
This gives a total of 6 × 6 = 36 possible outcomes.
Complete list of outcomes:
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
For product = 4: outcomes are (1,4), (2,2), (4,1) → 3 outcomes
For product = 9: outcome is (3,3) → 1 outcome
For product = 25: outcome is (5,5) → 1 outcome
Total favorable outcomes = 3 + 1 + 1 = 5
Probability, P(product is square of prime) =
Given: sin⁴[(x + 90°) ÷ 10] = 1⁄16
This can be written as:
sin⁴[(x + 90°) ÷ 10] = (±1⁄2)⁴
Now, taking the fourth root on both sides, we get:
sin[(x + 90°) ÷ 10] = ±1⁄2
The sine function equals +1⁄2 at angles (θ) = 30°, 150°
and the sine function equals −1⁄2 at angles (θ) = 210°, 330° within one cycle 0° to 360°.
So, we have:
(x + 90°) ÷ 10 = 30°, 150°, 210°, 330°
Now we have to solve for x.
For each value of θ, solve the equation:
(x + 90°) ÷ 10 = θ
So, x + 90° = 10θ → x = 10θ − 90°
For θ = 30°:
Value of x is: x = 300° − 90° = 210°
Similarly,
For θ = 150° → x = 1410°
For θ = 210° → x = 2010°
For θ = 330° → x = 3210°
Since we need the value of x in the range 0° ≤ x ≤ 360°,
this is only possible when θ = 30°.
Hence there is only 1 solution in the required range.
Hence the correct answer is (A).
Let's solve the first inequality:
100 − 99x ≤ 98 − 97x
100 − 98 ≤ 99x − 97x
2 ≤ 2x
Divide both sides by 2:
1 ≤ x → x ≥ 1
Let's solve the second inequality:
96 + 95x > 94 + 93x
−93x + 95x > 94 − 96
2x > −2
Divide both sides by 2:
x > −1
Now we have to take the intersection of the two results:
x > −1 and x ≥ 1
Therefore, the complete set of values of x that satisfies both inequalities is:
x ≥ 1
The given equation of circle is:
First, we need to write the circle’s equation in standard form by completing the square.
The standard equation of a circle is:
(x − h)² + (y − k)² = r²
Here, h, k and r are the coordinates of the centre of the circle and the radius of the circle.
For the x – terms:
For the y – terms:
Substitute the completed square forms back to the original equation, we get:
Solving this gives:
Comparing this with the standard equation, we get: h = 5, k = −6 and r = 2.
So, the given equation of circle has a radius, r = 2 and coordinates of its centre are (5, −6).
The distance from the centre to the x-axis is 5 and to the y-axis is 6. The minimum distance to either axis would be the smaller of these distances minus the radius of the circle:
Therefore, Minimum distance = 5 − 2 = 3
We have to simplify the expression:
√(16x + 8x) / (4x + 2x)
Let's simplify the powers first:
16x = (2⁴)x = 24x
8x = (2³)x = 23x
4x = (2²)x = 22x
2x = 2x
Now substitute these into the original expression:
√(24x + 23x) / (22x + 2x)
Simplify numerator and denominator:
= √[23x(2x + 1)] / [2x(2x + 1)]
= √[23x / 2x] → √[22x] → 2x
Final Answer: 2x
Mass of point mass A: m₁ = m
Initial speed of point mass A: u₁ = v
Final speed of point mass A: v₁ = vA
Mass of point mass B: m₂ = 2m
Initial speed of point mass B: u₂ = 0
Final speed of point mass B: v₂ = vB
Velocity of A after collision:
vA = [(m₁ − m₂)/(m₁ + m₂)] · u₁ + [2m₂/(m₁ + m₂)] · u₂
Substituting values:
v₁ = vA = [(m − 2m)/(m + 2m)] · v + [2(2m)/(m + 2m)] · 0
v₁ = vA = (−m / 3m) · v = −1⁄3v
Note: The negative sign indicates a change in direction. Since only speed (magnitude) is asked, ignore the sign:
Speed of A after collision = ⅓v
Velocity of B after collision:
vB = [(m₂ − m₁)/(m₁ + m₂)] · u₂ + [2m₁/(m₁ + m₂)] · u₁
Substituting values:
v₂ = vB = [(2m − m)/(m + 2m)] · 0 + [2m/(m + 2m)] · v
v₂ = vB = (2m / 3m) · v = 2⁄3v
Speed of B after collision = ⅔v
Given: The gas initially expands isothermally, so its temperature remains constant.
Initial temperature, T₁ = 25°C = 25 + 273 = 298 K
After the expansion, the pressure of the gas is its initial pressure P₁, and temperature T₁ = 298 K.
After transferring thermal energy to the trapped gas, pressure becomes half:
Final pressure P₂ = P₁ / 2
We are to find the final temperature T₂ of the gas after thermal energy is transferred.
Using Ideal Gas Law: PV = nRT
Where:
P = Pressure (Pa)
V = Volume (m³)
n = Number of moles
R = 8.314 J·K⁻¹·mol⁻¹
T = Temperature (K)
Since the volume is constant, we apply Gay-Lussac’s Law:
P₁ / T₁ = P₂ / T₂ → T₂ = T₁ × (P₂ / P₁)
Substitute values:
T₂ = 298 × (P₁/2) / P₁ = 298 × 1/2 = 149 K
Convert to Celsius:
T₂ = 149 K = 149 − 273 = −124°C
According to the law of calorimetry, we can say that:
Heat lost by water = Heat gained by ice
As the water cools from T₁ to T₂, heat lost by water is:
Qwater = M×c×(T₁ − T₂)
Where:
c = specific heat capacity of water
M = mass of water at temperature T₁
Heat gained by ice includes:
- Heat to melt the ice: m×Lf
- Heat to raise melted ice from 0°C to T₂: m×c×(T₂ − 0)
Total heat gained by ice:
Qice = m×Lf + m×c×T₂
Now, applying the heat balance:
m×Lf + m×c×T₂ = M×c×(T₁ − T₂)
Factor out m:
m×(Lf + c×T₂) = M×c×(T₁ − T₂)
Solving for m (mass of ice):
m = [M × c × (T₁ − T₂)] / (Lf + c T₂)
The vehicle travels east for 6 km and then south for 8 km. We use the Pythagorean theorem to find the straight-line displacement:
Displacement = √(6² + 8²) = √(36 + 64) = √100 = 10 km
The trip takes 15 minutes. Since the options are in km/h, we convert time into hours:
15 mins = 15 ÷ 60 = 0.25 hours
Average velocity is total displacement divided by time:
Average Velocity = Displacement ÷ Time = 10 km ÷ 0.25 h = 40 km/h
So, the magnitude of the average velocity is 40 km/h.
Here the spheres are perfectly insulating sphere. Since the spheres are insulating, no charge will transfer between them when they are placed in contact. Thus, the charges on each sphere will remain as they were originally.
So, the charge on the sphere with radius R1 will remain Q1.