CBSE · Class 10 · Board preparation
Practice questions for CBSE Class 10 Science, Mathematics and Social Science, organised by chapter rather than by year, with a worked answer under every question. Free to read, no sign-in. These are practice questions built to the CBSE pattern, not scans of past papers.
Most pages that rank for “previous year question papers class 10” are link farms pointing at PDF scans. This one is different, and the difference is worth a sentence: we do not host past CBSE papers. What we have is a very large bank of CBSE-pattern questions with worked answers, sorted by chapter. For official past papers and sample papers, go to cbseacademic.nic.in. Use both.
Half the paper is now competency-based — case studies, application, reasoning — which is why rote-learning answers from a guide stopped working. Another fifth is objective, including assertion–reason. Only the last 30% is the classic short and long answer writing that older question banks drill.
| Section | Marks | Share |
|---|---|---|
| Competency-based (case study, application, reasoning) 50% of the paper | 40 | |
| Objective (MCQ + assertion–reason) 20% of the paper | 16 | |
| Short and long answer 30% of the paper | 24 | |
| Total | 80 |
Exam length is 3 hours plus 15 minutes of reading time. Use the reading time to decide which optional questions you will attempt — not to start writing in your head.
February
Every candidate sits this. It is the main board examination.
May
Optional. Used to improve the score in selected subjects; same syllabus and same marking scheme as Phase 1. The better of the two scores counts.
All 13 chapters, each with a mix of question types so you meet the objective, the short answer and the reasoning version of the same idea.
Respiration is considered an exothermic process because:
Correct option: (c)
(c) energy is released during the breakdown of glucose. Explanation: In respiration, glucose reacts with oxygen to release energy required for cellular activities.
Distinguish between the reaction of calcium oxide with water and the burning of coal in terms of reactants and products.
CaO + H₂O is a combination of a compound and an element; C + O₂ is a combination of two elements. Explanation: Both are combination reactions forming a single product, but the nature of reactants differs.
Count and compare the number of atoms of each element on the LHS and RHS of the arrow for the skeletal chemical equation Fe + H₂O → Fe₃O₄ + H₂.
LHS: Fe = 1, H = 2, O = 1 RHS: Fe = 3, H = 2, O = 4 Comparison: The number of Fe atoms and O atoms are not equal on both sides. Therefore, the equation is unbalanced.
How is hydrogen gas typically tested in the laboratory using a burning candle?
Correct option: (a)
(a) It produces a pop sound when a burning candle is brought near it. Explanation: Hydrogen gas is highly flammable and burns with a characteristic 'pop' sound when exposed to a flame.
Why does a chemist add acid to water and not water to acid during dilution?
Adding water to acid is highly exothermic and can cause the mixture to splash, leading to burns. Adding acid to water allows the heat to dissipate safely.
How does the concentration of hydronium ions (H₃O⁺) change when an acid solution is diluted with water? Explain how this change affects the pH value of the solution.
When an acid is diluted with water, the number of hydronium ions per unit volume decreases. Since pH is inversely related to the concentration of H₃O⁺ ions, a decrease in concentration leads to an increase in the pH value, making the solution less acidic.
Which metal reacts with dilute hydrochloric acid to produce hydrogen gas?
Correct option: (b)
(b) Magnesium. Explanation: Magnesium is a reactive metal that displaces hydrogen from dilute acids, releasing hydrogen gas bubbles.
In the reaction of metals with dilute hydrochloric acid, which metal among magnesium, aluminium, zinc, and iron produces the highest temperature rise? State the reason.
Magnesium produces the highest temperature rise. This is because magnesium is the most reactive among these metals, leading to the fastest reaction rate and the most vigorous exothermic release of energy.
Describe the formation of magnesium chloride (MgCl₂) by the transfer of electrons. State the electronic configurations of the ions formed and the type of bond present.
Magnesium (2,8,2) loses two electrons to form Mg²⁺ (2,8). Two chlorine atoms (2,8,7) each gain one electron to form Cl⁻ ions (2,8,8). The electrostatic attraction between Mg²⁺ and two Cl⁻ ions forms MgCl₂. The bond is ionic (electrovalent).
When ethanoic acid reacts with sodium carbonate, a gas is evolved. Which test confirms the identity of this gas?
Correct option: (c)
(c) It turns lime water milky. Explanation: The reaction produces carbon dioxide gas. Carbon dioxide turns lime water (calcium hydroxide solution) milky due to the formation of a white precipitate of calcium carbonate.
Why can't carbon form a C⁴⁻ anion?
Carbon cannot form a C⁴⁻ anion because its nucleus, with only six protons, would find it difficult to hold on to ten electrons (four extra electrons). The electrostatic attraction would not be strong enough to stabilize the anion.
Explain why diamond and graphite, both being allotropes of carbon, exhibit vastly different physical properties such as hardness and electrical conductivity. Base your answer on the structural arrangement of carbon atoms in each allotrope.
Diamond is hard and an insulator because each carbon atom is covalently bonded to four other carbon atoms in a rigid three-dimensional lattice, leaving no free electrons. Graphite is soft and a good conductor because each carbon atom is bonded to only three others in hexagonal layers, leaving one free electron per atom that allows charge flow. The weak forces between these layers allow them to slide over each other, making graphite slippery.
In an industrial setting, yeast is used to produce ethanol. If the process is carried out in the presence of excess oxygen, what change in the metabolic pathway and end products would be observed compared to anaerobic conditions?
Correct option: (a)
(a) Yeast will perform aerobic respiration, producing carbon dioxide and water instead of ethanol.
Why is excretion necessary for living organisms?
Excretion is necessary to remove toxic waste products generated during metabolic processes. If these wastes accumulate in the body, they can cause poisoning and disrupt normal cellular functions, ultimately leading to death.
Describe the five steps of holozoic nutrition.
Holozoic nutrition involves five steps: ingestion (taking in food), digestion (breaking down food), absorption (uptake of nutrients), assimilation (utilization of nutrients by cells), and egestion (removal of undigested waste). These steps ensure the organism obtains energy and raw materials for growth.
Inside the skull, the brain is contained within a fluid-filled balloon. What is the primary function of this fluid?
Correct option: (b)
(b) To provide shock absorption. Explanation: The fluid-filled cavity around the brain provides shock absorption, protecting the delicate brain tissue from mechanical impacts.
Explain the mechanism by which pea plant tendrils coil around a support.
The part of the tendril in contact with the support grows slower than the part away from it, causing the tendril to circle around the object.
In a reflex action, such as withdrawing a hand from a hot object, the spinal cord initiates the response. Explain the role of the brain in this process. Why do we feel pain only after the hand has already moved?
1. The spinal cord acts as the reflex center, initiating the immediate withdrawal response to protect the body from injury. 2. Simultaneously, a parallel signal is sent from the spinal cord to the brain. 3. The brain processes this signal to register the sensation of pain and the awareness of the event. 4. Since the brain is located further away than the spinal cord reflex arc, the perception of pain occurs slightly after the protective reflex action has been executed.
In *Spirogyra*, new individuals are formed through fragmentation. What characteristic of *Spirogyra* allows this simple mode of reproduction to be effective?
Correct option: (c)
(c) *Spirogyra* has a relatively simple body organization with filamentous structures that can break into smaller pieces, each capable of growing into a new individual.
Spores of Rhizopus are covered by thick walls. How does this structural feature benefit the organism when environmental conditions become unfavorable?
The thick walls protect the spores from desiccation and extreme temperatures. This allows them to remain dormant for extended periods until favorable moist conditions return, ensuring the survival of the species.
Sperms are produced in the testes but are transported in a fluid medium called semen. Explain the composition of semen and the function of the glands that contribute to it.
Semen is a fluid mixture containing sperms and secretions from the seminal vesicles and prostate gland. These glandular secretions provide nutrition to the sperms and make the medium alkaline and slippery. This facilitates the easy transport of sperms through the urethra and protects them from the acidic environment of the female reproductive tract.
Which type of reproduction results in greater genetic diversity and variation among the offspring?
Correct option: (b)
(b) Sexual reproduction. Explanation: Sexual reproduction involves the fusion of gametes from two parents, leading to a mixing of genetic material and greater variation compared to asexual reproduction.
Critique the common societal belief that the mother is responsible for the sex of the child. Use genetic principles to justify your answer.
(a) Father determines sex. Explanation: This belief is scientifically incorrect. Since mothers only possess X chromosomes, they always contribute an X chromosome to the zygote. The sex is determined by whether the father contributes an X (resulting in a girl) or a Y chromosome (resulting in a boy).
If a child has attached earlobes and both parents have free earlobes, explain the possible genotypes of the parents and the child.
Attached earlobes are a recessive trait. For a child to have attached earlobes (genotype 'ee'), both parents must carry at least one 'e' allele. Since both parents have free earlobes, they must be heterozygous (genotype 'Ee'). The child inherited one 'e' allele from each parent, resulting in the 'ee' genotype.
A beam of light parallel to the principal axis of a concave mirror, after reflection, passes through:
Correct option: (a)
(a) The principal focus. Explanation: By definition, rays parallel to the principal axis converge at the principal focus (F) after reflecting from a concave mirror.
In an activity with a concave mirror, a student tries to obtain the image of a candle flame on a screen but fails for one specific object position. Identify this position and explain why the image cannot be obtained on the screen.
The object is placed at the principal focus (F). The reflected rays become parallel and never meet, so the image is formed at infinity and cannot be captured on a finite screen.
A convex lens has a focal length of 20 cm. An object is placed 30 cm from the lens. Find the position, nature, and magnification of the image.
Given: f = +20 cm, u = -30 cm. Using the lens formula: 1/v - 1/u = 1/f => 1/v = 1/f + 1/u = 1/20 + 1/(-30) = 1/20 - 1/30 = (3-2)/60 = 1/60. So, v = 60 cm. The image is formed 60 cm on the other side of the lens. Magnification (m) = v/u = 60/(-30) = -2. The image is real, inverted, and magnified.
Stars twinkle at night, but planets do not. What is the main reason for this difference?
Correct option: (a)
(a) Stars are point sources of light, while planets are extended sources. Explanation: Stars are very far away and act as point sources of light. Their light undergoes continuous atmospheric refraction, causing fluctuations in brightness (twinkling). Planets are much closer and act as extended sources (discs), so the twinkling effect from different points cancels out.
Why does the sky appear dark blue or black to an astronaut in space, whereas it appears bright blue to an observer on the surface of the Earth? Relate your answer to the scattering of light.
(d) On Earth, the atmosphere scatters shorter wavelengths (blue) of sunlight in all directions, making the sky appear blue. In space, there is no atmosphere to scatter sunlight, so the sky appears dark/black as there is no scattered light reaching the astronaut's eyes.
A rainbow is a natural spectrum appearing in the sky. Explain the three main optical processes involved in the formation of a rainbow. Mention the role of water droplets in this process.
The formation of a rainbow involves dispersion, internal reflection, and refraction of sunlight. Water droplets in the atmosphere act as small prisms. Sunlight enters the droplet, disperses into constituent colors, undergoes total internal reflection inside the droplet, and then refracts out, creating the visible spectrum arc.
A current of 2 A flows through a bulb for 5 minutes. Find the total charge that flows through the circuit.
Correct option: (b)
(b) 600 C. Explanation: Charge Q = I × t. Here I = 2 A, t = 5 minutes = 300 s. So, Q = 2 × 300 = 600 C.
Define the unit of current.
The SI unit of electric current is the ampere (A). One ampere is constituted by the flow of one coulomb of charge per second, that is, 1 A = 1 C/1 s.
A charge of 100 C flows through a conductor in 20 seconds. Calculate the potential difference across the conductor if the work done is 600 J.
Given: Charge Q = 100 C, Work done W = 600 J. Formula: Potential difference V = W / Q. Calculation: V = 600 J / 100 C = 6 V. Answer: The potential difference across the conductor is 6 volts.
The SI unit of magnetic field strength is the:
Correct option: (b)
(b) Tesla. Explanation: The SI unit for magnetic field strength (magnetic flux density) is the Tesla (T). The oersted is a CGS unit, but the Tesla is the standard SI unit used in modern physics.
Why is a soft iron core used inside a current-carrying solenoid to make an electromagnet? State one property of soft iron that makes it suitable for this purpose.
(b) High magnetic permeability. Explanation: Soft iron has high magnetic permeability, which means it can be easily magnetized by the solenoid's field, significantly strengthening the magnetic field. It also loses its magnetism quickly when the current is switched off.
Define the direction of a magnetic field at a given point and state the convention for field lines.
The direction of the magnetic field at a point is the direction in which the North pole of a compass needle points. By convention, field lines emerge from the North pole and merge at the South pole outside the magnet.
Which of the following organisms is a producer in an aquatic ecosystem?
Correct option: (a)
(a) Phytoplankton. Explanation: Phytoplankton are microscopic algae that perform photosynthesis, making them the primary producers in aquatic food chains.
Explain why an ecosystem is considered a self-sustaining unit in terms of energy and nutrients.
An ecosystem is self-sustaining because producers capture solar energy and convert it into food, which flows through consumers. Decomposers recycle nutrients from dead matter back to the soil, making them available for producers again, thus closing the nutrient loop.
Explain two specific ways in which non-biodegradable substances like plastics and heavy metals affect the environment negatively.
First, non-biodegradable substances like plastics accumulate in the soil, reducing its porosity and fertility, which hinders plant growth and root development. Second, these substances often end up in water bodies, where they can block sunlight from reaching aquatic plants and entangle or poison aquatic animals. Additionally, when broken down into microplastics, they enter the food chain, causing biological magnification of toxins in higher organisms, including humans.
All 14 chapters, each with a mix of question types so you meet the objective, the short answer and the reasoning version of the same idea.
Using Euclid's division algorithm, if $a = 5q + r$, what are the possible values of the remainder $r$?
Correct option: (a)
(a) 0, 1, 2, 3, 4. Explanation: According to Euclid's division lemma, for any two positive integers $a$ and $b$, there exist unique integers $q$ and $r$ such that $a = bq + r$, where $0 \le r < b$. Here, the divisor $b$ is 5. Therefore, the remainder $r$ must be less than 5 and non-negative. The possible integer values for $r$ are 0, 1, 2, 3, and 4.
Does the rational number $\frac{35}{50}$ have a terminating decimal expansion? Justify your answer.
Yes, it has a terminating decimal expansion. We simplify $\frac{35}{50}$ by dividing numerator and denominator by 5, getting $\frac{7}{10}$. The denominator is 10, which factors into $2 \times 5$. Since the prime factorization of the denominator is of the form $2^n \times 5^m$, the decimal expansion terminates. Specifically, $\frac{7}{10} = 0.7$.
Show that the number 7 × 11 × 13 + 13 is a composite number by expressing it as a product of its prime factors.
Let the number be N = 7 × 11 × 13 + 13. We can factor out the common term 13: N = 13 × (7 × 11 + 1). Calculate the value inside the parenthesis: 7 × 11 = 77. So, N = 13 × (77 + 1) = 13 × 78. Now, factorize 78 further into primes: 78 = 2 × 39 = 2 × 3 × 13. Substituting this back, N = 13 × 2 × 3 × 13 = 2 × 3 × 13². Since N can be expressed as a product of prime factors (2, 3, and 13) and has more than two factors, it is a composite number.
Find a quadratic polynomial whose sum and product of zeroes are 4 and 1 respectively.
Correct option: (d)
(d) x² - 4x + 1. Explanation: A quadratic polynomial is given by k[x² - (sum of zeroes)x + (product of zeroes)]. Substituting sum = 4 and product = 1, we get k[x² - 4x + 1]. For k=1, the polynomial is x² - 4x + 1.
If $\alpha, \beta, \gamma$ are zeroes of $x^3 - 3x^2 + x + 1$, find $\alpha + \beta + \gamma$.
(d) 3. Explanation: For a cubic polynomial $ax^3 + bx^2 + cx + d$, sum of zeroes = $-b/a$. Here $a=1, b=-3$. Sum = $-(-3)/1 = 3$.
What does it mean if a parabola representing a quadratic polynomial does not intersect the x-axis?
If a parabola does not intersect the x-axis, it means the quadratic polynomial has no real zeroes. The graph lies entirely above or below the x-axis, depending on whether 'a' is positive or negative.
A library has a fixed charge for the first 3 days and an additional charge for each day thereafter. Saritha paid ₹ 27 for 7 days and Susy paid ₹ 21 for 5 days. What is the charge for each extra day?
Correct option: (d)
(d) ₹ 3. Explanation: Let fixed charge be x and extra day charge be y. For Saritha (7 days, 4 extra): x + 4y = 27. For Susy (5 days, 2 extra): x + 2y = 21. Subtracting second from first: 2y = 6 => y = 3.
State whether the pair of equations x + y = 3 and 2x + 2y = 6 has a unique solution, no solution, or infinitely many solutions.
The pair of equations has infinitely many solutions because a₁/a₂ = b₁/b₂ = c₁/c₂ (1/2 = 1/2 = 3/6).
Determine whether the following pair of linear equations is consistent or inconsistent by comparing the ratios of their coefficients: 2x - 3y = 8 and 4x - 6y = 9.
The equations are 2x - 3y - 8 = 0 and 4x - 6y - 9 = 0. Here, a1 = 2, b1 = -3, c1 = -8 and a2 = 4, b2 = -6, c2 = -9. Calculate the ratios: a1/a2 = 2/4 = 1/2 b1/b2 = -3/-6 = 1/2 c1/c2 = -8/-9 = 8/9 Since a1/a2 = b1/b2 ≠ c1/c2 (1/2 = 1/2 ≠ 8/9), the lines are parallel. Therefore, the pair of linear equations is inconsistent.
A researcher in Bengaluru is modeling population growth with the equation 2x² - 7x + 3 = 0. Which of the following is a root of this equation?
Correct option: (a)
(a) 3. Explanation: Substituting x = 3 gives 2(3)² - 7(3) + 3 = 18 - 21 + 3 = 0. So, 3 is a root.
A cottage industry produces toys. The cost of production of each toy (in ₹) is $55$ minus the number of toys produced. If the total cost of production on a day was ₹ 750, write the quadratic equation for the number of toys $x$.
Number of toys is $x$. Cost per toy is $55 - x$. Total cost is $x(55 - x) = 750$. This simplifies to $55x - x^2 = 750$, or $x^2 - 55x + 750 = 0$.
A scientist in Chandigarh is studying a reaction where the concentration c follows c² - 5c + 6 = 0. Verify if c = 2 and c = 3 are roots of this equation.
For c = 2: (2)² - 5(2) + 6 = 4 - 10 + 6 = 0. So, c = 2 is a root. For c = 3: (3)² - 5(3) + 6 = 9 - 15 + 6 = 0. So, c = 3 is a root. Both values satisfy the equation.
In the AP 20, 17, 14, 11, ..., which term is the first negative term?
Correct option: (b)
(b) 8th term. Explanation: Here a = 20 and d = 17 - 20 = -3. We need to find n such that a_n < 0. a_n = 20 + (n-1)(-3) < 0. 20 - 3n + 3 < 0 => 23 < 3n => n > 23/3 => n > 7.66. Since n must be an integer, the first negative term is the 8th term. Let's verify: a_7 = 20 + 6(-3) = 2. a_8 = 20 + 7(-3) = -1.
Does the sequence 2, 4, 8, 16, ... form an AP? Justify your answer by calculating the differences between consecutive terms.
Calculate the differences: 4 - 2 = 2, 8 - 4 = 4, and 16 - 8 = 8. Since the differences (2, 4, 8) are not constant, the sequence does not have a common difference. Therefore, it is not an Arithmetic Progression.
Find the missing terms in the following arithmetic progression: $\square$, 13, $\square$, 3. Determine the first, third, and fifth terms if the sequence continues.
Let the AP be $a_1, a_2, a_3, a_4, ...$ Given $a_2 = 13$ and $a_4 = 3$. $a_2 = a + d = 13$ ... (i) $a_4 = a + 3d = 3$ ... (ii) Subtract (i) from (ii): $2d = -10 \Rightarrow d = -5$. From (i): $a - 5 = 13 \Rightarrow a = 18$. The AP is 18, 13, 8, 3, ... The missing term between 13 and 3 is $a_3 = 13 + (-5) = 8$. The term before 13 is $a_1 = 18$. The next term $a_5 = 3 + (-5) = -2$. The missing terms are 18 and 8. The sequence is 18, 13, 8, 3, -2.
In triangles ABC and DEF, angle B = angle E. Which additional condition would make the triangles similar by the SAS criterion?
Correct option: (c)
(c) AB/DE = BC/EF Explanation: The SAS (Side-Angle-Side) similarity criterion requires that two sides are proportional and the included angle is equal. Here, angle B and angle E are the included angles.
Two similar triangles have areas of 100 cm² and 49 cm² respectively. If the perimeter of the larger triangle is 40 cm, calculate the perimeter of the smaller triangle.
(b) 28 cm. Explanation: The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding perimeters. Let P1 and P2 be the perimeters. Area1/Area2 = (P1/P2)². So, 100/49 = (40/P2)². Taking the square root of both sides gives 10/7 = 40/P2. Solving for P2: P2 = (40 * 7) / 10 = 28 cm.
In the light bulb activity, a quadrilateral ABCD with sides 3 cm, 4 cm, 5 cm, 6 cm casts a shadow A'B'C'D' with sides 6 cm, 8 cm, 10 cm, 12 cm. What is the scale factor?
The scale factor is the ratio of corresponding sides, e.g., 6/3 = 2. So, the shadow is an enlargement with a scale factor of 2.
What are the coordinates of the points of trisection of the line segment joining A(2, -2) and B(-7, 4)?
Correct option: (a)
(a) (-1, 0) and (-4, 2). Explanation: Trisection points divide the segment in ratios 1:2 and 2:1. Point P (1:2) = ((1(-7)+2(2))/3, (1(4)+2(-2))/3) = ((-7+4)/3, (4-4)/3) = (-3/3, 0) = (-1, 0). Point Q (2:1) = ((2(-7)+1(2))/3, (2(4)+1(-2))/3) = ((-14+2)/3, (8-2)/3) = (-12/3, 6/3) = (-4, 2).
If A(3, 4) and B(5, 8) are two vertices of a rectangle and C is the midpoint of the diagonal joining A and B, find the coordinates of C.
C is the midpoint of AB. x = (3+5)/2 = 4. y = (4+8)/2 = 6. Coordinates of C are (4, 6).
Determine if the points (1, 5), (2, 3), and (–2, –11) are collinear by using the distance formula.
Let A(1, 5), B(2, 3), and C(–2, –11). AB = √((2-1)² + (3-5)²) = √(1 + 4) = √5. BC = √((-2-2)² + (-11-3)²) = √(16 + 196) = √212 = 2√53. AC = √((-2-1)² + (-11-5)²) = √(9 + 256) = √265. For points to be collinear, the sum of two distances must equal the third (e.g., AB + BC = AC). √5 + 2√53 ≈ 2.23 + 14.56 = 16.79. AC = √265 ≈ 16.28. Since AB + BC ≠ AC, the points are not collinear.
An architect in Mumbai is designing a roof with a slope angle of 30°. What is the value of sin 30°?
Correct option: (a)
(a) 1/2. Explanation: From the standard trigonometric table, the value of sin 30° is 1/2.
If cos A = 12/13, find the value of cot A.
Given cos A = Adjacent/Hypotenuse = 12/13. Let Adjacent = 12k and Hypotenuse = 13k. Opposite side = √((13k)² - (12k)²) = √(169k² - 144k²) = √25k² = 5k. Therefore, cot A = Adjacent/Opposite = 12k/5k = 12/5.
In a right triangle ABC, right-angled at B, if angle A is 30°, prove that tan A = sin A / cos A.
tan A = BC/AB. sin A / cos A = (BC/AC) / (AB/AC) = BC/AB. Therefore, tan A = sin A / cos A. Explanation: We substitute the values of sin A, cos A, and tan A in terms of the sides of the triangle and simplify.
From the top of a lighthouse, the angle of depression of a ship in the sea is 30°. If the line of sight is drawn from the top of the lighthouse to the ship, what is the angle of elevation of the top of the lighthouse from the ship?
Correct option: (a)
(a) 30°. Explanation: The angle of depression from a horizontal line is equal to the alternate interior angle of elevation from the horizontal line at the lower point.
An electrician needs to reach a point 3.7 m up a pole. She uses a ladder inclined at 60° to the horizontal. Find the length of the ladder. (Take √3 = 1.73)
Let ladder length be L. sin 60° = 3.7/L. So, √3/2 = 3.7/L => L = 7.4/√3 = 7.4 × 1.73 / 3 = 12.802 / 3 = 4.27 m (approx).
A cable of length 50 m is attached to the top of a tower and makes an angle of 30° with the ground. Find the height of the tower.
Let the height be h m. In the right-angled triangle, sin 30° = h/50. Since sin 30° = 1/2, we have 1/2 = h/50. Therefore, h = 25 m.
A tangent to a circle intersects the circle at exactly how many points?
Correct option: (b)
(b) One. Explanation: By definition, a tangent is a line that touches the circle at exactly one point, known as the point of contact.
From an external point P, two tangents PA and PB are drawn to a circle with centre O. If the angle subtended by the chord AB at the centre ∠AOB is 110°, find the angle between the tangents ∠APB.
(a) 70°. Explanation: The quadrilateral OAPB is formed by two radii and two tangents. The angles between the radius and tangent at points of contact are 90°, so ∠OAP = ∠OBP = 90°. The sum of angles in quadrilateral OAPB is 360°. Therefore, ∠APB + ∠OAP + ∠AOB + ∠OBP = 360°. Substituting the known values, ∠APB + 90° + 110° + 90° = 360°, which gives ∠APB = 360° - 290° = 70°.
What is the meaning of the word 'tangent' and how does it relate to its geometric definition?
The word 'tangent' comes from the Latin 'tangere', meaning 'to touch'. Geometrically, a tangent touches the circle at exactly one point, aligning with the etymological meaning.
The area of the major sector of a circle with radius 10 cm and minor sector angle 90° is (use π = 3.14):
Correct option: (b)
(b) 235.5 cm². Explanation: Major sector angle = 360 - 90 = 270°. Area = (270/360) × 3.14 × 10² = (3/4) × 314 = 235.5 cm².
Find the area of the minor segment of a circle of radius 21 cm and ∠ AOB = 120°. (Use π = 22/7, √3 = 1.73)
Area of sector = (120/360) × (22/7) × 21² = 462 cm². Area of triangle = (1/2) × 21 × 21 × sin(120°) = 190.9 cm². Segment area = 462 - 190.9 = 271.1 cm².
In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find the length of the arc and the area of the sector formed by the arc. (Use π = 22/7)
Length of arc = (θ/360) × 2πr = (60/360) × 2 × (22/7) × 21 = (1/6) × 2 × 22 × 3 = (1/6) × 132 = 22 cm. Area of sector = (θ/360) × πr² = (60/360) × (22/7) × 21² = (1/6) × (22/7) × 441 = (1/6) × 22 × 63 = 231 cm².
A toy is in the shape of a hemisphere surmounted by a cone. If the radius is 7 cm and the total surface area is 528 cm², what is the slant height of the cone? (Use π = 22/7)
Correct option: (b)
(b) 12 cm. Explanation: TSA = 2πr² + πrl = πr(2r + l). 528 = (22/7)*7*(14 + l) => 528 = 22(14 + l) => 24 = 14 + l => l = 10 cm. I will adjust to l=10. Options: (a) 8 (b) 10 (c) 12 (d) 14. Correct is (b).
A decorative block is made of two solids — a cube and a hemisphere. The base of the block is a cube with edge 5 cm, and the hemisphere fixed on the top has a diameter of 4.2 cm. Find the total surface area of the block. (Take π = 22/7)
TSA of cube = 6a² = 6(5)² = 150 cm². Radius of hemisphere r = 2.1 cm. Base area of hemisphere = πr². CSA of hemisphere = 2πr². Total Surface Area = TSA of cube - Base area of hemisphere + CSA of hemisphere = 150 - πr² + 2πr² = 150 + πr². TSA = 150 + (22/7)(2.1)² = 150 + (22/7)(4.41) = 150 + 13.86 = 163.86 cm².
A wooden article was made by scooping out a hemisphere from each end of a solid cylinder. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the total surface area of the article. (Take π = 22/7)
Radius r = 3.5 cm. Height of cylinder h = 10 cm. TSA = CSA of cylinder + 2 × CSA of hemisphere = 2πrh + 2(2πr²) = 2πr(h + 2r). TSA = 2 × (22/7) × 3.5 × (10 + 7) = 22 × (10 + 7) = 22 × 17 = 374 cm².
In the step-deviation method, why is the variable $u_i$ introduced?
Correct option: (a)
(a) To simplify calculations. $u_i$ reduces large deviations $d_i$ to smaller numbers, making the multiplication with frequencies and summation easier and less prone to error.
If the mean of a grouped data is 25 and ∑fᵢ = 12, find ∑fᵢxᵢ.
Using the formula Mean = (∑fᵢxᵢ) / (∑fᵢ), we substitute the given values: 25 = (∑fᵢxᵢ) / 12. Therefore, ∑fᵢxᵢ = 25 × 12 = 300.
A survey collected data on the number of plants in 20 houses. Find the mean number of plants per house using the direct method. | Number of Plants | 0-2 | 2-4 | 4-6 | 6-8 | 8-10 | 10-12 | 12-14 | | :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | | Number of Houses | 1 | 2 | 1 | 5 | 6 | 2 | 3 |
Midpoints: 1, 3, 5, 7, 9, 11, 13. f_i * x_i: 1(1)=1, 2(3)=6, 1(5)=5, 5(7)=35, 6(9)=54, 2(11)=22, 3(13)=39. Σf_i = 1+2+1+5+6+2+3 = 20. Σf_i x_i = 1+6+5+35+54+22+39 = 162. Mean = Σf_i x_i / Σf_i = 162 / 20 = 8.1 plants per house.
A standard deck of 52 playing cards is well-shuffled. What is the probability of drawing the King of Hearts?
Correct option: (a)
(a) 1/52. Explanation: There is exactly one King of Hearts in a standard deck of 52 cards. P(King of Hearts) = 1/52.
Can the probability of an event be -0.5? Give a reason for your answer.
No, the probability of an event cannot be -0.5. The probability of any event always lies between 0 and 1 (inclusive). A negative value is not possible.
A lot of 20 bulbs contains 4 defective ones. One bulb is drawn at random from the lot. Find the probability that the bulb drawn is (i) defective, (ii) non-defective.
Total bulbs = 20. Defective bulbs = 4. Non-defective bulbs = 20 - 4 = 16. (i) P(Defective) = 4/20 = 1/5. (ii) P(Non-defective) = 16/20 = 4/5. Check: P(Defective) + P(Non-defective) = 1/5 + 4/5 = 1.
Social Science is one 80-mark paper drawn from four books. Students lose marks here by revising History hard and leaving Economics until the night before — the paper does not weight them that way.
In January 1871, where was the new German Empire proclaimed, with William I as the Emperor?
Correct option: (b)
(b) Hall of Mirrors, Versailles. Explanation: The German Empire was proclaimed in the Hall of Mirrors at the Palace of Versailles in a ceremony attended by princes and army representatives.
Giuseppe Mazzini founded 'Young Italy' and 'Young Europe' with the vision of democratic republics. Why was his approach considered a direct threat to the conservative order established by the Vienna Congress?
Correct option: (c)
(c) Because he opposed monarchy and sought to unify nations into single democratic republics, challenging the principle of legitimate monarchy.
Discuss the emergence of the new middle class in Western and Central Europe during the nineteenth century. How did their social and economic position influence their political demands?
The growth of industrial production and trade led to the emergence of a new middle class comprising industrialists, businessmen, and professionals. Unlike the landed aristocracy, this class was based on production for the market and wealth rather than birth. They demanded an end to autocracy and clerical privileges, advocating for a constitution and representative government. Their economic power drove them to seek political rights, such as suffrage and equality before the law, to protect their property and interests, aligning with the ideology of liberal nationalism.
Interpret the impact of the July Revolution of 1830 in France on the political landscape of Europe. How does Metternich’s quote reflect this impact?
The July Revolution of 1830 overthrew the Bourbon kings in France and installed a constitutional monarchy, sparking liberal-nationalist uprisings elsewhere. It led to Belgium breaking away from the United Kingdom of the Netherlands. Metternich’s quote, 'When France sneezes, the rest of Europe catches cold,' reflects the idea that political changes in France had a contagious effect, inspiring similar revolutionary movements across the continent.
Explain how the French Revolutionaries used cultural and administrative measures to forge a sense of national unity among the French people. Discuss the significance of uniform laws, a common language, and the commemoration of martyrs in this process.
To forge national unity, French revolutionaries implemented a centralized administrative system with uniform laws for all citizens. They abolished internal customs duties and adopted a uniform system of weights and measures. Culturally, they discouraged regional dialects and promoted French, as spoken in Paris, as the common language. Hymns were composed, oaths taken, and martyrs commemorated in the name of the nation to create shared symbols of identity. These measures broke down regional divisions and created a cohesive national community, laying the foundation for the modern nation-state by ensuring that all citizens shared common legal, linguistic, and cultural experiences.
Explain the changes in political rights and suffrage during the French Revolution and the subsequent Napoleonic era. How did the Napoleonic Code affect the status of women?
During the French Revolution, political rights were initially granted exclusively to property-owning men, excluding women and non-propertied men. However, under the radical Jacobin regime, all adult males briefly enjoyed suffrage. After Napoleon came to power, the Napoleonic Code reversed these gains. It restored limited suffrage and significantly reduced the status of women, subjecting them to the authority of fathers and husbands. Women were treated as minors with no political rights. Throughout the 19th and early 20th centuries, women and non-propertied men organized opposition movements to demand equal political rights, highlighting the persistent struggle for democracy and equality.
In arid soils, the lower horizons are often occupied by Kankar. What is the primary consequence of the Kankar layer formation in the bottom horizons?
Correct option: (c)
(c) It restricts the infiltration of water. Explanation: Kankar is a calcareous concretion that forms a hard layer, preventing water from percolating deeper into the soil profile.
Why is resource planning particularly important for a country like India?
Correct option: (b)
(b) Because India has enormous diversity in the availability of resources across different regions.
What are 'Shelter Belts'? Explain their dual role in soil conservation and desert stabilization.
Shelter belts are rows of trees planted to create windbreaks. They protect crops from strong winds and reduce soil erosion. They also help in stabilizing sand dunes, which is crucial for preventing desert expansion in arid regions.
Analyze the difference between 'Net Sown Area' and 'Gross Cropped Area'. Why is the Gross Cropped Area in India significantly larger than the Net Sown Area?
Net Sown Area is the total physical extent of land on which crops are sown and harvested in a year. Gross Cropped Area is the sum of the Net Sown Area and the area sown more than once in the same agricultural year. In India, the Gross Cropped Area is larger because farmers practice multiple cropping (growing two or more crops on the same piece of land in a year) to maximize yield and income, especially in regions with favorable climate and irrigation.
Analyze the causes of land degradation in the states of Punjab, Haryana, and western Uttar Pradesh compared to Jharkhand and Chhattisgarh. Suggest specific conservation measures for each region based on the root causes identified.
In Punjab, Haryana, and western Uttar Pradesh, land degradation is primarily caused by over-irrigation, leading to waterlogging and increased soil salinity and alkalinity. In contrast, Jharkhand and Chhattisgarh face degradation due to deforestation caused by mining and quarrying activities. For the northern region, conservation measures include better water management systems, crop rotation, and use of organic manure to reduce chemical dependency. For the eastern/central mining states, measures include afforestation, proper management of mining sites, and rehabilitation of mined areas with vegetation to prevent soil erosion.
Identify the major human activities contributing to land degradation in India. Describe specific measures to check land degradation in arid regions like Rajasthan and Gujarat.
Major human activities causing land degradation include deforestation, overgrazing, mining, quarrying, over-irrigation, and industrial pollution. In arid regions like Rajasthan and Gujarat, overgrazing is a primary cause, leading to soil erosion and desertification. Specific measures to check degradation in these areas include: (1) Afforestation and planting shelter belts to reduce wind speed; (2) Controlling overgrazing through rotational grazing and managed pastures; (3) Stabilizing sand dunes by growing thorny bushes; and (4) Proper management of waste lands to prevent further encroachment and degradation.
How does the population of Belgium compare to the Indian state of Haryana?
Correct option: (a)
(a) Belgium's population is about half the population of Haryana. Belgium has a population of a little over one crore, about half the population of Haryana.
The Sri Lankan Tamils demanded regional autonomy and equality of opportunity. How did the central government's response to these demands contribute to the escalation of conflict?
Correct option: (c)
(c) The repeated denial of autonomy led to the formation of political organizations demanding an independent state. Explanation: By repeatedly denying the demands for provincial autonomy and recognizing Tamil as an official language, the government fueled distrust, leading to the formation of groups demanding an independent Tamil Elam.
Define 'vertical division of power' in the context of modern democracies. How does the Indian Constitution implement this form of power sharing between the Centre and the States?
Vertical division of power refers to the sharing of authority among governments at different levels, such as the federal (Central) government and state (provincial) governments. The Indian Constitution implements this by clearly laying down the powers of the Union Government and the State Governments. This ensures that while the Centre handles national issues, States manage regional matters, preventing concentration of power.
Describe the ethnic composition of Belgium.
Belgium has a complex ethnic composition. 59% of the population lives in the Flemish region and speaks Dutch. 40% live in the Wallonia region and speak French. The remaining 1% speak German.
Describe the causes and consequences of the civil war in Sri Lanka.
The civil war in Sri Lanka was caused by the distrust between the Sinhala and Tamil communities, stemming from majoritarian policies like the 1956 Act and constitutional provisions favoring Buddhism. The Tamils felt alienated and discriminated against, leading to demands for autonomy and eventually an independent Tamil Eelam. The consequences were severe: thousands were killed, many families became refugees, livelihoods were lost, and the social, cultural, and economic life of the country suffered a terrible setback. The war ended in 2009 with the defeat of the LTTE.
Describe the ethnic composition of Belgium and Sri Lanka based on the NCERT chapter.
Belgium: 59% Dutch-speaking (Flemish), 40% French-speaking (Wallonia), 1% German-speaking. Sri Lanka: 74% Sinhala-speakers, 18% Tamil-speakers (13% Sri Lankan Tamils, 5% Indian Tamils), 7% Christians.
Why is per capita income considered an inadequate sole indicator of development when comparing two regions?
Correct option: (c)
(c) It does not account for public facilities like health, education, and environmental quality.
In a society, women are often restricted from working outside the home due to lack of safety and unequal distribution of housework. How does addressing these non-income factors contribute to development?
Correct option: (b)
(b) It enhances women's dignity, freedom, and economic participation, leading to holistic development.
How is per capita income calculated, and why is it useful for comparing states within a country?
Per capita income is calculated by dividing the total national or state income by the total population. It is useful for comparing states because it provides an average income figure that helps assess the relative economic prosperity and standard of living across different regions.
How does the World Bank classify countries based on per capita income? Mention the income criteria for 'High Income' and 'Low Income' countries and state the category of India.
The World Bank classifies countries based on their per capita income to compare development levels. Countries with a per capita income of US$ 66,500 per annum and above are classified as 'High Income' or rich countries. Countries with a per capita income of about US$ 2,300 or less are classified as 'Low Income' countries. India falls into the category of 'Lower Middle Income' countries, with a per capita income of approximately US$ 11,000 per annum.
Discuss the statement: 'Development means different things to different people.' Support your answer with examples of varying developmental goals from the NCERT chapter.
The statement is true because individuals and groups have different socioeconomic backgrounds, needs, and aspirations. For example, a landless rural labourer aspires for more days of work, better wages, and quality local education. In contrast, a prosperous farmer from Punjab seeks higher support prices for crops and cheap labour. An urban unemployed youth might desire job opportunities in cities, while a girl from a rich urban family aspires for equal freedom and the ability to pursue studies abroad. These examples show that development is subjective and context-dependent.
Define per capita income and explain how it is calculated. Why is it widely used to compare the economic development of different countries?
Per capita income is the average income earned per person in a country during a specific year. It is calculated by dividing the total national income of the country by its total population. It is widely used to compare economic development because: 1) It provides a simple, standardized metric that is easy to calculate and understand. 2) It allows for direct comparison of the average economic standing of populations across different nations. 3) It serves as a foundational indicator for broader economic analysis and policy-making.