Classwise Practice Tests

Q. Identify scenarios requiring statistical survey data versus factual inquiries with known constants.📘 Data Handling and Presentation📕 NCERT Book — p. 75, 4.1 · Data Collection & Organisation

Q. Find missing numbers in equivalent fractions: 5/4 = ?/8, 4/3 = 12/?, and 7/5 = ?/10.📘 Fractions📕 NCERT Book — p. 168, 7.6 · Equivalent Fractions & Simplification

Q. Evaluate differences using tokens: (+10)-(+7), (-8)-(-4), (+9)-(+12), (-5)-(-7), (-2)-(-6).📘 The Other Side of Zero📕 NCERT Book — p. 258, 10.2 · Additive Inverses & Zero Pairs

Q. For three non-collinear points A, B, C, how many distinct lines can be drawn and how many angles are formed?📘 Lines and Angles📕 NCERT Book — p. 20, 2.5 · Angles & Notation

Q. Compare Charan's (130 ft) and Sharan's (134 ft) houses: show they have identical area but different perimeters.📘 Perimeter and Area📕 NCERT Book — p. 147, 6.3 · Area of Rectangles and Squares

Q. Identify and correct discrepancies between a 2006–2022 tiger population data table and its plotted bar heights.📘 Data Handling and Presentation📕 NCERT Book — p. 99, 4.4 · Bar Graphs & Interpretation

Q. Leena makes 5 cups of tea using 1/4 L milk. Calculate milk volume per cup using reciprocal division (1/4 / 5 = 1/20 L).📘 Working with Fractions📕 NCERT Book — p. 190, In-Text Exploration · Division of Fractions

Q. According to the 2011 Census, the population of Chintamani was about 75,000. How much less than one lakh is 75,000?📘 Large Numbers Around Us📕 NCERT Book — p. 3, Figure it Out 1.1 · Indian & International Numeration Systems

Q. Calculate unknown angles from transversal diagrams: i = 54° and j = 97°.📘 Parallel and Intersecting Lines📕 NCERT Book — p. 123, Figure it Out 5.4 · Angle Calculations in Parallel Lines

Q. For base angles 30°, 70°, 54°, 144°, find pairs for which triangle is possible (sum < 180°) and not possible (sum >= 180°).📘 A Tale of Three Intersecting Lines📕 NCERT Book — p. 163, Figure it Out 7.7 · Angle Sum Property of Triangle

Q. Execute Euclid's rigorous proof that the sum of angles of any triangle is 180° using an auxiliary parallel line; verify via paper folding.📘 A Tale of Three Intersecting Lines📕 NCERT Book — p. 165-166, In-Text Exploration · Angle Sum Property of Triangle

Q. A tap fills 7/10 tank in 1 hr: calculate fill for 1/3 hr (7/30), 2/3 hr (14/30), 3/4 hr (21/40), 7/10 hr (49/100), and time to fill full tank (10/7 hr).📘 Working with Fractions📕 NCERT Book — p. 183-184, Figure it Out 8.3 · Applied Fractional Models

Q. Formulate 3x3 magic square with center m: [m+3, m-4, m+1; m-2, m, m+2; m-1, m+4, m-3]; prove each line sums to 3m.📘 Number Play📕 NCERT Book — p. 136-137, In-Text Exploration · Magic Squares

Q. Express given repeated products like 6*6*6*6, b*b*b*b, and 2*2*a*a in exponential form.📘 Power Play📕 NCERT Book — p. 22, Figure it Out 2.1 · Concept of Powers & Exponents

Q. Fold paper in half and quarter to create specific crease patterns forming rhombuses and squares.📘 Quadrilaterals📕 NCERT Book — p. 111, Puzzle Time · Constructions & Theorems

Q. Analyze how the Chinese used alternating Zong and Heng rod numerals for decimal place value.📘 A Story of Numbers📕 NCERT Book — p. 77, In-Text Exploration · Ancient Positional Systems

Q. Construct landmark numbers for a base-5 system (1, 5, 25, 125, 625) and represent 143.📘 A Story of Numbers📕 NCERT Book — p. 63, In-Text Exploration · Base-n Number Systems

Q. Find all pairs (a, b) for 48a23b divisible by 18 and (p, q) for 3p7q8 divisible by 44.📘 Number Play📕 NCERT Book — p. 132, Figure it Out 5.4 · Divisibility Rules for 9 and 11

Q. Demonstrate 4 different algebraic interpretations of dot pattern Step k leading to k^2+2k.📘 We Distribute, Yet Things Multiply📕 NCERT Book — p. 152, In-Text Exploration · Geometric & Visual Patterns

Q. Referring to Fig. 1.3: What are the coordinates of D₁?📘 Orienting Yourself: The Use of Coordinates📕 NCERT Book — p. 5, 1.1 · Cartesian Coordinate System

Q. ABCD is a parallelogram. P and Q are any two points on side AB. What can you say about the ratio area(ΔPCD) : area(ΔQCD)?📘 Measuring Space: Perimeter and Area📕 NCERT Book — p. 142, 6.2 · Area of Quadrilaterals & Polygons

Q. An equilateral triangle is inscribed in a circle of radius r. Show that the ratio of triangle area to circle area is (3√3)/(4π) ≈ 0.413.📘 Measuring Space: Perimeter and Area📕 NCERT Book — p. 148, 6.3 · Area of Quadrilaterals & Polygons

Q. Semicircles are drawn on all three sides of a right-angled triangle. Show that Area(A) + Area(B) = Area(C).📘 Measuring Space: Perimeter and Area📕 NCERT Book — p. 153, End-of-Chapter · Area Related to Circles & Segments

Q. Prove that √5 is an irrational number using proof by contradiction.📘 The World of Numbers📕 NCERT Book — p. 64, End-of-Chapter · Irrational Numbers & Real Numbers

Q. A toy car of mass 100 g is moving with a constant velocity of 0.5 m/s. What is the magnitude of the net force acting on the toy car? (0 N)📘 How Forces Affect Motion📕 NCERT Book — p. 106, Pause and Ponder · Balanced & Unbalanced Forces

Q. Differentiate between cell membrane and cell wall based on their permeability to water and solutes.📘 Cell: The Building Block of Life📕 NCERT Book — p. 24, Revise, Reflect, Refine · Cell Membrane & Transport (Osmosis)

Q. Differentiate between Rough Endoplasmic Reticulum (RER) and Smooth Endoplasmic Reticulum (SER) based on ribosome attachment and structure.📘 Cell: The Building Block of Life📕 NCERT Book — p. 24, Revise, Reflect, Refine · Cell Structure & Organelles

Q. Discuss how industrial combustion, deforestation, and livestock agriculture elevate greenhouse gas levels. Outline individual actions under Mission LiFE.📘 Earth as a System: Energy, Matter, and Life📕 NCERT Book — p. 266, Pause and Ponder · Anthropogenic Impacts & Climate Change

Q. Truck driver slows from 54 km/h (15 m/s) to 36 km/h (10 m/s) in 36 s. Calculate the distance travelled during this time under constant acceleration (450 m).📘 Describing Motion Around Us📕 NCERT Book — p. 69, Revise, Reflect, Refine · Acceleration & Kinematic Equations

Q. Detail how deforestation dismantles carbon sequestration, reduces atmospheric oxygen replenishment, diminishes transpiration rainfall, and accelerates soil loss.📘 Earth as a System: Energy, Matter, and Life📕 NCERT Book — p. 267, Revise, Reflect, Refine · Anthropogenic Impacts & Climate Change

Q. True/False: sin(A + B) = sin A + sin B. Justify your answer.📘 Introduction to Trigonometry📕 NCERT Book — p. 127, Ex 8.2 · Algebraic & Monotonic Properties of Trig Ratios

Q. Rohan's mother is 26 years older than him. Product of their ages 3 years from now will be 360. Represent as quadratic equation.📘 Quadratic Equations📕 NCERT Book — p. 42, Ex 4.1 · Applied Word Problems on Quadratics

Q. D on side BC of triangle ABC such that angle ADC = angle BAC. Show that CA² = CB · CD.📘 Triangles📕 NCERT Book — p. 97, Ex 6.3 · Applications & Proofs of Similarity

Q. Solve: John and Jivanti have 45 marbles. Both lost 5 marbles, product is 124. Find initial marbles (x² - 45x + 324 = 0).📘 Quadratic Equations📕 NCERT Book — p. 44, Ex 4.2 · Applied Word Problems on Quadratics

Q. Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre.📘 Circles📕 NCERT Book — p. 152, Ex 10.2 · Theorems & Proofs on Tangents

Q. Prove: (cos A - sin A + 1)/(cos A + sin A - 1) = cosec A + cot A using cosec² A = 1 + cot² A.📘 Introduction to Trigonometry📕 NCERT Book — p. 131, Ex 8.3 · Trigonometric Identities & Proofs

Q. 200 logs stacked: 20 in bottom row, 19 in next, 18 in next. How many rows and how many logs in the top row?📘 Arithmetic Progressions📕 NCERT Book — p. 70, Ex 5.3 · Word Problems & Real-Life AP Models

Q. How is the concentration of hydronium ions (H3O+) affected when a solution of an acid is diluted?📘 Acids, Bases and Salts📕 NCERT Book — p. 25, In-Text 3 · Aqueous Solutions & Ionisation (pH Scale)

Q. What are the primary outside raw materials used by an organism to sustain life?📘 Life Processes📕 NCERT Book — p. 81, In-Text 1 · Autotrophic & Heterotrophic Nutrition

Q. Why should a magnesium ribbon be cleaned before burning in air?📘 Chemical Reactions and Equations📕 NCERT Book — p. 6, In-Text 1 · Chemical Equations & Balancing

Q. Why do HCl, HNO3 show acidic character in aqueous solutions while alcohol and glucose do not?📘 Acids, Bases and Salts📕 NCERT Book — p. 25, In-Text 3 · Aqueous Solutions & Ionisation (pH Scale)

Q. Explain the complete mechanism of the cleaning action of soaps with a neat diagram of a micelle.📘 Carbon and its Compounds📕 NCERT Book — p. 78, Exercise · Soaps, Detergents & Micelles

Q. State which of the following sets are finite and which are infinite: (i) {x in Z : (x+1)(x+2)=0} (ii) {x in N : x^2-1=3} (iii) {x: x is an odd natural number} (iv) {x in Z : -1 < x < 0} (v) {x in Z : x < 0} (vi) {x: x satisfies the identity cos^2 x + sin^2 x = 1}.📘 Set📕 NCERT Book — p. 71, 3.3 · Finite and Infinite Sets

Q. Find the domain and range of each of the following real functions: (i) f(x) = x^2 (ii) f(x) = 1/x.📘 Relations📕 NCERT Book — p. 122, 4.5 · Functions - Domain and Range

Q. In how many ways can 4 men and 4 women be seated at a round table if: (i) no restriction is imposed (ii) two particular women must sit together (iii) all women must sit together?📘 Permutations and Combinations📕 NCERT Book — p. 211-212, 6.5 · Circular Permutations with Restrictions

Q. There are 9 points in a plane of which only 5 are collinear. Find the number of: (i) straight lines that can be formed joining two points (ii) triangles that can be formed joining any three points.📘 Permutations and Combinations📕 NCERT Book — p. 222-223, 6.6 · Collinear Points and Polygons

Q. A ball is dropped from a height of 90 feet and always rebounds one-third the distance from which it falls. Find the total vertical distance the ball travelled when it hits the ground for the 3rd time. Also find the total distance travelled by the ball before it comes to rest.📘 Sequences and Series📕 NCERT Book — p. 164-165, 5.6 · Bouncing Ball Rebound - Infinite GP

Q. Find the number of words with or without meaning which can be made using all the letters of the word MOTHER. If these words are written as in a dictionary, find the rank of the word MOTHER.📘 Permutations and Combinations📕 NCERT Book — p. 213-214, 6.5 · Dictionary Rank of a Word

Q. Find the principal value of sin^-1(-1/2).📘 Inverse Trigonometric Functions📕 NCERT Book — p. 26, 2.1 · Principal Value Branches

Q. Evaluate the indefinite integral of (sqrt(x) - 1/sqrt(x))^2 dx.📘 Integrals📕 NCERT Book — p. 234, 7.1 · Indefinite Integrals & Elementary Forms

Q. Evaluate the integral of sin^3(x) dx using trigonometric reduction.📘 Integrals📕 NCERT Book — p. 242, Ex. · Integration by Substitution

Q. Find k such that f(x) = {k cos x / (pi - 2x) for x != pi/2; 3 for x = pi/2} is continuous at x = pi/2.📘 Continuity and Differentiability📕 NCERT Book — p. 118, 5.1 · Continuity of Functions at a Point/Interval

Q. Differentiate y = tan^-1((3x - x^3)/(1 - 3x^2)) with respect to x for -1/sqrt(3) < x < 1/sqrt(3).📘 Continuity and Differentiability📕 NCERT Book — p. 125, 5.3 · Differentiation Rules (Chain, Product, Quotient)

Q. A 28m wire is cut into two pieces to form a square and a circle. Find piece lengths so that combined area is minimum.📘 Application of Derivatives📕 NCERT Book — p. 176, 6.3 · Maxima and Minima & Optimization Problems

Q. For A=[[1,1,-1],[2,0,3],[3,-1,2]], B=[[1,3],[0,2],[-1,4]], C=[[1,2,3,-4],[2,0,-2,1]], verify (AB)C = A(BC).📘 Matrices📕 NCERT Book — p. 54, Ex. · Multiplication of Matrices & Properties

Q. Differentiate (x + 1/x)^x + x^(1 + 1/x) with respect to x.📘 Continuity and Differentiability📕 NCERT Book — p. 134, 5.5 · Implicit & Logarithmic Differentiation