Daily Practice

Q1. Which one among 64², 108², 292², and 36² has last digit 4?📘 Chapter 1 — A Square and A CubeTopic: Properties of Square NumbersQID: M08-01-564Page: 10

Q2. Prove that the sum of all interior angles in any quadrilateral is 360° by triangular division.📘 Chapter 4 — QuadrilateralsTopic: Angle Sum Property of QuadrilateralsQID: M08-04-656Page: 95

Q3. Calculate outfit combinations for Estu (4 dresses, 3 caps) and Roxie (7 dresses, 2 hats, 3 shoes).📘 Chapter 2 — Power PlayTopic: Applied Combinatorics & Large NumbersQID: M08-02-596Page: 26

Q4. Verify algebraic statements and find remainders mod 7 for sum, difference, product of given remainders.📘 Chapter 6 — We Distribute, Yet Things MultiplyTopic: Algebraic Modeling & Word ProblemsQID: M08-06-723Page: 155

Q5. Explain base-60 place value notation in ancient Babylon and how 640 and 7530 were represented.📘 Chapter 3 — A Story of NumbersTopic: Ancient Positional SystemsQID: M08-03-639Page: 71

Q6. Convert the base-10 number 25 into base-8 (31), base-5 (100), and base-2 (11001).📘 Chapter 3 — A Story of NumbersTopic: Base-n Number SystemsQID: M08-03-644Page: 80

Q7. Solve cryptarithms PQ\*8 = RS, GH\*H = 9K, and BYE\*6 = RAY using place value constraints.📘 Chapter 5 — Number PlayTopic: Cryptarithms & Mathematical GamesQID: M08-05-691Page: 132

Q8. Use (a+1)² = a² + 2a + 1 to find 51² from 50².📘 Chapter 1 — A Square and A CubeTopic: Consecutive Square CalculationQID: KV-ORIG-08-01Page: —

Q9. A parallelogram has one angle 65°. Find its other three angles.📘 Chapter 4 — QuadrilateralsTopic: Angles of a ParallelogramQID: KV-ORIG-08-02Page: —

Q10. Determine whether 2⁶ is divisible by 2⁴ and justify using laws of exponents.📘 Chapter 2 — Power PlayTopic: Divisibility Using PowersQID: KV-ORIG-08-03Page: —

Q1. Let A and B be two points on a circle with centre O. Are there points X, Y on the circle, on the same side of AB, such that ∠AXB is different from ∠AYB?📘 Chapter 5 — I'm Up and Down, and Round and RoundTopic: Angles Subtended by Chords & ArcsQID: M09-05-1046Page: 111

Q2. Referring to Fig. 1.3: If D₁R₁ represents the door to Reiaan's room, how far is the door from the left wall (the y-axis) of the room? How far is the door from the x-axis?📘 Chapter 1 — Orienting Yourself: The Use of CoordinatesTopic: Cartesian Coordinate SystemQID: M09-01-759Page: 5

Q3. What is the least possible radius of a circle through two points A and B?📘 Chapter 5 — I'm Up and Down, and Round and RoundTopic: Circles & Circumcircles of TrianglesQID: M09-05-1033Page: 98

Q4. A driver attempts to start a car: Does the car starting or not starting constitute equally likely outcomes? Explain why not.📘 Chapter 7 — The Mathematics of Maybe: Introduction to ProbabilityTopic: Compound & Equally Likely EventsQID: M09-07-1182Page: 170

Q5. In a circle with centre O, the central angle AOB is 60°. If the radius of the circle is 12 cm, what is the length of the chord AB?📘 Chapter 5 — I'm Up and Down, and Round and RoundTopic: Angles Subtended by Chords & ArcsQID: M09-05-1045Page: 110

Q6. One diagonal of a rhombus is twice as long as the other diagonal. If the rhombus has area 128 cm², find the length of the shorter diagonal.📘 Chapter 6 — Measuring Space: Perimeter and AreaTopic: Area of Quadrilaterals & PolygonsQID: M09-06-1101Page: 142

Q7. Using an isosceles triangle decomposition from a diameter AB with center O and point C on circumference, justify that the angle in a semicircle is 90°.📘 Chapter 5 — I'm Up and Down, and Round and RoundTopic: Angles Subtended by Chords & ArcsQID: M09-05-1073Page: 116

Q8. The parallel sides of a trapezium are 40 cm and 20 cm. If its non-parallel sides are both equal, each being 26 cm, find the area of the trapezium.📘 Chapter 6 — Measuring Space: Perimeter and AreaTopic: Area of Quadrilaterals & PolygonsQID: M09-06-1098Page: 142

Q9. If the mid-points of the sides of a quadrilateral (4-gon) are joined in order, prove that the area of the parallelogram formed is half the area of the quadrilateral.📘 Chapter 6 — Measuring Space: Perimeter and AreaTopic: Area of Quadrilaterals & PolygonsQID: M09-06-1104Page: 142

Q10. A chord of a circle of radius 15 cm subtends 60° at the centre. Find the areas of the corresponding minor and major segments. (Use π ≈ 3.14, √3 ≈ 1.73)📘 Chapter 6 — Measuring Space: Perimeter and AreaTopic: Area Related to Circles & SegmentsQID: M09-06-1113Page: 148

Q1. True/False: The value of tan A is always less than 1. Justify your answer.📘 Chapter 8 — Introduction to TrigonometryTopic: Algebraic & Monotonic Properties of Trig RatiosQID: M10-08-1865Page: 121

Q2. In triangle ABC, DE || BC. Find EC if AD=1.5cm, DB=3cm, AE=1cm.📘 Chapter 6 — TrianglesTopic: Basic Proportionality Theorem (Thales)QID: M10-06-1794Page: 84

Q3. For AP: 3, 1, -1, -3..., write first term a and common difference d.📘 Chapter 5 — Arithmetic ProgressionsTopic: Common Difference & Identification of APQID: M10-05-1703Page: 55

Q4. State if triangles ABC and PQR are similar with sides 2, 3, 2.5 and 4, 6, 5. Write similarity criterion.📘 Chapter 6 — TrianglesTopic: Criteria for Similarity (AAA, SSS, SAS)QID: M10-06-1808Page: 95

Q5. In figure, if triangle ABE congruent to ACD, show that triangle ADE \~ ABC.📘 Chapter 6 — TrianglesTopic: Applications & Proofs of SimilarityQID: M10-06-1817Page: 96

Q6. In triangle PQR, E and F on PQ and PR. PE=3.9cm, EQ=3cm, PF=3.6cm, FR=2.4cm. State whether EF || QR.📘 Chapter 6 — TrianglesTopic: Basic Proportionality Theorem (Thales)QID: M10-06-1796Page: 84

Q7. If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B.📘 Chapter 8 — Introduction to TrigonometryTopic: Algebraic & Monotonic Properties of Trig RatiosQID: M10-08-1858Page: 121

Q8. Diagonals AC and BD of trapezium ABCD with AB || DC intersect at O. Using similarity criterion, show OA/OC = OB/OD.📘 Chapter 6 — TrianglesTopic: Applications & Proofs of SimilarityQID: M10-06-1814Page: 95

Q9. Sides AB, BC and median AD of triangle ABC proportional to PQ, QR and median PM of PQR. Show ABC \~ PQR.📘 Chapter 6 — TrianglesTopic: Applications & Proofs of SimilarityQID: M10-06-1823Page: 97

Q10. How many terms of the AP: 9, 17, 25... must be taken to give a sum of 636?📘 Chapter 5 — Arithmetic ProgressionsTopic: Sum of First n Terms of APQID: M10-05-1769Page: 69

Q1. In a class there are 20 boys and 15 girls. The teacher wants to select either a boy or a girl to represent the class in a competition. In how many ways can this be done?📘 Chapter 6 — Permutations and CombinationsTopic: Fundamental Principle of AdditionQID: M11-06-2567Page: 188

Q2. The dramatics club of a college has selected six boys and five girls for a play. From this group the director can cast his leading couple (a boy and a girl) in how many ways?📘 Chapter 6 — Permutations and CombinationsTopic: Fundamental Principle of MultiplicationQID: M11-06-2568Page: 189

Q3. If the ordered pairs (2x, y-3) and (2, 1) are equal, then find x and y.📘 Chapter 4 — RelationsTopic: Ordered Pairs EqualityQID: M11-04-2523Page: 109

Q4. Find the number of subsets of the set B = {a, b, c, d}.📘 Chapter 3 — SetTopic: Power Set & SubsetsQID: M11-03-2507Page: 80

Q5. An insect population is growing in such a way that each generation is 2.5 times as large as the previous one. If there are 10,000 insects in the first generation, how many are there in the 5th generation?📘 Chapter 5 — Sequences and SeriesTopic: Biological Growth - GP ApplicationQID: M11-05-2553Page: 154

Q6. Let A = {2, 3} and B = {4, 5}. Find: 1. A x B 2. B x A 3. n(A x B) 4. number of subsets of A x B.📘 Chapter 4 — RelationsTopic: Cartesian Product & SubsetsQID: M11-04-2526Page: 111-112

Q7. If p times the pth term of an A.P. is q times the qth term, then show that its (p + q)th term is zero.📘 Chapter 5 — Sequences and SeriesTopic: AP Algebraic ProofsQID: M11-05-2539Page: 134-135

Q8. If (a^n + b^n) / (a^(n-1) + b^(n-1)) is the A.M. between 'a' and 'b', then find the value of 'n'.📘 Chapter 5 — Sequences and SeriesTopic: Arithmetic Mean PropertyQID: M11-05-2546Page: 144-145

Q9. A courier service company sends 30% of its orders by air, 50% by bus and 20% by train. Past records show courier is delivered late 2%, 7% and 5% of the time by air, bus and train respectively. Find: (i) the probability order will be delivered late (ii) the probability parcel delivered late was sent by train.📘 Chapter 9 — ProbabilityTopic: Bayes' Theorem - Courier Transit RoutingQID: M11-09-2622Page: 324

Q10. An insurance company insures scooter drivers, car drivers and bus drivers in the ratio 4:5:3. The probability of a scooter driver, car driver and bus driver meeting with an accident is 0.7%, 0.4% and 1.2% respectively. If an insured person meets with an accident find the probability that the person is a scooter driver.📘 Chapter 9 — ProbabilityTopic: Bayes' Theorem - Insurance Risk AssessmentQID: M11-09-2623Page: 324

Q1. Find the principal value of sin⁻¹(1/√2).📘 Chapter 2 — Inverse Trigonometric FunctionsTopic: Principal Value BranchesQID: M12-02-2700Page: 26

Q2. Find the area of the triangle whose vertices are (3,8), (−4,2), (5,1) using determinants.📘 Chapter 4 — DeterminantsTopic: Applications to Triangles & CollinearityQID: M12-04-2722Page: 82

Q3. For f(x)=cos x and g(x)=3x², find g∘f and f∘g and show that g∘f ≠ f∘g.📘 Chapter 1 — Relations and FunctionsTopic: Composition and Invertibility of FunctionsQID: M12-01-2839Page: 12

Q4. Show that the points A(a, b+c), B(b, c+a), C(c, a+b) are collinear.📘 Chapter 4 — DeterminantsTopic: Applications to Triangles & CollinearityQID: M12-04-2723Page: 83

Q5. For A=ℝ−{3} and B=ℝ−{1}, check if f:A→B defined by f(x)=(x−2)/(x−3) is one-one and onto.📘 Chapter 1 — Relations and FunctionsTopic: Composition and Invertibility of FunctionsQID: M12-01-2697Page: 11

Q6. Find values of a and b such that f(x) is continuous, where f(x)=5 for x≤2, f(x)=ax+b for 2<x<10, and f(x)=21 for x≥10.📘 Chapter 5 — Continuity and DifferentiabilityTopic: Continuity of Functions at a Point/IntervalQID: M12-05-2734Page: 118

Q7. Differentiate y=√(x−3)(x²+4)3x²+4x+5 with respect to x.📘 Chapter 5 — Continuity and DifferentiabilityTopic: Implicit & Logarithmic DifferentiationQID: M12-05-2737Page: 131

Q8. Evaluate ∫₀^π (x sin x)/(1+cos²x) dx.📘 Chapter 7 — IntegralsTopic: Definite Integrals & PropertiesQID: M12-07-2766Page: 277

Q9. For f(x) = 5x − 2, find f(3) and f(−1).📘 Chapter 1 — Relations and FunctionsTopic: Evaluation of a FunctionQID: KV-ORIG-12-01Page: —

Q10. Evaluate the determinant |1 2; 3 4|.📘 Chapter 4 — DeterminantsTopic: Evaluation of a 2×2 DeterminantQID: KV-ORIG-12-02Page: —