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CBSE Class 10 Maths Question of the Day: chapters 5–8

36 CBSE Class 10 Mathematics puzzles from the Question of the Day rotation, chapters 5–8. Each puzzle is three board-style questions on one chapter, shown as an image with the question text written out below it; the answers, hints and step-marked solutions are on the daily puzzle page.

Chapter 5: Arithmetic Progressions

Chapter 5: Arithmetic Progressions
Three board-style questions on Arithmetic Progressions (CBSE Class 10 Mathematics). No calculator.
1. The common difference of the AP 73, 2, 53, … is Options: A) 13; B) -1; C) -13; D) 23
2. If 2k + 1, 13, 5k - 3 are three consecutive terms of an AP, then k equals Options: A) 3; B) 5; C) 4; D) 27/7
3. The 15th term of the AP -4, -1, 2, … is Options: A) -46; B) 41; C) 35; D) 38
Chapter 5: Arithmetic Progressions · From the sum to the terms
Three board-style questions on Arithmetic Progressions (CBSE Class 10 Mathematics). No calculator. The sum of the first n terms of an AP is S_n = 3n² + 4n.
1. The first term is Options: A) 10; B) 4; C) 7; D) 3
2. The common difference is Options: A) 13; B) 6; C) 4; D) 3
3. The nth term is Options: A) 3n + 4; B) 6n + 7; C) 6n + 1; D) 6n - 1
Chapter 5: Arithmetic Progressions · Reasoning with an AP
Three board-style questions on Arithmetic Progressions (CBSE Class 10 Mathematics). No calculator.
1. In the following question, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option. Assertion (A): The sum of the first n odd natural numbers is n^2. Reason (R): The sum of the first n terms of an AP is S_n = n/2[2a + (n - 1)d]. Options: A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).; B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).; C) Assertion (A) is true but Reason (R) is false.; D) Assertion (A) is false but Reason (R) is true.
2. Three numbers in AP have sum 27 and product 504. The largest of them is Options: A) 13; B) 16; C) 12; D) 14
3. The middle term of the AP 6, 13, 20, …, 216 is Options: A) 111; B) 108; C) 104; D) 118
Chapter 5: Arithmetic Progressions · First term, last term and sum
Three board-style questions on Arithmetic Progressions (CBSE Class 10 Mathematics). No calculator. An AP has first term 5, last term 100 and the sum of all its terms is 1050.
1. The number of terms is Options: A) 19; B) 21; C) 20; D) 10
2. The common difference is Options: A) 19/4; B) 4; C) 6; D) 5
3. The 8th term from the end is Options: A) 40; B) 60; C) 70; D) 65
Chapter 5: Arithmetic Progressions · nth term
Three board-style questions on Arithmetic Progressions (CBSE Class 10 Mathematics). No calculator. Consider the AP 7, 11, 15, 19, …
1. Its common difference is Options: A) 11; B) 4; C) 7; D) -4
2. Its 20th term is Options: A) 83; B) 79; C) 87; D) 80
3. Is 101 a term of this AP? Options: A) Yes, the 24th term; B) Yes, the 25th term; C) No; D) Yes, the 23rd term
Chapter 5: Arithmetic Progressions · Sum of n terms
Three board-style questions on Arithmetic Progressions (CBSE Class 10 Mathematics). No calculator.
1. The sum of the first 15 terms of the AP 3, 8, 13, … is Options: A) 600; B) 1140; C) 570; D) 540
2. The common difference of the AP whose nth term is 5n - 2 is Options: A) -2; B) 3; C) 5; D) 2
3. The sum of the first n terms of that AP (with nth term 5n - 2) is Options: A) (n(5n + 3))/2; B) n(5n + 1); C) (n(5n + 1))/2; D) (n(5n - 1))/2
Chapter 5: Arithmetic Progressions · Two terms given
Three board-style questions on Arithmetic Progressions (CBSE Class 10 Mathematics). No calculator. The 4th term of an AP is 14 and its 9th term is 34.
1. The common difference is Options: A) 4; B) 20; C) 6; D) 5
2. The first term is Options: A) 2; B) 10; C) -2; D) 6
3. The sum of the first 10 terms is Options: A) 180; B) 400; C) 380; D) 200
Chapter 5: Arithmetic Progressions · Counting terms
Three board-style questions on Arithmetic Progressions (CBSE Class 10 Mathematics). No calculator.
1. How many two-digit numbers are divisible by 6? Options: A) 17; B) 16; C) 14; D) 15
2. The sum of all two-digit numbers divisible by 6 is Options: A) 900; B) 810; C) 864; D) 756
3. How many terms of the AP 24, 21, 18, … must be taken so that their sum is 78? Options: A) 4 or 13; B) 6; C) 4 only; D) 13 only
Chapter 5: Arithmetic Progressions · Weekly savings
Three board-style questions on Arithmetic Progressions (CBSE Class 10 Mathematics). No calculator. Riya saves ₹50 in the first week of the year, ₹60 in the second week, ₹70 in the third, and so on.
1. How much does she save in the 15th week? Options: A) ₹180; B) ₹190; C) ₹150; D) ₹200
2. Her total savings after 15 weeks are Options: A) ₹1750; B) ₹2100; C) ₹1900; D) ₹1800
3. In which week does she first save ₹300 in that week? Options: A) 25; B) 30; C) 26; D) 27

Chapter 6: Triangles

Chapter 6: Triangles
Three board-style questions on Triangles (CBSE Class 10 Mathematics). No calculator.
1. All ________ triangles are similar. Options: A) isosceles; B) equilateral; C) right-angled; D) scalene
2. Which of the following pairs of shapes are always similar? Options: A) Two rectangles; B) Two rhombuses; C) Two isosceles triangles; D) Two squares
3. Which of the following statements is true? Options: A) Any two similar triangles are congruent.; B) Any two right triangles are similar.; C) Any two congruent triangles are similar.; D) Any two isosceles triangles are similar.
Chapter 6: Triangles · Proportion in triangles
Three board-style questions on Triangles (CBSE Class 10 Mathematics). No calculator.
1. In the following question, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option. Assertion (A): In △ ABC, DE ∥ BC with D on AB, E on AC and AD/DB = 23. Then DE/BC = 25. Reason (R): If a line parallel to one side of a triangle meets the other two sides, it divides them in the same ratio. Options: A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).; B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).; C) Assertion (A) is true but Reason (R) is false.; D) Assertion (A) is false but Reason (R) is true.
2. In △ ABC, DE ∥ BC with D on AB and E on AC. If AD = 2.4 cm, AE = 3.2 cm and EC = 4.8 cm, then DB equals Options: A) 3.6 cm; B) 6.4 cm; C) 1.6 cm; D) 4.0 cm
3. △ ABC △ DEF. Their perimeters are 30 cm and 45 cm, and AB = 8 cm. Then DE equals Options: A) 15 cm; B) 12 cm; C) 10 cm; D) 16/3 cm
Chapter 6: Triangles · Altitude to the hypotenuse
Three board-style questions on Triangles (CBSE Class 10 Mathematics). No calculator. In △ ABC, ∠ ABC = 90^∘ and BD ⊥ AC with D on AC. AD = 4 cm and DC = 9 cm.
1. Which similarity statement is correct? Options: A) △ ADB △ CDB; B) △ ADB △ BDC; C) △ ABD △ BDC; D) △ ADB △ DBC
2. BD equals Options: A) 5 cm; B) 6 cm; C) 36 cm; D) 6.5 cm
3. AB equals Options: A) 3√13 cm; B) 13 cm; C) 52 cm; D) 2√13 cm
Chapter 6: Triangles · Basic Proportionality Theorem
Three board-style questions on Triangles (CBSE Class 10 Mathematics). No calculator. In △ ABC, D lies on AB and E on AC with DE ∥ BC. AD = 3 cm, DB = 5 cm and AE = 4.5 cm.
1. EC equals Options: A) 2.7 cm; B) 6.5 cm; C) 8 cm; D) 7.5 cm
2. AD/AB equals Options: A) 5/8; B) 3/8; C) 8/3; D) 3/5
3. If BC = 16 cm, then DE equals Options: A) 6 cm; B) 9.6 cm; C) 5 cm; D) 10 cm
Chapter 6: Triangles · Similarity criteria
Three board-style questions on Triangles (CBSE Class 10 Mathematics). No calculator.
1. One triangle has sides 5, 7 and 9 cm; another has sides 7.5, 10.5 and 13.5 cm. The triangles are Options: A) similar, with scale factor 2; B) congruent; C) not similar; D) similar, with scale factor 32
2. Two angles of one triangle are 50^∘ and 60^∘; two angles of another are 60^∘ and 70^∘. The triangles are Options: A) similar by AA; B) not similar; C) similar by SSS; D) congruent
3. △ ABC △ PQR, AB = 6 cm, PQ = 9 cm and BC = 8 cm. Then QR equals Options: A) 10 cm; B) 11 cm; C) 16/3 cm; D) 12 cm
Chapter 6: Triangles · Converse of BPT
Three board-style questions on Triangles (CBSE Class 10 Mathematics). No calculator. In △ PQR, S lies on PQ and T on PR, with PS = 4 cm, SQ = 6 cm, PT = 6 cm and TR = 9 cm.
1. Is ST ∥ QR? Options: A) Yes, because PS/SQ = PT/TR; B) No, because PS ≠ PT; C) Yes, because PS + SQ = PT + TR; D) No, because SQ ≠ TR
2. ST/QR equals Options: A) 2/3; B) 2/5; C) 3/5; D) 4/9
3. If QR = 20 cm, then ST equals Options: A) 13 cm; B) 40/3 cm; C) 8 cm; D) 12 cm
Chapter 6: Triangles · Shadows
Three board-style questions on Triangles (CBSE Class 10 Mathematics). No calculator. At the same time of day, a girl 1.5 m tall casts a shadow 2 m long and a vertical pole casts a shadow 12 m long.
1. The triangles formed by each object, its shadow and the sun's rays are similar by Options: A) SSS; B) SAS; C) AA; D) none of these
2. The height of the pole is Options: A) 9 m; B) 8 m; C) 16 m; D) 10 m
3. Later in the day the girl's shadow is 2.5 m long. The pole's shadow is then Options: A) 18 m; B) 12.5 m; C) 15 m; D) 13.5 m
Chapter 6: Triangles · Diagonals of a trapezium
Three board-style questions on Triangles (CBSE Class 10 Mathematics). No calculator. ABCD is a trapezium with AB ∥ DC, AB = 12 cm and DC = 8 cm. Its diagonals meet at O.
1. AO/OC equals Options: A) 3/2; B) 3/5; C) 2/5; D) 2/3
2. If AC = 15 cm, then AO equals Options: A) 9 cm; B) 7.5 cm; C) 6 cm; D) 10 cm
3. If BD = 10 cm, then OD equals Options: A) 4 cm; B) 6 cm; C) 5 cm; D) 20/3 cm
Chapter 6: Triangles · BPT with an unknown
Three board-style questions on Triangles (CBSE Class 10 Mathematics). No calculator. In △ ABC, DE ∥ BC with D on AB and E on AC. AD = x, DB = x - 2, AE = x + 2 and EC = x - 1 (all in cm).
1. x equals Options: A) 5; B) 2; C) 4; D) 3
2. AB equals Options: A) 8 cm; B) 4 cm; C) 9 cm; D) 6 cm
3. DE: BC equals Options: A) 2: 3; B) 1: 2; C) 2: 1; D) 3: 4

Chapter 7: Coordinate Geometry

Chapter 7: Coordinate Geometry
Three board-style questions on Coordinate Geometry (CBSE Class 10 Mathematics). No calculator.
1. The distance between the points (-3, 4) and (5, -2) is Options: A) 8; B) 14; C) √28; D) 10
2. The distance of the point (5, -12) from the origin is Options: A) 13; B) 17; C) 7; D) √119
3. If the distance between (4, p) and (1, 0) is 5, then p equals Options: A) 4 only; B) ± 3; C) -4 only; D) ± 4
Chapter 7: Coordinate Geometry · Identifying a figure
Three board-style questions on Coordinate Geometry (CBSE Class 10 Mathematics). No calculator. A(1, 1), B(5, 4) and C(2, 8).
1. AB equals Options: A) 25; B) 5; C) 7; D) √7
2. Triangle ABC is Options: A) equilateral; B) right-angled and isosceles; C) scalene; D) right-angled and scalene
3. D is chosen so that ABCD is a square. D is Options: A) (6, 11); B) (4, 5); C) (-3, 4); D) (-2, 5)
Chapter 7: Coordinate Geometry · Distance, mid-point and section
Three board-style questions on Coordinate Geometry (CBSE Class 10 Mathematics). No calculator. A is the point (2, 3) and B is (8, 11).
1. The length AB is Options: A) 100; B) 14; C) 10; D) 2 √7
2. The mid-point of AB is Options: A) (10, 14); B) (6, 8); C) (5, 7); D) (3, 4)
3. The point that divides AB internally in the ratio 1: 3 is Options: A) (72, 5); B) (5, 7); C) (13/2, 9); D) (4, 7)
Chapter 7: Coordinate Geometry · Distance formula
Three board-style questions on Coordinate Geometry (CBSE Class 10 Mathematics). No calculator.
1. How far is the point (-7, 24) from the origin? Options: A) 25; B) √527; C) 17; D) 31
2. The distance between (3, -4) and (-1, -1) is Options: A) 5; B) 7; C) √41; D) √13
3. The point on the x-axis equidistant from (2, 3) and (6, -1) is Options: A) (0, 3); B) (5, 0); C) (4, 0); D) (3, 0)
Chapter 7: Coordinate Geometry · Division by the axes
Three board-style questions on Coordinate Geometry (CBSE Class 10 Mathematics). No calculator. A is (-4, 5) and B is (6, -3).
1. The y-axis divides AB in the ratio Options: A) 5: 3; B) 1: 1; C) 3: 2; D) 2: 3
2. The point where AB meets the y-axis is Options: A) (0, 1); B) (0, 9/4); C) (0, 95); D) (0, 11/5)
3. The x-axis divides AB in the ratio Options: A) 5: 3; B) 3: 2; C) 3: 5; D) 2: 3
Chapter 7: Coordinate Geometry · Parallelogram vertices
Three board-style questions on Coordinate Geometry (CBSE Class 10 Mathematics). No calculator. A(1, 2), B(4, 3), C(6, 6) and D are the vertices, in order, of a parallelogram ABCD.
1. The mid-point of the diagonal AC is Options: A) (5, 4); B) (52, 52); C) (7, 8); D) (72, 4)
2. The vertex D is Options: A) (3, 5); B) (4, 5); C) (9, 7); D) (-1, -1)
3. The length of side AD is Options: A) 5; B) √5; C) √10; D) √13
Chapter 7: Coordinate Geometry · Points on a line
Three board-style questions on Coordinate Geometry (CBSE Class 10 Mathematics). No calculator. A(1, -1), B(3, 3) and C(5, 7).
1. AB equals Options: A) 2 √5; B) 4 √5; C) 2 √3; D) √10
2. Which statement is true? Options: A) A, B, C form a right-angled triangle; B) AB + BC > AC; C) B is the mid-point of AC; D) AC = 2√5
3. The point dividing AC internally in the ratio 3: 1 is Options: A) (2, 1); B) (3, 3); C) (4, 11/2); D) (4, 5)
Chapter 7: Coordinate Geometry · Unknown coordinates
Three board-style questions on Coordinate Geometry (CBSE Class 10 Mathematics). No calculator.
1. If the distance between (x, 3) and (5, 7) is 5, then x equals Options: A) 8 only; B) 2 or 8; C) -2 or 8; D) 2 only
2. If P(k, 4) is equidistant from A(2, 1) and B(8, 3), then k equals Options: A) 11/3; B) 4; C) 13/3; D) 5
3. The point (-1, 6) divides the segment joining (-3, 10) and (6, -8) in the ratio Options: A) 7: 2; B) 1: 2; C) 2: 9; D) 2: 7
Chapter 7: Coordinate Geometry · Points of trisection
Three board-style questions on Coordinate Geometry (CBSE Class 10 Mathematics). No calculator. A is (-2, 1) and B is (7, 4). Points P and Q trisect AB, with P nearer to A.
1. P is Options: A) (52, 52); B) (3, 2); C) (1, 2); D) (4, 3)
2. Q is Options: A) (4, 3); B) (1, 2); C) (5, 3); D) (4, 2)
3. AB equals Options: A) 12; B) 3 √10; C) √10; D) 9 √10

Chapter 8: Introduction to Trigonometry

Chapter 8: Introduction to Trigonometry
Three board-style questions on Introduction to Trigonometry (CBSE Class 10 Mathematics). No calculator.
1. In △ PQR, right-angled at Q, PQ = 20 cm and QR = 21 cm. The value of sin R is Options: A) 20/29; B) 21/29; C) 20/21; D) 21/20
2. If cos A = 5/13, where A is acute, then tan A equals Options: A) 5/12; B) 12/13; C) 12/5; D) 13/12
3. The value of 2tan² 45^∘ + cos² 30^∘ - sin² 60^∘ is Options: A) 0; B) 1; C) 2; D) 3/2
Chapter 8: Introduction to Trigonometry · Ratios in a right triangle
Three board-style questions on Introduction to Trigonometry (CBSE Class 10 Mathematics). No calculator. In △ ABC, ∠ B = 90^∘, AB = 5 cm, BC = 12 cm and AC = 13 cm.
1. sin A equals Options: A) 12/13; B) 12/5; C) 13/12; D) 5/13
2. tan C equals Options: A) 5/12; B) 12/5; C) 5/13; D) 13/5
3. sin² A + cos² A equals Options: A) 119/169; B) 1; C) 144/169; D) 17/13
Chapter 8: Introduction to Trigonometry · Standard angles
Three board-style questions on Introduction to Trigonometry (CBSE Class 10 Mathematics). No calculator.
1. sin 30^∘ + cos 60^∘ equals Options: A) √3; B) 1/2 + (√3)/2; C) 1; D) 1/2
2. 2 sin 30^∘ cos 30^∘ equals Options: A) 1/2; B) (√3)/4; C) (√3)/2; D) √3
3. (1 - tan² 30^∘)/(1 + tan² 30^∘) equals Options: A) 1; B) 1/2; C) 2/3; D) (√3)/2
Chapter 8: Introduction to Trigonometry · From one ratio to the others
Three board-style questions on Introduction to Trigonometry (CBSE Class 10 Mathematics). No calculator. A is an acute angle with sin A = 35.
1. cos A equals Options: A) 2/5; B) 5/4; C) 3/4; D) 4/5
2. tan A equals Options: A) 3/4; B) 5/3; C) 4/3; D) 3/5
3. sec A + tan A equals Options: A) 7/4; B) 8/5; C) 1/2; D) 2
Chapter 8: Introduction to Trigonometry · Simple identities
Three board-style questions on Introduction to Trigonometry (CBSE Class 10 Mathematics). No calculator.
1. (1 - sin²θ)sec²θ equals Options: A) sin² θ; B) tan² θ; C) 1; D) 0
2. sinθ cotθ equals Options: A) tanθ; B) cosθ; C) secθ; D) 1
3. If secθ + tanθ = 3, then secθ - tanθ equals Options: A) -3; B) 1/3; C) 2; D) 3
Chapter 8: Introduction to Trigonometry · Finding angles
Three board-style questions on Introduction to Trigonometry (CBSE Class 10 Mathematics). No calculator.
1. If tan 2A = √3 and 2A is acute, then A equals Options: A) 30^∘; B) 60^∘; C) 15^∘; D) 45^∘
2. If sin(A - B) = 12 and cos(A + B) = 12, where 0^∘ < A + B ≤ 90^∘ and A > B, then A equals Options: A) 45^∘; B) 15^∘; C) 30^∘; D) 60^∘
3. With the same conditions, B equals Options: A) 60^∘; B) 30^∘; C) 15^∘; D) 45^∘
Chapter 8: Introduction to Trigonometry · Using a given tangent
Three board-style questions on Introduction to Trigonometry (CBSE Class 10 Mathematics). No calculator. θ is acute and 5tanθ = 12.
1. sinθ equals Options: A) 5/13; B) 12/13; C) 13/12; D) 12/5
2. (5sinθ - 3cosθ)/(4sinθ + 2cosθ) equals Options: A) 45/58; B) 75/58; C) 45/62; D) 3/2
3. sec²θ - tan²θ equals Options: A) 1; B) 25/169; C) 1/5; D) 13/5
Chapter 8: Introduction to Trigonometry · Reasoning with ratios
Three board-style questions on Introduction to Trigonometry (CBSE Class 10 Mathematics). No calculator.
1. In the following question, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option. Assertion (A): There is no acute angle θ with sinθ = 43. Reason (R): For an acute angle in a right triangle, the hypotenuse is the longest side, so sinθ < 1. Options: A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).; B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).; C) Assertion (A) is true but Reason (R) is false.; D) Assertion (A) is false but Reason (R) is true.
2. If θ is acute and sinθ = cosθ, then sin⁴θ + cos⁴θ equals Options: A) 1/4; B) 2; C) 1; D) 1/2
3. If x = 3secθ and y = 2tanθ, then (x²)/9 - (y²)/4 equals Options: A) 13/36; B) 0; C) 1; D) 5
Chapter 8: Introduction to Trigonometry · Simplifying expressions
Three board-style questions on Introduction to Trigonometry (CBSE Class 10 Mathematics). No calculator.
1. (2sinθ + cosθ)² + (sinθ - 2cosθ)² equals Options: A) 8 sin θ cos θ; B) 5; C) 1; D) 3
2. (1 + tan²θ)(1 - sinθ)(1 + sinθ) equals Options: A) tan² θ; B) sec² θ; C) cos² θ; D) 1
3. If θ is acute and cosθ = 12, then tanθ + cotθ equals Options: A) 2; B) 2 √3; C) (4 √3)/3; D) 1 + √3

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