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CBSE Class 10 Maths starter questions: weeks 19–31

33 short questions to open a lesson for CBSE Class 10 Mathematics, weeks 19–31 of the teaching year, three or four a week. Each question is shown as an image with its text underneath; the answers and mark schemes are free on the free weekly starters page, to show or project in class.

Week 19

Question 1: Section formula
The y-axis divides the segment joining (-4, 5) and (6, -3) in the ratio (a) 2: 3 (b) 3: 2 (c) 4: 5 (d) 5: 3
Question 2: Applications to geometric shapes
The points (0, 0), (4, 0) and (2, 2√3) are the vertices of (a) a right-angled triangle (b) an equilateral triangle (c) an isosceles right triangle (d) a scalene triangle
Question 3: Similar figures
Which of the following pairs of shapes are always similar? (a) Two rectangles (b) Two rhombuses (c) Two isosceles triangles (d) Two squares

Week 20

Question 1: Ratios of specific angles
Which of the following trigonometric ratios is not defined? (a) sin 90° (b) cos 0° (c) tan 90° (d) cot 45°
Question 2: Applications to geometric shapes
A(1, 2), B(4, 3) and C(6, 6) are three vertices of parallelogram ABCD. The fourth vertex D is (a) (3, 5) (b) (9, 7) (c) (-1, -1) (d) (5, 3)
Question 3: Basic Proportionality Theorem and its converse
In △ ABC, D lies on AB and E on AC such that AD/DB = AE/EC. Then (a) AD = AE (b) DE = BC (c) DE ⊥ BC (d) DE ∥ BC

Week 21

Question 1: Trigonometric identities
(sinθ+cosθ)²+(sinθ-cosθ)² equals (a) 0 (b) 1 (c) 2 (d) 4
Question 2: Ratios of specific angles
The value of 2tan² 45° + cos² 30° - sin² 60° is (a) 0 (b) 1 (c) 2 (d) 3/2
Question 3: Distance formula
The distance of the point (5, -12) from the origin is (a) 13 (b) 17 (c) 7 (d) √119

Week 22

Question 1: Two-triangle problems
Points A and B on level ground are on the same side of a tower of height h and in line with its foot. The angles of elevation of the top of the tower from A and B are 45° and 60° respectively. Then AB equals (a) (h(√3-1))/(√3) (b) h(√3-1) (c) h/(√3) (d) (h(√3+1))/(√3)
Question 2: Angle of elevation
The shadow of a vertical tower on level ground is equal to its height. The angle of elevation of the Sun is (a) 30° (b) 45° (c) 60° (d) 90°
Question 3: Trigonometric ratios
In △ PQR, right-angled at Q, PQ = 20 cm and QR = 21 cm. The value of sin R is (a) 20/29 (b) 21/29 (c) 20/21 (d) 21/20

Week 23

Question 1: Length of tangent
The length of the tangent to a circle of radius 9 cm from a point 41 cm from its centre is (a) 40 cm (b) 32 cm (c) 50 cm (d) √1762 cm
Question 2: Tangent to a circle
How many tangents can a circle have? (a) one (b) infinitely many (c) two (d) four
Question 3: Angle of elevation
A 14 m ladder leans against a wall and makes an angle of 60° with the ground. The distance of its foot from the wall is (a) 7√3 m (b) 7 m (c) 14√3 m (d) 7/(√3) m

Week 24

Question 1: Tangent to a circle
The common point of a tangent and a circle is called the (a) centre (b) point of contact (c) end of a secant (d) chord point
Question 2: Angle of depression
From a window 15 m above the ground, the angle of depression of a car parked on the road is 60°. The distance of the car from the foot of the building is (a) 15√3 m (b) 5√3 m (c) 15 m (d) 30 m
Question 3: Ratios of specific angles
If 2sin 2θ = √3 and 2θ is acute, then θ is (a) 15° (b) 30° (c) 45° (d) 60°

Week 27

Question 1: Tangent perpendicular to radius
AB is a diameter of a circle. The tangents at A and B are (a) parallel (b) perpendicular (c) inclined at 45° (d) coincident
Question 2: Tangents from an external point
PA and PB are tangents from P to a circle with centre O. If ∠ AOB = 130°, then ∠ OPA is (a) 25° (b) 50° (c) 65° (d) 130°
Question 3: Angle of elevation
A straight zip-line cable, 80 m long, runs from the top of a platform down to a point on level ground and makes an angle of 30° with the ground. The height of the platform is (a) 40 m (b) 40√3 m (c) 80√3 m (d) 40/(√3) m

Week 28

Question 1: Area of a segment
The area of the minor segment of a circle of radius 6 cm, whose chord subtends 90° at the centre, is (a) (9π+18) cm² (b) (9π-18) cm² (c) (9π-36) cm² (d) (36π-18) cm²
Question 2: Length of an arc
The perimeter of a sector of radius r and central angle θ is (a) (θ)/360×2π r (b) 2r+(θ)/360×2π r (c) r+(θ)/360×2π r (d) 2r+(θ)/360×π r²
Question 3: Consistency and number of solutions
The pair of equations 5x - 4y + 8 = 0 and 7x + 6y - 9 = 0 is (a) consistent with infinitely many solutions (b) inconsistent (c) consistent with a unique solution (d) neither consistent nor inconsistent

Week 29

Question 1: Volume of combined solids
A cone and a hemisphere have the same base radius r, and the height of the cone is r. The ratio of the volume of the cone to that of the hemisphere is (a) 1:1 (b) 2:1 (c) 1:3 (d) 1:2
Question 2: Surface area of basic solids
The total surface area of a solid hemisphere of radius r is (a) 2π r² (b) 4π r² (c) 3π r² (d) π r²
Question 3: Area of a sector
The area of a sector is 1/6 of the area of the circle. Its central angle is (a) 30° (b) 45° (c) 60° (d) 90°

Week 30

Question 1: Mean of grouped data
The class mark of the class 25–35 is (a) 10 (b) 25 (c) 30 (d) 35
Question 2: Volume of combined solids
The largest right circular cone is carved out of a solid cube of edge 14 cm. The volume of the cone is (π=22/7) (a) 2156 cm³ (b) 1437.33 cm³ (c) 718.67 cm³ (d) 2744 cm³
Question 3: Area of a sector
The hour hand of a clock is 6 cm long. The area swept by it between 12 noon and 4 p.m. is (a) 6π cm² (b) 24π cm² (c) 4π cm² (d) 12π cm²

Week 31

Question 1: Empirical relationship
The empirical relationship between the three measures of central tendency is (a) 3 Median=Mode+2 Mean (b) 3 Mean=Median+2 Mode (c) 3 Mode=Mean+2 Median (d) 2 Median=Mode+3 Mean
Question 2: Mode of grouped data
The modal class of a grouped frequency distribution is the class with the (a) largest cumulative frequency (b) largest class mark (c) highest frequency (d) middle position
Question 3: Surface area of basic solids
The slant height of a cone with base radius 5 cm and height 12 cm is (a) 13 cm (b) 17 cm (c) √119 cm (d) 7 cm

More starter questions

Other weeks: Weeks 1–18 · Weeks 19–31 · Weeks 33–46. Answers and mark schemes, free for everyone, are on the free weekly starters page.

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