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CBSE Class 10 Maths starter questions: weeks 33–46

30 short questions to open a lesson for CBSE Class 10 Mathematics, weeks 33–46 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 33

Question 1: Complementary events
If P(E) = 0.05, then P(not E) is (a) 0.5 (b) 0.05 (c) 0.95 (d) 1.05
Question 2: Mode of grouped data
In the formula Mode=l+((f_1-f_0)/(2f_1-f_0-f_2))h, f_0 is the frequency of the (a) modal class (b) class succeeding the modal class (c) first class (d) class preceding the modal class
Question 3: Area of a sector
The area of a sector of angle 90° of a circle of radius 14 cm is (π=22/7) (a) 154 cm² (b) 308 cm² (c) 44 cm² (d) 616 cm²

Week 34

Question 1: Complementary events
For an event E, P(E): P(not E) = 3: 5. Then P(E) is (a) 3/5 (b) 3/8 (c) 5/8 (d) 2/5
Question 2: Volume of basic solids
The volume of a hemisphere of radius 21 cm is (π=22/7) (a) 38808 cm³ (b) 19404 cm³ (c) 2772 cm³ (d) 9702 cm³
Question 3: Mean of grouped data
If every observation in a data set is increased by 5, the mean (a) is unchanged (b) increases by 5 (c) is multiplied by 5 (d) increases by 5 times the number of observations

Week 35

Question 1: Basic properties of probability
A die is thrown once. Which of the following is an impossible event? (a) getting 6 (b) getting 0 (c) getting an odd number (d) getting a number less than 7
Question 2: Nature of roots
The discriminant of 3x² - 4x + 2 = 0 is (a) 40 (b) -8 (c) 8 (d) -40
Question 3: nth term of an AP
If the nth term of an AP is a_n = 5 - 3n, then its common difference is (a) 5 (b) 3 (c) 2 (d) -3

Week 38

Question 1: Basic properties of probability
Which one of these numbers could never be the probability of an event? (a) 2/3 (b) 0.7 (c) -1.5 (d) 15%
Question 2: Basic Proportionality Theorem and its converse
In △ ABC, D and E are points on AB and AC with DE ∥ BC. If AD = 3 cm, DB = 5 cm and AE = 4.5 cm, then EC is (a) 7.5 cm (b) 6 cm (c) 2.7 cm (d) 8 cm
Question 3: Distance formula
The distance between the points (-3, 4) and (5, -2) is (a) 8 (b) 14 (c) √28 (d) 10

Week 39

Question 1: Probability with coins
Two coins are tossed together. The probability of getting at least one head is (a) 1/4 (b) 1/2 (c) 1 (d) 3/4
Question 2: Trigonometric ratios
For 0° < θ ≤ 90°, the greatest value of 1/(cosecθ) is (a) 0 (b) 1/2 (c) 1 (d) (√3)/2
Question 3: Angle of elevation
The ratio of the height of a pole to the length of its shadow is 1:√3. The angle of elevation of the Sun is (a) 60° (b) 45° (c) 30° (d) 90°

Week 42

Question 1: Tangent to a circle
A straight line cuts a circle at two different points. Such a line is called (a) a secant (b) a tangent (c) a radius (d) a diameter
Question 2: Area of a sector
Two sectors of the same circle have central angles 40° and 120°. The ratio of their areas is (a) 1:3 (b) 1:9 (c) 3:1 (d) 2:3
Question 3: Volume of basic solids
A cylinder and a cone have equal base radii and equal heights. The ratio of their volumes is (a) 1:3 (b) 3:1 (c) 2:1 (d) 1:1

Week 43

Question 1: Mean of grouped data
The mean of the data with classes 0–4, 4–8, 8–12 and frequencies 2, 3, 5 is (a) 6 (b) 7.2 (c) 8 (d) 6.8
Question 2: Probability with dice
A die is thrown once. The probability of getting a number that is a multiple of 2 or of 3 is (a) 1/3 (b) 1/2 (c) 2/3 (d) 5/6
Question 3: Relationship between zeroes and coefficients
If α and β are the zeroes of x² + 5x + 6, then 1α + 1β equals (a) 5/6 (b) -6/5 (c) 6/5 (d) -5/6

Week 44

Question 1: Substitution method
If x = 2, y = -1 is a solution of 3x + ky = 8, then k equals (a) -2 (b) 2 (c) 14 (d) -14
Question 2: Standard form of a quadratic equation
If x = -2 is a root of 3x² + 7x + p = 0, then p equals (a) 26 (b) -2 (c) 2 (d) -26
Question 3: Arithmetic progressions and common difference
In the AP √2, 3√2, 5√2, …, each term is obtained from the one before it by adding (a) 3 (b) √2 (c) 2 (d) 2√2

Week 45

Question 1: Criteria for similarity of triangles
ABCD is a trapezium with AB ∥ DC and AB = 2 DC. Its diagonals meet at O. If OC = 4 cm, then OA is (a) 2 cm (b) 4 cm (c) 6 cm (d) 8 cm
Question 2: Mid-point formula
The mid-point of the segment joining (-4, 7) and (6, -1) is (a) (2, 6) (b) (5, -4) (c) (1, 3) (d) (-1, 3)
Question 3: Trigonometric identities
cos²θ (1+tan²θ)+sin²θ (1+cot²θ), for 0°<θ<90°, is equal to (a) 1 (b) 2 (c) sec²θ+cosec²θ (d) 0

Week 46

Question 1: Angle of elevation
The angle of elevation of the top of a tower 100√3 m high from a point on the ground is 60°. The distance of the point from the foot of the tower is (a) 100√3 m (b) 300 m (c) 50√3 m (d) 100 m
Question 2: Number of tangents from a point
The number of tangents that can be drawn to a circle from a point inside it is (a) 0 (b) 1 (c) 2 (d) infinitely many
Question 3: Length of an arc
The length of an arc of a circle of radius 21 cm subtending an angle of 60° at the centre is (π=22/7) (a) 44 cm (b) 22 cm (c) 231 cm (d) 66 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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