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; answers and mark schemes stay with teachers.
Week 33
Question 1: Complementary events
For an event E, P(E): P(not E) = 3: 5. Then P(E) is (a) 35 (b) 38 (c) 58 (d) 25
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: 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: 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: 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) 13 (b) 12 (c) 23 (d) 56
Question 2: Nature of roots
The discriminant of 3x² - 4x + 2 = 0 is (a) 40 (b) -8 (c) 8 (d) -40
Question 3: Arithmetic progressions and common difference
If 2k + 1, 13, 5k - 3 are three consecutive terms of an AP, then k equals (a) 3 (b) 5 (c) 4 (d) 27/7
Week 38
Question 1: Probability with dice
Two dice are thrown together. The probability that the sum of the numbers is 8 is (a) 16 (b) 5/36 (c) 19 (d) 7/36
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: Simple events
A number is chosen at random from 1 to 30. The probability that it is a multiple of 4 is (a) 1/4 (b) 2/15 (c) 7/30 (d) 4/15
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: 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 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: Basic properties of probability
The probability of a sure event is (a) 0 (b) 1 (c) 12 (d) more than 1
Question 3: Relationship between zeroes and coefficients
If α and β are the zeroes of x² + 5x + 6, then 1α + 1β equals (a) 56 (b) -65 (c) 65 (d) -56
Week 44
Question 1: 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
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: nth term of an AP
Which term of the AP 21, 18, 15, … is -81? (a) 34th (b) 35th (c) 36th (d) -81 is not a term
Week 45
Question 1: Criteria for similarity of triangles
△ ABC △ PQR with AB = 6 cm and PQ = 9 cm. If the perimeter of △ ABC is 24 cm, the perimeter of △ PQR is (a) 16 cm (b) 27 cm (c) 36 cm (d) 54 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: Tangents from an external point
Quadrilateral ABCD circumscribes a circle. If AB = 7 cm, BC = 9 cm and CD = 8 cm, then DA is (a) 8 cm (b) 10 cm (c) 6 cm (d) 24 cm
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 are in the teacher tools.