CBSE Maths 2019

CBSE Class 10 Maths 2019 — all 30 questions from the paper

The complete question list from the CBSE Class 10 Mathematics 2019 board examination is below. Every question can be attempted in the timed interactive test above, with visual step-by-step solutions and AI coaching after each answer. Three fully worked solutions from this paper follow the question list.

Questions from the 2019 paper

1. Q1.If x = 3 is one root of the equation x² − 2kx − 6 = 0, then the value of k is:A) 1/2B) −1/2C) 3D) 1
2. Q2.The total number of factors of a prime number is:A) 1B) 0C) 2D) 3
3. Q3.If the common difference of an AP is 5, then a₁₈ − a₁₃ is:A) 5B) 20C) 25D) 30
4. Q4.In ΔABC, ∠B = 90°. If AB = 12 cm and BC = 5 cm, then what is the radius of the circle inscribed in the triangle?A) 2 cmB) 3 cmC) 4 cmD) 5 cm
5. Q5.If tanθ = 12/5, then the value of (1 + sinθ)/(1 − sinθ) is:A) 25B) 9C) 4D) 16
6. Q6.A number is selected at random from the numbers 1 to 30. The probability that it is a prime number is:A) 1/3B) 2/15C) 7/15D) 11/30
7. Q7.Find the LCM of 12, 15 and 20 using prime factorisation.A) 60B) 120C) 180D) 240
8. Q8.Find a quadratic polynomial whose sum and product of zeroes are −1 and −20 respectively.A) x² + x − 20B) x² − x + 20C) x² − x − 20D) x² + x + 20
9. Q9.The 4th term of an AP is zero. Prove that its 25th term is triple its 11th term. What is a₂₅/a₁₁?A) 2B) 3C) 4D) 5
10. Q10.Find the area of the triangle with vertices A(1, −1), B(−4, 6) and C(−3, −5).A) 24 sq unitsB) 12 sq unitsC) 48 sq unitsD) 32 sq units
11. Q11.Prove that (sinA − 2sin³A)/(2cos³A − cosA) = tanA. The expression equals:A) sinAB) cosAC) tanAD) cotA
12. Q12.The length of a tangent from a point A at a distance 5√2 cm from the centre of a circle is 5 cm. Find the radius of the circle.A) 5 cmB) 5√2 cmC) 10 cmD) 5/√2 cm
13. Q13.Show that 5 + 2√7 is an irrational number, given that √7 is irrational.A) RationalB) IrrationalC) IntegerD) Natural number
14. Q14.If α and β are zeroes of 6x² − 5x + k such that α − β = 1/6, find the value of k.A) 1B) 2C) −1D) 3
15. Q15.5 pencils and 7 pens together cost ₹50, whereas 7 pencils and 5 pens together cost ₹46. Find the cost of one pen.A) ₹5B) ₹3C) ₹4D) ₹6
16. Q16.The sum of the reciprocals of Rehman's ages (in years) 3 years ago and 5 years from now is 1/3. Find his present age.A) 7 yearsB) 8 yearsC) 10 yearsD) 12 years
17. Q17.The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.A) −13, −8, −3B) −8, −3, 2C) −3, 2, 7D) 2, 7, 12
18. Q18.If the point P(k, 0) divides the line segment joining A(2, −2) and B(−7, 4) in the ratio 1 : 2, find k.A) -1B) 1C) -3D) 3
19. Q19.Prove that (cosA − sinA + 1)/(cosA + sinA − 1) = cosecA + cotA. This uses the identity:A) cosec²A − cot²A = 1B) sin²A + cos²A = 1C) sec²A − tan²A = 1D) 1 + tan²A = sec²A
20. Q20.Prove that the parallelogram circumscribing a circle is a rhombus. If ABCD is such a parallelogram with AB = 10 cm, what is BC?A) 10 cmB) 5 cmC) 20 cmD) 15 cm
21. Q21.Find the mean of the following frequency distribution:
    Class: 10–25 (f=2), 25–40 (f=3), 40–55 (f=7), 55–70 (f=6), 70–85 (f=6), 85–100 (f=6). The mean is:A) 62B) 58.5C) 61.75D) 63.25
22. Q22.A bag contains 15 white and some black balls. If the probability of drawing a black ball is thrice that of drawing a white ball, find the number of black balls.A) 45B) 30C) 60D) 35
23. Q23.The speed of a boat in still water is 11 km/h. It can go 12 km upstream and return downstream to the original point in 2 hours 45 minutes. Find the speed of the stream.A) 5 km/hB) 4 km/hC) 3 km/hD) 6 km/h
24. Q24.If the sum of the first 14 terms of an AP is 1050 and its first term is 10, find the 20th term.A) 200B) 190C) 180D) 210
25. Q25.In ΔABC, if AD is the median and AM ⊥ BC, prove that AB² = AD² + BC·DM + (BC/2)². If AB = 10, AD = 8, BC = 12, find DM.A) 1B) 2C) 3D) 0
26. Q26.A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and of the top of the pedestal is 45°. Find the height of the pedestal.A) 0.8(√3 + 1) mB) 0.8(√3 − 1) mC) 1.6(√3 − 1) mD) 1.6√3 m
27. Q27.A solid metallic sphere of radius 4.2 cm is melted and recast into a cone of radius 6 cm. Find the height of the cone.A) 8.232 cmB) 7.8 cmC) 9.6 cmD) 6.4 cm
28. Q28.The following data gives the heights of students:
    Height (cm): 150–155 (f=15), 155–160 (f=8), 160–165 (f=20), 165–170 (f=12), 170–175 (f=5). Find the modal height.A) 161.76 cmB) 162.35 cmC) 160.00 cmD) 163.50 cm
29. Q29.Two different dice are rolled together. Find the probability that the numbers obtained have a product that is a perfect square.A) 2/9B) 1/6C) 1/4D) 5/36
30. Q30.A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter of the hemisphere is equal to the edge of the cube. If the edge of the cube is 14 cm, find the total surface area of the remaining solid.A) 1ea cm² ... 1484 cm²B) 1484 cm²C) 1176 cm²D) 1596 cm²

Worked solutions from the CBSE 2019 paper

Start the test above to see visual step-by-step solutions for all 30 questions — free, with AI coaching when you get stuck.