ISC 2020 Maths Question Paper for Class 12

About this paper

This is the ISC Class 12 Mathematics paper from the 2020 CISCE board examination, with a worked solution written under the questions. It carries 100 marks and runs for three hours, with fifteen minutes extra for reading only. Section A is worth 80 marks and is all compulsory. Question 1 has ten two-mark parts, and there is an internal choice in three four-mark questions and two six-mark questions. Candidates then attempt either Section B or Section C, each worth 20 marks, with an internal choice in two four-mark questions. Section B is vectors, planes, the image of a point and area between curves. Section C is profit and break-even, demand, regression and correlation. Mathematical tables and graph paper are provided.

Exam

ISC Class 12

Subject

Mathematics

Year

2020

Maximum marks

100

Time allowed

3 hours + 15 min reading

Questions

22

Pages

12

Answers included

Yes

Paper pattern

• Section A

  80 marks

  Questions 1–14, all compulsory. Question 1 has ten parts of two marks each; internal choice in three four-mark questions and two six-mark questions

• Section B or Section C

  20 marks

  Attempt every question in one section only. Section B (Questions 15–18) is vectors, lines, planes and area; Section C (Questions 19–22) is revenue, cost, regression and correlation. Each has an internal choice in two four-mark questions

Topics covered

• Binary operations and functions
• Inverse trigonometric functions
• Determinants and matrices
• Rolle's theorem and tangents
• L'Hospital's rule
• Indefinite integrals
• Differential equations
• Probability and binomial distribution
• Maxima and minima
• Vectors and three-dimensional geometry
• Area between curves
• Cost, revenue, correlation and regression

Questions from this paper

1. A binary operation on real numbers is defined by a * b = |a − b|. Show that it is commutative, and find (−3) * 2.
2. Prove that tan²(sec⁻¹ 2) + cot²(cosec⁻¹ 3) = 11.
3. Verify Rolle's theorem for f(x) = −1 + cos x on [0, 2π].
4. The tangent at (2, 3) on the curve y² = px + q is y = 4x − 7. Find p and q.
5. The probability that a bulb will fuse after 150 days is 0.05. For 5 such bulbs, find the probability that none fuse, that not more than one fuses, that more than one fuses, and that at least one fuses.
6. Show that a closed right circular cylinder of given surface area has maximum volume when its radius is half its height.