# CBSE Class 12 Maths Sample Paper 2019 with Answers & Marking Scheme

CBSE Sample Paper 2019 for Class 12 Maths Subject is available in this article for download in PDF format along with its Marking Scheme.  CBSE Sample Paper for Class 12 Maths Board Exam 2019

CBSE Solved Sample Paper for Class 12 Maths Board Exam 2019 is available here for download in PDF format along with its Marking Scheme. CBSE Class 12 Maths Sample Paper is based on the latest CBSE Class 12 Maths Syllabus 2019. With the help of this Sample Paper, students can easily understand the latest pattern of CBSE Class 12 Maths Board Exam.

Maths is considered as one of the most challenging subjects of Class 12, but with a little practice, one can easily score well in board exams. For practice, candidates should check the latest Sample Papers. As CBSE itself publishes this Sample Paper, so it is one of the best resources for the preparation of CBSE 12th Maths Board Exam 2019.

CBSE Syllabus for Class 12 Maths Board Exam 2019 - Check here!

## Content from CBSE Class 12 Maths Sample Paper 2019

• Time Allowed: 3 hours • Maximum Marks: 100

General Instructions:

1. All questions are compulsory.

2. This question paper contains 29 questions.

3. Questions 1 – 4 in Section A are very short-answer type questions carrying 1 mark each.

4. Questions 5 – 12 in Section B are short-answer type questions carrying 2 marks each.

5. Questions 13 – 23 in Section C are long-answer I type questions carrying 4 marks each.

6. Questions 24 – 29 in Section D are long-answer II type questions carrying 6 marks each.

Section A

Question1. If A and B are invertible matrices of order 3, |A| = 2 and | (AB)‒1| = ‒1/6. Find |B|.

Solution1:

| 1/(AB)| = ‒1/6 ⇒  1/(|A||B|) = ‒1/6 ⇒  |B| = ‒3.

NCERT Exemplar Questions & Solutions: Class 12 Mathematics - All Chapters

Question2. Differentiate sin2(x2) w.r.t  x2.

Solution2:

2 sin(x2) cos (x2) or sin (2x2)

Question3. Write the order of the differential equation: log (d2y/dx2) = (dy/dx)3 + x.

Solution3:

2

Question4. Find the acute angle which the line with direction cosines 1/√3, 1/√6, n makes with positive direction of z-axis.

Solution4:

l2 + m2 + n2 = 1 ⇒(1/√3)2 + (1/√6)2 + n2 = 1 ⇒ cos γ = 1/√2 ⇒ γ = 45o or π/4.

OR

Question4. Find the direction cosines of the line: (x ‒ 1)/2 = ‒ y = (z + 1)/2.

Solution4:

Direction ratios of the given line are 2, –1, 2.

Hence, direction cosines of the line are:

2/3, ‒1/3, 2/3 or ‒2/3, 1/3, ‒2/3

Section B

Question5. Let A = Z × Z and * be a binary operation on A defined by

(a,b)*(c,d) = (ad + bc, bd).

Find the identity element for * in the set A.

Solution5:

An element (e, f) ϵ Z × Z be the identity element, if

(a, b) * (e, f) = (a, b) = (e, f) * (a, b) ∀ (a, b) ϵ Z × Z

i.e., if, (af + be, bf) = (a, b) = (eb + fa, fb)

i.e., if, af + be = a = eb + fa and bf = b = fb …(1)

i.e., if, f = 1, e = 0 …(2)

Hence, (0, 1) is the identity element.

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Rest questions are available in the PDF of the Sample Paper. Questions and Solutions (with Marking Scheme) are available in different PDF.