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CBSE Class 12 Maths Sample Paper 2019

Oct 28, 2018 19:10 IST
    CBSE Class 12 Maths Sample Paper 2019
    CBSE Class 12 Maths Sample Paper 2019

    CBSE Solved Sample Paper 2019 for Class 12 Maths Subject is available in this article for download in PDF format along with its Marking Scheme. CBSE recently publishes this Sample Paper for students who are going to write upcoming CBSE Class 12 Maths Board Exam 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 refer 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

    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.

    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 indifferent PDFs.

    Download CBSE Sample Paper 2019 for Class 12 Maths

    Download Solution of this Sample Paper (with Marking Scheme)

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