# CBSE Question Paper 2018 class 12 Mathematics

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CBSE Question Paper 2018 class 12 Mathematics conducted by Central Board of Secondary Education, New Delhi in the month of March 2018. CBSE previous year question papers with solution are available in myCBSEguide mobile app and cbse guide website. The Best CBSE App for students and teachers is myCBSEguide which provides complete study material and practice papers to cbse schools in India and abroad.

Question Paper 2018 class 12 Maths

## Class 12 Mathematics list of chapters

1. Relations and Functions
2. Inverse Trigonometric Functions
3. Matrices
4. Determinants
5. Continuity and Differentiability
6. Application of Derivatives
7. Integrals
8. Application of Integrals
9. Differential Equations
10. Vector Algebra
11. Three Dimensional Geometry
12. Linear Programming
13. Probability

## CBSE Question Paper 2018 class 12 Mathematics

Time allowed : 3 hours
Maximum Marks: 100

General Instructions :

1. All questions are compulsory.
2. The question paper consists of 29 questions divided into four sections A, B, C and D. Section A comprises of 4 questions of one mark each, Section B comprises of 8 questions of two marks each, Section C comprises of 11 questions of four marks each and Section D comprises of 6 questions of six marks each.
3. All questions in Section A are to be answered in one word, one sentence or as per the exact requirement of the question.
4. There is no overall choice. However, internal choice has been provided in 3 questions of four marks each and 3 questions of six marks each. You have to attempt only one of the alternatives in all such questions.
5. Use of calculators is not permitted. You may ask for logarithmic tables if required.

SECTION A

Question numbers 1 to 4 carry 1 mark each.

1. Find the value of ${\tan ^{ - 1}}\sqrt 3 - {\cot ^{ - 1}}\left( { - \sqrt 3 } \right)$.
2. If the matrix $A = \left[ {\begin{array}{*{20}{c}} 0&a&{ - 3} \\ 2&0&{ - 1} \\ b&1&0 \end{array}} \right]$ is skew-symmetric, find the values of ‘a’ and ‘b’.
3. Find the magnitude of each of the two vectors $\vec a$ and $\vec b$, having the same magnitude such that the angle between them is 60° and their scalar product is.$\frac{9}{2}$
4. If a * b denotes the larger of ‘a’ and ‘b’ and if a $\circ$ b = (a * b) + 3, then write the value of (5) $\circ$ (10), where * and $\circ$ are binary operations.

SECTION B

Question numbers 5 to 12 carry 2 marks each.

1. Prove that: $3 \; {\sin ^{ - 1}}x = {\sin ^{ - 1}}(3x - 4{x^3})$, $x \in \left[ {\frac{{ - 1}}{2},\;\frac{1}{2}} \right]$
2. Given $A = \left[ {\begin{array}{*{20}{c}} 2&{ - 3} \\ { - 4}&7 \end{array}} \right]$, compute A-1 and show that 2A-1 = 9I – A.
3. Differentiate ${\tan ^{ - 1}}\left( {\frac{{1 + \cos x}}{{\sin x}}} \right)$ with respect to x.
4. The total cost C(x) associated with the production of x units of an item is given by C(x) = 0·005x3 – 0·02x2 + 30x + 5000. Find the marginal cost when 3 units are produced, where by marginal cost we mean the instantaneous rate of change of total cost at any level of output.
5. Evaluate : $\int {\frac{{\cos 2x + 2{{\sin }^2}x}}{{{{\cos }^2}x}}} dx$
6. Find the differential equation representing the family of curves y = a ebx+5, where a and b are arbitrary constants.
7. If $\theta$ is the angle between two vectors $\hat i - 2\hat j + 3\hat k$ and $3\hat i - 2\hat j + \hat k$ find sin.$\theta$
8. A black and a red die are rolled together. Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.

SECTION C

Question numbers 13 to 23 carry 4 marks each.

1. Using properties of determinants, prove that
$\left| {\begin{array}{*{20}{c}} 1&1&{1 + 3x} \\ {1 + 3y}&1&1 \\ 1&{1 + 3z}&1 \end{array}} \right|$ = 9 (3xyz + xy + yz + zx)
2. If (x2 + y2)2 = xy, find $\frac{{dy}}{{dx}}$.
OR

If $x = a(2\theta - \sin 2\theta )$ and $y = a(1 - \cos 2\theta )$, find $\frac{{dy}}{{dx}}$ when $\theta = \frac{\pi }{3}$.

3. If y = sin (sin x), prove that $\frac{{{d^2}y}}{{d{x^2}}} + \tan x\frac{{dy}}{{dx}} + y{\cos ^2}x = 0$.
4. Find the equations of the tangent and the normal, to the curve 16x2 + 9y2 = 145 at the point (x1, y1), where x1 = 2 and y1 > 0.
OR

Find the intervals in which the function f(x) = $\frac{{{x^4}}}{4}$ – x3 – 5x2 + 24x + 12 is (a) strictly increasing, (b) strictly decreasing.

5. An open tank with a square base and vertical sides is to be constructed from a metal sheet so as to hold a given quantity of water. Show that the cost of material will be least when depth of the tank is half of its width. If the cost is to be borne by nearby settled lower-income families, for whom water will be provided, what kind of value is hidden in this question?
6. Find : $\int {\frac{{2\cos x}}{{(1 - \sin x)(1 + {{\sin }^2}x)}}} dx$
7. Find the particular solution of the differential equation ex tan y dx + (2 – ex) sec2y dy = 0, give that $y = \frac{\pi }{4}$ when x = 0.
OR

Find the particular solution of the differential equation $\frac{{dy}}{{dx}} + 2y$ tanx = sinx, given that y = 0 when.$x = \frac{\pi }{3}$

8. Let $\vec a = 4\hat i + 5\hat j - \hat k,\;\vec b = \hat i - 4\hat j + 5\hat k$ and $\vec c = 3\hat i + \hat j - \hat k$. Find a vector $\vec d$ which is perpendicular to both $\vec c$ and $\vec b$ and $\vec d \cdot \vec a$ = 21.

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## Mathematics Question Paper 2018 with solution

Download class 12 Mathematics question paper with solution from best CBSE App the myCBSEguide. CBSE class 12 Mathematics question paper 2018 in PDF format with solution will help you to understand the latest question paper pattern and marking scheme of the CBSE board examination. You will get to know the difficulty level of the question paper. CBSE question papers 2018 for class 12 Mathematics have 29 questions with solution.

## CBSE Question Paper 2018

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