# CBSE 12th Maths Sample Paper

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Central Board of Secondary Education is abbreviated as CBSE which is one of the most famous and the reputed one Board of Education in India. CBSE is a government body that serve best quality in terms of Education to both private as well as public Schools. Every year CBSE conducts Board Examination for Class X ans XII students and to get good marks in this exam is the dream of every appearing student. As a graduate, I have tried to set this CBSE 12th Maths Sample Paper in order to help you to achieve excellent marks in your Board Exams. Maths is one of the most toughest subject to prepare as it consists of various formula and derivation. So, practice is essential for gaining marks. This **Sample Paper of Class 12th CBSE Maths** will definitely help you in this regard. Keep practising.

** CBSE CLASS 12 ^{th }MATHS SAMPLE PAPER **

This is the **7th** paper of CBSE 12th Maths Sample Paper series and you will find more sample Papers in the below mentioned links. We will soon update the more sample paper also.

**GENERAL INSTRUCTIONS:**

**(i)** All the question are compulsory.

**(ii)** The question paper consists of **29** question divided into three

Sections A, B and C. Section A comprises of **10** questions of **one** marks each, Section B comprises of 12 questions for **four** marks each and Section C comprises of **7** question of **six** marks each.

**(iii)** All question in Section A are to be answered in **one** word, **one** sentence or as per the exact requirement of the question.

**(iv)** Use of calculator is not permitted.

*NOTE: THIS IS CBSE 12th MATHS SAMPLE PAPER FOR THE EFFECTIVE PREPARATION FOR 12th BOARD EXAM.

**SECTION A**

- A matrix A of order 3 × 3 has determinant 8. What is the value of | 3A |
**[1 Mark]** - Find the point on the curve
*y*=x^2-4x+3 where the tangent is parallel to*x*-axis.**[1 Mark]** - Write the formulae for the eccentricity of ellipse?
**[1 Mark]** - Cartesian equations of a line AB are:

(2x-1/3)= (4-y/6) = (z-1/2)

Write the direction ratios of a line parallel to AB.**[1 Mark]** - If matrix A = [3 4 8], write AA’, where A’ is the transpose of matrix A.
**[1 Mark]** - If the binary operation * on the set of integers Z, is defined by a*b = a+3b^2, then find the value of 4*8?
**[1 Mark]** - If A is an invertible matrix of order 3 and | A | = 10, then find |adj. A |.
**[1 Mark]** - Find the value of ∫sinx/x.
**[1 Mark]** - Find the value of x for which the vector â= 2i-6j+7k and ĉ=5i+3j-xk are perpendicular to each other.
**[1 Mark]** - Find the equation of the line perpendicular to y axis and passing through the origin.
**[1 Mark]**

**SECTION B**

- Using the method of integration find the area of region bounded by the line.
**[4 Mark]**

3x-2y+1=0

2x+3y-21=0 and

x-5y+2=0 - Using the method of integration find the area of region bounded by the line-
**[4 Mark]**

5x-3y+6=0

2x^2-2x+6 and

6x-3y=0 - Using matrices solve the following system of linear equation:
**[4 Mark]**

x-y+3z=8

3x+4y-4z=-4

2x-y+3z=11 - Using elementary operation find the inverse of the following matrix:
**[4 Mark]**

3 3 5

-1 2 2

2 4 3 - A water tank has the shape of an inverted right circular cone with its axis vertical and vertex lower most. Its semi-vertical angle is tan^-1*(1/2) . Water is poured into it at a constant rate of 5 cubic meters per minute. Find the rate at which the level of the water is rising at the instant when the depth of water in the tank is 20m.
**[4 Mark]** - A die is thrown again and again until three sixes are obtained. Find the probability of obtaining the third six in the sixth throw of the die.
**[4 Mark]** - Using Rolle’s theorem find the points on the curve y = x^2+5, x ε [-2,2], where the tangent is parallel to the x axis.
**[4 Mark]** - Solve the following differential equations:

dy/dx+y= sinx-cosx**[4 Mark]** - Using vectors prove that Medians of a triangle are concurrent.
**[4 Mark]** - Using determinants, find the area of the triangle whose vertices are (-2,7), (-1,6) and (-5,2). Are the given points collinear?
**[4 Mark]** - The probability of a bullet hitting a target is 1/3. How many minimum number of times it must be fired so that the probability of hitting the target at least once is more than 0.67
**[4 Mark]** - Find the probability of getting at least sum of 6 when 2 dice are thrown simultaneously.
**[4 Mark]**

**SECTION C**

- Find the volume of the largest cylinder that can be inscribed in a sphere of radius r.
**[6 Mark]** - Three bags contain balls as shown in the table below:

BAG NO OF WHITE BALL NO OF BLACK BALL NO OF RED BALL

1. 2 3 1

2. 5 1 4

3. 1 4 6

A bag is chosen at random and two balls are drawn from it. They happen to be black and red. What is the probability that they came from 3 bags?**[6 Mark]** - A tank with rectangular base and rectangular sides, Open at the top is to be constructed so that its depth is 4 cm and volume is 12 meter cube . If building of tank costs Rs. 70 per sq. meter for the basis and Rs. 40 per sq. meter for sides, what is the cost of least expensive tank?
**[6 Mark]** - Prove that the radius of the base of right circular cylinder of greatest curved surface area which can be inscribed in a given cone is half that of the cone.
**[6 Mark]** - Find the area of the region enclosed between the two circles:
**[6 Mark]**

x^2+y^2 = 1 and (x-1)^2 + y^2 = 1 - Solve the following: ʃ(x^2/(x^3+x^2+1)) dx.
**[6 Mark]** - Show that the rectangle of maximum area that can be inscribed in a circle is a square.
**[6 Mark]**

**NOTE:** To get pdf of above sample paper,follow:

**CBSE 12th Maths Sample Paper**

To get pdf of more maths sample paper, follow:

**CBSE Mathematics Sample Papers for Class 12**

**Sample Paper for Mathematics CBSE 12th**

**BLUEPRINT :
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**Best of Luck for your Exam preparations…!!!!**

**Related Links:**

**1) CBSE Sample Papers for Class 12th Maths**

**2) Sample Paper for Mathematics CBSE Class 12**

**3) Sample Question Papers for Class 12 CBSE Maths**

**4) Sample Paper for Class 12 CBSE Mathematics**

**5) CBSE Mathematics Sample Papers for Class 12**

**6) CBSE XII – Sample Paper FOR Maths**

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