## Unsolved CBSE Sample Papers Class 12 Maths

CBSE is one of the most reputed Board of Education that is serving quality education to their students across the country for both private as well as public. In order to get good marks in the Board Exam conducted by CBSE is must essential as it serve the basis of your career. Here in this post, I have tried to prepare** **this Unsolved** CBSE Sample Papers Class 12 Maths ** for the purpose of giving an idea about the type of questions asked in the Exam as per the latest pattern of CBSE Board. Maths is one of the subject which will help you to maintain good percentage as its a marks earning subject. So prepare it well and become able to earn excellent marks in your exam by practising this CBSE Sample Paper for Class 12 Maths.

This is the **10th CBSE Sample Papers Class 12 Maths ** series and you will get more sample paper of this series very soon to guide you.

**General Instructions:
**

**1.**All questions are compulsory.

**2.** The question paper consists of 29 questions divided into three sections A, B, C. Section A comprises of 10 questions of one mark each, section B comprises of 12 questions of 4 marks each and section C comprises of 7 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.

**CBSE Sample Paper for Class 12 Maths**

**SECTION A (One Mark Questions)**

**Question-1:** Give an example of two nonzero 3×3 matrices A,B such that AB=O

**Question-2:** Find the numerical value of tan[2tan-1(1/6)-π/2]

**Question-3:**Find the equation of the line parallel to x axis and passing through the origin.

**Question-4: **Find the value of ∫dx/25-x

**Question-5: **Find the angle between vectors â and ĉ with magnitude 3 and 2 respectively. Given â.ĉ= 6.

**Question-6:** Find the value of x for which the vector â= 3i+j-2k and ĉ=i+xj-3k are perpendicular to each other.

**Question-7: **What is the principal value of cosπ/3+sin2π/3.

**or,** is the degree of the following differential equation? y d’y +(d Y) = x(d3y) ‘ dx2dx dx’

**Question-8: **Find a matrix X such that B – 2A + X = O

**Question-9:** Let E={1,2,3} and F={1,2}. Then find the number of onto functions from E to F.

**Question-10: **Find the direction cosines of a line, passing through origin and lying the first octant, making equal angles with the three coordinate axes.

**SECTION B(Four Mark Questions)**

**Question-11:** Let f: N be a function defined as f ( x ) = 4×2 + 12x + 15 .Show that f: N where S is the range of f, is invertible .Find the inverse of f .

**Question-12:** Find the image of the point P( 6,5,9) on the plane determined by the points A ( 3,-1,2 ) , B ( 5,2,4 ) and C ( -1,-1,6 )

**Question-13:**The probability of a shooter hitting a target is 3/4. How many minimum number of times must he/ she fire so that the probability of hitting the target at least once is more than 0.99

**Question-14: **The dot products of a vector with the vectors i-3k, i-2k and i+j+4k are 0, 5 and 8 respectively. Find the vector.

**Question-15:** Find all the points of discontinuity of the function f(x) = (x’ ) on [1 , 2), where [.J denotes the greatest integer function.

**or, **Solve for x. tan-1(x+1) + tan-1( x) + tan-1(x-1) = tan-13

**Question-16:** If f is continuous at x = π/2 Find a and b

f(x)= 1 – sin3x if x < π/2 3cos2x

= a if x = π/2

= b(1-sinx) if x > π/2(π-2x)

**Question-17: **Using Rolle’s theorem find the points on the curve y = x2, x ε [-2,2], where the tangent is parallel to the x axis.

**Question-18: **If a = 5i-j-3k, b = i +3j-5k, then show that the vectors a+b and a-b are orthogonal.

**Question-19:** Differentiate tan-1 [ √1-cosx/1+cosx] with respect to tan-1x

**Question-20:** Form the differential equation representing the family of curves y2-2ay+x2 = a2(or) Prove that the differential equation is homogeneous and solve it 2xydx + (x2+2y2)dy = 0

**Question-21:** The radius of the balloon is increasing at the rate of 10 cm/sec. At what rate is the surface area of the balloon is increasing when its radius is 15 cm.

**SECTION C(Six mark Questions)**

**Question-22:** Find the area enclosed by the region in the first quadrant enclosed by the ellipse x2/4+y2/36=1 and the line 3x+y=6 .

**Question-23:** Suppose a girl throws a die. If she gets 5 or 6 she tosses the coin 3 times and notes the number of heads. If she gets 1,2,3 or 4 she tosses a coin once and notes whether a head or a tail is obtained f she obtained exactly one head what is the probability that she threw 1,2,3 or 4 with a die.

**or, ** A dealer wishes to purchase a number of fans and sewing machines. He has only Rs 5760 to invest and has space for at the most 20 items. A fan costs him Rs 360 and sewing machine Rs 240. He expects to sell a fan at a profit of Rs 22 and a sewing machine for a profit of Rs 18. Assuming that he can sell all the items he buys, how should he invest his money to maximize his profit. Solve it graphically.

**Question-24:** Show that the volume of the greatest cylinder which can be inscribed in a cone of height h and semi vertical angle a ,is ~rrh’ tan’ a .

**Question-25:** Show that the rectangle of maximum area that can be inscribed in a circle is a square.

**or,** Find the equation of the plane passing through the point (-1,-1,2) and perpendicular to each of the following planes:

**Question-26: **Two bags A and B contain 4 white and 3 black balls and 2 white and 2 black ball s respectively. From bag A. two balls are drawn at random and then transferred to bag B. A ball is then drawn from bag B and is found to be a black ball. What is the probability that the transferred balls were I white and I black.

**Question-27: **Show that the normal at any point e to the curve x=a cos e +a e sin e and y=a sin ea e cos e is at a constant distance from the origin.

**Question-28: **Find the area bounded by the curve y2=4a(x-1) and the lines x=1 and y=4a.

**Question-29: **Find the equation of a plane parallel to x axis and has intercepts 5 and 7 on y and z axis respectively.

**Question-30:** Solve the differential equation: (tan-1y–x)dy=(1+y2) dx.

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

**Unsolved CBSE Sample Papers Class 12 Maths.**

**To get pdf of more maths sample paper, follow:**

**Class 12 Mathematics Sample papers CBSE**

** Maths Sample Paper for Class 12 CBSE**

For any kind of suggestion related to the content of this paper or the post, please let me know through the comment section given below the post.

**ALL THE BEST…!!!!**

**For more Sample papers click on the following 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)** **Sample Paper of Class 12th CBSE Maths**

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