# CBSE Maths Sample Paper for Class 12

Central Board of Secondary Education is one of the most reputed and famous Board of Education that serve the standards of quality education to their students. Mathematics is the toughest subject thus students need to be very attentive while preparing for it as per exam point of view. Here in this we have tried to provide a series of CBSE Maths Sample paper for Class 12 for the purpose of providing help to the appearing students of Class 12. The choice of questions has been taken from the previous year sample papers and referred NCERT textbooks. Hope this paper will help you to sort out your problems. For better preparation you can also take help from **CBSE 12th Maths Sample Paper.**

This is the 2nd** CBSE Maths Sample paper for Class 12 **in the sample paper series and you will find more sample Papers in the below mentioned links. We will soon update more sample paper also.

**CBSE Mathematics Sample Papers for Class 12**

Time: 3 Hours Max.Marks:100

**General Instructions**

**1.** All questions are compulsory.

**2.** The question paper consists of 29 questions divided into three sections A, B, C.

**(a) Section A** comprises of 10 questions of one mark each,

**(b) Section B** comprises of 12 questions of 4 marks each

(**c) Section C** comprises of of 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 questions.

**4.** There is no overall choice. However, internal choice has been provided in 04 questions of four marks each and 02 questions of six marks each.

**SECTION A**

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

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

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

**4.** Find the value of ∫dx/25-x

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

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

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

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

**9.** Find a matrix X such that B – 2A + X = O

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

**SECTION B**

**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 .

**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)

**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

**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.

OR

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

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

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

**17. **If f is continuous at x = π/2 Find a and b

f(x) = 1 – sin3x if x < π/2 3cos2x

= a x = π/2

= b(1-sinx) if x > π/2(π-2x)

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

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

**20.** Differntiate tan-1 [ √1-cosx/1+cosx] with respect to tan-1x

**21.** 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

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

**SECTION C**

**23.** 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 .

**OR**

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

**24.** 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.

**25.** 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.

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

**OR**

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

**27.** Show that the rectangle of maximum area that can be inscribed in a circle is a square.

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

**29.** 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.

**To get pdf of more Sample paper for Class 12 CBSE Maths, follow:**

**For more CBSE Maths Sample paper for Class 12, 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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