Cbse 12 Class Maths Sample Paper
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The document is a mathematics sample test paper for Class XII, consisting of 29 questions divided into three sections: A (10 questions of 1 mark each), B (12 questions of 4 marks each), and C (7 questions of 6 marks each), with internal choices in some questions. The contents cover various mathematical topics including calculus, matrices, probability, and geometry, requiring both theoretical knowledge and problem-solving skills. Use of calculators is not permitted, and all questions are compulsory.
![MATHEMATICS
SAMPLE TEST PAPER
CLASS XII
Class:12
Time 3hrs
Max Mks:100
No of pages: 3
General Instructions:
rit
e.
co
m
Ò All questions are compulsory.
Ò The question paper consists of 29 questions divided into three sections - A, B and C.
Ò Section - A comprises of 10 questions of one mark each, Section B is of 12 questions of four
marks each, Section C comprises of 7 questions of six marks each.
Ò Internal choice has been provided in four marks question and six marks question. You have to
attempt any one of the alternatives in all such questions
Ò use of calculator not permitted.
1. Find the value of x , if
w
w
sin2x
2. Evaluate: ∫ ( 3+ secx )dx
.e
du
SECTION A
Question number 1 to 10 carry 1 mark each
w
3. If A is irreversible matrix or order 5 and ∣ A∣ = 5, then find [adj,A]
a
a b
b
b
i
k
4. Find the projection of ⃗ on ⃗ , if ⃗ . ⃗ = 6 and ⃗ =4 ⃗ + ⃗j +8 ⃗
2
2x
5. Evaluate: ∫ ( 1+ 3x ) dx
3π
6. what is the value of tan-1 4
7. write the order of the matrix
8. write the position vector of the mid point of the vector join g the points p(2,3,4 and q (4,-1,2))
9. write the distance from following plane from the origin2x-y+2z+1 = 0
0
i
k
i
k
10. Find λ if (2 ⃗ +6 ⃗j +14 ⃗ )*( ⃗ -λ ⃗j +7 ⃗ ) = ⃗](https://image.slidesharecdn.com/cbse-12-class-maths-sample-paper-model-1-131218012321-phpapp02/85/Cbse-12-Class-Maths-Sample-Paper-1-320.jpg)
Cbse 12 Class Maths Sample Paper
- 1. MATHEMATICS SAMPLE TEST PAPER CLASS XII Class:12 Time 3hrs Max Mks:100 No of pages: 3 General Instructions: rit e. co m Ò All questions are compulsory. Ò The question paper consists of 29 questions divided into three sections - A, B and C. Ò Section - A comprises of 10 questions of one mark each, Section B is of 12 questions of four marks each, Section C comprises of 7 questions of six marks each. Ò Internal choice has been provided in four marks question and six marks question. You have to attempt any one of the alternatives in all such questions Ò use of calculator not permitted. 1. Find the value of x , if w w sin2x 2. Evaluate: ∫ ( 3+ secx )dx .e du SECTION A Question number 1 to 10 carry 1 mark each w 3. If A is irreversible matrix or order 5 and ∣ A∣ = 5, then find [adj,A] a a b b b i k 4. Find the projection of ⃗ on ⃗ , if ⃗ . ⃗ = 6 and ⃗ =4 ⃗ + ⃗j +8 ⃗ 2 2x 5. Evaluate: ∫ ( 1+ 3x ) dx 3π 6. what is the value of tan-1 4 7. write the order of the matrix 8. write the position vector of the mid point of the vector join g the points p(2,3,4 and q (4,-1,2)) 9. write the distance from following plane from the origin2x-y+2z+1 = 0 0 i k i k 10. Find λ if (2 ⃗ +6 ⃗j +14 ⃗ )*( ⃗ -λ ⃗j +7 ⃗ ) = ⃗
- 2. SECTION B Question numbers 11 to 22 carry 4 marks each. 11. State whether the function is one -one, onto or objective. Justify your answer a) f:R→R defined by f (x) = 4+5x b) f:R→R defined by f (x) = 4x+5x2 dy 12. use mathematical induction prove that dx (xn)=nx(n-1)for all n belongs N for all positive integers n. 13. rit e. co m 1+ 1− √ x− √ x π 14. prove that tan-1( √ x+ √ x )= 2 1+ 1− 15. Find the derivative of the function given by f(x) = (1+x) (1+x2) (1+x4)(1+x8) and hence find f(3) 16. using properties of determinants, prove that w prove that w w .e du or 17. solve the differential equation 2 2 x dy - y dx= √x + y or dy 2 dx = log(x+2) 18. A speaks truth 10 times out of 15 times. A dice is tossed. He reports that it was 6. What is the probability it was actually 6.' sin− 1( x) d2y dy 19. If y = , show that (1-x2) dx2 -3x dx -y = 0 2 √1− x 20. Express the following matrix as the sum of symmetric and skew symmetric matrix, and verify your answer.
- 3. rit e. co m 21. On multiplying choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answer just by guessing? 22. Finds the shortest between the following lines: r ⃗ = (1+λ) ⃗ +(2-λ) ⃗j + (λ+1)7 ⃗ ; ⃗ = (2 ⃗ - ⃗j + - ⃗ )+μ(2 ⃗ + ⃗j +2 ⃗ ) i i i k r k k SECTION C Question numbers 23 to 29 carry 6 marks each. 23. solve using matrices: 2x-y+3z = 5 3x+2y-z = 7 4x+5y-5z = 9 or using matrix method solve the following system of equations: 2x+y+z = 3 3x-y+z = 0 x-2y+3z = -6 du 24. Find the area of the region bounded by y2 = 4x, x = 1, x = 4 and x -a xis in the first quadrant .e or Evaluate lim 0− 2 ∫ as limit of a sum. 25. Show that the height of the cylinder of maximum volume that can be inscribed in a cone of 1 height h is 3 h. w w w x 2 + x+ 1 dx 26. Find the equation of the plane passing through the (-1,-1,2) are perpendicular to each of the following planes 2x+3y-3z = 2 and 5x-4y+z = 6 or Find the point on the curve y2 = 4x which is nearest to the point (-,-8) 27. Sketch the graph of y = Ix + 5I and evaluate the area under the curve y = x + 5 above x-axis and between x = -7 to x = O. 28. Using the method of integration, find the area of region bounded by the lines 2x+y = 4, 3x-2y = 6, x-3y+5 = 0 29. A can hit a target 4 times in 5 shots,B 3 times in 4 shots and C, 2 times in 3 shots. Calculate the probability that: a)A,B,C all may hit b) none of them ii hit the target