CBSE Sample Papers for Class 12 Maths Paper 6

CBSE Sample Papers for Class 12 Maths Paper 6 are part of CBSE Sample Papers for Class 12 Maths. Here we have given CBSE Sample Papers for Class 12 Maths Paper 6.

CBSE Sample Papers for Class 12 Maths Paper 6

Board CBSE
Class XII
Subject Maths
Sample Paper Set Paper 6
Category CBSE Sample Papers

Students who are going to appear for CBSE Class 12 Examinations are advised to practice the CBSE sample papers given here which is designed as per the latest Syllabus and marking scheme as prescribed by the CBSE is given here. Paper 6 of Solved CBSE Sample Paper for Class 12 Maths is given below with free PDF download solutions.

Time: 3 Hours
Maximum Marks: 100

General Instructions:

  • All questions are compulsory.
  • Questions 1-4 in section A are very short answer type questions carrying 1 mark each.
  • Questions 5-12 in section B are short answer type questions carrying 2 marks each.
  • Questions 13-23 in section C are long answer I type questions carrying 4 marks each.
  • Questions 24-29 in section D are long answer II type questions carrying 6 marks each.

SECTION A

Question 1.
If A is a matrix of order 2 x 3 and B is of order 3 x 4, what is the order of (AB)’?

Question 2.
If \(\vec { P }\) is a unit vector and \(\left( \vec { x } -\vec { P } \right) \cdot \left( \vec { x } +\vec { P } \right) =80\), then find the value of \(\left| \vec { x } \right|\).

Question 3.
Evaluate \(\int { \sqrt { \frac { x }{ 1-{ x }^{ 3 } } } } dx\)

Question 4.
Find the point at which tangent to the curve y = x2 makes an angle of 45° with x-axis.

SECTION B

Question 5.
Express the matrix \(A=\begin{pmatrix} 3 & 5 \\ 1 & -1 \end{pmatrix}\) as the sum of symmetric and skew symmetric matrix.

Question 6.
If xy = yx, find \(\frac { dy }{ dx }\)

Question 7.
Verify Rolle’s theorem for f(x) = sin 2x in [0, \(\frac { \pi }{ 2 }\)] and find the value of ]0, \(\frac { \pi }{ 2 }\)[

Question 8.
Discuss continuity of the function at x = 0
CBSE Sample Papers for Class 12 Maths Paper 6 Q8

Question 9.
Find the coordinate of point of intersection of lines
CBSE Sample Papers for Class 12 Maths Paper 6 Q9

Question 10.
If P(A) = \(\frac { 1 }{ 4 }\), P(A | B) = \(\frac { 1 }{ 2 }\), P(B | A) = \(\frac { 2 }{ 3 }\) then find P(B).

Question 11.
If 3 tan-1x + cot-1x = π then find the value of x.

Question 12.
CBSE Sample Papers for Class 12 Maths Paper 6 Q12

SECTION C

Question 13.
CBSE Sample Papers for Class 12 Maths Paper 6 Q13

Question 14.
CBSE Sample Papers for Class 12 Maths Paper 6 Q14

Question 15.
CBSE Sample Papers for Class 12 Maths Paper 6 Q15

Question 16.
CBSE Sample Papers for Class 12 Maths Paper 6 Q16

Question 17.
CBSE Sample Papers for Class 12 Maths Paper 6 Q17

Question 18.
Solve the differential equation (1 + y2) dx = (tan-1 y – x) dy ; y(0) = 0

Question 19.
The scalar product of the vector \(\hat { i } +\hat { j } +\hat { k }\) with a unit vector along the sum of vectors \(2\hat { i } +4\hat { j } -5\hat { k }\) and \(\lambda \hat { i } +2\hat { j } +3\hat { k }\) is equal to one. Find the value of λ.

Question 20.
CBSE Sample Papers for Class 12 Maths Paper 6 Q20

Question 21.
A and B throw a die alternately till one of them gets a 5 and wins the game. F ind their respective probabilities of winning if A starts the game. Why gambling is not a good way of earning money?

Question 22.
In a bolt factory, machine A, B and C manufacture respectively 25%, 35% and 40% of the bolts. of their output, 5%, 4% and 2% are respectively defective bolts. A bolt is drawn at random from the total production and is found to be defective. Find the probability that it is manufactured by machine B.

Question 23.
A binary operation * on the set {0, 1, 2, 3, 4, 5} is defined as
CBSE Sample Papers for Class 12 Maths Paper 6 Q23
Show that zero is the identity element for. this operation and each non-zero element ‘a’ of the set is invertible with 6 – a being the inverse of a.

SECTION D

Question 24.
CBSE Sample Papers for Class 12 Maths Paper 6 Q24

Question 25.
Prove that the radius of the right circular cylinder of greatest curved surface area which can be inscribed in a given cone is half of that of the cone.
OR
An open box with square base is to be made out of a given quantity of sheet of area a2 sq.units. Show that the maximum volume of the box is \(\frac { { a }^{ 3 } }{ 6\surd 3 }\) cubic units.

Question 26.
Using integration find the area bounded by the lines x + 2y = 2, y – x = 1 and 2x + y = 7.
OR
Find the area of the region in the first quadrant enclosed by the y-axis, the line y = x and the circle x2 + y2 = 32 using integration.

Question 27.
A dealer wishes to purchase a number of fans and sewing machines. He has only ₹ 5760 to invest and has space for at most 20 items. A fan cost him ₹ 360 and a sewing machine ₹ 240. On selling he get a profit of ₹ 22 on a fan and ₹ 18 on a sewing machine. Assuming that he can sell all the items that he store, how should he invest his money in order to maximize profit? Formulate this as L.P.P. and solve it graphically.

Question 28.
Find the image of the point (1, 2, 3) in the plane x + 2y + 4z = 38.
OR
Find the equation of the plane passing through the points A(3, -1, 2), B (5, 2, 4) and C(-1, -1, 6). Also find the distance of the point P(6, 5, 9) from the plane.

Question 29.
Show that the differential equation x dy – y dx = \(\sqrt { { x }^{ 2 }+{ y }^{ 2 } }\) dx is homogeneous and hence solve it.

Solutions

Solution 1.
A = [aij]2×3
B = [bij]3×4
Order of AB = 2 x 4
Order of (AB)’ = 4 x 2

Solution 2.
CBSE Sample Papers for Class 12 Maths Paper 6 S2

Solution 3.
CBSE Sample Papers for Class 12 Maths Paper 6 S3

Solution 4.
Let the point is (x, y)
y = x2
CBSE Sample Papers for Class 12 Maths Paper 6 S4

Solution 5.
CBSE Sample Papers for Class 12 Maths Paper 6 S5

Solution 6.
CBSE Sample Papers for Class 12 Maths Paper 6 S6
CBSE Sample Papers for Class 12 Maths Paper 6 S6.1

Solution 7.
CBSE Sample Papers for Class 12 Maths Paper 6 S7

Solution 8.
CBSE Sample Papers for Class 12 Maths Paper 6 S8
CBSE Sample Papers for Class 12 Maths Paper 6 S8.1

Solution 9.
CBSE Sample Papers for Class 12 Maths Paper 6 S9

Solution 10.
CBSE Sample Papers for Class 12 Maths Paper 6 S10

Solution 11.
CBSE Sample Papers for Class 12 Maths Paper 6 S11

Solution 12.
CBSE Sample Papers for Class 12 Maths Paper 6 S12

Solution 13.
CBSE Sample Papers for Class 12 Maths Paper 6 S13
CBSE Sample Papers for Class 12 Maths Paper 6 S13.1

Solution 14.
CBSE Sample Papers for Class 12 Maths Paper 6 S14
CBSE Sample Papers for Class 12 Maths Paper 6 S14.1
CBSE Sample Papers for Class 12 Maths Paper 6 S14.2

Solution 15.
y = sinpt
x = sint
CBSE Sample Papers for Class 12 Maths Paper 6 S15
CBSE Sample Papers for Class 12 Maths Paper 6 S15.1

Solution 16.
CBSE Sample Papers for Class 12 Maths Paper 6 S16
CBSE Sample Papers for Class 12 Maths Paper 6 S16.1
CBSE Sample Papers for Class 12 Maths Paper 6 S16.2

Solution 17.
CBSE Sample Papers for Class 12 Maths Paper 6 S17

Solution 18.
CBSE Sample Papers for Class 12 Maths Paper 6 S18
CBSE Sample Papers for Class 12 Maths Paper 6 S18.1

Solution 19.
CBSE Sample Papers for Class 12 Maths Paper 6 S19
CBSE Sample Papers for Class 12 Maths Paper 6 S19.1

Solution 20.
CBSE Sample Papers for Class 12 Maths Paper 6 S20

Solution 21.
CBSE Sample Papers for Class 12 Maths Paper 6 S21
CBSE Sample Papers for Class 12 Maths Paper 6 S21.1

Solution 22.
Let E1 is the event the bolt is manufactured by machine A
E2 is the event the bolt is manufactured by machine B
E3 is the event the bolt is manufactured by machine C
A is the event bolt drawn is defective
CBSE Sample Papers for Class 12 Maths Paper 6 S22

Solution 23.
CBSE Sample Papers for Class 12 Maths Paper 6 S23
CBSE Sample Papers for Class 12 Maths Paper 6 S23.1

Solution 24.
CBSE Sample Papers for Class 12 Maths Paper 6 S24
CBSE Sample Papers for Class 12 Maths Paper 6 S24.1

Solution 25.
CBSE Sample Papers for Class 12 Maths Paper 6 S25
CBSE Sample Papers for Class 12 Maths Paper 6 S25.1

Solution 26.
x + 2y = 2 ……. (1)
y – x = 1 …… (2)
2x + y = 7 ……. (3)
From (1) and (2), (0, 1)
From (2) and (3), (2, 3)
From (1) and (3), (4, -1)
CBSE Sample Papers for Class 12 Maths Paper 6 S26
CBSE Sample Papers for Class 12 Maths Paper 6 S26.1
CBSE Sample Papers for Class 12 Maths Paper 6 S26.2

Solution 27.
Let dealer purchases x fans and y sewing machines.
Objective function is maximize profit Z = 22x + 18y
CBSE Sample Papers for Class 12 Maths Paper 6 S27

Solution 28.
CBSE Sample Papers for Class 12 Maths Paper 6 S28
CBSE Sample Papers for Class 12 Maths Paper 6 S28.1

Solution 29.
CBSE Sample Papers for Class 12 Maths Paper 6 S29

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