ncert.nic.in : Class XII Mathematics Question Paper Model National Council of Education Research & Training

Board : National Council of Education Research & Training
Subject : Class XII Mathematics
Document type : Model Question Paper
Website : ncert.nic.in

Download Model/ Sample Question Papers : https://www.pdfquestion.in/uploads/6162-Math.pdf

NCERT Model Question Paper Mathematics

Class XII
Time Allowed : 3 hours
Max Marks : 100

Related : National Council Of Educational Research & Training Class XII Chemistry Question Paper Model : www.pdfquestion.in/6158.html

General Instructions

(i) The question paper consists of three parts A, B and C.Each question of each
part is compulsory.
(ii) Part A Question number 1 to 20 are of 1 mark each.

(iii) Part B Question number 21 to 31 are of 4 marks each
(iv) Question number 32 to 37 are of 6 marks each

Model Questions

Part A
Choose the correct answer in each of the questions from 1 to 20. Each of these question
contain 4 options with just one correct option.
Part A :
Choose the correct answer in each of the questions from 1 to 20. Each of these question contain 4 options with just one correct option.
1. Let N be the set of natural numbers and R be the relation in N defined as
R = {(a, b) : a = b – 2, b > 6}. Then
(A) (2, 4) < R
(B) (3, 8) < R
(C) (6, 8) > R
(D) (8, 7) > R.

2. The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is
(A) 27
(B) 18
(C) 81
(D) 512

3. Let A be a square matrix of order 3 × 3, then kA is equal to
(A) k A
(B) k2 A
(C) k3 A
(D) 3k A

4. The rate of change of the area of a circle with respect to its radius r when r = 6 is
(A) 10 p
(B) 12 p
(C) 8 p
(D) 11 p

5. The interval in which y = x2 e–x is increasing is
(A) (– 8, 8)
(B) (–2, 0)
(C) (2, 8)
(D) (0, 2)

6. xsec2 x dx is equal to
(A) tanx2 + C
(B) tan2x + C
(C) x tanx – log sin x
(D) x tanx + log cos x + C

7. Area bounded by the curve y = sinx between x = 0 and x = 2p is
(A) 2sq. units
(B) 4 sq. units
(C) 8sq. units
(D) 16sq. units

8. The general solution of the differential equation dy ex y dx = + is
(A) ex + e–y = C
(B) ex + ey = C
(C) e–x + ey = C
(D) e–x + e–y = C

9. The vector 2 ˆi + a ˆj + ˆ k is perpendicular to the vector 2 ˆi – ˆj – kˆ if
(A) a = 5
(B) a = – 5
(C) a = – 3
(D) a = 3

10. The angle between the planes r .(3iˆ – 4 ˆj +5kˆ) r = 0 and r .(2iˆ – ˆj – 2kˆ) r is
(A) 3 /p
(B) 2/p
(C) 6/p
(D) 4

The probability of obtaining an even prime numbr on each die, when a pair of dice is rolled is
(A) 0
(B) 1/3
(C) 1/12
(D) 1/36

Part – B :

1. Find the solution of the differential equation (x2 + y2) dx = 2xy dy
OR
Find the equation of the curve passing through the origin and satisfying the differential equation (1 + x2) dy dx + 2xy = 4x

2. If the magnitude of the vectors, a , b , c are 3, 4, 5 respectively and a and b + c , b and ( c + a ), c and ( a + b ) are mutually perpendicular, then find the magnitude of ( a + b + c )

3. Find the equation of the straight line passing through (1, 2, 3) and perpendicular to the plane x + 2y – 5z + 9 = 0
OR
Find the equation of the plane passing through the point (–1, 3, 2) and perpendicular to each of the planes x + 2y + 3z = 5 and 3x + 3y + z = 0

4. A man and his wife appear for an interview for two posts. The probability of husband’s selection is 1/7 and that of the wife’s selection is 1/5 . Find the probability that only one of them will be selected

Part-C :
1. Obtain the inverse of the following matrix using elementary operations
2. Show that the function f given by f (x) = tan–1 (sinx + cosx), x > 0 is always an strictly increasing function in 0, 4
OR
An open box is to be constructed by removing equal squares from each corner of a 3 metre by 8 metre rectangular sheet of aluminium and folding up the sides. Find the volume of the largest such box.

2. Find the area of the region enclosed between the two circles x2+ y2 = 4 and (x – 2)2 + y2 = 4.
OR
Prove that the curves y2 = 4x and x2 = 4y divide the area of the square bounded by x = 0, x = 4, y = 4 and y = 0 into three equal parts.