ncert.nic.in : ISC Mathematics Question Paper Model National Council Of Educational Research & Training

Board : National Council Of Educational Research & Training
Exam : ISC Mathematics
Document Type : Model Question Paper
Website : ncert.nic.in

Download Model/ Sample Question Papers : https://www.pdfquestion.in/uploads/6672-Math.pdf

NCERT Model Question Paper Mathematics

Class XII
Time Allowed : 3 hours
Max Marks: 100

Related : National Council Of Educational Research & Training ISC English Question Paper Model : www.pdfquestion.in/6670.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 :

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.

3. A dietician has to develop a special diet using two foods P and Q. Each packet (containing 30g) of food P contains 12 units of calcium, 4 units of iron, 6 units of cholesterol and 6 units of vitamin A. Each packet of the same quantity of food Q contains 3 units of calcium, 20 units of iron, 4 units of cholesterol, and 3 units of vitamin A. The diet requires atleast 240 units of calcium, atleast 460 units of iron and atmost 300 units of cholesterol. How many packets of each food should be used to minimize the amount of vitamin A in the diet? What is the minimum amount of vitamin A?

4. A doctor is to visit a patient. From the past experience, it is known that the probabilities that he will come by train, bus, scooter or by any other means of transport are respectively 3 , 1 , 1 and 2 10 5 10 5 . The probabilities that he will be late are 1 , 1 and 1 4 3 12 if he comes by train, bus and scooter respectively, but if he comes by other means of transport, then he will not be late. When he arrives, he is late. What is the probability that he comes by train.
OR
Let a pair of dice be thrown and the random variable X be the sum of the numbers that appear on the two dice. Find the mean or expectation of X.