The ISC Class 12 Maths paper was conducted on 16th March 2015. The exam started at 2 PM. The paper was of 3 hours of time duration and 100 Marks. Students can find the ISC Class 12 Maths Question Paper Solution 2015 on this page. Going through the answers after solving the ISC Class 12 Maths Previous Year Question Papers will help students in understanding their strong and weak points. They will also be able to analyse the time taken by them in solving the paper. Students are advised to have a deep look at the ISC Class 12 Maths Question Paper Solution 2015. They can download the ISC Class 12 Maths Question Paper and Solution pdf 2015 from the link below.
ISC Class 12 Maths Question Paper 2015
ISC Class 12 Maths Question Paper Solution 2015 PDF
Science Stream students can also access the Solved ISC Class 12 Previous Year Question Papers with Solutions for all subjects compiled at one place. They can have a look at the ISC Class 12 Maths Question Paper Solution 2015 below.
Difficult Topics of ISC Class 12 Maths Paper 2015
Topics which students found difficult while solving the Maths 2015 paper are mentioned below:
 Determinant properties and their use.
 Conics (parabola, ellipse, hyperbola)
 Application of L Hospitalâ€™s rule.
 Indefinite Integrals, Definite Integrals.
 Inverse trigonometric functions.
 Area of curves.
 Probability (Both sections) and probability distribution.
 Differential equations.
 Complex numbers.
 Vectors.
 3D plane & straightline.
 Annuities.
 Linear programming.
 Regression lines.
Confusing ISC Class 12 Maths Questions 2015
Maths concepts between which students got confused during the exam are mentioned below.
 Conics (parabola, ellipse, hyperbola)
 Open & closed intervals for Mean value theorem.
 Conversion of inverse trigonometric functions.
 Regression coefficient byx & bxy and r.
 Differential equations (Linear & Homogeneous form)
 Geometrical problem in vectors.
 Annuity due & ordinary annuity.
 Bankerâ€™s discount & bankerâ€™s gain.
 Price relative and aggregate method in Index No.
 Shortest distance between skew lines and parallel lines.
 Probability distribution (conceptual problem)
ISC Class 12 Maths Question Paper Solution 2015
Question 1:
(i) Find the value of k if
and M^{2} â€“ kM â€“ I_{2} = 0
(ii) Find the equation of an ellipse whose latus rectum is 8 and eccentricity is 1/3.
(iii) Solve: cos^{1}(sin cos^{1}x) = Ï€/6
(iv) Using Lâ€™Hospitalâ€™s rule, evaluate:
(v) Evaluate:
(vi) Evaluate:
(vii) The two lines of regressions are 4x + 2y â€“ 3 = 0 and 3x + 6y + 5 = 0. Find the correlation coefficient between x and y.
(viii) A card is drawn from a well shuffled pack of playing cards. What is the probability that it is either a spade or an ace or both?
(ix) If 1, w and w^{2} are the cube roots of unity, prove that
(x) Solve the differential equation: sin^{1 }dy/dx = x+y
Answer:
Question 2:
find AB and use this result to solve the following system of equations:
x â€“ 2y + 3z = 6, x + 4y + z = 12, x â€“ 3y + 2z = 1
Answer: (a)
(b)
Question 3:
(a) Solve the equation for x:
(b) A, B and C represent switches in â€˜onâ€™ position and A’, B’ and C’ represent them in â€˜offâ€™ position. Construct a switching circuit representing the polynomial ABC + ABâ€™C + Aâ€™Bâ€™C. Using Boolean Algebra, prove that the given polynomial can be simplified to C(A + Bâ€™). Construct an equivalent switching circuit.
Answer: (a)
(b) ABC+ABâ€™C +Aâ€™Bâ€™C
= ACB+ACBâ€™ + Aâ€™Bâ€™C
=AC ( B+Bâ€™) + Aâ€™Bâ€™C (B+Bâ€™ =1)
= AC + Aâ€™Bâ€™C
= (A+Aâ€™Bâ€™)C
=(A+Aâ€™)(A+Bâ€™) C
= (A+Bâ€™) C
Question 4:
(a) Verify Lagrangeâ€™s Mean Value Theorem for the following function:
f(x) = 2 sin x + sin2x on [0, Ï€]
(b) Find the equation of the hyperbola whose foci are (0, Â±âˆš10) and passing through the point (2, 3).
Answer: (a) f(x) = (2 sinx + sin 2x) is continuous in [ 0, Ï€]
f ‘(x) exists in (0,Ï€)
f ‘(x) = 2cos x + 2cos2x f(0) =0, f(Ï€) =0
All the conditions of Lagrangeâ€™s Mean Value theorem are satisfied there exist ‘ c ‘ in ( 0, Ï€)
such that
c = Ï€ /3 which lies between 0 to Ï€ , hence, LMV theorem is verified.
(b)
Question 5:
(a)
(b) Show that the rectangle of maximum perimeter which can be inscribed in a circle of radius 10 cm is a square of side 10âˆš2 cm.
Answer:
Question 6:
(a)
(b) Find the smaller area enclosed by the circle x^{2} + y^{2} and the line x + y = 2.
Answer: (a)
Question 7:
(a) Given that the observations are:
(9, 4), (10, 3), (11, 1), (12, 0), (13, 1), (14, 3), (15, 5), (16, 8).
Find the two lines of regression and estimate the value of y when x = 13Â·5.
(b) In a contest the competitors are awarded marks out of 20 by two judges. The scores of the 10 competitors are given below. Calculate Spearmanâ€™s rank correlation.
Competitors 
A 
B 
C 
D 
E 
F 
G 
H 
I 
J 
Judge A 
2 
11 
11 
18 
6 
5 
8 
16 
13 
15 
Judge B 
6 
11 
16 
9 
14 
20 
4 
3 
13 
17 
Answer: (a)
x = 0Â·596 y + 11Â·83
y, when x = 13Â·5
y = 1Â·63x – 19Â·25
y = 1Â·63 Ã— 13Â·5 – 19Â·25 = 2Â·755 = 2Â·76
(b)
Judge A 
Judge B 
R_{x} 
R_{y} 
d = R_{x }– R_{y} 
d^{2} 
2 
6 
10 
8 
2 
4 
11 
11 
5.5 
6 
0.5 
0.25 
11 
16 
5.5 
3 
2.5 
6.25 
18 
9 
1 
7 
6 
36 
6 
14 
8 
4 
4 
16 
5 
20 
9 
1 
8 
64 
8 
4 
7 
9 
2 
4 
16 
3 
2 
10 
8 
64 
13 
13 
4 
5 
1 
1 
15 
17 
3 
2 
1 
1 
d^{2 }= 196.5 
Question 8:
(a) An urn contains 2 white and 2 black balls. A ball is drawn at random. If it is white, it is not replaced into the urn. Otherwise, it is replaced with another ball of the same colour. The process is repeated. Find the probability that the third ball drawn is black.
(b) Three persons A, B and C shoot to hit a target. If A hits the target four times in five trials, B hits it three times in four trials and C hits it two times in three trials, find the probability that:
(i) Exactly two persons hit the target.
(ii) At least two persons hit the target.
(iii) None hit the target.
Answer:
Question 9:
Answer: (a)
(b)
Question 10:
(a) Using vectors, prove that angle in a semicircle is a right angle.
(b) Find the volume of a parallelepiped whose edges are represented by the vectors:
Answer:
Question 11:
(a) Find the equation of the plane passing through the intersection of the planes:
x + y + z +1 = 0 and 2x – 3y + 5z – 2 = 0 and the point ( 1, 2, 1).
(b)
Answer: (a) Equation of plane passing through the intersection of the given planes is:
(x + y + z + 1) + k(2x 3y + 5z 2) = 0
If this plane passes through (1,2,1) then
(1+2+1+1) + k( 2 â€“ 6 + 5 2) = 0
3 = 5k
K = 3/5
5(x+y+z+1) + 3(2x3y+5z 2) = 0
11x 4y + 20z 1=0
Or equivalent form
(b)
âˆ´ shortest distance = 0.415
Question 12:
(a) Box I contains two white and three black balls. Box II contains four white and one black balls and box III contains three white and four black balls. A dice having three red, two yellow and one green face, is thrown to select the box. If red face turns up, we pick up box I, if a yellow face turns up we pick up box II, otherwise, we pick up box III. Then, we draw a ball from the selected box. If the ball drawn is white, what is the probability that the dice had turned up with a red face?
(b) Five dice are thrown simultaneously. If the occurrence of an odd number in a single dice is considered a success, find the probability of maximum three successes.
Answer:
Question 13:
(a) Mr. Nirav borrowed â‚¹ 50,000 from the bank for 5 years. The rate of interest is 9% per annum compounded monthly. Find the payment he makes monthly if he pays back at the beginning of each month.
(b) A dietician wishes to mix two kinds of food X and Y in such a way that the mixture contains at least 10 units of vitamin A, 12 units of vitamin B and 8 units of vitamin C. The vitamin contents of one kg food is given below:
Food 
Vitamin A 
Vitamin B 
Vitamin C 
X 
1 Unit 
2 Unit 
3 Unit 
Y 
2 Unit 
2 Unit 
1 Unit 
One kg of food X costs â‚¹ 24 and one kg of food Y costs â‚¹ 36. Using Linear Programming, find the least cost of the total mixture which will contain the required vitamins.
Answer:
Question 14:
(a) A bill for â‚¹ 7,650 was drawn on 8th March, 2013, at 7 months. It was discounted on 18th May, 2013 and the holder of the bill received â‚¹ 7,497. What is the rate of interest charged by the bank?
(b) The average cost function, AC for a commodity is given by AC = x + 5 + 36/x, in terms of output x. Find:
(i) The total cost, C and marginal cost, MC as a function of x.
(ii) The outputs for which AC increases.
Answer: (a) Face value of the bill= â‚¹ 7650 = A
Discounted value of the bill = â‚¹ 7497
Bankers discount = (7650 – 7497)
= â‚¹153
Nominal due date is 8th October (âˆ´ 8th October + 3 days of grace).
Legal due date of the bill is 11 October
Number of unexpired days from 8 May to 11 October is 146 days n = (2/5)year
Bankers discount = Ani
153 = 7650 x r x (2/5)
r =(1/20) = 0.05 r = 5%
(b)
Question 15:
(a) Calculate the index number for the year 2014, with 2010 as the base year by the weighted aggregate method from the following data:
Commodity 
Price in Rs 
Weight 

2010 
2014 

A 
2 
4 
8 
B 
5 
6 
10 
C 
4 
5 
14 
D 
2 
2 
19 
(b) The quarterly profits of a small scale industry (in thousands of rupees) is as follows :
Year 
Quarter 1 
Quarter 2 
Quarter 3 
Quarter 4 
2012 
39 
47 
20 
56 
2013 
68 
59 
66 
72 
2014 
88 
60 
60 
67 
Answer: (a)
Commodity 
2010 
2014 
p_{1}w 
p_{0}w 

p_{0} 
w 
p_{1} 
w 

A 
2 
8 
4 
8 
32 
16 
B 
5 
10 
6 
10 
60 
50 
C 
4 
14 
5 
14 
70 
56 
D 
2 
19 
2 
19 
38 
38 
200 
60 
The index number for the year 2014 with 2010 as the base year is 200/160 x 100 = 125
(b)
Year 
Quarter 
Quarterly Profit 
4 Yearly Moving Total 
4 Yearly Average 
4 Yearly Centered Moving Average 
2010 
1 
39 

2 
47 

162 
40.5 

3 
20 
44.125 

191 
47.75 

4 
56 
49.25 

203 
50.75 

2013 
1 
68 
56.5 

249 
62.25 

2 
59 
64.25 

265 
66.25 

3 
66 
68.75 

285 
71.25 

4 
72 
71.375 

286 
71.5 

2014 
1 
88 
70.75 

280 
70 

2 
60 
69.375 

275 
68.75 

3 
60 

4 
67 
ISC Class 12 Maths Question Paper Solution 2015 must have helped students in analysing their current level of exam preparation. Keep practising more questions and stay tuned to BYJUâ€™S for the latest update on ICSE/CBSE/State Boards/Competitive exams. Also, download the BYJUâ€™S App to get interactive study related videos.
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