The ISC Class 12 Maths exam was conducted on 15th March 2017 for 100 marks and 3 hours of time duration. The exam started at 2 PM. Many times students get stuck while practising the questions from previous years ISC Class 12 Maths Question Papers. So, to help them, we have provided the ISC Class 12 Maths Question Paper Solution 2017 along with marking scheme. The answers are provided in detail, along with step marking for each question. Students can download the ISC Class 12 Maths Question Paper and Solution pdf 2017 from the link below.
ISC Class 12 Maths Question Paper 2017
ISC Class 12 Maths Question Paper Solution 2017 PDF
Students can also access the Solved ISC Class 12 Previous Year Question Papers for Maths, Maths, Maths and Biology subjects compiled at one place. They can have a look at the ISC Class 12 Maths Question Paper Solution 2017 below.
Difficult Topics of ISC Class 12 Maths Paper 2017
Topics which students found difficult while solving the Maths 2017 paper are mentioned below:
 Conic Section in general
 Integrals, definite Integrals and curve sketching
 Vectors and Interchange of vector equation to Cartesian form (vice versa) of plane and Straightline equations of 3D Geometry and their applications
 Conditional Probability and their applications, Binomial Probability distribution
 Complex numbers and Inverse circular functions
 Maxima and Minima.
Confusing ISC Class 12 Maths Questions 2017
Maths concepts on which students got confused during the exam are mentioned below.
 Hyperbola and Ellipse: Their standard form and other relations
 Lagrange’s Mean Value Theorem
 Product and sum rule of probability and concepts of dependent and independent events
 Definite Integrals and their properties
 Dot and Cross product of vectors
 Present value of annuity and Amount of annuity at the end of the period
ISC Class 12 Maths Question Paper Solution 2017
Question 1:
(a) The regression equation y on x.
(b) What is the most likely value of y when x = 60?
(c) What is the coefficient of correlation between x and y?
(viii) A problem is given to three students whose chances of solving it are 1/4,1/5 and 1/3 respectively. Find the probability that the problem is solved.
Answer:
Question 2:
Answer:
Question 3:
(a) Solve the equation for x:
sin^{1} x + sin^{1} (1–x) = cos^{1}x, x ≠ 0
(b) If A, B and C are the elements of Boolean algebra, simplify the expression
(Aʹ+Bʹ)(A + Cʹ) + Bʹ (B + C). Draw the simplified circuit.
Answer:
Question 4:
(a) Verify Lagrange’s mean value theorem for the function:
f(x) = x (1 – log x) and find the value of ‘c’ in the interval [1, 2]
(b) Find the coordinates of the centre, foci and equation of directrix of the hyperbola
x^{2}–3y^{2} – 4x = 8.
Answer: (a)
(b)
Question 5:
(a) If y = cos (sin x), show that:
(b) Show that the surface area of a closed cuboid with square base and given volume is minimum when it is a cube.
Answer:
Question 6:
(a)
(b) Draw a rough sketch of the curve y^{2} = 4x and find the area of the region enclosed by the curve and the line y = x.
Answer:
Question 7:
(a) Calculate the Spearman’s rank correlation coefficient for the following data and interpret the result:
x 
35 
54 
80 
95 
73 
73 
35 
91 
83 
81 
y 
40 
60 
75 
90 
70 
75 
38 
95 
75 
70 
(b) Find the line of best fit for the following data, treating x as dependent variable (Regression equation x on y):
x 
14 
12 
13 
14 
16 
10 
13 
12 
y 
14 
23 
17 
24 
18 
25 
23 
24 
Hence, estimate the value of x when y = 16.
Answer: (a)
(b)
x 
y 
dx 
dy 
dx^{2} 
dy^{2} 
dx.dy 
14 
14 
1 
7 
1 
49 
7 
12 
23 
1 
2 
1 
4 
2 
13 
17 
0 
4 
0 
16 
0 
14 
24 
1 
3 
1 
9 
3 
16 
18 
3 
3 
9 
9 
9 
10 
25 
3 
4 
9 
16 
12 
13 
23 
0 
2 
0 
4 
0 
12 
24 
1 
3 
1 
9 
3 
Question 8:
(a) In a class of 60 students, 30 opted for Mathematics, 32 opted for Biology and 24opted for both Mathematics and Biology. If one of these students is selected at random, find the probability that:
(i) The student opted for Mathematics or Biology.
(ii) The student has opted neither Mathematics nor Biology.
(iii) The student has opted Mathematics but not Biology.
(b) Bag A contains 1 white, 2 blue and 3 red balls. Bag B contains 3 white, 3 blue and 2red balls. Bag C contains 2 white, 3 blue and 4 red balls. One bag is selected at random and then two balls are drawn from the selected bag. Find the probability that the balls drawn are white and red.
Answer: (a) Let A: event that candidates opted Mathematics.
Let B: event that candidates opted Biology.
(b) Probability of selecting each bag = 1/3.
A 
B 
C 

White 
1 
3 
2 
Blue 
2 
3 
3 
Red 
3 
2 
4 
Prob of (1W and 1R) 
1×^{3}C_{1 }/ ^{6}C_{2} 
^{3}C_{1}×^{2}C_{1 }/ ^{8}C_{2} 
^{2}C_{1}×^{4}C_{1 }/ ^{9}C_{2} 
Question 9:
(a) Prove that locus of z is circle and find its centre and radius if (𝑧𝑖) / (𝑧−1) is purely imaginary.
(b) Solve: (𝑥^{2}−𝑦𝑥^{2})𝑑y +(𝑦^{2}+𝑥y^{2}) 𝑑𝑥 = 0
Answer:
Question 10:
Answer: (a)
(b)
Question 11:
(a) Show that the lines
intersect. Find the coordinates of their point of intersection.
(b) Find the equation of the plane passing through the point (1,−2,1) and perpendicular to the line joining the points A (3, 2, 1) and B (1, 4, 2).
Answer: (a)
(b) Any plane passing through the point (1, −2, 1)
a(x −1) + b(y+2)+ c(𝑧−1) = 0
D.R. of normal to the plane: a, b, c
This plane is perpendicular to the line joining points A (3, 2, 1), B (1, 4, 2)
∴𝐷. 𝑅′′ of line perpendicular to 3−1, 2−4,1−2 i.e, 2−2, −1
∵ D. ’R’ of normal to the plane and D.R’ line perpendicular to the plane are proportional.
a/2 = b/(−2) = c/(−1) = k
a = 2k, b = −2k, c = −k
∴ Required equation of the plane is:
2k (x−12k (y+2)−k(z−1)=0
⇒2x−2−2y−4−z+1=0
2x−2y−z−5=0
Question 12:
(a) A fair die is rolled. If face 1 turns up, a ball is drawn from Bag A. If face 2 or 3 turns up, a ball is drawn from Bag B. If face 4 or 5 or 6 turns up, a ball is drawn from Bag C. Bag A contains 3 red and 2 white balls, Bag B contains 3 red and 4 white balls and Bag C contains 4 red and 5 white balls. The die is rolled, a Bag is picked up and a ball is drawn. If the drawn ball is red, what is the probability that it is drawn from Bag B?
(b) An urn contains 25 balls of which 10 balls are red and the remaining green. A ball is drawn at random from the urn, the colour is noted and the ball is replaced. If 6 balls are drawn in this way, find the probability that:
(i) All the balls are red.
(ii) Not more than 2 balls are green.
(iii) Number of red balls and green balls are equal.
Answer:
Question 13:
(a) A machine costs₹ 60,000 and its effective life is estimated to be 25 years. A sinking fund is to be created for replacing the machine at the end of its life time when its scrap value is estimated as ₹5,000. The price of the new machine is estimated to be 100%more than the price of the present one. Find the amount that should be set aside at the end of each year, out of the profits, for the sinking fund if it accumulates at an interest of 6% per annum compounded annually.
(b) A farmer has a supply of chemical fertilizer of type A which contains 10% nitrogenand 6% phosphoric acid and of type B which contains 5% nitrogen and 10%phosphoric acid. After soil test, it is found that at least 7 kg of nitrogen and the same quantity of phosphoric acid is required for a good crop. The fertilizer of type A costs₹5.00 per kg and the type B costs ₹8.00 per kg. Using Linear programming, find how many kilograms of each type of the fertilizer should be brought to meet the requirement and for the cost to be minimum. Find the feasible region in the graph.
Answer: (a)
(b)
Question 14:
(a) The demand for a certain product is represented by the equation p = 500 + 25x − 𝑥^{2}/3 in rupees where x is the number of units and p is the price per unit. Find:
(i) Marginal revenue function.
(ii) The marginal revenue when 10 units are sold.
(b) A bill of ₹60,000 payable 10 months after date was discounted for ₹57,300 on 30th June, 2007. If the rate of interest was 11¼% per annum, on what date was the bill drawn?
Answer: (a)
(b)
Question 15:
(a) The price relatives and weights of a set of commodities are given below:
Commodity 
A 
B 
C 
D 
Price Relative 
125 
120 
127 
119 
Weights 
x 
2x 
y 
y+3 
If the sum of the weights is 40 and the weighted average of price relatives index number is 122, find the numerical values of x and y.
(b) Construct 3 yearly moving averages from the following data and show on a graph against the original data:
Years 
2000 
2001 
2001 
2003 
2004 
2005 
2006 
2007 
2008 
2009 
Annual Sales in Lakhs 
18 
22 
20 
26 
30 
22 
24 
28 
32 
35 
Answer: (a)
Commodity 
PR = R 
Weight 
RW 
A 
125 
x 
125x 
B 
120 
2x 
240x 
C 
127 
y 
127y 
D 
119 
y+3 
119y+357 
3x + 2y + 3 = 40
3x + 2y = 37 —————— (1)
Index number: 122 = 365𝑥+246𝑦+357/40
365x + 246y = 4880 – 357
365x +246y = 4523 —– (2)
Solving (1) & (2) x = 7, y = 8
(b)
Year 
Annual Sales 
3 Yearly Moving total 
3 Yearly Moving average 
2000 
18 
– 
– 
2001 
22 
60 
20 
2002 
20 
68 
22.7 
2003 
26 
76 
25.3 
2004 
30 
78 
26 
2005 
22 
76 
25.3 
2006 
24 
74 
24.7 
2007 
28 
84 
28 
2008 
32 
95 
31.7 
2009 
35 
– 
– 
We hope, solving ISC Class 12 Maths Question Paper Solution 2017 has boosted students’ exam preparation. Be continuous in your studies and keep practising more questions. Stay tuned to BYJU’S for the latest update on ICSE/CBSE/State Boards/Competitive exams. Also, download the BYJU’S App for interactive study videos.
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