ISC Maths 2013 Class-12 Solved Previous Year Question Papers

ISC Maths 2013 Class-12 Solved Previous Year Question Paper for practice. Step by step Solutions with section-A, B and C. Visit official website CISCE for detail information about ISC Board Class-12 Maths.

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ISC Maths 2013 Class-12 Previous Year Question Papers Solved


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Section-A

Section-B

Section-C


Time Allowed: 3 Hours
Maximum Marks: 100

(Candidates are allowed additional 15 minutes for only reading the paper. They must NOT start writing during this time.)

  • The Question Paper consists of three sections A, B and C.
  • Candidates are required to attempt all questions from Section A and all questions either from Section B or Section C.
  • Section A: Internal choice has been provided in three questions of four marks each and two questions of six marks each.
  • Section B: Internal choice has been provided in two questions of four marks each.
  • Section C: Internal choice has been provided in two questions of four marks each.
  • All working, including rough work, should be done on the same sheet as, and adjacent to the rest of the answer.
  • The intended marks for questions or parts of questions are given in brackets [ ].
  • Mathematical tables and graph papers are provided.

Section – A (80 Marks)

ISC Maths 2013 Class-12 Previous Year Question Papers Solved

Que 1:
(i) If (A – 2I) (A – 3I) = 0, where A=\left(\begin{array}{cc}{4} & {2} \\ {-1} & {x}\end{array}\right) \text { and } I=\left(\begin{array}{ll}{1} & {0} \\ {0} & {1}\end{array}\right), find the value of x. [3] (ii) Find the value (s) of k so that the line 2x + y + k = 0 may touch the hyperbola 3x2 – y2 = 3. [3] (iii) Prove that: \tan ^{-1} \frac{1}{4}+\tan ^{-1} \frac{2}{9}=\frac{1}{2} \sin ^{-1} \frac{4}{5} [3] (iv) Using L’Hospital’s Rule, evaluate: [3] \lim _{x \rightarrow 0}\left(\frac{e^{x}-e^{-x}-2 x}{x-\sin x}\right)
(v) Evaluate: \int \frac{1}{x+\sqrt{x}} d x [3] (vi) Evaluate: \int_{0}^{1} \log \left(\frac{1}{x}-1\right) d x [3] (vii) Two regression lines are represented by 4x + 10y = 9 and 6x + 3y = 4. Find the line of regression of y on x. [3] (viii) If 1, w and w2 are the cube roots of unity, evaluate: (1 – w4 + w8) (1 – w8 + w16) [3] (ix) Solve the differential equation: [3] \log \left(\frac{d y}{d x}\right)=2 x-3 y
(x) If two balls are drawn from a bag containing three red balls and four blue balls, find the probability that: [3] (a) They are of the same colour
(b) They are of different colours
Solution 1:
ISC Class 12 Maths Previous Year Question Papers Solved 2013 Q1
ISC Class 12 Maths Previous Year Question Papers Solved 2013 Q1.1
ISC Class 12 Maths Previous Year Question Papers Solved 2013 Q1.2
ISC Class 12 Maths Previous Year Question Papers Solved 2013 Q1.3
ISC Class 12 Maths Previous Year Question Papers Solved 2013 Q1.4
ISC Class 12 Maths Previous Year Question Papers Solved 2013 Q1.5
ISC Class 12 Maths Previous Year Question Papers Solved 2013 Q1.6
ISC Class 12 Maths Previous Year Question Papers Solved 2013 Q1.7

Que 2:
(a) Using properties of determinants, prove that: [5]
\left|\begin{array}{ccc}{x} & {y} & {z} \\ {x^{2}} & {y^{2}} & {z^{2}} \\ {y+z} & {z+x} & {x+y}\end{array}\right|=(x-y)(y-z)(z-x)(x+y+z)
(b) Find A-1, where A=\left[\begin{array}{ccc}{4} & {2} & {3} \\ {1} & {1} & {1} \\ {3} & {1} & {-2}\end{array}\right]
Hence, solve the following system of linear equations: [5]
4x + 2y + 3z = 2
x + y + z = 1
3x + y – 2z = 5
Solution 2:
ISC Class 12 Maths Previous Year Question Papers Solved 2013 Q2
ISC Class 12 Maths Previous Year Question Papers Solved 2013 Q2.1
ISC Class 12 Maths Previous Year Question Papers Solved 2013 Q2.2
ISC Class 12 Maths Previous Year Question Papers Solved 2013 Q2.3

Que 3:
(a) Solve for x: \sin ^{-1} x+\sin ^{-1}(1-x)=\cos ^{-1} x. [5] (b) Construct a circuit diagram for the following Boolean Function:
(BC + A) (A’B’ + C) + A’B’C’
Using laws of Boolean Algebra, simplify the function and draw the simplifed circuit. [5]
Solution 3:
ISC Class 12 Maths Previous Year Question Papers Solved 2013 Q3
ISC Class 12 Maths Previous Year Question Papers Solved 2013 Q3.1

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Que 4:
(a) Verify Lagrange’s Mean Value Theorem for the function f(x)=\sqrt{x^{2}-x} in the interval [1, 4]. [5] (b) From the following information, find the equation of the Hyperbola and the equation of its Transverse Axis.
Focus: (-2, 1), Directrix: 2x – 3y + 1 = 0, e=\frac{2}{\sqrt{3}} [5] Solution 4:
ISC Class 12 Maths Previous Year Question Papers Solved 2013 Q4
ISC Class 12 Maths Previous Year Question Papers Solved 2013 Q4.1
ISC Class 12 Maths Previous Year Question Papers Solved 2013 Q4.2
Which is the required equation of the hyperbola
Transverse axis is ⊥ to directrix
Equation of transverse axis be 3x + 2y + k = 0 ……(ii)
Focus (-2, 1) lies on transverse axis
3 × (-2) + 2 × 1 + k = 0
⇒ -4 + k = 0
⇒ k = 4
Now putting the value of k = 4 in (ii), we have
Equation of transverse axis is 3x + 2y + 4 = 0

Que 5:
(a) If y = (cot-1x)2, show that \left(1+x^{2}\right)^{2} \frac{d^{2} y}{d x^{2}}+2 x\left(1+x^{2}\right) \frac{d y}{d x}=2 [5] (b) Find the maximum volume of the blinder which can be inscribed in a sphere of radius 3√3 cm. (Leave the answer in terms of π).
Solution 5:
ISC Class 12 Maths Previous Year Question Papers Solved 2013 Q5
ISC Class 12 Maths Previous Year Question Papers Solved 2013 Q5.1
ISC Class 12 Maths Previous Year Question Papers Solved 2013 Q5.2

Que 6:
(a) Evaluate: \frac{\cos ^{-1} x}{x^{2}} d x [5] (b) Find the area bounded by the curve y = 2x – x2, and the line y = x. [5] Solution 6:
(a) Put cos-1x = t
⇒ x = cos t
⇒ dx = -sin t dt
ISC Class 12 Maths Previous Year Question Papers Solved 2013 Q6
ISC Class 12 Maths Previous Year Question Papers Solved 2013 Q6.1

Que 7:
(a) Find Karl Pearson’s coefficient of correlation between x and y for the following data: [5]
ISC Class 12 Maths Previous Year Question Papers Solved 2013 Q7
(b) The following table shows the mean and standard deviation of the marks of Mathematics and Physics scored by the students in a School: [5]
ISC Class 12 Maths Previous Year Question Papers Solved 2013 Q7.1
The correlation coefficient between the given marks is 0.86. Estimate the likely marks in Physics if the marks in Mathematics are 92.
Solution 7:
(a) Assume mean A = 20 for the x-variate and B = 30 for the y-variate.
ISC Class 12 Maths Previous Year Question Papers Solved 2013 Q7.2
ISC Class 12 Maths Previous Year Question Papers Solved 2013 Q7.3

Que 8:
(a) Bag A contains three red and four white Balls; bag B contains two red and three white Balls. If one ball is drawn from bag A and two Balls from bag B, find the probability that: [5]
(i) One ball is red and two balls are white
(ii) All the three balls are of the same colour.
(b) Three persons, Aman, Bipin and Mohan attempt a Mathematics problem independently. The odds in favour of Aman and Mohan solving the problem are 3 : 2 and 4 : 1 respectively and the odds against Bipin solving the problem are 2 : 1. Find: [5] (i) The probability that all three will solve the problem.
(ii) The probability that the problem will be solved.
Solution 8:
(a) Here, the possible selection is as follows:
(i) 1 Red from bag A, 2 white from bag B
1 White from bag A, 1 white from bag B 1 Red from B
P (one ball is red and two balls are white)
ISC Class 12 Maths Previous Year Question Papers Solved 2013 Q8
(ii) Possible selection is as follows:
(a) 1 Red from Bag A, 2 Red from Bag B
(b) 1 White from Bag A, 2 white from Bag B
P (All the three balls are of the same colour)
ISC Class 12 Maths Previous Year Question Papers Solved 2013 Q8.1
ISC Class 12 Maths Previous Year Question Papers Solved 2013 Q8.2
ISC Class 12 Maths Previous Year Question Papers Solved 2013 Q8.3
ISC Class 12 Maths Previous Year Question Papers Solved 2013 Q8.4

Que 9:
(a) Find the locus of the complex number z = x + iy, satisfying relations arg (z – 1) = \frac{\pi}{4} and |z – 2 – 3i| = 2. Illustrate the locus oh the Argand plane. [5] (b) Solve the following differential equation:
y e^{y} d x=\left(y^{3}+2 x e^{y}\right) d y, given that x = 0, y = 1 [5] Solution 9:
ISC Class 12 Maths Previous Year Question Papers Solved 2013 Q9
ISC Class 12 Maths Previous Year Question Papers Solved 2013 Q9.1
ISC Class 12 Maths Previous Year Question Papers Solved 2013 Q9.2
ISC Class 12 Maths Previous Year Question Papers Solved 2013 Q9.3


Section – B (20 Marks)

ISC Maths 2013 Class-12 Previous Year Question Papers Solved

Que 10:
(a) If \vec{a} \text { and } \vec{b}, are unit vectors and 0 is the angle between them, then show that |\vec{a}-\vec{b}|=2 \sin \frac{\theta}{2}. [5] (b) Find the value of λ for which the four points A, B, C, D with position vectors -\hat{j}-\hat{k} : 4 \hat{i}+5 \hat{j}+\lambda \hat{k} : 3 \hat{i}+9 \hat{j}+4 \hat{k} \text { and }-4 \hat{i}+4 \hat{j}+4 \hat{k} are coplanar. [5] Solution 10:
ISC Class 12 Maths Previous Year Question Papers Solved 2013 Q10
ISC Class 12 Maths Previous Year Question Papers Solved 2013 Q10.1

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