# 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**.

By the practice of** ISC Maths 2013 Class-12** Solved Previous Year Question Paper you can get the idea of solving. Try Also other year except **ISC Maths 2013** **Class-12 **Solved Question Paper of Previous Year for more practice. Because only **ISC Maths 2013 Class-12** is not enough for complete preparation of next council exam.

## ISC Maths 2013 Class-12 Previous Year Question Papers Solved

**-: Select Your Topics :-**

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 , 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 3x^{2} – y^{2} = 3. [3]
(iii) Prove that: [3]
(iv) Using L’Hospital’s Rule, evaluate: [3]

(v) Evaluate: [3]
(vi) Evaluate: [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 w^{2} are the cube roots of unity, evaluate: (1 – w^{4} + w^{8}) (1 – w^{8} + w^{16}) [3]
(ix) Solve the differential equation: [3]

(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:

Que 2:

**(a) Using properties of determinants, prove that: [5]**

(b) Find A^{-1}, where

**Hence, solve the following system of linear equations: [5]**

4x + 2y + 3z = 2

x + y + z = 1

3x + y – 2z = 5

Solution 2:

Que 3:

(a) Solve for 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:

Que 4:

(a) Verify Lagrange’s Mean Value Theorem for the function 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, [5]
Solution 4:

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^{-1}x)^{2}, show that [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:

Que 6:

(a) Evaluate: [5]
(b) Find the area bounded by the curve y = 2x – x^{2}, and the line y = x. [5]
Solution 6:

(a) Put cos^{-1}x = t

⇒ x = cos t

⇒ dx = -sin t dt

Que 7:

**(a) Find Karl Pearson’s coefficient of correlation between x and y for the following data: [5]**

**(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]**

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.

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)

**(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)

Que 9:

(a) Find the locus of the complex number z = x + iy, satisfying relations arg (z – 1) = and |z – 2 – 3i| = 2. Illustrate the locus oh the Argand plane. [5]
(b) Solve the following differential equation:

, given that x = 0, y = 1 [5]
Solution 9:

**Section – B (20 Marks)**

### ISC Maths 2013 Class-12 Previous Year Question Papers Solved

Que 10:

(a) If , are unit vectors and 0 is the angle between them, then show that . [5]
(b) Find the value of λ for which the four points A, B, C, D with position vectors are coplanar. [5]
Solution 10:

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