# ISC Maths 2011 Class-12 Solved Previous Year Question Papers

**ISC Maths 2011 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 2011 Class-12** Solved Previous Year Question Paper you can get the idea of solving. Try Also other year except **ISC Maths 2011** **Class-12 **Solved Question Paper of Previous Year for more practice. Because only **ISC Maths 2011 Class-12** is not enough for complete preparation of next council exam.

## ISC Maths 2011 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 2011 Class-12 Previous Year Question Papers Solved

Que 1:

(i) If , find x such that A^{2} = xA – 2I. Hence find A^{-1}. [3]

(ii) Find the values of k, if the equation 8x^{2} – 16xy + ky^{2} – 22x + 34y = 12 represents an elhpse. [3]

**(iii) Solve for x: sin (2 tan ^{-1}x) = 1 [3]**

(iv) Two regression lines are represented by 2x + 3y – 10 = 0 and 4x + y – 5 = 0. Find the line of regression of y on x. [3]

(v) Evaluate: [3]

**(vi) Evaluate: [3]**

**(vii) Evaluate: [3]**

(viii) Find the modulus and argument of the complex number [3]

(ix) A word consists of 9 different alphabets, in which there are 4 consonants and 5 vowels. Three alphabets are chosen at random. What is the probability that more than one vowel will be selected? [3]

(x) Solve the differential equation: [3]

Solution 1:

Que 2:

**(a) Using properties of determinants, show that pα ^{2} + 2qα + r = 0, given that p, q and r are not in GP and [5]**

**(b) Solve the following system of equations using matrix method: [5]**

Solution 2:

Que 3:

**(a) Prove that: [5]**

(b) P, Q and R represent switches in ‘ON position’ and P’, Q’ and R’ represent switches in ‘OFF position’. Construct a switching circuit representing the polynomial: [5]

P(P + Q)Q(Q + R’)

Use Boolean Algebra to show that the above circuit is equivalent to a switching circuit in which when P and Q are in ‘ON position’, the light is on.

Solution 3:

(b) P, Q, R represent switches in ON position and P’, Q’, R’ represent in OFF position.

Given polynomial is

P(P + Q) Q (Q + R’) = (PP + PQ) (QQ + QR’)

= (P + PQ) (Q + QR’)

= P(1 + Q)Q(1 + R’)

= P.1.Q.1

= PQ

Que 4:

(a) Verify Lagrange’s mean value theorem for the function f(x) = sin x – sin 2x in the interval [0, π]. [5]

(b) Find the equation of the hyperbola whose foci are (0, ±13) and the length of the conjugate axis is 20. [5]

Solution 4:

Que 5:

(a) Evaluate: [5]

(b) Draw a rough sketch of the curves y = (x – 1)^{2} and y = |x – 1|. Hence, find the area of the region bounded by these curves.

Solution 5:

Que 6:

**(a) If the sum of the lengths of the hypotenuse and a side of a right-angled triangle is given, show that the area of the triangle is maximum when the angle between them is [5]**

(b) If y = x^{x}, prove that: [5]

Solution 6:

Que 7:

**(a) The following observations are given:**

(1, 4), (2, 8), (3, 2), (4, 12) (5, 10), (6, 14), (7, 16), (8, 6), (9, 18)

Estimate the value of y when the value of x is 10 and also estimate the value of x when the value of y = 5. [5]

**(b) Compute Karl Pearson’s Coefficient of Correlation between sales and expenditures of a firm for six months. [5]**

Solution 7:

Que 8:

(a) A purse contains 4 silver and 5 copper coins. A second purse contains 3 silver and 7 copper coins. If a coin is taken out at random from one of the purses, what is the probability that it is a copper coin? [5]

(b) Aman arid Bhuvan throws a pair of dice alternately. In order to win, they have to get a sum of 8. Find their respective probabilities of winning if Aman starts the game. [5]

Solution 8:

**(a) Let E _{1} = selecting the first purse, E_{2} selecting the second purse and A = coin drawn is silver.**

Que 9:

**(a) Using De Moivre’s theorem, find the value of: [5]**

**(b) Solve the following differential equation for a particular solution: [5]**

Solution 9:

**Section – B (20 Marks)**

### ISC Maths 2011 Class-12 Previous Year Question Papers Solved

Que 10:

(a) Prove that: [5]

**(b) If D, E, F are mid-points of the sides of a triangle ABC, prove by vector method that:**

Area of ∆DEF = (Area of ∆ABC). [5]

Solution 10:

Que 11:

(a) Find the vector equation of the line passing through the point (-1, 2, 1) and parallel to the line . Also, find the distance between these lines. [5]

(b) Find the equation of the plane passing through the points A (2, 1, -3), B (-3, -2, 1) and C(2, 4, -1). [5]

Solution 11:

(a) …(i)

The given fine is parallel to the vector and the required line is parallel to given line So, required line is parallel to the vector

It is given that the required line passes through the point (-1, 2, 1)

The equation of the required line is

**(b) Let the equation of the plane passing through the point A(2, 1, -3) be**

A (x – 2) + B(y – 1) + C(z + 3) = 0 ….. (i)

Points B (-3, -2,1) and C (2, 4, -1) lies on the plane.

⇒ A(-3 – 2) + B (-2 – 1) + C(1 + 3) = 0

⇒ -5A – 3B + 4C = 0 ……(ii)

And A(2 – 2) + B(4 – 1) + C(-1 + 3) = 0

⇒ A.0 + 3B + 2C = 0 ….(iii)

Now, eliminating A, B, C from (i), (ii) and (iii), we have

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