# ISC Maths 2012 Class-12 Solved Previous Year Question Papers

**ISC Maths 2012 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 2012 Class-12** Solved Previous Year Question Paper you can get the idea of solving. Try Also other year except **ISC Maths 2012** **Class-12 **Solved Question Paper of Previous Year for more practice. Because only **ISC Maths 2012 Class-12** is not enough for complete preparation of next council exam.

## ISC Maths 2012 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 2012 Class-12 Previous Year Question Papers Solved

Que 1:

(i) Solve for x if [3]
(ii) Prove that [3]
(iii) Find the equation of the hyperbola whose Transverse and Conjugate axes are the x and y axes respectively, given that the length of conjugate axis is 5 and distance between the foci is 13. [3]
(iv) From the equations of the two regression lines, 4x + 3y + 7 = 0 and 3x + 4y + 8 = 0, find: [3]
(a) Mean of x and y.

(b) Regression coefficients.

(c) Coefficient of correlation.

(v) Evalulate: [3]
(vi) Evaluate: [3]

(vii) Find the locus of the complex number, Z = x + iy given [3]
(viii) Evaluate: [3]
**(ix) Three persons A, B and C shoot to hit a target. If in trials, A hits the target 4 times in 5 shots, B hits 3 times in 4 shots and C hits 2 times in 3 trials. Find the probability that: [3]**

(a) Exactly two persons hit the target.

(b) At least two persons hit the target.

(x) Solve the differential equation: [3]
(xy^{2} + x)dx + (x^{2}y + y) dy = 0

Solution 1:

Que 2:

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

**(b) Find the product of the matrices A and B where: [5]**

**Hence, solve the following equations by matrix method:**

x + y + 2z = 1

3x + 2y + z = 7

2x + y + 3z = 2

Solution 2:

Que 3:

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

**(i) Write the Boolean expression corresponding to the circuit given below: [5]**

**(ii) Simplify the expression using laws of Boolean Algebra and construct the simplified circuit.**

Solution 3:

(b)

**(i) The statement using the given switching circuits is as:**

CA + A(B + C) (C + A) (C + B) ….. (i)

using laws of Boolean Algebra, we have

CA + A(B + C) (C + A) (C + B) = (CA + AB + AC) (C + A) (C + B)

= (AC + AB + AC) (C + A) (C + B)

= ACC + ACA + ABC + ABA (C + B)

= AC + AC + ABC + AB (C + B)

= AC + ABC + ABC + AB

= AC + ABC + AB

= AC + AB (1 + C)

= AC + AB (1)

= AC + AB

= A(C + B)

**Hence, the simplified switching network can be shown as in the figure.**

Que 4:

**(a) Verify Rolle’s theorem for the function: [5]**

in the interval [a, b] where, 0 ∉ [a, b].

(b) Find the equation of the ellipse with its centre at (4, -1) focus at (1, -1) and given that it passes through (8, 0). [5]
Solution 4:

(a) Given

**Algorithmic function is differentiable and so continuous on .its domain. Therefore f(x) is continuous on [a, b] and differentiable on (a, b)**

f(a) = f(b)

**(b) Coordinate of the centre and focus are the same.**

Therefore both lie on y = -1 & hence the major axis of the ellipse is parallel to the x-axis. & minor axis is parallel to the y-axis.

Let 2a and 2b be the length of major & minor axes respectively. Then the equation of the ellipse is

Que 5:

(a) If e^{y} (x + 1) = 1, then show that: [5]

(b) A printed page is to have a total area of 80 sq. cm with a margin of 1 cm at the top and on each side and a margin of 1.5 cm at the bottom. What should be the dimensions of the page so that the printed area will be maximum? [5]
Solution 5:

Que 6:

(a) Evaluate [5]
(b) Find the area of the region bounded by the curve x = 4y – y^{2} and the y-axis. [5]
Solution 6:

Que 7:

**(a) Ten candidates received percentage marks in two subjects as follows: [5]**

Calculate Spearman’s rank correlation coefficient and interpret your result.

**(b) The following results were obtained with respect to two variables x and y: [5]**

Σx = 30, Σy = 42, Σxy = 199, Σx^{2} = 184, Σy^{2} = 318, Σn = 6

**Find the following:**

(i) The regression coefficients.

(ii) Correlation coefficient between x and y.

(iii) Regression equation ofy on x.

(iv) The likely value ofy when x = 10.

Solution 7:

**(a) In the case of Mathematics:**

88 is scored by 1 student, so we assign rank 1 to it.

Again, 80 is scored by the two students So we assign common rank to each of them.

And 76 is scored by only one thus we assign rank 4 to him.

74 is scored by only one, so we assign rank 5 to him.

68 is scored by only one so, we assign rank 6 to him.

65 is scored by only one so, we assign rank 7 to him.

43 is scored by only one so, we assign rank 8 to him.

40 is scored by two persons so, we assign common rank to each of them.

In Statistics

90 is scored by only one thus we assign rank 1 to him.

84 is scored by only one thus we assign rank 2 to him.

72 is scored by only one thus we assign rank 3 to him.

66 is scored by only one thus we assign rank 4 to him.

54 is scored by two candidates thus we assign common rank to both of them.

50 is scored by only one thus we assign rank 7 to him.

43 is scored by only one thus we assign rank 8 to him.

38 is scored by only one thus we assign rank 9 to him.

30 is scored by only one thus we assign rank 10 to him.

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