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.

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

Que 1:
(i) Solve for x if \left(\begin{array}{c}{x^{2}} \\ {y^{2}}\end{array}\right)+2\left(\begin{array}{l}{2 x} \\ {3 y}\end{array}\right)=3\left(\frac{7}{-3}\right) [3] (ii) Prove that \sec ^{2}\left(\tan ^{-1} 2\right)+\csc ^{2}\left(\cot ^{-1} 3\right)=15 [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: \int e^{x}(\tan x+\log \sec x) d x [3] (vi) Evaluate: [3] ISC Class 12 Maths Previous Year Question Papers Solved 2012 Q1.9
(vii) Find the locus of the complex number, Z = x + iy given \left|\frac{x+i y-2 i}{x+i y+2 i}\right|=\sqrt{2} [3] (viii) Evaluate: \int_{1}^{2} \frac{\sqrt{x}}{\sqrt{3-x}+\sqrt{x}} d x [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] (xy2 + x)dx + (x2y + y) dy = 0
Solution 1:
ISC Class 12 Maths Previous Year Question Papers Solved 2012 Q1
ISC Class 12 Maths Previous Year Question Papers Solved 2012 Q1.1
ISC Class 12 Maths Previous Year Question Papers Solved 2012 Q1.2
ISC Class 12 Maths Previous Year Question Papers Solved 2012 Q1.3
ISC Class 12 Maths Previous Year Question Papers Solved 2012 Q1.4
ISC Class 12 Maths Previous Year Question Papers Solved 2012 Q1.5
ISC Class 12 Maths Previous Year Question Papers Solved 2012 Q1.6
ISC Class 12 Maths Previous Year Question Papers Solved 2012 Q1.7
ISC Class 12 Maths Previous Year Question Papers Solved 2012 Q1.8

Que 2:
(a) Using properties of determinants, prove that: [5]
\left|\begin{array}{ccc}{a} & {a+b} & {a+b+c} \\ {2 a} & {3 a+2 b} & {4 a+3 b+2 c} \\ {3 a} & {6 a+3 b} & {10 a+6 b+3 c}\end{array}\right|=a^{3}
(b) Find the product of the matrices A and B where: [5]
A=\left(\begin{array}{ccc}{-5} & {1} & {3} \\ {7} & {1} & {-5} \\ {1} & {-1} & {1}\end{array}\right), B=\left(\begin{array}{lll}{1} & {1} & {2} \\ {3} & {2} & {1} \\ {2} & {1} & {3}\end{array}\right)
Hence, solve the following equations by matrix method:
x + y + 2z = 1
3x + 2y + z = 7
2x + y + 3z = 2
Solution 2:
ISC Class 12 Maths Previous Year Question Papers Solved 2012 Q2
ISC Class 12 Maths Previous Year Question Papers Solved 2012 Q2.1
ISC Class 12 Maths Previous Year Question Papers Solved 2012 Q2.2

Que 3:
(a) Prove that: \cos ^{-1} \frac{63}{65}+2 \tan ^{-1} \frac{1}{5}=\sin ^{-1} \frac{3}{5} [5] (b)

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(i) Write the Boolean expression corresponding to the circuit given below: [5]
ISC Class 12 Maths Previous Year Question Papers Solved 2012 Q3
(ii) Simplify the expression using laws of Boolean Algebra and construct the simplified circuit.
Solution 3:
ISC Class 12 Maths Previous Year Question Papers Solved 2012 Q3.1
(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.
 simplified switching network can be shown

Que 4:
(a) Verify Rolle’s theorem for the function: [5]
f(x)=\log \left\{\frac{x^{2}+a b}{(a+b) x}\right\} 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
f(x)=\log \left(\frac{x^{2}+a b}{x(a+b)}\right) \log \left(x^{2}+a b\right)-\log x-\log (a+b)
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)
ISC Class 12 Maths Previous Year Question Papers Solved 2012 Q4
(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
ISC Class 12 Maths Previous Year Question Papers Solved 2012 Q4.1

Que 5:
(a) If ey (x + 1) = 1, then show that: [5] \frac{d^{2} y}{d x^{2}}=\left(\frac{d y}{d x}\right)^{2}
(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:
ISC Class 12 Maths Previous Year Question Papers Solved 2012 Q5
ISC Class 12 Maths Previous Year Question Papers Solved 2012 Q5.1
ISC Class 12 Maths Previous Year Question Papers Solved 2012 Q5.2

Que 6:
(a) Evaluate \int \frac{d x}{x\left\{6(\log x)^{2}+7 \log x+2\right\}} [5] (b) Find the area of the region bounded by the curve x = 4y – y2 and the y-axis. [5] Solution 6:
ISC Class 12 Maths Previous Year Question Papers Solved 2012 Q6
ISC Class 12 Maths Previous Year Question Papers Solved 2012 Q6.1

Que 7:
(a) Ten candidates received percentage marks in two subjects as follows: [5]
ISC Class 12 Maths Previous Year Question Papers Solved 2012 Q7
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, Σx2 = 184, Σy2 = 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 \frac{2+3}{2}=2.5 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 \frac{9+10}{2}=9.5 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 \frac{5+6}{2}=5.5 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.
ISC Class 12 Maths Previous Year Question Papers Solved 2012 Q7.1
ISC Class 12 Maths Previous Year Question Papers Solved 2012 Q7.2
ISC Class 12 Maths Previous Year Question Papers Solved 2012 Q7.3

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