# Question Bank Solutions for ISC (Commerce) Class 12 - CISCE - Mathematics

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Evaluate : int(x1+x^2)/(1+x^4)dx

[0.01] Relations and Functions (Section A)
Chapter: [0.01] Relations and Functions (Section A)
Concept: Introduction of Relations and Functions

Solve the differential equation  dy/dx = (x + y+2)/(2(x+y)-1)

[0.01] Relations and Functions (Section A)
Chapter: [0.01] Relations and Functions (Section A)
Concept: Introduction of Relations and Functions

Evaluate: int_-6^3 |x+3|dx

[0.01] Relations and Functions (Section A)
Chapter: [0.01] Relations and Functions (Section A)
Concept: Introduction of Relations and Functions

Solve the following system of linear equation using matrix method:
1/x + 1/y +1/z = 9

2/x + 5/y+7/z = 52

2/x+1/y-1/z=0

[0.021] Matrices and Determinants
Chapter: [0.021] Matrices and Determinants
Concept: Introduction of Matrices

Draw a rough sketch and find the area bounded by the curve x2 = y and x + y = 2.

[0.07] Application of Integrals (Section B)
Chapter: [0.07] Application of Integrals (Section B)
Concept: Area Under Simple Curves

Find the equation of the regression line of y on x, if the observations (x, y) are as follows :
(1,4),(2,8),(3,2),(4,12),(5,10),(6,14),(7,16),(8,6),(9,18)
Also, find the estimated value of y when x = 14.

[0.09] Linear Regression (Section C)
Chapter: [0.09] Linear Regression (Section C)
Concept: Lines of Regression of X on Y and Y on X Or Equation of Line of Regression

Write the negation of the following statements :
(a) Radha likes tea or coffee.
(b) ∃x cc R such that x + 3 ≥ 10.

[0.021] Matrices and Determinants
Chapter: [0.021] Matrices and Determinants
Concept: Introduction of Matrices

If A = [(1,2), (1,3)], find A2 - 3A

[0.021] Matrices and Determinants
Chapter: [0.021] Matrices and Determinants
Concept: Introduction of Matrices

If y – 2x – k = 0 touches the conic 3x2 – 5y2 = 15, find the value of k.

[0.06] Three - Dimensional Geometry (Section B)
Chapter: [0.06] Three - Dimensional Geometry (Section B)
Concept: Equation of a Line in Space

Prove that 1/2 "cos"^(-1) ((1-"x")/(1+"x")) = "tan"^-1 sqrt"x"

[0.031] Continuity, Differentiability and Differentiation
Chapter: [0.031] Continuity, Differentiability and Differentiation
Concept: Concept of Continuity

A problem is given to three students whose chances of solving it are 1/4, 1/5 and 1/3 respectively. Find the probability that the problem is solved.

[0.04] Probability (Section A)
Chapter: [0.04] Probability (Section A)
Concept: Introduction of Probability

If a + ib = ("x" + "iy")/("x" - "iy"), prove that "a"^2 +"b"^2 = 1 and "b"/"a" = (2"xy")/("x"^2 - "y"^2)

[0.034] Differential Equations
Chapter: [0.034] Differential Equations
Concept: Basic Concepts of Differential Equation

If A, B and C are the elements of Boolean algebra, simplify the expression (A’ + B’) (A + C’) + B’ (B + C). Draw the simplified circuit.

[0.01] Relations and Functions (Section A)
Chapter: [0.01] Relations and Functions (Section A)
Concept: Introduction of Relations and Functions

Find the coordinates of the centre, foci and equation of directrix of the hyperbola x2 – 3y2 – 4x = 8.

[0.034] Differential Equations
Chapter: [0.034] Differential Equations
Concept: Basic Concepts of Differential Equation

The two lines of regressions are x + 2y – 5 = 0 and 2x + 3y – 8 = 0 and the variance of x is 12. Find the variance of y and the coefficient of correlation.

[0.09] Linear Regression (Section C)
Chapter: [0.09] Linear Regression (Section C)
Concept: Lines of Regression of X on Y and Y on X Or Equation of Line of Regression

For the given lines of regression, 3x – 2y = 5 and x – 4y = 7, find:
(a) regression coefficients byx and bxy
(b) coefficient of correlation r (x, y)

[0.09] Linear Regression (Section C)
Chapter: [0.09] Linear Regression (Section C)
Concept: Lines of Regression of X on Y and Y on X Or Equation of Line of Regression

Calculate the Spearman’s rank correlation coefficient for the following data and interpret the result:

 X 35 54 80 95 73 73 35 91 83 81 Y 40 60 75 90 70 75 38 95 75 70
[0.09] Linear Regression (Section C)
Chapter: [0.09] Linear Regression (Section C)
Concept: Lines of Regression of X on Y and Y on X Or Equation of Line of Regression

A pair of dice is thrown. What is the probability of getting an even number on the first die or a total of 8?

[0.04] Probability (Section A)
Chapter: [0.04] Probability (Section A)
Concept: Introduction of Probability

Solve the differential equation:

"x"("dy")/("dx")+"y"=3"x"^2-2

[0.034] Differential Equations
Chapter: [0.034] Differential Equations
Concept: Basic Concepts of Differential Equation

Bag A contains 1 white, 2 blue and 3 red balls. Bag B contains 3 white, 3 blue and 2 red balls. Bag C contains 2 white, 3 blue and 4 red balls. One bag is selected at random and then two balls are drawn from the selected bag. Find the probability that the balls draw n are white and red.

[0.04] Probability (Section A)
Chapter: [0.04] Probability (Section A)
Concept: Introduction of Probability
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