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

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Using integration find the area of the triangle formed by positive x-axis and tangent and normal of the circle

x^2+y^2=4 at (1, sqrt3)

[7] Application of Integrals (Section B)
Chapter: [7] Application of Integrals (Section B)
Concept: Area Under Simple Curves

Find the value of constant ‘k’ so that the function f (x) defined as

f(x) = {((x^2 -2x-3)/(x+1), x != -1),(k, x != -1):}

is continous at x = -1

[3.01] Continuity, Differentiability and Differentiation
Chapter: [3.01] Continuity, Differentiability and Differentiation
Concept: Concept of Continuity

Show that the function f(x) = {(x^2, x<=1),(1/2, x>1):} is continuous at x = 1 but not differentiable.

[3.01] Continuity, Differentiability and Differentiation
Chapter: [3.01] Continuity, Differentiability and Differentiation
Concept: Concept of Continuity

Find the equation of an ellipse whose latus rectum is 8 and eccentricity is 1/3

[7] Application of Integrals (Section B)
Chapter: [7] Application of Integrals (Section B)
Concept: Area Under Simple Curves

If 1, omega and omega^2 are the cube roots of unity, prove (a + b omega + c omega^2)/(c + s omega +  b omega^2) =  omega^2

[3.04] Differential Equations
Chapter: [3.04] Differential Equations
Concept: Basic Concepts of Differential Equation

Solve the equation for x: sin^(-1)  5/x + sin^(-1)  12/x = pi/2, x != 0

[3.04] Differential Equations
Chapter: [3.04] Differential Equations
Concept: Basic Concepts of Differential Equation

Given that the observations are: (9, -4), (10, -3), (11, -1), (12, 0), (13, 1), (14, 3), (15, 5), (16, 8). Find the two lines of regression and estimate the value of y when x = 13·5.

[9] Linear Regression (Section C)
Chapter: [9] Linear Regression (Section C)
Concept: Lines of Regression of X on Y and Y on X Or Equation of Line of Regression

Solve the following initial value problem:-

$y' + y = e^x , y\left( 0 \right) = \frac{1}{2}$

[3.04] Differential Equations
Chapter: [3.04] Differential Equations
Concept: Basic Concepts of Differential Equation

Evaluate :  int sec^2x/(cosec^2x)dx

[3.03] Integrals
Chapter: [3.03] Integrals
Concept: Introduction of Integrals

Show that the function f(x) = |x-4|, x ∈ R is continuous, but not diffrent at x = 4.

[3.01] Continuity, Differentiability and Differentiation
Chapter: [3.01] Continuity, Differentiability and Differentiation
Concept: Concept of Continuity

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

[1] Relations and Functions (Section A)
Chapter: [1] Relations and Functions (Section A)
Concept: Introduction of Relations and Functions

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

[1] Relations and Functions (Section A)
Chapter: [1] Relations and Functions (Section A)
Concept: Introduction of Relations and Functions

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

[1] Relations and Functions (Section A)
Chapter: [1] 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

[2.01] Matrices and Determinants
Chapter: [2.01] Matrices and Determinants
Concept: Introduction of Matrices

Evaluate: int_0^x (xtan x)/(sec x + tan x) dx

[3.03] Integrals
Chapter: [3.03] Integrals
Concept: Introduction of Integrals

Given three identical Boxes A, B and C, Box A contains 2 gold and 1 silver coin, Box B contains 1 gold and 2 silver coins and Box C contains 3 silver coins. A person choose a Box at random and takes out a coin. If the coin drawn is of silver, find the probability that it has been drawn from the Box which has the remaining two coins also of silver.

[3.03] Integrals
Chapter: [3.03] Integrals
Concept: Introduction of Integrals

Find the equation of the lines passing through the point (2, 1, 3) and perpendicular to the lines

[6] Three - Dimensional Geometry (Section B)
Chapter: [6] Three - Dimensional Geometry (Section B)
Concept: Direction Cosines and Direction Ratios of a Line

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

[7] Application of Integrals (Section B)
Chapter: [7] 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.

[9] Linear Regression (Section C)
Chapter: [9] 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.

[2.01] Matrices and Determinants
Chapter: [2.01] Matrices and Determinants
Concept: Introduction of Matrices
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