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Question Bank Solutions for ISC (Science) 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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Question Bank Solutions for ISC (Science) Class 12 CISCE Mathematics. You can further filter Question Bank Solutions by subjects and topics. Solutions for most of the questions for CISCE can be found here on Shaalaa.com. You can use these solutions to prepare for your studies and ace in exams. Solving questions is a great way to practice and with Shaalaa.com, you can answer a question and then also check your answer with the solutions provided.
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