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Option 2

150

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√3e

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• Faculty Support #### If  for  then Option: 1 Option: 2 Option: 3 Option: 4 Use

Correct Option (3)

Option d

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• Faculty Support #### The length of the minor axis (along y-axis) of an ellipse in the standard form is If this ellipse touches the line, then its eccentricity is :  Option: 1 Option: 2 Option: 3 Option: 4 What is Ellipse? -

Ellipse

Standard Equation of Ellipse:

The standard form of the equation of an ellipse with center (0, 0) and major axis on the x-axis is 1. a > b

2.  the length of the major axis is 2a

3.  the coordinates of the vertices are (±a, 0)

4.  the length of the minor axis is 2b

5.  the coordinates of the co-vertices are (0, ±b)

-

Equation of Tangent of Ellipse in Parametric Form and Slope Form -

Slope Form: -  Correct Option (2)

#### If is false, then the truth values of p and q are respectively :   Option: 1 F, TOption: 2 T, F Option: 3 F, F Option: 4 T, T

Relation Between Set Notation and Truth Table -

Sets can be used to identify basic logical structures of statements. Statements have two fundamental roles either it is true or false.

Let us understand with an example of two sets p{1,2} and q{2,3}.  Using this relation we get -

Practise Session - 2 -

Q1. Write the truth table for the following statement pattern: - Correct Option (4)

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• Faculty Support #### The following system of linear equations   has  Option: 1 infinitely many solutions, satisfying Option: 2 infinitely many solutions, satisfying Option: 3 no solution Option: 4 only the trivial solution.

System of Homogeneous linear equations - If ? ≠ 0, then x= 0, y = 0, z = 0 is the only solution of the above system. This solution is also known as a trivial solution.

If ? = 0, at least one of x, y and z are non-zero. This solution is called a non-trivial solution.

Explanation: using equation (ii) and (iii), we have  This is the condition for a system have Non-trivial solution.

-  so infinite non-trivial solution exist

now equation (1) + 3 equation (3)

10x - 20z = 0

x = 2z

Correct Option 2

#### Given : and Then the area (in sq. units) of the region bounded b the curves, and between the lines, is :  Option: 1 Option: 2 Option: 3 Option: 4 Area Bounded by Curves When Intersects at More Than One Point -

Area bounded by the curves  y = f(x),  y = g(x)  and  intersect each other in the interval [a, b]

First find the point of intersection of these curves  y = f(x) and  y = g(x) , let the point of intersection be x = c  When two curves intersects more than one point

rea bounded by the curves  y=f(x),  y=g(x)  and  intersect each other at three points at  x = a, x = b amd x = c.

To find the point of intersection, solve f(x) = g(x).

For x ∈ (a, c), f(x) > g(x) and for x ∈ (c, b), g(x) > f(x).

Area bounded by curves,  - Required area = Area of trapezium ABCD -  Correct Option (1)  