HOLIDAY HOMEWORK CLASS-XII SCIENCE Englishra 24 HOLIDAY HOMEWORK CLASS-XII SCIENCE English 1.Write on

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    HOLIDAY HOMEWORK

    CLASS-XII SCIENCE

    English 1.Write on following topics in your respective English Registers.

    a) Value Based Education Remedy to Decrease Crime

    b) Hazards of Environmental Pollution.

    c) Circus- “A Menace to Animals”.

    d) The Role of Youth in Combatting Corruption.

    e) Minimizing of Human Rights is the way to cleanse society from corruption.

    f) Teaching Profession is better Medical profession.

    2. Prepare a power point presentation or write review of chapters : 1 to 13.

    3. Learn the syllabus completed in class till 30May 2018 for Selection Test in June month.

    Maths

    Q.1 Show that A’A and AA’ are both symmetric matrices for any matrix A.

    Q.2 If A=*

    + *

    +

    Q.3 Find the value of x for which the matrix product

    [

    ] [

    ]

    Q.4 If A =[

    ]

    Q.5 Find a matrix A such that 2A-3B+5C=0 where B= [

    ] [

    ]

    Q.6 If A= *

    + , B=*

    + and (A+B)2=A2+B2, find a and b.

    Q.7 If A=*

    + , f(x)=x2-2x-3, show that f(A)=0.

    Q.8 If A=*

    +, find .

    Q.10 Given A=[

    ] [

    ] find BA and use this to solve the system of

    equations y+2z=7 , x-y=3 , 2x+3y+4z=17.

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    Q.11 If A=[

    ] ?

    Q.12 Two factories decided to award their employees for three values of (a) adaptable to new techniques, (b) careful and alert in difficult situations and (c) keeping clam in tense situations, at the rate of RS. X, Rs. Y and Rs. Z per person respectively. The first factory decided to honour respectively 2,4 and 3 employees with a total prize money of Rs. 29000. The second factory decided to honour respectively 5,2,and 3 employees with the prize money of 30500. If the three prizes per person together cost Rs. 9500 , then i) Represent above situation by a matrix equation and form linear equations using matrix multiplication. ii) Solve these equations using matrices.

    Q.13 Two institutions decided to award their employees for the three values of

    resourcefulness ,competence and determination in the form of prizes at the rate of Rs. X, Rs. Y and Rs. Z respectively per person.. The first institution decided to award respectively 4,3 and 2 employees with a total prize money of 37000 and the second institution decided to award respectively 5,3 and 4 employees with a total prize money of 47000. If all the three prizes per person together amount to Rs. 2000 then using matrix method find the value of x, v and z

    Q.14 Using properties of determinants, solve for x:|

    |

    Q.15 Using properties of determinants, Show that |

    ( )( ) ( )( ) ( )( )

    |

    Q.16 Write the value of |

    |

    Q.18 The slope of the curve 2y2=ax2 at (1,1) is -1. Find a.

    Q.19 Show that the acute angle of intersection between the curves xy=6 and x2y=12 is

    (

    )

    Q.20 Show that the acute angle of intersection between the curves y2=4x and x2=4y is (

    ).

    Q.22 Find the equation of tangent to the curve y=(x3-1)(x-2)at the points where the curve cuts at

    the x-axis.

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    Q.23 The volume o a cube is increasing at a constant rate. Prove that the increase in surface area

    varies inversely s the length of edge of cube.

    Q.24 Show that f(x)=sin x -2cos x -2 is increasing in (

    )

    Q.27 Determine the value of x, the function f(x)=

    is increasing or decreasing. Also find the

    points on the graph of function at which the tangent is parallel to x-axis.

    Q.30 For the curve y=5x-2x3 , if x increases at the rate of 2 units/sec, then find the rate of change

    of the slope of the curve when x=3.

    Q.31 Show that the points (a+5,a-4), (a-2,a+3) and (a,a) do not lie on a straight line for any value

    of a.

    Q.32 To raise money for an orphanage, students of three schools A, B and C organized an exhibition in their locality, where they sold paper-bags, scrap-books and pastel-sheets made by them using recycled paper, at the rate of Rs. 20, Rs. 15 and Rs. 5 per unit respectively. School A sold 25 paper bags, 12 scrap-books and 34 pastel sheets. School B sold 22 paper- bags, 25 scrap-books and 28 pastel sheets while School C sold 26 paper-bags, 18 scrap- books and 36 pastel sheets. Using matrices, find the total amount raised by each school. By such exhibitions, which values are inculcated in the students?

    Q.33 Ishan wants to donate a rectangular plot of land for a school in his village. When he was asked to give dimensions of the plot, he told that if its length is decreased by 50 m and breadth is increased by 50 m, then its area will remain same, but if length is decreased by 10 m and breadth is decreased by 20 m, then its area will decrease by 5300m2 . Using matrices, find the dimensions of the plot. Also give reason why he wants to donate the plot for a school.

    Q.35 Using properties of determinants, |

    |

    Q.36 For what value of x the matrix A=[

    ]

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    Q.37 Determine the value of x for which the matrix [

    ] is singular.

    Q.38 Evaluate |

    |

    Q.39 Without expanding show that |

    |=0

    Q.40 Let A=*

    + Using this result calculate A3 and A5.

    Q.41 If A=|

    | . Using , solve the system of linear

    equation x-2y=10, 2x-y-z=8 and -2y+z=7.

    Q.42 Find the intervals in which the function f(x)=

    +51 is

    i) Strictly increasing ii) Strictly deceasing

    Q.48 Show that the function f(x)=tan-1(sinx+cosx) ,x>0 is always increasing in (0,

    ).

    Q.49 Find the intervals in which the function f given by f(x) = sin x + cos x, 0 ≤ x ≤ 2π is (i) Strictly increasing (ii) Strictly decreasing

    Q.50 Prove that the radius of the right circular cylinder of greatest curved surface area which can be inscribed in a given cone is half of that of the cone.

    Q.51 If log(x2+y2)=2 ( )

    Q.52 If y=log tan(

    ) , show that

    Q.53 If y= ( )( ) ( )( )

    , Find

    Q.54 If y = √ ( )

    ( )

    ⁄ , Find

    Q.55 If a+b+c and |

    |

    Q.56 If x,y,x R then show that |

    ( ) ( )

    ( ) ( )

    ( ) ( )

    |

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    Q.57 If x=-9 is a root of [

    ]

    Q58 Prove that |

    | is divisible by a+b+c then find the quotient.

    Q.59 In a triangle ABC , if [

    ]=0 then prove that

    is an isosceles triangle.

    Q.60 Solve the following determinant equations:

    i) |

    | ii) |

    |

    Q.61 Without expanding Show that |

    | |

    |

    Q.62 show that i) |

    |=0

    Q.63

    Q.64 Show that |

    |

    Q.65 Without expanding the determinant show that (a+b+c) is a factor of the |

    |

    Q.66 Expand |

    ( ) ( )

    ( ) ( )

    ( ) ( )

    |

    Q.67 Expand |

    |

    Q.68 Prove that |

    | ( )( )( )

    Q.69 Solve the following determinant equations:

    I ) |

    | ii) |

    |

    Q.70 Solve the following determinant equations:

    i) |

    | ii) |

    |

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    Q.71 Using properties of determinants, Prove that:|

    |

    Q.72 Prove that:|

    | ( )( )( )

    Q.73 Using properties of determinants, Solve for x:|

    |

    Q.74 Using properties of determinants, Prove that |

    |

    Q.75 Using properties of determinants, Prove that :|

    |

    Q.76 Using properties of determinants, Prove that :|

    | (

    )

    Q.77 Prove that: |

    | ( )( )( )

    Q.78 A school wants to award its students for the values of honesty, Regularity and Hard work

    with a total cash award of Rs. 6000. Three times the award money for hard work added to

    that given for honesty amounts to Rs. 11000. The award money given for Honesty and Hard

    work together is double the one given for Regularity. Represent the above