28 June 2011

MATRICES

1. Find x, 

2.If A= then prove by M.I that

  3.A =          , find  f(A) , where  f(x) =

4.Find  K such that    ,if   A= satisfies the equation

5.If  A=                 B =              Express  3A  +  2B  as the sum of  symmetric and skew symmetric matrices.

DETERMINANTS

1.If A  is a 3 x 3 matrix ,  =12,      Find

2.If A  is a 3 x3 matrix   =-4        .Find

3.Find   , =3 and A is a 4 x4  matrix.  

  4.For what values of k,           A  =    is not invertible.

5.Show  that  the points ( a, b+c )  ;  (b, c+a) ; ( c, a+b )  are collinear using determinants.

6. Find the equation of the line joining  (1,2) ; (3,6) using determinants.

7. If  the area of triangle is 35 sq. units with vertices (2,-6) ; (5,4) ; (k,4) . Find the value of k

using determinants.

8. IfA= Find  A. adj A , without  finding  adjA.

10.  Show that the matrix, A=satisfies the equation. Hence               find.

11.Using properties of determinants, prove that=+

  1 2. Using properties of determinants, prove =

13.        Solve the equation,   =0                                         14.       Using properties of determinants, prove that               =ab+bc+ca+abc                 

15.         Using properties of determinants, prove that

=1+ +

16.  If x,y,z are different and  =0 , then show that 1+xyz=0.

17.Solve the equation,

18.Using properties of determinants, Solve the equation,  if.=0

19.Show that A. adj A =.      where A =   

20.Find the inverse of A, If  A=  .

Date of submission: 27 June 2011

Click here to download the homework

Date of submission: 07-01-2011 by   CLASS-XII-B.

CLASS-XII-B            -  MATHS( 1mark  QUESTIONS)

1.    If        .Find .

2     If     ,      .Find (-1.2) * (3, -4).

  3.Find the principal value of 

4.Find the principal value of 

5.  If        ,    Find x.

6.If A  is a 3 x 3 matrix ,   =12,     Find

7.If A  is a 3 x3 matrix     =-4       .Find

8.Find   , =3 and A is a 4 x4  matrix.

9.Find the derivative of  sinx  w.r. to logx.

10.Find the derivative of

11. Find x.

12.

13.

14.

  15,         

16.Find the direction ratios of line, 6x-2 = 2y =z-3.

17.Find the direction cosines if ratios are , 2, 1, 3.

18.Find the order and degree of,

19. .Find the integrating factor of ,

20.Find the value of  p, line             is parallel to the plane, px +3y-z+5=0

21.Abag contains 5 red, 6 blue, 4 black balls. Three balls are drawn .Find the probability that none of them is red.

.22.Find the rate of change of area of circle with respect to its radius r , when r= 6.

23.If sum of two unit vectors is also a unit vector, find  the angle between them

24.If A and B are independent events, such that, P( AU B)= 0.8,       P(A)=0.5,.find P(B).

25.At what points on the curve  ,       does the ordinate decrease as same rate as abscissa increases

    26.For what values of k, A=                        is not invertible.

27.A coin is tossed 5 times , and getting a head is considered as success. Find the probability of getting no success.

28.Find adj(adj A). If  A=

29.If A is an   invertible matrix of order 2. Find .

30. Find the identity element for the operation  a*b=ab/4,   in QxQ, Q is set of rational numbers.

31.   

32.Find x.       

33.

34.

35.Evaluate      .

36.

37.If A  is any matrix such that  I AI = 12. find  A. adj A.

38.Find whether f(x) = 1/x is strictly increasing  or decreasing function.

39.For  any vector  a , ,find (a .i) i + (a. j) .j +a .k) .k .

40.Find sine of angle between the vectors a and b,  a x b = 3i -6j-5k  and I a I =    and   Ib I= .

Mrs,PRASANNA KUMARI . K . P, TGT(Maths)

1. Find the 25^th term of the A.P: 9, 6,  3 , 0 , …
2. Which term of the A. P  :  7 , 3 , -1 , -5 , …  is  -389 ?
3. How many terms are there in the A. P :  18 , 15.5 , 13 , …  , -47 ?
4. The 6th term of an A. P is 23 and 8^th term is 33.Find its 3^rd term and the general term ( i.e.  n^th term )
5. How many 3 – digit numbers are divisible by 11 ?
6. Find the 26^th term from the end of  the A . P : 6 , 9 , 12 , … ,120 .
7. In an A .P five times the 5^th term is equal to ten times the 10^th term. Find its 15^th term.
8. In an A .P the 24^th term is twice  the 10^th term . Show that  its 72^nd  term is twice the 34^th term.
9. If  a , b , c  are in A . P , show that  ak , bk , ck are also in A . P .
10. Find the sum of all natural numbers between 100 and 250, which are divisible by 6 .
11. The sum of three numbers in A . P  is 21 and the sum of their squares is 155. Find the numbers .
12. The sum of 1^st n terms  of an A . P is given by  n² + 5n . Find its 1^st four terms and also its 10^th term .
13. If   a ,7 , b , 23 , c are in A . P . Find  a , b  & c .
14. Which term of the sequence  : 114 , 109 , 104 , … is the first negative term ?
15. A sum of Rs. 6240 is paid off in 30 installments, such that each installment is Rs. 10 more than the preceding installment. Find the value of the 1^st and the 25^th installments.

January 2010

THE WORLD IN MY HOME

1. Who is Anil?
2. Does Akshay’s grandmother like Anil?
3. What did grandmother ask Akshay not to do?
4. What was her reason for that?
5. Why was Akshay confused?
6. Who takes decision in Dhondu’s family?
7. What is the new job that Dhondu planned to do?
8. Who takes important decisions in your house?

Date: 20/01/10

POCHAMPALLI

Find out and write:

1. Talk to an ironsmith a carpenter and a potter about the nature of their work.
2. Where did they learn to do their work?
3. What else did they need to learn to be able to do this work?
4. Have they taught this work to any body in their family or to anyone else?

Date: 04-01-10

1. Name some natural calamites.
2. Name the resources and facilities you share with your neighbors.
3. Stick pictures of some natural calamites.

HOMEWORK FOR NOVEMEBER FIRST WEEK

1. Recently ‘A Seminar on Growing violence in the society’ was organized in your school in which several eminent personalities of your city participated. A renowned psychologist, Mr. K.K. Kakkad also showed up and threw light on the causes of growing violence and discussed various strategies and techniques of anger management. Write a report on the seminar in about 100 words for your school magazine.

For Nov. Third week

1.A leading news channel recently gave a live coverage of some young slum dwellers being beaten up mercilessly by the police for crimes not committed by them.  Such atrocities shake the very faith of people.  Write a letter to the Commissioner of Police urging him to adopt effective measures to curb such brutality against innocent people.  You are Nita/Nitesh, 5/6, Brahmaputra Road, Guwahati-5.