HSSC-I Mathematics Lectures & Assignments

(Section – B)

 

 

 

     i.        Prove that;

a.   

2.   Simplify:                                  

3.   Find multiplicative inverse of complex number

4.   Simplify and write in the form of a + bi?

a.   

5.   Construct truth table for the statement:

a.   

6.   If A=[aij]3x3 then show that;

a.   

7.   Solve the following matrix equation for A.

a.   

8.   Prove that  is irrational number?

9.   Separate into real and imaginary parts:

10.                By constructing truth table prove that(A

11.                Show that = ²(a+b+c+

12.                If the matrices A and B are symmetric and AB=BA,show that AB is symmetric.

13.                If the roots of px²+qx+q=0 are  then prove that

                                         i.   

14.                Resolve into partial fraction

15.                Find the sum of all integers in the first 1000 integers which are neither divisible by 5 nor by 2.

16.                If 5 and 8 are two A.ms between a and b,find a and b.

17.                How many permutation of the letters of the word PANAMA can be       made, if P is to be first letter in each arrangement?

18.                Use mathematical induction to prove that:1+nx ⁿfor n  and x>-1.

19.                Prove that =

20.                Find the period of .

21.                Solve the triangle if ABC ,if

22.                When the polynomial x⁴+2x³+kx²+3 is divided by x-2, the remainder is 1. Find the value of k.

23.                Show that :

24.                Find the solution set of the equation: