Visit the previous page for Part1 Maths model 5 mark questions.
1) State and prove reversal law for inverses of matrices.
2) Solve the following non-homogenous equations of 3 unknowns:
x + y + 2z = 4
2x + 2y + 4z = 8
3x + 3y + 6z = 10
by determinant method.
3) (1) The planes = 10)
and  = 5)
are perpendicular. Find 
.
(2) Find the centre and radius of the sphere| = 4 )
4) Prove that.(\overrightarrow{c}\times \overrightarrow{d}) \;+ \; (\overrightarrow{b}\times \overrightarrow{c}).(\overrightarrow{a}\times \overrightarrow{d}) \;+ \;(\overrightarrow{c}\times \overrightarrow{a}).(\overrightarrow{b}\times \overrightarrow{d}) =0 )
5) State and prove the triangle inequality of complex numbers.
6) Prove that^{n}-(1+cos\Theta -isin\Theta)^{n}=2^{n+1}\;cos^{n}(\frac{\Theta}{2})cos(\frac{n\Theta}{2}) )
7) The tangent at any point of the R.H
makes intercepts a,b and the normal at the point makes intercepts p,q on the axes. Prove that ap+bq=0.
8) Evaluate: limit^{cosx} )
9) Find
if 
if  )
, when 
, 
.
10) Show that of all the rectangles with a given perimeter the one with the greater area is a square.
11) Find the area of the circle whose radius is
using integration.
12) Solve )
13) Show that\; \vee \; q) \; \wedge \; ((\sim q)\vee \; p) )
14) Two cards are drawn without replacement from a well shuffled deck of 52 cards. Find the mean and variance for the number of aces.
15) (1) Show that the set of all
non singular matrices form a non ableian infinite group under matrix multiplication (where the entries belong to R).
(2) The life of army shoes is normally distributed with mean 8 months and standard deviation 2 months. If 5000 pairs are issued, how many pairs would be expected to need replacement after 12 months.=0.4772, \; P(0\leqZ\leq1.2)=0.3849] )
1) State and prove reversal law for inverses of matrices.
2) Solve the following non-homogenous equations of 3 unknowns:
x + y + 2z = 4
2x + 2y + 4z = 8
3x + 3y + 6z = 10
by determinant method.
3) (1) The planes
(2) Find the centre and radius of the sphere
4) Prove that
5) State and prove the triangle inequality of complex numbers.
6) Prove that
7) The tangent at any point of the R.H
8) Evaluate: limit
9) Find
10) Show that of all the rectangles with a given perimeter the one with the greater area is a square.
11) Find the area of the circle whose radius is
12) Solve
13) Show that
14) Two cards are drawn without replacement from a well shuffled deck of 52 cards. Find the mean and variance for the number of aces.
15) (1) Show that the set of all
(2) The life of army shoes is normally distributed with mean 8 months and standard deviation 2 months. If 5000 pairs are issued, how many pairs would be expected to need replacement after 12 months.
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