Visit the previous pages for Plus2 Maths Part1 , HSC Maths Sample Part2 and +2 Mathematics practice Part3 Important 5 Mark questions.
1) Solve the non-homogenous system of linear equations by determinant method
2x + y - z = 4,
x + y – 2z = 0,
3x + 2y – 3z = 4.
2) Examine the consistency of the equations:
2x + 3y + 7z = 5,
3x + y – 3z = 13,
2x + 19y – 47z = 32.
3) Solve by matrix inversion method for the system of linear equations: 7x + 3y = –1; 2x + y =0.
4) Show the adjoint of A is
, where 
5) Find the rank of the matrix:
6) Solve the non-homogenous system of three unknowns by determinant method.
x + y + 2z = 4,
2x + 2y + 4z = 8,
3x + 3y + 6z = 10.
7) Prove that
8) Solve the equation
, if one root is 1+2i.
9) If
, prove that:
(i) )
(ii) )
10) A standard rectangular hyperbola has its vertices at (5, 7) and (-3, –1). Find its equation and asymptotes.
11) Find the equation of the tangent and normal to the curves
at 
.
12) Obtain the Maclaurin’s series expansion for:
13) (i) The radius of a sphere was measured and found to be 21 cm with a possible error in measurement of atmost 0.05 cm. What is the maximum error in using this value of the radius to compute the volume of the sphere?
(ii) Determine:
if =x^{4}+y^{3}+3x^{2}y^{2}+3x^{2}y )
14) If
of the normal distribution whose probability function is given by =ke^{-2x^{2}+4x-2} )
.
15) (i) Solve:y=sinx\;cosx )
(or)
(ii) State and prove the cancellation laws.
16) Of
, prove that 
17) Evaluate:
18) Solve:\frac{\mathrm{d}y }{\mathrm{d} x}+2xy=cos\;x )
19) The life of army shoes is normally distributed with mean 8 months and standard deviation 2 months. If 5000 pairs are given, how many pairs would be expected to need replacement within 12 months.
20) Obtain the Maclarin’s expansion for
(OR)
In a Poisson distribution. Prove that the total probability is one.
1) Solve the non-homogenous system of linear equations by determinant method
2x + y - z = 4,
x + y – 2z = 0,
3x + 2y – 3z = 4.
2) Examine the consistency of the equations:
2x + 3y + 7z = 5,
3x + y – 3z = 13,
2x + 19y – 47z = 32.
3) Solve by matrix inversion method for the system of linear equations: 7x + 3y = –1; 2x + y =0.
4) Show the adjoint of A is
5) Find the rank of the matrix:
6) Solve the non-homogenous system of three unknowns by determinant method.
x + y + 2z = 4,
2x + 2y + 4z = 8,
3x + 3y + 6z = 10.
7) Prove that
8) Solve the equation
9) If
(i)
(ii)
10) A standard rectangular hyperbola has its vertices at (5, 7) and (-3, –1). Find its equation and asymptotes.
11) Find the equation of the tangent and normal to the curves
12) Obtain the Maclaurin’s series expansion for:
13) (i) The radius of a sphere was measured and found to be 21 cm with a possible error in measurement of atmost 0.05 cm. What is the maximum error in using this value of the radius to compute the volume of the sphere?
(ii) Determine:
14) If
15) (i) Solve:
(or)
(ii) State and prove the cancellation laws.
16) Of
17) Evaluate:
18) Solve:
19) The life of army shoes is normally distributed with mean 8 months and standard deviation 2 months. If 5000 pairs are given, how many pairs would be expected to need replacement within 12 months.
20) Obtain the Maclarin’s expansion for
(OR)
In a Poisson distribution. Prove that the total probability is one.
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