2015 (A)
Roll No: _________________
th
INTERMEDIATE PART-I (11 CLASS)
MATHEMATICS PAPER-I GROUP-II
TIME ALLOWED: 2.30 Hours
SUBJECTIVE
MAXIMUM MARKS: 80
NOTE: - Write same question number and its part number on answer book,
as given in the question paper.
SECTION-I
2.
8 × 2 = 16
Attempt any eight parts.
(i)
Find the multiplicative inverse of ( − 4, 7 )
(ii)
Separate
(iii)
Write the power set of
(iv)
State the De. Morgan’s Laws.
(v)
For A = {1, 2, 3, 4 } , find the relation in A satisfying
(vi)
Define Semi-group.
(vii)
−2 3
Find the inverse of A = 

−4 5
2 − 7i
into real and imaginary parts.
4 + 5i
{ a, { b, c }}.
{ ( x, y ) | x +
bc ca ab
1 1 1
=0
a b c
a b c
(viii) Without expansion show that
(ix)
If ' A ' is skew-symmetric, show that A 2 is symmetric.
(x)
Solve the equation 5 x 2 − 13x + 6 = 0
(xi)
Show that x 3 − y 3 = ( x − y ) ( x − ω y ) ( x − ω 2 y )
(xii)
If α , β are roots of 3x 2 − 2 x + 4 = 0 , find the values of
3.
y < 5}
α
β
+
β
α
8 × 2 = 16
Attempt any eight parts.
(i)
Define Improper Rational Fraction.
(ii)
Which term of an A.P 5, 2, –1, ----- is – 85 ?
(iii)
Find vulgar fraction equivalent to the recurring decimals 0. 7 .
(iv)
If 5 is the harmonic mean between 2 and b find b .
(v)
Insert two G. Ms between 2 and 16.
(vi)
How many signals can be given by 5 flags of different colours, using 3 flags at a time.
(vii)
Find the value of n when C =
•
n
10
12 × 11
2!
(viii) A natural number is chosen out of first fifty natural numbers, what is the probability that
the chosen number is multiple of 3.
(ix)
Find the number of the diagonals of 6 – sided figure.
(x)
Calculate ( 0.97 ) by means of Binomial Theorem.
(xi)
If x is so small that its square and higher powers can be neglected then show that
3
1 + 2x
1− x
≈1+
3
x
2
−1
(xii)
Expand up to 4 terms ( 1 + x ) 3
P.T.O.
(2)
4.
9 × 2 = 18
Attempt any nine parts.
(i)
Convert 3′′ into radians.
(ii)
Verify Sin 60 o Cos30 o − Cos 60 o Sin 30 o = Sin 30 o
(iii)
Prove that Sin (180 o + α
(iv)
π 
π 


Prove that Sin  θ +  + Cos  θ +  = Cos θ
6 
3 


(v)
Find Cos 2 α when Cos α =
(vi)
Express Sin 5 x + Sin 7 x as a product.
(vii)
Find the period of tan
) Sin ( 90
o
)
− α = − Sin α Cosα
3
π
,0<α <
5
2
x
7
(viii) Solve the right triangle ABC , in which γ = 90 o ,
β = 50 o 10′ , c = 0.832
(ix)
Define the Angle of Elevation and Depression.
(x)
Find the area of the triangle ABC , in which a = 4.33 , b = 9.25,
(xi)
Without using tables/calculator show that tan −1
(xii)
Find the solution of equation which lies in
(xiii) Find solution of equation which lies in
5
5
= Sin −1
12
13
[ 0, 2π ]
[ 0, 2π ]
r = 56 o 44′
when 1 + Cos x = 0
when Cos x = −
3
2
SECTION-II
3 × 10 = 30
NOTE: - Attempt any three questions.
5.(a)
(b)
6.(a)
(b)
7.(a)
(b)
8.(a)
Use Crammer’s rule to solve the system.
3x1 + x 2 − x3 = − 4 ,
x1 + x 2 − 2 x3 = − 4,
If the 7th and 10th terms of an H.P. are
n −1
Cr +
7
9.(a)
(b)
1
5
and
respectively, find its 14th term.
3
21
5
Cr − 1 = n Cr
5
1 1 .3 1 .3 .5
+
+
+ − − − − as a binomial expansion and find its sum.
3 3 .6 3 .6 .9
5
and the Terminal arm of the angle is not in the 3rd quad,
find the values of
(b)
5
n −1
Identify the series: 1 +
1
5
x2
( x2 + 4 ) ( x + 2 )
Resolve into Partial Fractions.
If tan θ =
− x1 + 2 x 2 − x3 = 1
x −2 − 10 = 3 x −1
Solve the equation
Prove that
5
Csc 2θ − Sec 2θ
Csc 2θ + Sec 2θ
5
Prove without using calculator Cos 20 o Cos 40 o Cos 60 o Cos 80 o =
Solve the triangle in which a = 4584 ,
Prove that Sin −1
1
5
+ Cot −1 3 =
b = 5140 ,
1
16
c = 3624
π
5
5
5
4
15-2015(A)-9000 (MULTAN)