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Guess
Papers
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Class 1st Year) |
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Class
1TH YEAR Federal Board 2009
Paper:Mathematics
(Objective Type) Time
Allowed: Max.Marks:
Note:Use this
paper to write the answers to the objective questions.No marks will
be awarded for cutting,over-writing or using a pencil.This paper must
be tagged with the answer-book.
1- Insert
the correct option. 20
(i) If sin-1ß =π -cos-1
a, what is the value of ß ?
2
(a) -a (b)
a (c)
π + a (d)
π -a
2
2
(ii) What is the number of solutions
to the equation sin 0 + cos 0 = 0?
(a)
3 (b)
0 (c)
1 (d)
2
(iii) In the triangle ABC, what is the sum
1 + 1 + 1 equal to?
ab
bc ca
(a)
2rR (b) 1
(c)
1 rR (d)
2R
2rR
2
r
(iv) If the period of sec (0p) is 3π what
is the value of p?
2
(a)
4 (b)
2π
(c) 3π (d)
2
3
2
3
(v) If the hour hand of a clock moves
0 radians in 39 minutes,what is the value of 0?
(a)
0.3 (b) 20 (c)
0.4 (d)
39
(vi) If the sin99 = p, What is sin 198 equal
to?
(a)
2p2 - 1 (b) 2p√1-p2 (c)
2p√1+p2 (d) 2p
(vii) If cos A = - cos B,which of the following
represents a relation between A and B?
(a) A + B =π (b)
A + B = 0 (c) A -
B =π (d)
A = B
(viii) If sin x + cos x = 0,what quadrant does x
lie in ?
(a)
1st (b)
2nd (c)
2nd or 4th (d)
4th
(ix) Which of the following is true, if Z
= Z?
(a)
Z is purely real.
(b) Z is purely imaginary
(c)
Z is any complex number (d)
Real part of Z = lmaginary part of Z.
(x) What is the converse of the contra positive
of p→q.
(a)
q→ p (b) ~q→ ~p
(c) ~P→q (d)
P→q
(xi) If A.adj A = O (i.e null matrix),then:
(a) |A|
= 0 (b) |A| = |adj A| (c)
|A| = 1 (d)
Both A and B
|adj
A|
(xii) If x is positive real number,what is the least
value of x + 1 ?
x
(a) -2
(b)
0 (c)
1 (d)
2
(xiii) What is the number of diagonals of a polygon with
n-sides?
(a) nP2 (b)
nC2 - n (c) nP2 - n (d)
n2
(xiv) Under which of the following conditions is the expansion
of (2-3x)-3 is valid?
(a)
|x| = 2 (b) |x| = -
2 (c) |x|> 2 (d)
|x|< 2
3
3
3
3
(xv) If 3x + 2 2x = 5x, what is the value of x ?
(a) 3
(b)
2 (c)
1 (d)
0
(xvi) 1 + 1
- 1 are the partial fractions of
which of the following?
x-1
x+1 x
(a)
x2 + 1 (b) x2 - 1 (c)
1 (d)
x2 + 1
x(x2-1)
x(x2-1) x(x2-1)
x2-1
(xvii) Which of the following statements is correct if 'a' and
'b' are distinct positive real numbers?
(a) 2√ab = a+b (b)
2√ab> a+b (c)
2√ab <a+b (d)
2 (a+b) =√ab
(xviii) If w is one of the complex cube roots of unity,what
is the conjugate of w?
(a)
w2 (b)
-w2 (c)
-w (d)
i
(xix) The series y = 1 + x + x2 + x3
+ ----- is convergent in the interval.
2
4 8
(a)
-2 < x < 2 (b) -1 < x < 1 (c)
-4 < x < 4 (d) -3 < x < 3
(xx) The product of 'n' consecutive positive integers
is divisible by.
(a)
n2 (b)√n
(c)
None of these (d)
n!
2. Attempt any
TEN parts. 40
(i) Find the matrix A if
(ii) Find the condition that a
+ b =
5 may have roots, equal in magnitude but opposite in signs.
x
- a x - b
(iii) Prove that v5 is an irrational
number.
(iv) Resolve 3x3
into partial fractions.
(x+1)2
(x2-1)
(v) Solve cos ec x = √3
+ cot x
(vi) Show that (x + y) is a factory
of x2n-1 + y2n -1; x = -y by mathematical induction for nε
z+.
(vii) The moon subtends an angle of 0.5 at
the eye of an observer on earth.The distance of the moon
from
earth is 3.844 x 10 5 km (approx).what is the length of the diameter
of the moon?
(viii) Show that the sum of n - Ams between 'a'
and 'b' is equal to n - times their Am.
(ix) Express cos 50 + cos 0 as product
and deduce cos 5 0 = 5cos0 - 20cos 30 +16cos 50
(x) One side of triangle garden
is 30m. if its two carner angle are 22 1/2 and 112 1/2,find the cost
of planting
grass in the garden at the rate of Rs.10 per square meter.
(xi) Prove that tan ( 1 sin-1
2x + 1 cos -1 1 - x2)
= 2x
2
1-x2 2
1+x2
1-x2
(xii) If A and B are subsets of U,then prove
in general that (A n B)' = A' U B'
(xiii) There are 9 girls and 12 boys in a class.
One-third of the boys and two-third of the girls have green eyes.
Find the probability that one student chosen as monitor is either
a girls or has green eyes.
(xiv) Prove that sine is a periodic function and
its period is 2π.
Attempt
any FIVE questions. 40
(3) Find the rank of the matrix
(4) A man invests a total of Rs.100,000 in
two companies. His total profit is Rs.5060. If he receives Rs.1980
from one company and rate 1 % more from the other,find the amount
of each investment.
(5) If the numbers 1 , 4 and
1 are subtracted from the three consecutive terms of G.P,the
resulting
2
21 36
numbers
are in H.P. Find the numbers If their product is 1 .
27
(6) Prove that Cos -1 63 and + 2 Tan -1 1
= sin -1 3
65
5
5
(7) Measures of two sides of a triangle are in the
ratio 3:2 and they include an angle of measure 57 .Find the
remaining two angle.
(8) On the same axes and to the same scale, draw
the graph of y = sinx and y = sin2x for their complete periods.
(9) Solve cos2x = sin3x
The
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