fazaia inter college lahore Send up examination class xi and xii 2017-18

1. 2
Roll No.
FAZAIA SCHOOLS & COLLEGES SEND-
UP EXAM: MATHEMATICS HSSC-I
(Session 2017 – 18)
Name of Candidate
Time Allowed : 2:35 Hours Total Marks: 80
NOTE: Sections ‘B’ and ‘C’ comprise pages 1-2 and questions therein are to be answered
on the separately provided Answer Book. Use supplementary answer sheet i.e.
Sheet – B if required. Write your answers neatly and legibly.
SECTION – B (Marks 40)
Q. 2 Attempt any TEN parts. All parts carry equal marks. (10 X 4 = 40)
(i) Simplify 2
by expressing in the form of a + ib .
5 + − 8
(ii) Construct truth table for the statement: (P∧ ~ P) → q
(iii) Verify that
a +
l a
a
a
a +
l a
a
a
a + l
= 
2
(3a + )
(iv) Determine that p is tautology, absurdity or contingency.
(v) Find the values of the trigonometric function:
− 71π
6
(vi) Reduce cos
4
θ to an expression involving only function of multiples of θ, raised to
(vii)
the first power.
m
2
− 1
If cotθ =
2m
(0 < θ < π ) find the value of remaining trigonometric ratios.
(viii) Draw the graph of y = tan x, x ∈[−π , π ]
(ix)
Show that
1
=
2rR
1
+
1
+
1
ab bc ca
(x) Solve the triangle ABC, by using law of cosine given that b = 3, c = 5,α = 120

.
(xi) Show that cos
−1
(−x) = π − cos
−1
x
(xii) Solve the equation: sin 2x = cos x

2. (xiii) Find the measure of greatest angle, if sides of the triangle are 16, 20, 33.
(xiv) Prove that Z = Z if and only if Z is real.
SECTION – C (Marks 40)
Note: Attempt any FIVE questions. All questions carry equal marks. (5 X 8= 40)
 1 −
5
3i 
Q. 3 Find out real and imaginary parts of :
  1 + 3i 
Q. 4 Solve the system of linear equations by Cramer’s rule
2x + 2y + z = 3
3x − 2y − 2z = 1
5x + y − 3z = 2
Q. 5
Q. 6 Prove that:
1
cosecθ − cotθ −
1
sinθ =
1
sinθ −
1
cosecθ + cotθ
Q. 7 Prove without using tables / calculator that sin19

cos11

+ sin 71

sin11

=
1
2
Q. 8
The sides of a triangle are
triangle is120

.
x
2
+ x +
1,
2x + 1 and x
2
− 1 . Prove that greatest angle of
the
Q. 9 Prove that: sin
−1
5
+ sin
−1
13
7
= cos
−1 253
25 325
Prove that cot ሺ� + �ሺ=
𝐶𝑜� � 𝐶𝑜� �−1
𝐶𝑜� �+𝐶𝑜� �