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We will try to emphasize on the graphs
 Particularly, in case of screening, to solve
coordinate and area problems.
 Here are some examples:

The area is bounded by the curve , the x-axis
and the tangent line to the graph of y=x^2
at the point(1,1) expressed as a function of n
is given by
 2(n+1)/n(n-1)
 (n-1)/2n(n+1)
 2(n-1)/n(n+1)
 (n+1)/2n(n-1)

79. The area of the quadrilateral formed by the
tangents to the ellipse
x2 y2
 1
,
at
9 5
the ends of each of its latus-rectum, is

(A)27/4
(B) 9

(C)27/2
(D) 27
 Ans:D

78.Let (0, 0), (21, 0) and (0, 21) be the
vertices of a triangle. The number of
points having integer coordinates which
are strictly inside the given triangle is

(A) 231 (B) 105

(C) 190 (D) 133
 Ans c






82. In the interval [0, 1], the mean value theorem is NOT
applicable to the function
(A) f (x) =1/2-x
x<1/2
(½-x)^2 x>=1/2
(B) f(x) =
(sin x)/x
x ≠0
(C) f (x) = x|x|
(D) f (x) = |x|
ANS: A
1
X=0
The orthocenter of the triangle with
vertices (0, 0), (4, 0) and (3, 4)
(A)(5/4,-4/3)
(B) (3, 12)
(C)(3,5/4
)
(D) (3,3/4)
74.If z is a complex number satisfying |z|
= 1 and z  –1, then the real part of =
 (z-1)/(z+1) is
1
1
 (A)
(B)| z  1| (C) | z  1|
(D) 0

2
| z  1|2
2
2
59. If the angles of a triangle are in the
ratio 4 : 1 : 1, then the longest side and the
perimeter are in the ratio
(A) 3 : 2 + 3 (B) 1: 6
(C) 1 : 2 + 3 (D) 2 : 3
Now
some problems can be
solved by putting some
convenient numbers and
satisfying some conditions.
83. Two numbers are drawn at random, one
after another and without replacement, from
the set {1, 2, 3, 4, 5, 6}. The probability that
minimum of the chosen numbers is smaller
than 4 is
(A) 1/15
(B) 14/15
(C)1/5
(D) 4/5
5. The edge of a cube is measured to be 1.2 
102m. Its volume should be recorded as

(A) 1.7  106 m3.(B) 1.73  106 m3.

(C) 1.70  106 m3.
(D) 1.728  106
m3.


11. A circular loop of wire is
carrying a current i (as shown
in the figure). On applying a
uniform magnetic field inward
perpendicular to the plane of
the loop, the loop
(A) move
along the positive x-direction
(B) move along the
negative x-direction
(C) contract
(D)
expand















 
 
 
 
i 










x
18.A nucleus with mass number A = 220
decays by -emission. The energy
released is 5.5 MeV, a good estimate for
the kinetic energy of the -particle will be

(A) 4.4 MeV (B) 5.4 MeV

(C) 5.6 MeV (D) 6.5 MeV
 18.B



28. A phase difference of /4
is observed between the
current (I) and voltage (V) in
an a.c. circuit with source
voltage E = E0 sin(100t) (see
figure). The combination of
components that would lead to
this (A)
R = 1 k, C = 10
F (B)
R =1k, C=1 F
(C)
R = 100 k, L =
10 H (D)
R =1 k, L = 1
H28. A
V
V
t
/4
i
Comprehension based questions

A quadratic polynomial y=f(x) with absolute
term 3 neither touches nor intersects the
abscissa axis and is symmetric about the line
x=1.The coefficient of the leading term of the
polynomial is unity.A point A(x1,y1)with
abscissa x1=1 and a point B(x2,y2)with ordinate
y2=11 are given in a cartesian rectangular
system of co-ordinate OXY in the first quadrant
on the curve y=f(x) where ‘O’ is the origin.Now
answer the following question.
Vertex
of the quadratic
polynomial is
a.(1,1) b.(2,3) c.(1,2)
d. none
Ans c

The scalar product of the vectors OA and OB is
a.
d.
–18
26
22
-22
e.
Ans b
b.
c.
The area bounded by the curves y=f(x)
and the line y=3 is
A 4/3
B 5/3
C 7/3
D 28/3
Ans C

The graph of y=f(x) represents a parabola
whose focus has the co-ordinates
A (1,7/4)
B (1,5/4)
C (1,5/2)
D (1,9/4)

Ans B