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SRI SRI ACADEMYIIT RAMAIAH MODEL QUESTION PAPER 2010
MATHEMATICSTime : TWO HOURS MAX Marks : 50
(8.30am 10.30am)
NOTE:-1. Attempt all questions2. Rough work must be enclosed
with answer book
3. While answering, refer to a question by its serial number as
well assection heading (eg. Q2/Sec.A)
4. There is no negative marking5. Answer each of Section A, B, C
at one place
6. Elegant solutions will be rewarded7. Use of calculators,
slide rule, graph paper and logarithmic,
trigonometric and statistical tables is not permitted.
Note: All answers to questions in Section A , Section B and
Section C must
be supported by mathematical arguments. In each of these
sections order of thequestions must be maintained.
SECTION A 5 x 2 = 10 M
This section has Five Questions. Each question is provided with
five alternativeanswers. Only one of them is the correct answer.
Indicate the correct answer by A,
B, C, D, E.1. Find the highest power of 5 in 2010 !
A) 500 B) 402 C) 482 D) 501 E) 401
2. A circle touches the y - axis at A (0,9) and cuts the x- axis
at B (3,0). Find theother point on the x- axis through which the
circle passes.
A) (0,27) B) (9,0 ) C) (0,9) D) (27,0) E) (9,27)3. Let be the
roots of x2 x + p = 0 and be the roots of x2 - 4 x + q = 0. If
,
, , , are in G.P then integral values of P and q respectively
areA) 2 , -32 B) 2, 3 C) 6, 3 D) 6 , -32 E) 2,3
4. 50 x 50 x 50 (where there are hundred 50s) is how many times
100 x 100 x100 x (where there are fifty 100s)?
A) 252525 x .(where there are fifty 25s)
B) 4 x 4 x 4 x (where there are fifty 4s)
C) 2 x 2 x 2 x (where there are fifty 2s)D) 1 time E) None of
these
5. D,G are points on the side AB of ABC , E and F are points on
the sidesACand BC respectively such that DE|| BC , EF || AB and FG
|| CA .Then D,E,F,G are the consecutive vertices of a quadrilateral
.
A) always B) only if AD
AB>
C) onlyAD
ABif = D) only if
AD
AB<
E) none of these
SECTION B 5 x 2 = 10 M
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This section has Five Questions. In each question a blank is
left. Fill in theblank.
1. ___ is the remainder when x2010 is divided by x2 -1
2. In the binomial expansion of (a - b)n, n 5 the sum of the 5th
and 6th terms is
zero. Then a/b is equal to
3. The number of points P strictly lying inside an equilateral
triangle ABC such thatthe sum of the perpendicular distances from P
to the three sides of the triangle
is minimum, is________
4. In ABC , AB =15 , BC =18 , CA =25. A semicircle is inscribed
in triangle ABC
such that diameter of semi circle lies on AC . If O is the
centre of circle thelength of AO_________
5. The quadratic equation ax2 + bx + a=0 has a positive
coincident root . Then
=____________
SECTION C 5 x 2 = 10M
1. Find the sum of the series12 22 + 32 42 + + 20092 - 20102
2. Determine the radius of the circle inscribed in a rhombus
whose diagonals
measure 10 units and 24 units.3. The sum of three numbers in G.P
is 14 . If the first two terms are each increased
by 1 and third term decreased by 1 the resulting numbers are in
A.P. Find the
numbers?
4. The measure of the vertex angle of isosceles triangle ABC is
and sides oftriangle are
, sin ,Sin Sin . Compute the area of ABC.
5. Find out the unequal pairs of sets, if any, among the
following sets.
i) ( ) ( )A B B A ii) ( ) ( )A B A B
iii) ( ) ( ) 'A B A B iv) ( ') ( ')A B B A
v) ( ) ( ' ')A B A B
SECTION D 5 x 4 = 20 M
1. Solve for positive integers x and y such that
x2 + y2 + 37 ( x + y ) + 2xy - 2010 = 0
2. If a triangle and a convex quadrilateral are drawn on the
same base and no partof the quadrilateral is outside the triangle,
show that the perimeter of the
triangle is greater than the perimeter of the quadrilateral.
3. Lines l and m intersect in O. Explain how you will construct
a triangle OPQ such
that P l, Q m, OP and OQ are equal in length and PQ is of given
lengtha.
4. f and g are two real variable real valued functions defined
by
( ) ( ),3 7, 2
2, 0 1, 2 2.2 3, 0 1, 2
x if xx if xf x g x x if x Find gof
x if x x if x
+ + = =
