olympiad preparatory test
1
Click here to load reader
description
mathematical olympiad preparatory test by resonance
Transcript of olympiad preparatory test
7/21/2019 olympiad preparatory test
http://slidepdf.com/reader/full/olympiad-preparatory-test-56da680f95092 1/1
Corporate Office : CG Tower, A-46 & 52, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)-324005
Website : www.resonance.ac.in | E-mail : [email protected]
Toll Free : 1800 200 2244 | 1800 258 5555 | CIN: U80302RJ2007PTC024029 MOPT3051114-1
OLYMPIAD PREPARATORY TEST - 3 (OPT-3)STAGE - I
SUBJECT : MATHEMATICS
Date: 05-11-2014 Time : 3 hr. Maximum marks : 60
Instructions :Calculators (in any form) and protractors are not allowed.
Rulers and compasses are allowed.
Answer all the questions, each question carry equal marks. Q.1 has each part worth 5 Marks
1. Find the last three digits of 79999
.
2. ABC is a triangle and 'P' is any point inside it. Perpendiculars let fall from P on BC, CA, AB be A', B' and
C'. The triangle A'B'C' is said to be pedal triangle of triangle ABC. From the point 'P' we draw second
pedal triangle to A', B', C' which is let A" B"C". If third pedal triangle is now drawn from P to A"B"C",
show that it is similar to ABC.
3. Find the positive solutions of the system of equations
x1 +2
1
x = 4, x2 +
3
1
x = 1; x3 +
4
1
x = 4 ......., x99 +
100
1
x = 4, x100 +
1
1
x = 1
4. Find the number of divisors of 20! of the form 4k + 1 where k ! w
5. Let A = (0, 0) and B = (b, 2) be points in the co-ordinate plane. Let ABCDEF be a convex equilateral
hexagon such that "FAB = 120°, AB||DE, BC||EF, CD||FA and the y co-ordinates of its vertices are
distinct elements of the set {0, 2, 4, 6, 8, 10}. Find the area of hexagon ABCDEF ?
6. Find the sum of the series1
2+
1.3
2.4
1
4
# $% &' (
+1.3.5
2.4.6
21
4
# $% &' (
+ .........
