Team 1
Team 2
Team 3
Team 4
Team 5
100

find HCF & LCM of 135 & 225.

HCF=45

LCM=675

100

find a quadratic polynomial whose zeros are 2+ root 3 & 2- root 3.

p(x)= x2-4x 1

100

find the HCF by using euclid's division lemma.

4052 & 12576

HCF:4

100

find zeroes of x2-5

x=-root 5,root 5

100

if the product of zeroes of the polynomial ax2-6x-6 is 4, find a

a= -3/2

200

if alpha, beta are zeroes of the quadratic polynomial f(x)= 6x2+x-2. find alpha/beta + beta/alpha.

alpha=-2/3

beta=1/2

alpha/beta+beta/alpha=-25/12

200

prove that 2 root 3+2 is irrational.

root 3 =a-2b/2b

the RHS is a rational which never equal to an irrational number root3

so,it is irrational number.

200

form a quadratic equation whose alpha is 3-root3/5 & beta is 3+ root3/5.

p(x)=x2-6/5x + 6/25

200

if m & n are zeroes of the polynomial 3x2+11x-4. find m/n + n/m.

-145/12

200

the HCF of two numbers is 27& their LCM is 162.if one of the number is 54. find the other number.

81

300

find the zeroes of 3x2+x.

x=0 & -1/3

300

find the least number by which when divided by 6,15 & 18 leave remainder 5 in each case.

LCM of 6,15,18 = 90

the number which leave remainder 5 in each case = 90+5=95.

300

find the smallest 4 digit number which is divisible by 18,24 & 32.

LCM=288

smallest 4 digit number=1000/288

[quotient=3,remainder=136]

288x3+288=864+288

=1152

300

if alpha,beta are the zeroes of the polynomial f[x]=kx2+4x+4 such that alpha2+beta2=24.

find k.

k= -1 or 2/3

300

using bpt prove that the line drawn through the mid point of one side of a triangle parallel to another side bisects the 3rd side.

step by step:

by BPT=AM/MB=AN/NC

AM=MB

AN/NC=1

=>AN=NC

so,N is the mid point of AC

400

rhombus PQRS is inscribed in triangle ABC such that angleB is one of its angle. P,Q & R lie on AB,AC&BC respectively.

if AB=12cm & BC=6cm, find the sides PQ,RB of rhombus.

angle A=common

angle P=corresponding angles.

by AA it is similar

AP/AB=PQ/BC=AQ/AC

{Cpst or sss}

12-9/12=9/6

a=4

400

to enhance the reading skills of grade x students ,the school nominates you & 2 of your friends to set up a class library.there are 2 sections A & B.

there are 32 students in sect A & 36 students in sect B. what is the minimum no. of books you will aquire for the class library,so that they can be distributed equally among students of sect A or sect B?

LCM= 288

400

in trapezium ABCD,AB||DC, E&F are points on non-parellel sides AD & BC respectively, such that EF||AB. show that AE/ED=BF/FC.

by BPT= AQ/CQ=AE/ED

in triangle ABC

by BPT= BF/FC=AQ/CQ

so,AE/ED=BF/FC

Hence,prooved.

400

what is the remainder of the polynomial 6x4+8x3+17x2+21x+7 ,if it is divided by another polynomial 3x2+4x+1