CBSE 11TH MATHEMATICS - Online Test

Given equation is 3x2 + 4y2 = 24

dividing throught by 24 we get,

x28 + y26 = 1

This implies a2 = 8 and b2 = 6

e = a2−b2√a =12

A team of 4 players are to be selected.

2 out of 6 men can be done in 6C2 ways. 2 out of 4 women can be done in 4C2ways. 

So the number of ways to select 4 players is 6C2x 4C2= 90.

Now we can arrange these people to form  mixed doubles.

 If M1,M2,W1,W2, are the 4 members selected then one team can be chosen as (M1,W1)or(M1,W2)  in 2 different ways 

Therefore the required number of arrangements= 90x2 = 180.

The equation ( x – 1 ) ( x – 2 ) = 0 represents , in three dimensional space , a pair of parallel planes

( x – 1 ) ( x – 2 ) = 0    => ( x – 1 )=0  ,   ( x – 2 ) = 0

          x =1 and x=2 

According to the equation ax +by +cz = d and by the formula a1a2=b1b2=c1c2we have both the planes represent pair of parallel planes

3 − 2x ≤ 9

⇒−2x≤9−3⇒−2x≤6⇒−x≤3⇒x≥−3