CBSE 11TH MATHEMATICS - Online Test

Answer : Option A
Explaination / Solution:

use,r(x,y)=1n∑i=1n(Xi−X¯)(Yi−Y¯)1n∑i=1n(Xi−X¯)2√1n∑i=1n(Yi−Y¯)2√

Answer : Option A
Explaination / Solution:

Distance between parallel lines is given by |C1−C2|A√2+B2

Now substituting the values we get,

|13−(13)|3√2+42=265 

Answer : Option B
Explaination / Solution:

iff means a double implication statement so symbolic form has ↔

Answer : Option D
Explaination / Solution:

If n = 0 the given expression becomes 1.2.3.4........r = r! Also when n = 1 one more extra term will be there in the product  2.3.4........(r+1)which is also divisible by r!.

Answer : Option D
Explaination / Solution:

Answer : Option B
Explaination / Solution:

We have  nCr - 1  + nCr = n+1Cr

Hence 12C4 + 12C5 = 13C5 ................(i)

But given 12C4 + 12C5 =nC5 ................(ii)

Comparing (i) and (ii) we get  n = 13

Answer : Option A
Explaination / Solution:

Answer : Option A
Explaination / Solution:

we know that general equation of sphere is  x2+y2+z2+2gx+2fy+2hz+c=0

since sphere passing through the points  ( 4 ,3 , 0 ) , ( 0 , 4 , 3 ) ,( 0 , 5 , 0 ) and ( 4 , 0 , 3 ) so putting these values one by one in given equation , we get

16+ 9+ 8g + 6f + c=0    =>8g +6f +c = -25  -------------1)

16 +9 +8f +6h +c=0    =>8f + 6h +c= -25   -----------2)

25 + 10f +c  = 0       -----------------------3)

16+ 9+ 8g + 6h +c=0    =>8g +6h +c= -25  -------------4)

by 2) - 4 ) we have  f = g

using this in 1) we have 16f +c = -25 -------5)

Now solving 3) and 5) we get f=0 

using value of f  we have g= 0 , h= 0 , c= -25

Now radius =(−g)2+(−f)+(−h)2−c−−−−−−−−−−−−−−−−−−−−√  = 25−−√ =5

Answer : Option C
Explaination / Solution:

Answer : Option A
Explaination / Solution: