CBSE 11TH MATHEMATICS - Online Test

n(A) = 3

n(B)=6

n(AUB) = n(A)+n(B)-n(A∩B)

for minimum number of elements in A U B

n(A∩B)= 3

so n(AUB = 6

Given in the mixture ,amount of coffee= x grams

Amount of choco=y grams

Amount of coffee is greater than that of choco ⇒ x > y$$

Each coffee powder pack is atmost 10 grams ⇒ x + y ≤ 10    

mean=1n∑i=1nXi⇒36=150∑i=150Xi⇒∑i=150Xi=36×50=1800

After deleting the observations 30 and 42

new sum =1800−30−42=1728

new mean =1728/48=36

Thslope of the given line 2x+6y = 7 is -1/3

Hence the line which is parallel to the above line is 

y = (-1/3)x+c

That is the y intercept is (0,c) and the x intercept is (3c,0)

Using the distance formula

d2 = (0-3c)2 + (3c-0)2

= 10c2

since the distance is 10 is given,

100 = 10c2

therefore c = ±$\pm$10

Since two values are possible, two lines can be drawn.

∼(∼p)≡p

T↔T≡T

F↔F≡T

y = m x + c ---(i)

y2=4ax ---(ii)

putting the value of y from (i) in (ii), we get

(mx+c)2=4ax

=> (mx)2+x(2mc−4a)+c2=0

here

discriminant =(2mc−4a)2−4m2c2−−−−−−−−−−−−−−−−−√

                     =16a2−16amc−−−−−−−−−−−√

when discriminant >0 line touches parabola at two points,

when discriminant < 0 line do not  touches parabola and

when discriminant = 0 line touches parabola at one point

and we know that tangent is a line that touches the curve at exactly one point

so putting discriminat = 0 and solving

we get c=am,m≠0

on putting the value of y from line in the parabola and solving for equal roots.