CBSE 11TH MATHEMATICS - Online Test

Answer : Option A
Explaination / Solution:

let us assume that y = 3x – 5 and y = 2x – 4 are lines of regression of x on y and y on x respectively,therefore

bxy=1/3byx=2

ρ=±bxybyx−−−−−√=±2/3−−−√

but sign of ρ$\rho$ is same as byx and bxy

therefore ρ=2/3−−−√

Answer : Option B
Explaination / Solution:

The required condition for concurrency is a3(b1c2 - b2c1) + b3(c1a2 - c2a1) + c3(a1b2 - a2b1) = 0

Here a1 = l, a2 =m, a3 = n and b1 = m, b2 = n, b3 = l and c1 = n, c2 = l and c3 = m

Substituting the values  we get

n(ml - n2) + l(nm - l2) +m(ln - m2) = 0

This implies l3 + m3 + n3 - 3lmn = 0

That is (l + m+ n)(l2 + m2 + n2 -lm -mn - nl) = 0

This implies l + m + n = 0

Answer : Option C
Explaination / Solution:

p:22=5

q:I get first class

the contrapositive of p→q is∼q→∼p. hence the answer is If I do not get a first class , then 22≠5

Answer : Option A
Explaination / Solution:

x2+y2=25

After completing the square,we get

(x−0)2+(y−0)2=52

so center is (0,0) and radius is 5 units.

As the normal should pass through the centre of the circle, center should satisfy the equation of normal

so 3x – 4y = 0 is the equation of normal as (0,0) satisfy this equation.

Answer : Option D
Explaination / Solution:

Answer : Option D
Explaination / Solution:

replace n = 1 we get the first term and n = 2 we get the sum of first two terms....

Answer : Option D
Explaination / Solution:

Total number of ways of getting even number is 3

Out of these 3 even number we have to get either 2 or 4 which can be done in 2 ways.

So required probability is 2/3

Answer : Option C
Explaination / Solution:

Since the lines intersect.Hence they have a common point in them.hence the distance will be zero

Answer : Option B
Explaination / Solution:

4 flowers which are always together can be considered as one SET, 

Therefore we have to arrange one SET ( 4 flowers ) and 4 other flowers into a garland. 

Which means, 5 things to be arranged in a garland. 

(5-1)! 

And the SET of flowers can arrange themselves within each other in 4! ways. 

Therefore 

(5-1)!*(4!) 

But, Garland, looked from front or behind does not matter. Therefore the clockwise and anti clockwise observation does not make difference. 

Therefore 

(5-1)! * (4!)/ 2 

= 288.

Answer : Option A
Explaination / Solution: