CBSE 11TH MATHEMATICS - Online Test

Answer : Option B
Explaination / Solution:

Answer : Option B
Explaination / Solution:

let us assume that 2x + y =7 and x + 2y = 7 are lines of regression of y on x and x on y respectively

therefore, byx=−1/2bxy=−1/2⇒ρ=±(byx−−−√bxy)=±(−12.−12)−−−−−−−√=±12

but sign of p will be same as byx and bxy

hence, ρ=−12

Answer : Option C
Explaination / Solution:

If the lines make equal angles of 450 with the given line, x+y =0.

Then these lines must be perpendicular with each other.

This is possible only when the two lines are parallel to X axis and Y axis.

That is the equations should be x = a constant and y  = a constant.

Since it passes through (1,1)

The equations should be x = 1 or x-1=0 and y=1 or y-1 =0

Answer : Option D
Explaination / Solution:

Associative law

Answer : Option A
Explaination / Solution:

After solving the equations we will get x+y = 2sec θ which represents a linear equation.

Answer : Option A
Explaination / Solution:

cosecθ+2=0⇒cosecθ=−2⇒sinθ=−12⇒sinθ=sin(−π6)⇒θ=nπ+(−1)n(−π6),nϵZ

Hence the values of θ$\theta$ betwwen 0 and 360 are  210o,330o         [when n=1,n=2]

Answer : Option C
Explaination / Solution:

When n = 1 9<4 not valid. when n = 2 27<16 not true. when n = 3 81<64 is in correct. when n = 4 243<256, is true.

Answer : Option D
Explaination / Solution:
No Explaination.

Answer : Option C
Explaination / Solution:
No Explaination.

Answer : Option C
Explaination / Solution:

First we will find the  number of three digit numbers (i.e, numbers from 100 to 999)which can be formed using the digits 0,1,2,3,4,5,6,7,8and 9 with repitition allowed .

Now we have the first place can be filled by any of the 9 digits other than 0 and since repetition is allowed the second and third can be filled by any of the ten digits.

Hence the total number of three digit numbers will be = 9×10×10=900

Now we will consider the case that the number does not have the digit 5.

Now the  first place can be filled by any of the 8 digits other than 0 and 5 and since repetition is allowed the second and third can be filled by any of the 9 digits other than 5.

Hence the total number of ways we can form a  three digit number with out 5 will be =8×9×9=648

Therefore the number of three digit numbers with atleast one 5=900−648=252