CBSE 11TH MATHEMATICS - Online Test

Answer : Option D
Explaination / Solution:

Using the formulae,

ρ=cov(x,y)σxσy

tanθ=1−ρ2ρ.σxσyσ2x+σ2y

here ρ=0

therefore θ=π2

Answer : Option A
Explaination / Solution:

Area of the triangle formed by the coordiates( x1,y1), (x2,y2) and (x3,y3) is given by

12[x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)]

On solving the lines 1 and 2, the point of intersection is (0,0)

On solving the lines 2 and 3, the point of intersection is (4,8)

\On solving the line 3 and 1 , the point of intersection is (-2,-2)

Now substituting the values to find the area of the triangle,

Area = 12| [ 0 + 4(-2-0) +(-2)(0 - 8)] |

 = 4 sq units

Answer : Option D
Explaination / Solution:

the contrapositive of p→q is∼q→∼p

Answer : Option D
Explaination / Solution:

Solving the above two equations we get,

x=acosα−bsinα---(i) 

y=asinα−bcosα ---(ii)

Squaring both sides of (i) and (ii) and adding both the equation we get  x2+y2=a2+b2.

which represents the locus of circle as

(i) it is quadratic equation

(ii) coeff of x2 = coeff of y2

(iiI) there is no trerm involving xy.

Answer : Option A
Explaination / Solution:

Answer : Option A
Explaination / Solution:

By the method of mathematical induction the given statement is true for n = 1,2,3.....

Answer : Option D
Explaination / Solution:
No Explaination.

Answer : Option B
Explaination / Solution:

Answer : Option B
Explaination / Solution:

First we will fix one person  from  the 6 boys  then  5 others can be  arranged in  5! ways=120 ways 

Now there are 6 places left in which 2 brothers can sit,so they can choose any 2 places from  the 6 places  in 6C2 ways=15 ways

Also 2 brothers can arrange themselves in 2! ways

So th ways in which the two brothers can be seated=15*2=30

Hence total ways in which all can be seated =120*30=3600

Answer : Option C
Explaination / Solution: