CBSE 12TH MATHEMATICS - Online Test

Answer : Option D
Explaination / Solution:

aˆ=a→∣∣a→∣∣, is called the unit vector of a given vector 
⃗ $\stackrel{}{\mathrm{a }}$ in the direction of   a⃗ 

Answer : Option B
Explaination / Solution:

It is given that :
P(A/B)=P(B/A)⇒P(A∩B)P(B)=P(B∩A)P(A)⇒1P(B)=1P(A)⇒P(A)=P(B)

Answer : Option C
Explaination / Solution:

The values of tanx repeats after an interval of π.

Answer : Option C
Explaination / Solution:

limx→k−(x−[x])=limx→k−x−−limx→k−[x] = k - (k - 1) = 1 for all x∈(k−1,k),[x]=(k−1)

Answer : Option C
Explaination / Solution:

Order = 1 , degree = 1. Since the equation has the highest derivative as y' and its power is 1

Answer : Option A
Explaination / Solution:

If a1, b1, c1 and a2, b2, c2 are the direction ratios of two lines and θ is the acute angle between the two lines; then , the cosine of the angle between these two lines is given by : 

Answer : Option D
Explaination / Solution:

Required area :
$∫1elogexdx= [xlogx−x]e1 =(eloge−e) - (1log1−1)= 1

Answer : Option A
Explaination / Solution:

[xyz]1 x 3 ⎡⎣⎢ahghbfgfc⎤⎦⎥3x3⎡⎣⎢xyz⎤⎦⎥3x1= [A]1 x 1${\left[A\right]}_{1x1}$ . ( where ; matrix A denotes the product of three given matrices.)

Answer : Option A
Explaination / Solution:

f′(x)=ddx(tan−1x)

Answer : Option C
Explaination / Solution:

Because , if A=B+C then |A|=|B+C|