CBSE 12TH MATHEMATICS - Online Test

Answer : Option C
Explaination / Solution:

f′(x)=1(1+x)2−11+x=−x(1+x)2<0.

Hence decreasing function.

Answer : Option A
Explaination / Solution:

Since g(x) and h(x) are integrals of the same function , therefore ; g(x) – h(x) is constant. 'OR'

[g(x)+C] - [f(x)+D]=0 => g(x) - f(x) = D-C, Which is a constant of integeration. 

 

Answer : Option D
Explaination / Solution:

If   a⃗   ,b⃗   and  c⃗      are any three vectors then the correct expression for distributivity of scalar product over addition is: 

Answer : Option C
Explaination / Solution:

If E and F are events then P (E ∩ F) = P (E) P (F|E), P (E) ≠ 0. By the defination of conditional probability of two events

Answer : Option B
Explaination / Solution:

The value of cos1050 =cos(90+15)0=−sin150=1−3√22√.

Answer : Option D
Explaination / Solution:

limx→0+f(x)=limx→0+(1+x)=1limx→0−f(x)=limx→0−x=0,∴limx→0f(x) Does not exist.

Answer : Option C
Explaination / Solution:

0 , because the particular solution is free from arbitrary constants.

Answer : Option A
Explaination / Solution:

If a line has the direction ratios – 18, 12, – 4, then its direction cosines are given by:

Answer : Option A
Explaination / Solution:

Upper Triangular matrix is given by :⎡⎣⎢a1100a12a220a13a23a33⎤⎦⎥ Here, aij=0 if i is greater than j.and aij≠0, if I is less than j.

Answer : Option B
Explaination / Solution:

The two curves parabola and the line meet where,
 3 - x =x2+1 ⇒x2+x−2 = 0 ⇒x=−2,1.$\mathrm{.}$
Required area ;
∫−21{3−x−(x2+1)}dx = [2x−x22−x33]1−2= 92