CBSE 12TH MATHEMATICS - Online Test

Answer : Option B
Explaination / Solution:

order = 2, degree not defined, because the function dy/dx present in angle of cosine function.

Answer : Option A
Explaination / Solution:

Equation of a line through a point (x1, y1, z1) and having direction cosines l, m, n is given by : x−x1l=y−y1m=z−z1n

Answer : Option B
Explaination / Solution:

 y = 4−x2>0⇒−2<x<2  And  y=4−x2<0⇒x<−2or...x>2
Required area:
 = ∫02(4−x2)dx+∣∣∣∫23(4−x2)dx∣∣∣= 163+∣∣−73∣∣ =233sq.units

Answer : Option C
Explaination / Solution:

If the product of any square matrix with itself is the matrix itself , then the matrix is called Idempotent.

Answer : Option A
Explaination / Solution:

Here , f′(x)=ddx(x2e−x)
=x2e−x(−1)+2xe−x
⇒f′(x)=e−x(2x−x2)>0
if(2x−x2)>0
i.e. if x(x – 2 )<0 i.e. if 0 < x < 2. Hence f is strictly increasing on [0,2]

Answer : Option B
Explaination / Solution:

Answer : Option C
Explaination / Solution:

In Corner point method for solving a linear programming problem the second step after finding the feasible region of the linear programming problem and determining its corner points is : To evaluate the objective function Z = ax + by at each corner point.

Answer : Option D
Explaination / Solution:

The number of elements in A x A is n x n = n2. hence ,the number of relations on A = number of subsets of A x A = 2nxn =2n2.

Answer : Option B
Explaination / Solution:

Answer : Option B
Explaination / Solution:

Two vectors having same magnitude as well as same direction are always equal.