CBSE 12TH MATHEMATICS - Online Test
Q1. is equal to
Answer : Option A
Explaination / Solution:
Q2. Determine order and degree (if defined) of +sin(y’’’) = 0
Answer : Option A
Explaination / Solution:
Order = 4 , degree not defined , because the function y’’’ present in the angle of sine function.
Q3. If and are the direction cosines of two lines; and is the acute angle between the two lines; then
Answer : Option A
Explaination / Solution:
If and are the direction cosines of two lines; and is the acute angle between the two lines; then the cosine of the angle between these two lines is given by : .
Q4.
The area bounded by y = 2cosx , x = 0 to x =2π and the axis of x in square units is
Answer : Option C
Explaination / Solution:
$= = == 2
Therefore , total area from x= 0 to x = 2 is 4 X 2= 8 sq. units.
Therefore , total area from x= 0 to x = 2 is 4 X 2= 8 sq. units.
Q5. If a square matrix A has two identical rows or columns , then det.A is :
Answer : Option C
Explaination / Solution:
If two rows or column of a matrix are identical then determinant of such a matrix is zero.
Q6. The function f (x) = m x + c where m, c are constants, is a strict decreasing function for all x∈R , if
Answer : Option D
Explaination / Solution:
f ( x) = mx + c is strict decreasing on R
if f ‘ ( x) < 0 i.e. if m < 0 .
is equal to
Q8. Let R be the feasible region for a linear programming problem,and let Z = ax + by be the objective function. If R is bounded, then the objective function Z has both a maximum and a minimum value on R and
Answer : Option D
Explaination / Solution:
Let R be the feasible region for a linear programming problem,and let Z = ax + by be the objective function. If R is bounded, then the objective function Z has both a maximum and a minimum value on R and each of these occurs at a corner point (vertex) of R.
Q9. Let A = {1, 2, 3}. Which of the following is not an equivalence relation on A ?
Answer : Option A
Explaination / Solution:
A relation R on a non empty set A is said to be reflexive iff xRx for all x R . A relation R on a non empty set A is said to be symmetric iff xRyyRx, for all x , y R .
A relation R on a non empty set A is said to be transitive iff xRy and yRzxRz, for all x R. An equivalence relation satisfies all these three properties. .
None of the given relations satisfies all three properties of equivalence relation.
A relation R on a non empty set A is said to be transitive iff xRy and yRzxRz, for all x R. An equivalence relation satisfies all these three properties. .
None of the given relations satisfies all three properties of equivalence relation.
