CBSE 12TH MATHEMATICS - Online Test
Q1. Area of the region bounded by the curves y = , x = a , x = b and the x- axis is given by
Answer : Option A
Explaination / Solution:
Required area
∫abexdx=[ex]ba=eb−ea
Q2. If P is of order 2 × 3 and Q is of order 3 × 2, then PQ is of order
Answer : Option B
Explaination / Solution:
Here, matrix P is of order and matrix Q is of order , then , the product PQ is defined only when : no. of columns in P = no. of rows in Q. And the order of resulting matrix is given by : rows in P x columns in Q.
Q3. In case of strict decreasing functions, slope of tangent and hence derivative is
Answer : Option B
Explaination / Solution:
In case of a strict decreasing function , slope of tangent and hence derivative is either negative or zero because decreasing function change sign from positive to negative and making obtuse angle measured clockwise.Hence negative and will be zero at peak.
Q4. A square matrix A is invertible iff det A is equal to
Answer : Option D
Explaination / Solution:
Only non-singular matrices possess inverse.
Q5. In linear programming infeasible solutions
Answer : Option C
Explaination / Solution:
In linear programming infeasible solutions fall outside the feasible region . In other words, it the region other than the feasible region is called the infeasible region.
Q6. Let R be the relation on N defined as x R y if x + 2 y = 8. The domain of R is
Answer : Option A
Explaination / Solution:
As x R y if x + 2 y = 8 , therefore , domain of the relation R is given by x = 8 – 2y∈N. When y = 1, ⇒x = 6 ,when y = 2, ⇒x =4 , when y =3 , ⇒x = 2 . therefore domain is { 2, 4, 6 }.
Q7. is equal to
Answer : Option A
Explaination / Solution:
Q8. Direction cosines
Answer : Option D
Explaination / Solution:
Cosines of the angles α,β,γ are called direction cosines.
Q9. A black and a red dice are rolled. Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.
Answer : Option A
Explaination / Solution:
Q10. If is equal to
Answer : Option A
Explaination / Solution:
secθ+ tanθsecθ−tanθ=1cosθ+sinθcosθ1cosθ−sinθcosθ=1+sinθ1−sinθ=1+351−35=4
