Mathematics - Online Test
Q1. If a vector is multiplied by any scalar then , the result is always a vector.
Answer : Option B
Explaination / Solution:
Addition of two vectors i.e. vector addition is commutative. i.e..
Q2. If P(A) = and P(B) = , find P (A ∩ B) if A and B are independent events.
Answer : Option B
Explaination / Solution:
Since A and B are independent events .
Therefore ,
Therefore ,
Q3. The conditional probability of an event E, given the occurrence of the event F is given by
Answer : Option C
Explaination / Solution:
The conditional probability of an event E, given the occurrence of the event F is given by :
Q4. The value ofis
Answer : Option B
Explaination / Solution:
Q5. The statement is true for all
Answer : Option C
Explaination / Solution:
when n = 1 , , which is not true.When n = 2, , which is false as well. Also when n = 3 we get .When n = 4 , Hence it is trure frm n = 4 .
Q6. Let f (x) = [x], then f (x) is
Answer : Option A
Explaination / Solution:
f(x) = [x] is derivable at all x except at integral points i.e. on R – I .
Q7. The length of the common chord of the parabolas and is
Answer : Option D
Explaination / Solution:
point of intersection is (0,0) and (1,1). Hence by using the distance formula
=
Q8. A function f(x,y) is said to be homogenous function of degree n if
Answer : Option C
Explaination / Solution:
A function is homogenous if we can write in the form of where n is an whole number .
Q9. Shortest distance between two skew lines is
Answer : Option B
Explaination / Solution:
Shortest distance between two skew lines is The line segment perpendicular to both the lines .
Q10.
In a , Is equal to
Answer : Option D
Explaination / Solution:
