Mathematics - Online Test
Q1. Let f (x) = x sin, x0, then the value of the function at x = 0, so that f is continuous at x = 0, is
Answer : Option D
Explaination / Solution:
Here, if we directly put x= 0, f(0) = 0 * sin (1/0) = 0.
At L.H.L, put x=0-h ,f(0-h) = = 0.
At R.H.L, put x = 0+h , , f(0+h) = = 0.
Hence, L.H.L = f(0) = R.H.L.
f(x) is continuous at x=0.
Q2. The next term of the series is
Answer : Option B
Explaination / Solution:
Terms of given sequence can be written as
so the required term is 33/32
Q3. If the angle between two lines of regression is , then it represents
Answer : Option B
Explaination / Solution:
here
hence r = 0, therefore there is no linear correlation.
Q4. Let A = { 2 , 3 , 6 }. Which of the following relations on A are reflexive ?
Answer : Option A
Explaination / Solution:
is a reflexive on A , because ( a,a ) ∈ R1 for each a ∈ A
Q5. Slope of a line is not defined if the line is
Answer : Option C
Explaination / Solution:
Vertical lines hve undefined slopes. Hence a line which is parallel to Y-axis has undefined slopes.
Q6. Let p and q be two prepositions given by p : I play cricket during the holidays, q : I just sleep throughout the day then , the compound statement p ∧q is
Answer : Option D
Explaination / Solution:
∧ is replaced by and in verbal form
Q7. dx is equal to
Answer : Option D
Explaination / Solution:
Q8. Direction angles are
Answer : Option C
Explaination / Solution:
the angles are called direction angles, which the position vector makes with the positive x-axis ,y-axis and z-axis respectively
Q9. A black and a red dice are rolled. Find the conditional probability of obtaining a sum greater than 9, given that the black die resulted in a 5.
Answer : Option C
Explaination / Solution:
n(S)=36.
Let A = event of getting sum greater than 9.
= {(4,6),(5,5),(6,4),(5,6),(6,5),(6,6)}
And B = event of getting 5 on black die.
={(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)}
Let A = event of getting sum greater than 9.
= {(4,6),(5,5),(6,4),(5,6),(6,5),(6,6)}
And B = event of getting 5 on black die.
={(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)}
Q10. The minimum value of sin x −− cos x is
Answer : Option B
Explaination / Solution:
(−12√)+(−12√)=−2–√
