Mathematics - Online Test
Q1. S.D. of a data is 6. When each observation is increased by 1, then the S.D. of new data is
Answer : Option D
Explaination / Solution:
so it depends only on number of observations not on individual observations.
Q2.
Let f (x) = then f (x) is strictly decreasing in
Answer : Option D
Explaination / Solution:
Hence , f is strictly increasing on [1,3].
Hence , f is strictly increasing on [1,3].
Q3. A relation R on a non – empty set A is an equivalence relation iff it is
Answer : Option B
Explaination / Solution:
By definition of Equivalence Relation,a relation is said to be equivalence if it is reflexive,symmetric and transitive
Q4. 
Answer : Option D
Explaination / Solution:
because , the value of the determinant is zero only when , the two of its rows or column are identical., Which is possible only when Either x = 3 or x = 4 .
because , the value of the determinant is zero only when , the two of its rows or column are identical., Which is possible only when Either x = 3 or x = 4 .
Q5. The distance between the parallel lines 4x + 3y + 11 = 0 and 8x + 6y = 15 is
Answer : Option A
Explaination / Solution:
Distance between two parallel lines is given by
c1 = 2 x 11 = 22 and c2 = 15 and A = 8 and B = 6
Now substituting the values we get
= 7/10
Q6. Negation of the statement ∼p→(q∨r) is
Answer : Option A
Explaination / Solution:
rules of negation ∼(p→q)≡p∧∼q
Hence ∼p∧(∼q∧∼r)
Q7. is equal to
Answer : Option D
Explaination / Solution:
∫e−logxdx=∫elogx−1dx=∫x−1dx=log|x|+C
Q8. Correct form of distributive law is
Answer : Option B
Explaination / Solution:
Distributive law is given by :
Q9. The conditional probability of the event E', given that F has occurred is given by
Answer : Option C
Explaination / Solution:
we know that P(S/F) =1
P(E U E'|F)=1 since EUE' =S
P(E/F) +P(E'/F) =1 since E and E' are disjoint events
P(E'/F) = 1- P(E/F)
Q10. is
Answer : Option D
Explaination / Solution:
Because both lies in 3rd quadrant. In 3rd quadrant values of both sine and cosine functions are negative.
