Mathematics - Online Test
Q1. The value of 
is
is
Answer : Option C
Explaination / Solution:
Q2. Vector has
Answer : Option C
Explaination / Solution:
A vector has both magnitude as well as direction.
Q3. A coin is tossed three times, if E : head on third toss , F : heads on first two tosses. Find P(E|F)
Answer : Option B
Explaination / Solution:
Q4.
The value of
is
is
Answer : Option D
Explaination / Solution:
Q5. If A = {(x, y) : y = ex, x∈R} and B = {(x, y) : y = e-x, x ∈ R} then n(A ∩ B) is
Answer : Option C
Explaination / Solution:
Q6. 
Answer : Option B
Explaination / Solution:
Q7. is equal to
Answer : Option C
Explaination / Solution:
Q8. Let P(n)P be a statement and let P(n)⇒P(n+1) for all natural numbers n , then what will the nature of P(n) ?
Answer : Option D
Explaination / Solution:
Since the statement is conditional statement ( if....then).
Q9. Let be a statement , where n is a natural number , then is true for
Answer : Option C
Explaination / Solution:
Since for example n = 4 will give LHS as 16 and RHS as 4! = 1.2.3.4= 24
Q10. In how many ways can the letters of the word ‘MATHEMATICS ‘be permuted so that consonants always occur together?
Answer : Option C
Explaination / Solution:
In the word 'MATHAEMATICS' there are 7 consonants which are M-2 ,,H-1,C-1,S-1, T-2 .Since they have to occur together we treat them as a single unit.
Now this single unit together with the remaining 4 vowels which are A-2,E-1,and I-1 will account for 5 letters.
Now in these 5 letters we have A is repeating twice these can be aarranged in different ways.
Corresponding to each of these arrangements the consonents can be arranged in different ways.
Hence the number of ways it can be arranged is =75600
