Mathematics - Online Test
Q1. If a function f is derivable at x = a, then is equal to
Answer : Option C
Explaination / Solution:
Q2. If the radius of the circumcircle of an isosceles triangle PQR is equal to PQ ( = PR), then the angle P is
Answer : Option A
Explaination / Solution:
Q3. 1.2.3 + 2.3.4 + 3.4.5 + ………..up to n terms is equal to 1/4 n ( n + 1 ) ( n + 2 ) ( n + 3 ) is true for
Answer : Option A
Explaination / Solution:
By the method of mathematical induction the given statement is true for n = 1,2,3.....
Q4. The total area under the standard normal curve is
Answer : Option D
Explaination / Solution:
No Explaination.
Q5. The points ( 1 , 1 , 0 ) , ( 0 , 1 , 1 ) , ( 1 , 0 , 1 ) , and ( 2/3 , 2/3 , 2/3 ) are
Answer : Option B
Explaination / Solution:
Q6. If A and B are any two square matrices of the same order, then
Answer : Option B
Explaination / Solution:
By the property of transpose , (AB )’ = B’A’.
Q7. A class is composed 2 brothers and 6 other boys. In how many ways can all the boys be seated at the round table so that the 2 brothers are not seated besides each other?
Answer : Option B
Explaination / Solution:
First we will fix one person from the 6 boys then 5 others can be arranged in 5! ways=120 ways
Now there are 6 places left in which 2 brothers can sit,so they can choose any 2 places from the 6 places in 6C2 ways=15 ways
Also 2 brothers can arrange themselves in 2! ways
So th ways in which the two brothers can be seated=15*2=30
Hence total ways in which all can be seated =120*30=3600
Q8. Vector equation of a plane that contains three non collinear points having position vectors 
is
is
Answer : Option D
Explaination / Solution:
Vector equation of a plane that contains three non collinear points having position vectors 
is given by: 
is given by:
Q9. In a bank, principal increases continuously at the rate of 5% per year. An amount of Rs1000 is deposited with this bank, how much will it worth after 10 years
Answer : Option D
Explaination / Solution:
Here P is the principal at time t
When P = 1000 and t = 0 ., then ,
c = 1000, therefore, we have :
When P = 1000 and t = 0 ., then ,
c = 1000, therefore, we have :
Q10. If are non real complex numbers such that and , then
Answer : Option C
Explaination / Solution:
