Mathematics - Online Test
Q1.
sin sin
Answer : Option B
Explaination / Solution:
Q2. For all is divisible by :
Answer : Option C
Explaination / Solution:
Replace n = 1 we get 209 which is divisible by 11.
Q3. A pair of dice is tossed once and a total of 8 has come up. The chance that both the dice show up same number is
Answer : Option C
Explaination / Solution:
on tossing a pair of dice total outcomes are 36
out of which getting a total of 8 have possiblities {(2,6),(6,2),(3,5),(5,3),(4,4)}=5
and from these 5 outcomes getting same no. on both dice is (4,4)=1
so, probability is 1/5
Q4. Volume of a tetrahedron is k X area of one face X length of perpendicular from the opposite vertex upon it, where k is
Answer : Option D
Explaination / Solution:
Volume of tetrahedron 
where a,b,c are co-terminus edges of tetrahedron.a X b is area of one face and c is the perpendicular from the opposite vertex
where a,b,c are co-terminus edges of tetrahedron.a X b is area of one face and c is the perpendicular from the opposite vertex
Q5. Each diagonal element of a skew-symmetric matrix is
Answer : Option A
Explaination / Solution:
The diagonal elements of a skew-symmetric is zero.
Q6. Different calendars for the month of February are made so as to serve for all the coming years. The number of such calendars is
Answer : Option C
Explaination / Solution:
The month of February has either 28 days (non-Leap Year) or 29 days(Leap Year).
Thus there are 2 possibility for the number of days in February.
Also the first day of the month of February can be any of the 7 days in a week.
So total number of February calendars = 2 * 7 =14
Q7. Two lines 
are coplanar if
are coplanar if
Answer : Option D
Explaination / Solution:
In vector form:
Two lines 
are coplanar if (
.
are coplanar if (
Q8. To form a differential equation from a given function
Answer : Option A
Explaination / Solution:
We shall differentiate the function equal to the number of arbitrary constant so that we get equations equal to arbitrary constant and then eliminate them to form a differential equation
Q9.
If is a complex a number such that then is
Answer : Option C
Explaination / Solution:
Q10. is
Answer : Option D
Explaination / Solution:
