Mathematics - Online Test
Q1. The solution of the differential equation, for 
with initial conditions y(0) = 0 and 
is (u(t) denotes the unit step function),
with initial conditions y(0) = 0 and is (u(t) denotes the unit step function),
Answer : Option A
Explaination / Solution:
Q2. is divisible by :
Answer : Option D
Explaination / Solution:
put n = 1 we get 11 .
Q3. From a pack of 52 cards, the cards are drawn one by one till an ace appears. The chance that an ace does not come up in first 26 cards is
Answer : Option A
Explaination / Solution:
No Explaination.
Q4. The equation 
represents
represents
Answer : Option D
Explaination / Solution:
The equation 
x=0 , y= , z= 0 which represent Y axis
x=0 , y= , z= 0 which represent Y axis
Q5. If , then ,which of the following is true :
Answer : Option A
Explaination / Solution:
The given matrix is a skew – symmetric matrix.,therefore , A = - A’.
Q6. The number of all even divisors of 1600 is
Answer : Option B
Explaination / Solution:
We have 1600=
To form factors we have to do selections from a lot of 2's and 5's and multiply them together.
To form even factor we should choose at least one 2's from the lot , which will ensure that what ever be the remaining selection, their multiplication will always result in an even factor.
The number of ways to select atleast one ‘2’ from a lot of six identical ‘2’s will be 6 (i.e. select 1 or select 2 or select 3 or select 4 or select 5 or select 6)
And, we’ll select any number of ‘5 from a lot of two identical ‘5’s in 3 ways(select 0, select 1,select 2)
There fore the total number of selection of even factors=6x3=18
Q7. Find the equation of the plane through the line of intersection of the planes x + y + z = 1 and 2x + 3y + 4z = 5 which is perpendicular to the plane x – y + z = 0.
Answer : Option D
Explaination / Solution:
The equation of the plane through the line of intersection of the planes
Q8. Forming a differential equation representing the given family of curves by eliminating arbitrary constants a and b from yields the differential equation
Answer : Option A
Explaination / Solution:
Q9. The points z = x + iy which satisfy the equation | z | = 1 lie on
Answer : Option B
Explaination / Solution:
which is the equation of a circle whose centre is origin and radius = 1
Q10.
In the expansion of, the term is 24 times the term . The value of x is
Answer : Option C
Explaination / Solution:
