Mathematics - Online Test
Q1. The smallest positive integer ‘ n ‘ for which P ( n ) : holds is :
Answer : Option D
Explaination / Solution:
Since the values of n as 1,2,3gives inavlid inequations but when n = 4 we have 16<24, which is valid.
Q2. In the vector form, equation of a plane which is at a distance d from the origin, and is the unit vector normal to the plane through the origin is
Answer : Option D
Explaination / Solution:
In the vector form, equation of a plane which is at a distance d from the origin, and is the unit vector normal to the plane through the origin is given by : 
Q3. Two dice are thrown. The number of sample points in the sample space when 6 does not appear on either dice is
Answer : Option C
Explaination / Solution:
total no. of outcomes=62=36
The pair which shows 6 on either dice are {(6,1),(6,2),(6,3),(6,4),(6,5),(1,6),(2,6),(3,6),(4,6),(5,6),(6,6)}=11
So total number of sample points in sample space when 6 on either dice do not appear=36-11=25
Q4. The equation 
represents
represents
Answer : Option C
Explaination / Solution:
The equation 
represents the plane z=0 as the equation can be written as 
represents the plane z=0 as the equation can be written as In this z-coordinate is zero .So , this represent XY plane i.e. the plane Z=0
Q5.
If A and B are two matrices such that AB = BA and BA = A, then
Answer : Option C
Explaination / Solution:
Q6. The number of even numbers that can be formed by using all the digits 1, 2, 3, 4, and 5 (without repetitions) is
Answer : Option C
Explaination / Solution:
| t th | th | h | t | o |
| 1 | 2 | 3 | 4 | 2 |
Since we need an even number , ones place can be occupied by only two numbers 2 and 4 in two ways.
Since repetition is not allowed tens place is occupied by remaining 4 numbers in 4 ways and the hundred's place by 3 ways and thousands place in 2 ways.
Hence total number of even numbers can be formed in 1x2x3x4x2 = 48.
Q7. Find a particular solution of dydx=ytanx;y=1whenx=0
Answer : Option C
Explaination / Solution:
Q8. If the cube roots of unity are 1, then roots of the equation are :
Answer : Option B
Explaination / Solution:
Q9. If and then
Answer : Option D
Explaination / Solution:
Q10. If A, B and C are any three sets , then A – (B∩∩C ) is equal to
Answer : Option B
Explaination / Solution:
