Mathematics - Online Test
Q1. The derivative of f(x) = | x | at x = 0 is
Answer : Option B
Explaination / Solution:
which does not exist at x = 0 .
Q2. The equation represents
Answer : Option B
Explaination / Solution:
On factorizing the given equation we get y+x-1=0 and y-x+1=0, which clearly represent a pair of straight lines which are intersecting.
Q3. The statement P ( n ) : “ “ is true for :
Answer : Option D
Explaination / Solution:
When n = 1 we get 16>16, which is false. when n = 2 we get 25>32,which is false as well. As n = 3,4,5....the inequalty does not hold correct.
Q4.
If then is equal to
Answer : Option C
Explaination / Solution:
Q5. Find the cartesian equations of the lines that passes through the origin and (5, – 2, 3).
Answer : Option C
Explaination / Solution:
The coordinates of the origin are ( 0 , 0 ,0 ) , therefore , , and l = 5 , m = - 2 and n = 3 ,
therefore the equation in Cartesian form is given by:
i.e. .
therefore the equation in Cartesian form is given by:
i.e. .
Q6. A coin is tossed n times, the number of all the possible outcomes is
Answer : Option D
Explaination / Solution:
There can either be a heads or tails, therefore for every toss, the possible outcomes are 2. hence for n number of toss the possibilities are 2n.
Q7. General solution of is
Answer : Option B
Explaination / Solution:
Q8. The direction cosines of the line joining ( 1 , - 1 , 1 ) , and ( -1 , 1 , 1 ) are
Answer : Option C
Explaination / Solution:
The direction ratio of the line joining ( x1 , y1 , z1 ) , and ( x2 , y2 , z2) = < x1-x2 , y1-y2 , z1-z2 >
The direction ratio of the line joining ( 1 , - 1 , 1 ) , and ( -1 , 1 , 1 ) = < 1+1 , -1-1 , 1-1> = < 2 , -2 , 0 >
Q9. If and then AB =
Answer : Option A
Explaination / Solution:
Q10. If then is equal to :
Answer : Option D
Explaination / Solution:
