Mathematics - Online Test
Q1. The direction cosines of X -axis are
Answer : Option B
Explaination / Solution:
As we know that if a lines makes angles a , b and c with X-axis , Y-axis and Z-axis respectively then direction cosines are given by < cos a , cos b ,cos c >
In our case line is X-axis itself which we know makes angle of 0 , 90 , 90 with X-axis , Y-axis and Z-axis respectively then direction cosine will be
<cos 0 , cos 90, cos 90>
= < 1 0 0 >
Q2. The number of all possible matrices of order 3×3 with each entry 0 or 1 is
Answer : Option C
Explaination / Solution:
The number of elements in a 3 X 3 matrix is the product 3 X 3=9.
Each element can either be a 0 or a 1.
Given this, the total possible matrices that can be selected is 29=512
Q3. If 
, then the value of k is
, then the value of k is
Answer : Option C
Explaination / Solution:
Q4. The value of ∑(in + in−1 ) is
Answer : Option A
Explaination / Solution:
Q5. The value of 
is
is
Answer : Option C
Explaination / Solution:
Q6. In an examination there are three multiple choice questions and each question has 5 choices .
Number of ways in which a student can fail to get all answer correct is
Answer : Option B
Explaination / Solution:
Q7. If the graph of a differentiable function y = f (x) meets the lines y = – 1 and y = 1, then the graph
Answer : Option C
Explaination / Solution:
Since the graph cuts the lines y = -1 and y = 1 , therefore ,it must cut y = 0 atleast once as the graph is a continuous curve in this case.
Q8. A number is selected from the set { 1, 2, 3,..., 20 }. The probability that the selected number is divisible by 3 or 4 is
Answer : Option C
Explaination / Solution:
Q9. A = {a,b, p}, B =
{2, 3}, C = {p,q,r,s} then n[(A
∪ C )× B] is
Answer : Option C
Explaination / Solution:
Q10. The differential equation representing the
family of curves y = A cos(x + B),
where A and B are parameters, is
Answer : Option B
Explaination / Solution:
