Mathematics - Online Test
Q1. The points ( 4,7 ,8) ,( 2, 3,4 ),( - 1 , -2 , 1 ) and (1 , 2, 5 ) are the vertices of a
Answer : Option A
Explaination / Solution:
The vertices of a quadrilateral are A( 4,7 ,8) , B( 2, 3,4 ) ,C (- 1 , -2 , 1 ) and D(1 , 2, 5 )
Here opposite sides of quadrilateral ABCD are equal , so it may be parallelogram or rectangle
Here length of diagonals AC and BD are different so ABCD is a parrallelogram
Q2. If a matrix A is symmetric as well as skew symmetric then A is a
Answer : Option B
Explaination / Solution:
Only a null matrix can be symmetric as well as skew symmetric.
In Symmetric Matrix AT =A,
Skew Symmetric Matrix AT = -A,
Given that the matrix is satisfying both the properties therefore Equating the RHS we get A= -A i.e 2A=0 .
Therefore A=0,which is a null matrix.
Q3. Let f (x) = then f (x) is decreasing in
Answer : Option B
Explaination / Solution:
Here ,
Q4. Let A and B be two sets in the universal set . Then A - B is equal to
Answer : Option D
Explaination / Solution:
Q5. The inequality | z − 6 | < | z − 2 | represents the region given by
Answer : Option A
Explaination / Solution:
Q6. 
Answer : Option B
Explaination / Solution:
Q7. If is non real cube root of unity , then 
Answer : Option B
Explaination / Solution:
expanding along R3
Q8. The coefficients of and ( p, q are + ve integers) in the binomial expansion of are
Answer : Option B
Explaination / Solution:
Q9. What is the solution set for ?
Answer : Option D
Explaination / Solution:
Q10. is equal to
Answer : Option D
Explaination / Solution:
Since the limit is in the form of 0/0. By applying L'hospital first time we get,
Again using L'Hospital;
Again using L'Hospital we get
