Mathematics - Online Test
Q1. dx is equal to
Answer : Option C
Explaination / Solution:
∫log(1−x)dx−∫logx dx⇒(x−1)log(1−x)+1−xlnx+C
Q2. Find the value of x for which is a unit vector
Answer : Option D
Explaination / Solution:
As x is a unit vector ,
therefore,
therefore,
Q3. is equal to
Answer : Option C
Explaination / Solution:
Q4. Let A be a 4 × 3 real matrix with rank 2. Which one of the following statement is TRUE?
Answer : Option B
Explaination / Solution:
Q5. The equations x = a cos + b sin , and , 0 2 represent
Answer : Option D
Explaination / Solution:
x = a cos + b sin , and
putting the value of x and y in x2+y2
we get a2+b2
=> x2+y2 =a2+b2
which is quadratic in nature,
coefficient of x2 = coefficient of y2
and no term involving xy
hence its locus represents a circle
Q6. If f (x) = x then f ‘ (1 ) is equal to
Answer : Option B
Explaination / Solution:
Q7.
sin sin
Answer : Option B
Explaination / Solution:
Q8. For all is divisible by :
Answer : Option C
Explaination / Solution:
Replace n = 1 we get 209 which is divisible by 11.
Q9. A pair of dice is tossed once and a total of 8 has come up. The chance that both the dice show up same number is
Answer : Option C
Explaination / Solution:
on tossing a pair of dice total outcomes are 36
out of which getting a total of 8 have possiblities {(2,6),(6,2),(3,5),(5,3),(4,4)}=5
and from these 5 outcomes getting same no. on both dice is (4,4)=1
so, probability is 1/5
Q10. Volume of a tetrahedron is k X area of one face X length of perpendicular from the opposite vertex upon it, where k is
Answer : Option D
Explaination / Solution:
Volume of tetrahedron 
where a,b,c are co-terminus edges of tetrahedron.a X b is area of one face and c is the perpendicular from the opposite vertex
where a,b,c are co-terminus edges of tetrahedron.a X b is area of one face and c is the perpendicular from the opposite vertex