Mathematics - Online Test
Q1. A balloon rises straight up at 10 m/s. An
observer is 40 m away from the spot
where the balloon left the ground. The rate of change of the balloon’s angle of
elevation in radian per second when the balloon is 30 metres above the ground.
Answer : Option B
Explaination / Solution:
Q2. Length of common chord of the circles and is
Answer : Option D
Explaination / Solution:
Applying the completing the square
Comparing the above equation with 
we get its center as (-1,-3) and radius (r1)=
we get its center as (-1,-3) and radius (r1)=Comparing the above equation with 
we get its center as (2,1) and radius (r2)=
we get its center as (2,1) and radius (r2)=So distance(d) between the centers is 
units
unitsAfter applying general formula of length of common chord as 
and putting the values of r1, r2 and d we get length as
. and putting the values of r1, r2 and d we get length as
Q3. Given that x, y and b are real numbers x < y, b > 0, then
Answer : Option A
Explaination / Solution:
Q4. Order of a differential equation is defined as
Answer : Option A
Explaination / Solution:
Order of a differential equation is defined as the order of the highest order derivative of the dependent variable present in the differential equation.
Q5. If A is a 3× 3 non-singular matrix such that AAT = AT A and B = A−1 AT , then BBT =
Answer : Option C
Explaination / Solution:
Q6. If l, m, n are the direction cosines of a line, then
Answer : Option D
Explaination / Solution:
we know that direction cosines is coefficient of i,j,k of unit vector along that line ,i.e those coefficient are l,m,n .the length of the line r is such that and magnitute of unit vector r is 1 and . on squaring both side we get
Q7. In a triangle ABC, if A = and B = then b + 2 c is equal to
Answer : Option B
Explaination / Solution:
Q8. The percentage error of fifth root of 31 is
approximately how many times the percentage error in 31?
Answer : Option B
Explaination / Solution:
Q9. If cos 28̊ + sin 28̊ = k3, then cos 17̊ is equal to
Answer : Option A
Explaination / Solution:
Q10. The area of the loop between the curve y = a sin x and the x – axis and x= 0 , x=π. is
Answer : Option D
Explaination / Solution:
Required area =
∫0πasinxdx=a[−cosx]π0=a(−cosπ+cos0)=a(1+1)=2a
