Mathematics - Online Test

Q1. With K as a constant, the possible solution for the first order differential equation  is
Answer : Option A
Explaination / Solution:



Q2. In how many ways can the letters of the word ‘MATHEMATICS ‘be permuted so that consonants always occur together?
Answer : Option C
Explaination / Solution:

In the word 'MATHAEMATICS'  there are   7 consonants which are M-2 ,,H-1,C-1,S-1, T-2 .Since they have to occur together we treat them as a single unit.

Now this single unit together with the remaining 4 vowels which are A-2,E-1,and I-1  will account for 5 letters.

Now in these 5 letters we have A is repeating twice  these can be aarranged in   different ways.

Corresponding to each of these arrangements the consonents can be arranged in  different ways.

Hence the number of ways it can be arranged is  =75600


Q3. 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:



Q4. 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)=

Comparing the above equation with  we get its center as (2,1) and radius (r2)=

So distance(d) between the centers is   units
After applying general formula of length of common chord as  and putting the values of r1, r2 and d we get length as 
.




Q5. Given that x, y and b are real numbers x < y, b > 0, then
Answer : Option A
Explaination / Solution:


Q6. 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.

Q7. If A is a 3× 3 non-singular matrix such that AAT = AT A and B = A1 AT , then BBT =
Answer : Option C
Explaination / Solution:


Q8. 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 
Q9. In a triangle ABC, if A =  and B =  then b + 2 c is equal to
Answer : Option B
Explaination / Solution:



Q10. The percentage error of fifth root of 31 is approximately how many times the percentage error in 31?
Answer : Option B
Explaination / Solution: