# Maths - Online Test

Q1. If  and  are parallel vectors, then [  ] is equal to
Explaination / Solution:
No Explaination.

Q2. 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.
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Q3. If A is a 3× 3 non-singular matrix such that AAT = AT A and B = A1 AT , then BBT =
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Q4. The percentage error of fifth root of 31 is approximately how many times the percentage error in 31?
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Q5. The value of  (i+ in1 )  is
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Q6. The value of  is
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Q7. The differential equation representing the family of curves y = A cos(x + B), where A and B are parameters, is
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Q8. If f and g are polynomials of degrees m and n respectively, and if h(x) = ( f o g )(x) , then the degree of h is
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Q9. If sin1 x + sin1 y (2π/3) ; then cos1 x + cos1 y is equal to
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Q10.

A rod of length 2l is broken into two pieces at random. The probability density function of the shorter of the two pieces is

The mean and variance of the shorter of the two pieces are respectively

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