Maths-2000-Set II

Q2) Find a matrix X such that A + 2B + X = 0, where
A= 2 -1
3 5
B=-1 1
0 2

Ans2) Here
A= 2 -1
3 5
B= -1 1
0 2

A + 2B + X = 0
X = -A – 2B
= – 2 -1 – -1 1
3 5 2 0 2

= 0 -1
-3 -9

Q4) Calculate Spearman’s rank correlation from the following Data:
x 1 2 3 4 5 6
y 2 3 1 6 5 4

Ans4) Here :-
X Y RX RY di=RX – RY di2
1 2 6 5 1 1
2 3 5 4 1 1
3 1 4 6 -2 4
4 6 3 1 2 4
5 5 2 2 0 0
6 4 1 3 -2 4
di2 = 14

R, the rank Correlation
= 1 – (6di2/n(n2 – 1))
= 1 – (6 x 14)/6(35)
= 1 – 14/35 = 21/35 = 0.6

Q7) Evaluate
1+ Cot x dx
x + log Sin x

Ans7) Let
I= 1 + Cot x dx
x + log Sin x
= log | x + log Sin x | + C [ f'(x)/f(x) dx = log|f(x)| + c and d/dx(x + logSin x) = 1+Cot x ]

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