Find the rank of the matrix \(\begin{pmatrix} -5 & -7 \\ 5 & 7 \end{pmatrix}\)

Integrate the following with respect to x.
\(\sqrt { 3x+5 } \)

Find the area of the region bounded by the parabola \(y=4{ - }x^{ 2 }\) , x −axis and the lines x = 0, x = 2.

Solve: \(\frac { dy }{ dx } \) = y sin 2x

Evaluate \({ \Delta }^{ 2 }\left( \frac { 1 }{ x } \right) \) by taking ‘1’ as the interval of differencing.

Construct cumulative distribution function for the given probability distribution.

X	0	1	2	3
P(X = x)	0.3	0.2	0.4	0.1

A fair coin is tossed 6 times. Find the probability that exactly 2 heads occurs.

Using the following Tippett’s random number table,

2952	6641	3992	9792	7969	5911	3170	5624
4167	9524	1545	1396	7203	5356	1300	2693
2670	7483	3408	2762	3563	1089	6913	7991
0560	5246	1112	6107	6008	8125	4233	8776
2754	9143	1405	9025	7002	6111	8816	6446

Draw a sample of 15 houses from Cauvery Street which has 83 houses in total.

Mention the components of the time series.

Write mathematical form of transportation problem.