Mathematics Tes...

If \(\mathrm{X}=\left\{8^{\mathrm{n}}-7 \mathrm{n}-1, \mathrm{n} \in \mathbf{N}\right\}\) and \(\mathrm{Y}=49(\mathrm{n}-1), \mathrm{n} \in \mathbf{N},\) then: \((\) given \(\mathrm{n}>1)\)

If \(\mathrm{f}(\mathrm{x}), \mathrm{g}(\mathrm{x})\) be twice differential functions on \([0,~2]\) satisfying \(\mathrm{f}^{\prime \prime}(\mathrm{x})=\mathrm{g}^{\prime \prime}(\mathrm{x}), \mathrm{f}^{\prime}(1)\) \(=2 g^{\prime}(1)=4\) and \(f(2)=3 g(2)=9,\) then:

Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the threeapply for the same house is:

If the parabola y² = 4ax passes through the point (2, 4), then the focus of parabola is ?

Solving an integer programming problem by rounding off answers obtained by solving it as a linear programming problem (using simplex), we find that:

The mean of a distribution is \(22\) and the standard deviation is \(10\). What is the value of variance coefficient?

An attempt is made to pull a roller of weight W over a curb (step) by applying a horizontal force F as shown in the figure.

The coefficient of static friction between the roller and the ground (including the edge of the step) is μ. Identify the correct free body diagram (FBD) of the roller when the roller is just about to climb over the step.

Find the minimum value of the function \(f(x)=2 x^{3}-3 x^{2}-12 x+6\).