Mathematics Tes...

The range of the real-valued function \(f(x)=\sqrt{9-x^{2}}\) is:

Let \(\mathrm{S}_{\mathrm{K}} \frac{1+2+\ldots+\mathrm{K}}{\mathrm{K}}\) and \(\sum_{\mathrm{j}=1}^{\mathrm{n}} \mathrm{S}_{\mathrm{j}}^2=\frac{\mathrm{n}}{\mathrm{A}}\left(\mathrm{Bn}^2+\mathrm{Cn}+\mathrm{D}\right)\), where \(\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D} \in \mathrm{N}\) and A has least value. Then:

All the pairs \((x, y)\) that satisfy the inequality \(2 \sqrt{\sin ^2 x-2 \sin x+5} \cdot \frac{1}{4 \sin ^2 y} \leq 1\) also satisfy the equation:

Evaluate the integral \(\int_{1}^{4} \frac{\sqrt{x}+3}{\sqrt{x}} d x\).

If \(A=\{2,3,4\}\) and \(B=\{5,6\}\), then how many subsets does \(A \times B\) have?

If \(\mathrm{P}\) and \(\mathrm{Q}\) be two sets such that \(\mathrm{P} \cup \mathrm{Q}=\mathrm{P},\) then \(\mathrm{P} \cap \mathrm{Q}\) will be:

Let \(\mathrm{S}\) be the set of all real roots of the equation, \(3^{\mathrm{x}}\left(3^{\mathrm{x}}-1\right)+2=3^{\mathrm{x}}-1\left|+3^{\mathrm{x}}-2\right|\). Then \(\mathrm{S}:\)

If the mean of 4, 7, 2, 8, 6 and a is 7, then the mean deviation from the median of these observations is:

Find the number of arrangements of letters in the word ASHUTOSH?

If the constraints in a linear programming problem are changed _______________.