TANCET 2025 Solved Papers

Concept:Standard deviation of a set of numbers can be found from the mean and the sum of squares of the numbers.Explanation:Statement (1): The sum $p+q+r+s=24$ gives the mean as $\frac{24}{4}=6$.But this alone does not tell how the values are spread around the mean.So statement (1) alone is not sufficient.Statement (2): The sum of squares $p^2+q^2+r^2+s^2=224$ is known, but the mean is still unknown.Without the mean, the standard deviation cannot be calculated.So statement (2) alone is not sufficient.Combining both statements:Mean $= \frac{24}{4}=6$.Variance $= \frac{p^2+q^2+r^2+s^2}{4} - (\text{mean})^2$.Variance $= \frac{224}{4} - 6^2 = 56 - 36 = 20$.Standard deviation $= \sqrt{20}$.Thus both statements together are needed and sufficient.Answer:Option C: BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.