Question : Which one of the following is the smallest?
Option 1: $\sqrt{101}-\sqrt{99}$
Option 2: $\sqrt{201}-\sqrt{199}$
Option 3: $\sqrt{301}-\sqrt{299}$
Option 4: $\sqrt{401}-\sqrt{399}$
Correct Answer: $\sqrt{401}-\sqrt{399}$
Solution : The expressions given are differences in square roots of numbers that are 2 units apart. For such expressions, the difference decreases as the numbers increase. The function $f(x) = \sqrt{x}$ is concave up, meaning the rate of increase of $f(x)$ decreases as $x$ increases. Therefore, the difference decreases as numbers increase. Therefore, among the given options, $\sqrt{401}-\sqrt{399}$ is the smallest. Hence, the correct answer is $\sqrt{401}-\sqrt{399}$.
Application | Eligibility | Selection Process | Result | Cutoff | Admit Card | Preparation Tips
Question : Which of the following ranges of the Air Pollutant index is considered hazardous?
Option 1: 301 - 500
Option 2: 201 - 300
Option 3: 101 - 200
Option 4: 401 - 500
Question : The smallest among $\sqrt[6]{12},\sqrt[3]{4},\sqrt[4]{5},\sqrt3$ is:
Option 1: $\sqrt[6]{12}$
Option 2: $\sqrt[3]{4}$
Option 3: $\sqrt3$
Option 4: $\sqrt[4]{5}$
Question : One of the factors of the expression $4\sqrt{3}x^{2}+5x-2\sqrt{3}$ is:
Option 1: $4x+\sqrt{3}$
Option 2: $4x+3$
Option 3: $4x-3$
Option 4: $4x-\sqrt{3}$
Question : $\frac{1}{3-\sqrt{8}}-\frac{1}{\sqrt{8}-\sqrt{7}}+\frac{1}{\sqrt{7}-\sqrt{6}}-\frac{1}{\sqrt{6}-\sqrt{5}}+\frac{1}{\sqrt{5}-2}=?$
Option 1: 5
Option 2: 4
Option 3: 3
Option 4: 2
Question : If $x=\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}$ and $y=\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}$, then the value of $x^{3} + y^{3}$ is:
Option 1: 950
Option 2: 730
Option 3: 650
Option 4: 970
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile