Distance equals the absolute difference of the two coordinates. In exams, treat the negative sign as direction, not distance.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{19}{6}\). Distance equals the absolute difference of the two coordinates. In exams, treat the negative sign as direction, not distance.
Step 3
Exam Tip
दूरी दोनों निर्देशांकों के अंतर के परिमाण के बराबर होती है। परीक्षा में ऋण चिह्न को दिशा मानें, दूरी नहीं।
Since \(7^2=49\) and \(8^2=64\), \(\sqrt{52}\) lies between them. In exams, locate square roots by comparing squares.
Step 2
Why this answer is correct
The correct answer is B. (7) और (8) / (7) and (8). Since \(7^2=49\) and \(8^2=64\), \(\sqrt{52}\) lies between them. In exams, locate square roots by comparing squares.
Step 3
Exam Tip
क्योंकि \(7^2=49\) और \(8^2=64\), इसलिए \(\sqrt{52}\) इनके बीच है। परीक्षा में वर्गों की तुलना करके स्थान पहचानें।
Since \(\sqrt{10}\) lies between (3) and (4), \(-\sqrt{10}\) lies between (-4) and (-3). In exams, place negative surds to the left.
Step 2
Why this answer is correct
The correct answer is A. (-4) और (-3) / (-4) and (-3). Since \(\sqrt{10}\) lies between (3) and (4), \(-\sqrt{10}\) lies between (-4) and (-3). In exams, place negative surds to the left.
Step 3
Exam Tip
क्योंकि \(\sqrt{10}\) (3) और (4) के बीच है, इसलिए \(-\sqrt{10}\) (-4) और (-3) के बीच होगा। परीक्षा में ऋणात्मक सुरद की दिशा बाईं ओर मानें।
This decimal is non-recurring and non-terminating, so it is irrational. In exams, identify non-recurring infinite decimals as irrational.
Step 2
Why this answer is correct
The correct answer is C. अपरिमेय संख्या / Irrational number. This decimal is non-recurring and non-terminating, so it is irrational. In exams, identify non-recurring infinite decimals as irrational.
Step 3
Exam Tip
यह दशमलव अनावर्ती और अनंत है, इसलिए यह अपरिमेय संख्या है। परीक्षा में अनावर्ती अनंत दशमलव को अपरिमेय पहचानें।
A. यह (2) और (3) के बीच (2.75) पर है/It is between (2) and (3) at (2.75)
Step 1
Concept
\(\frac{11}{4}=2.75\), so it lies between (2) and (3). In exams, convert fractions to decimals or mixed numbers for placement.
Step 2
Why this answer is correct
The correct answer is A. यह (2) और (3) के बीच (2.75) पर है / It is between (2) and (3) at (2.75). \(\frac{11}{4}=2.75\), so it lies between (2) and (3). In exams, convert fractions to decimals or mixed numbers for placement.
Step 3
Exam Tip
\(\frac{11}{4}=2.75\), इसलिए यह (2) और (3) के बीच आता है। परीक्षा में भिन्न को दशमलव या मिश्र भिन्न में बदलकर रखें।
\(-\frac{5}{2}=-2.5\), and (-2.45) is greater than (-2.5) but less than (-2.4). In exams, compare negative numbers carefully.
Step 2
Why this answer is correct
The correct answer is B. (-2.45). \(-\frac{5}{2}=-2.5\), and (-2.45) is greater than (-2.5) but less than (-2.4). In exams, compare negative numbers carefully.
Step 3
Exam Tip
\(-\frac{5}{2}=-2.5\), और (-2.45) (-2.5) से बड़ा तथा (-2.4) से छोटा है। परीक्षा में ऋणात्मक संख्याओं की तुलना सावधानी से करें।
\(-\frac{4}{5}=-0.8\), which is the smallest among the given values. In exams, the farthest-left number is the least number.
Step 2
Why this answer is correct
The correct answer is C. (C). \(-\frac{4}{5}=-0.8\), which is the smallest among the given values. In exams, the farthest-left number is the least number.
Step 3
Exam Tip
\(-\frac{4}{5}=-0.8\), जो दिए गए मानों में सबसे छोटा है। परीक्षा में सबसे बाईं संख्या सबसे छोटी होती है।
A. हर वास्तविक संख्या का एक अद्वितीय बिंदु होता है/Every real number has a unique point
Step 1
Concept
The number line represents real numbers, and each real number has a unique position. In exams, connect the number line with real numbers.
Step 2
Why this answer is correct
The correct answer is A. हर वास्तविक संख्या का एक अद्वितीय बिंदु होता है / Every real number has a unique point. The number line represents real numbers, and each real number has a unique position. In exams, connect the number line with real numbers.
Step 3
Exam Tip
संख्या रेखा वास्तविक संख्याओं का निरूपण करती है और हर वास्तविक संख्या का एक अद्वितीय स्थान होता है। परीक्षा में संख्या रेखा को वास्तविक संख्याओं से जोड़कर समझें।
\(\sqrt{\frac{1}{2}}\) lies between (0) and (1) and cannot be simplified to a rational form. In exams, identify square roots of non-perfect squares as irrational.
Step 2
Why this answer is correct
The correct answer is C. \(\sqrt{\frac{1}{2}}\). \(\sqrt{\frac{1}{2}}\) lies between (0) and (1) and cannot be simplified to a rational form. In exams, identify square roots of non-perfect squares as irrational.
Step 3
Exam Tip
\(\sqrt{\frac{1}{2}}\) (0) और (1) के बीच है और इसे परिमेय रूप में सरल नहीं किया जा सकता। परीक्षा में वर्गमूल वाले अपूर्ण वर्गों को अपरिमेय पहचानें।
B. (8) बराबर भागों में और (5)वां बिंदु लें/Into (8) equal parts and take the (5)th point
Step 1
Concept
In \(\frac{5}{8}\), the denominator is (8), so divide the unit into (8) equal parts and take the (5)th. In exams, the denominator gives the number of equal parts.
Step 2
Why this answer is correct
The correct answer is B. (8) बराबर भागों में और (5)वां बिंदु लें / Into (8) equal parts and take the (5)th point. In \(\frac{5}{8}\), the denominator is (8), so divide the unit into (8) equal parts and take the (5)th. In exams, the denominator gives the number of equal parts.
Step 3
Exam Tip
\(\frac{5}{8}\) में हर (8) है, इसलिए इकाई को (8) बराबर भागों में बांटकर (5)वां भाग लें। परीक्षा में हर भागों की संख्या बताता है।
\(\sqrt{80}\approx8.94\), so it lies slightly left of (9). In exams, connect approximation with direction near the nearest integer.
Step 2
Why this answer is correct
The correct answer is B. (9) के बाईं ओर / Left of (9). \(\sqrt{80}\approx8.94\), so it lies slightly left of (9). In exams, connect approximation with direction near the nearest integer.
Step 3
Exam Tip
\(\sqrt{80}\approx8.94\), इसलिए यह (9) के थोड़ा बाईं ओर होगा। परीक्षा में अनुमान को निकटतम पूर्णांक के साथ दिशा से जोड़ें।
