यदि संख्या रेखा पर (A=-2.75) और (B=1.25), तो (AB) का मध्य बिंदु क्या है?
If (A=-2.75) and (B=1.25) on the number line, what is the midpoint of (AB)?
#number-line
#midpoint
#decimals
A ( -0.75 )
B ( -1.50 )
C (0.75)
D (2.00)
Explanation opens after your attempt
Correct Answer
A. ( -0.75 )
Step 1
Concept
The midpoint is \( \frac{-2.75+1.25}{2}=-0.75 \). Take the average to find a midpoint.
Step 2
Why this answer is correct
The correct answer is A. ( -0.75 ). The midpoint is \( \frac{-2.75+1.25}{2}=-0.75 \). Take the average to find a midpoint.
Step 3
Exam Tip
मध्य बिंदु \( \frac{-2.75+1.25}{2}=-0.75 \) है। मध्य बिंदु निकालने में औसत लें।
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संख्या रेखा पर \( -\frac{17}{5} \) किस दो पूर्णांकों के बीच स्थित है?
Between which two integers is \( -\frac{17}{5} \) located on the number line?
#number-line
#negative-fraction
#interval
A ( -4 ) और ( -3 ) / ( -4 ) and ( -3 )
B ( -3 ) और ( -2 ) / ( -3 ) and ( -2 )
C (3) और (4) / (3) and (4)
D ( -5 ) और ( -4 ) / ( -5 ) and ( -4 )
Explanation opens after your attempt
Correct Answer
A. ( -4 ) और ( -3 ) / ( -4 ) and ( -3 )
Step 1
Concept
\( -\frac{17}{5}=-3.4 \). It lies between (-4) and (-3).
Step 2
Why this answer is correct
The correct answer is A. ( -4 ) और ( -3 ) / ( -4 ) and ( -3 ). \( -\frac{17}{5}=-3.4 \). It lies between (-4) and (-3).
Step 3
Exam Tip
\( -\frac{17}{5}=-3.4 \) है। यह (-4) और (-3) के बीच आता है।
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यदि \( \sqrt{n} \) संख्या रेखा पर (6.4) और (6.5) के बीच है, तो (n) के लिए कौन सा मान सही हो सकता है?
If \( \sqrt{n} \) lies between (6.4) and (6.5) on the number line, which value of (n) can be correct?
#number-line
#root-inequality
#estimation
A (42)
B (40)
C (45)
D (49)
Explanation opens after your attempt
Step 1
Concept
\(6.4^2=40.96\) and \(6.5^2=42.25\), so (n) must lie between them. (42) is in the correct range.
Step 2
Why this answer is correct
The correct answer is A. (42). \(6.4^2=40.96\) and \(6.5^2=42.25\), so (n) must lie between them. (42) is in the correct range.
Step 3
Exam Tip
\(6.4^2=40.96\) और \(6.5^2=42.25\), इसलिए (n) इनके बीच होना चाहिए। (42) सही सीमा में है।
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संख्या रेखा पर \(0.2727727772\ldots\) किस प्रकार की संख्या है?
What type of number is \(0.2727727772\ldots\) on the number line?
#number-line
#irrational-decimal
#classification
A अपरिमेय संख्या / Irrational number
B परिमेय संख्या / Rational number
C पूर्णांक / Integer
D प्राकृतिक संख्या / Natural number
Explanation opens after your attempt
Correct Answer
A. अपरिमेय संख्या / Irrational number
Step 1
Concept
This decimal is non-terminating and non-repeating. Hence it is an irrational number on the number line.
Step 2
Why this answer is correct
The correct answer is A. अपरिमेय संख्या / Irrational number. This decimal is non-terminating and non-repeating. Hence it is an irrational number on the number line.
Step 3
Exam Tip
यह दशमलव असांत और अनावर्ती है। इसलिए यह संख्या रेखा पर अपरिमेय संख्या है।
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यदि \(a=\sqrt{27}-\sqrt{12}\), तो संख्या रेखा पर (a) का सरल रूप क्या है?
If \(a=\sqrt{27}-\sqrt{12}\), what is the simplified form of (a) on the number line?
#number-line
#radical-simplification
#irrational
A \( \sqrt{3} \)
B \(3\sqrt{3}\)
C \(5\sqrt{3}\)
D \( \sqrt{15} \)
Explanation opens after your attempt
Correct Answer
A. \( \sqrt{3} \)
Step 1
Concept
\( \sqrt{27}=3\sqrt{3} \) and \( \sqrt{12}=2\sqrt{3} \), so the difference is \( \sqrt{3} \). Subtract like radicals.
Step 2
Why this answer is correct
The correct answer is A. \( \sqrt{3} \). \( \sqrt{27}=3\sqrt{3} \) and \( \sqrt{12}=2\sqrt{3} \), so the difference is \( \sqrt{3} \). Subtract like radicals.
Step 3
Exam Tip
\( \sqrt{27}=3\sqrt{3} \) और \( \sqrt{12}=2\sqrt{3} \) इसलिए अंतर \( \sqrt{3} \) है। समान मूलों को घटाएँ।
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कौन सा मान संख्या रेखा पर \( -\sqrt{3} \) और \( -\frac{5}{3} \) के बीच है?
Which value lies between \( -\sqrt{3} \) and \( -\frac{5}{3} \) on the number line?
#number-line
#negative-interval
#comparison
A ( -1.70 )
B ( -1.60 )
C ( -1.80 )
D ( -2.00 )
Explanation opens after your attempt
Correct Answer
A. ( -1.70 )
Step 1
Concept
\( -\sqrt{3}\approx-1.732 \) and \( -\frac{5}{3}\approx-1.667 \). Therefore (-1.70) lies between them.
Step 2
Why this answer is correct
The correct answer is A. ( -1.70 ). \( -\sqrt{3}\approx-1.732 \) and \( -\frac{5}{3}\approx-1.667 \). Therefore (-1.70) lies between them.
Step 3
Exam Tip
\( -\sqrt{3}\approx-1.732 \) और \( -\frac{5}{3}\approx-1.667 \) है। इसलिए (-1.70) इनके बीच है।
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संख्या रेखा पर \( \frac{2}{5} \) और \( \frac{3}{5} \) के ठीक बीच का बिंदु कौन सा है?
Which point is exactly midway between \( \frac{2}{5} \) and \( \frac{3}{5} \) on the number line?
#number-line
#midpoint
#fraction
A \( \frac{1}{2} \)
B \( \frac{5}{2} \)
C \( \frac{1}{5} \)
D \( \frac{4}{5} \)
Explanation opens after your attempt
Correct Answer
A. \( \frac{1}{2} \)
Step 1
Concept
The midpoint is \( \frac{\frac{2}{5}+\frac{3}{5}}{2}=\frac{1}{2} \). Use the average for the midpoint.
Step 2
Why this answer is correct
The correct answer is A. \( \frac{1}{2} \). The midpoint is \( \frac{\frac{2}{5}+\frac{3}{5}}{2}=\frac{1}{2} \). Use the average for the midpoint.
Step 3
Exam Tip
मध्य बिंदु \( \frac{\frac{2}{5}+\frac{3}{5}}{2}=\frac{1}{2} \) है। मध्य के लिए औसत लें।
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यदि संख्या रेखा पर (C) बिंदु ( -1 ) से बाईं ओर \( \sqrt{6} \) इकाई दूर है, तो (C) का निर्देशांक क्या होगा?
If point (C) is \( \sqrt{6} \) units to the left of (-1) on the number line, what is the coordinate of (C)?
#number-line
#direction
#coordinate
A \( -1-\sqrt{6} \)
B \( -1+\sqrt{6} \)
C \(1-\sqrt{6}\)
D \( \sqrt{6}-1 \)
Explanation opens after your attempt
Correct Answer
A. \( -1-\sqrt{6} \)
Step 1
Concept
Moving left means subtracting the distance. Therefore the coordinate is \( -1-\sqrt{6} \).
Step 2
Why this answer is correct
The correct answer is A. \( -1-\sqrt{6} \). Moving left means subtracting the distance. Therefore the coordinate is \( -1-\sqrt{6} \).
Step 3
Exam Tip
बाईं ओर जाने पर दूरी घटाई जाती है। इसलिए निर्देशांक \( -1-\sqrt{6} \) होगा।
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कौन सा कथन संख्या रेखा पर \( \sqrt{5} \) और (2.24) के लिए सही है?
Which statement is correct for \( \sqrt{5} \) and (2.24) on the number line?
#number-line
#root-decimal-comparison
#precision
A \( \sqrt{5}<2.24 \)
B \( \sqrt{5}>2.24 \)
C \( \sqrt{5}=2.24 \)
D \( \sqrt{5}<2 \)
Explanation opens after your attempt
Correct Answer
A. \( \sqrt{5}<2.24 \)
Step 1
Concept
\( \sqrt{5}\approx2.236 \), which is slightly less than (2.24). Compare close decimals to more places.
Step 2
Why this answer is correct
The correct answer is A. \( \sqrt{5}<2.24 \). \( \sqrt{5}\approx2.236 \), which is slightly less than (2.24). Compare close decimals to more places.
Step 3
Exam Tip
\( \sqrt{5}\approx2.236 \) है और यह (2.24) से थोड़ा छोटा है। निकट दशमलवों में अधिक स्थानों तक तुलना करें।
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यदि \(x=\frac{\sqrt{81}}{4}\), तो संख्या रेखा पर (x) किसके बराबर है?
If \(x=\frac{\sqrt{81}}{4}\), what is (x) equal to on the number line?
#number-line
#exact-root
#fractions
A \( \frac{9}{4} \)
B \( \frac{81}{4} \)
C \( \frac{4}{9} \)
D \( \frac{9}{2} \)
Explanation opens after your attempt
Correct Answer
A. \( \frac{9}{4} \)
Step 1
Concept
\( \sqrt{81}=9 \), so \(x=\frac{9}{4}\). Find the square root first and then divide.
Step 2
Why this answer is correct
The correct answer is A. \( \frac{9}{4} \). \( \sqrt{81}=9 \), so \(x=\frac{9}{4}\). Find the square root first and then divide.
Step 3
Exam Tip
\( \sqrt{81}=9 \), इसलिए \(x=\frac{9}{4}\) है। पहले वर्गमूल निकालें फिर भाग करें।
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संख्या रेखा पर \( -\sqrt{0.36} \) किस बिंदु के बराबर है?
On the number line, \( -\sqrt{0.36} \) is equal to which point?
#number-line
#negative-root
#decimal-root
A ( -0.6 )
B (0.6)
C ( -0.06 )
D ( -3.6 )
Explanation opens after your attempt
Correct Answer
A. ( -0.6 )
Step 1
Concept
\( \sqrt{0.36}=0.6 \), so \( -\sqrt{0.36}=-0.6 \). Treat the outside negative sign separately.
Step 2
Why this answer is correct
The correct answer is A. ( -0.6 ). \( \sqrt{0.36}=0.6 \), so \( -\sqrt{0.36}=-0.6 \). Treat the outside negative sign separately.
Step 3
Exam Tip
\( \sqrt{0.36}=0.6 \) है इसलिए \( -\sqrt{0.36}=-0.6 \)। बाहर के ऋण चिह्न को अलग से देखें।
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यदि (m) ऐसा पूर्णांक है कि \(m<\sqrt{57}<m+1\), तो (m) का मान क्या है?
If (m) is an integer such that \(m<\sqrt{57}<m+1\), what is the value of (m)?
#number-line
#integer-bounds
#square-roots
A (7)
B (6)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
Since (49<57<64), \(7<\sqrt{57}<8\). Therefore (m=7).
Step 2
Why this answer is correct
The correct answer is A. (7). Since (49<57<64), \(7<\sqrt{57}<8\). Therefore (m=7).
Step 3
Exam Tip
क्योंकि (49<57<64), इसलिए \(7<\sqrt{57}<8\)। अतः (m=7) होगा।
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संख्या रेखा पर \(2-\sqrt{10}\) का सही स्थान किस अंतराल में है?
In which interval is \(2-\sqrt{10}\) correctly located on the number line?
#number-line
#root-expression
#interval
A (-2) और (-1) के बीच / Between (-2) and (-1)
B (-1) और (0) के बीच / Between (-1) and (0)
C (0) और (1) के बीच / Between (0) and (1)
D (1) और (2) के बीच / Between (1) and (2)
Explanation opens after your attempt
Correct Answer
A. (-2) और (-1) के बीच / Between (-2) and (-1)
Step 1
Concept
\( \sqrt{10}\approx3.162 \), so \(2-\sqrt{10}\approx-1.162\). Estimation is important in root subtraction.
Step 2
Why this answer is correct
The correct answer is A. (-2) और (-1) के बीच / Between (-2) and (-1). \( \sqrt{10}\approx3.162 \), so \(2-\sqrt{10}\approx-1.162\). Estimation is important in root subtraction.
Step 3
Exam Tip
\( \sqrt{10}\approx3.162 \) इसलिए \(2-\sqrt{10}\approx-1.162\) है। घटाव वाले मूल में अनुमान जरूरी है।
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कौन सा मान संख्या रेखा पर \( \sqrt{18} \) और \( \sqrt{19} \) के बीच स्थित है?
Which value lies between \( \sqrt{18} \) and \( \sqrt{19} \) on the number line?
#number-line
#between-roots
#estimation
A (4.3)
B (4.1)
C (4.5)
D (4.0)
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{18}\approx4.243 \) and \( \sqrt{19}\approx4.359 \). So (4.3) lies between them.
Step 2
Why this answer is correct
The correct answer is A. (4.3). \( \sqrt{18}\approx4.243 \) and \( \sqrt{19}\approx4.359 \). So (4.3) lies between them.
Step 3
Exam Tip
\( \sqrt{18}\approx4.243 \) और \( \sqrt{19}\approx4.359 \) है। इसलिए (4.3) इनके बीच है।
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यदि संख्या रेखा पर \(A=-\frac{7}{3}\) और \(B=\frac{5}{6}\), तो (AB) की लंबाई क्या है?
If \(A=-\frac{7}{3}\) and \(B=\frac{5}{6}\) on the number line, what is the length of (AB)?
#number-line
#distance
#fractions
A \( \frac{19}{6} \)
B \( \frac{3}{2} \)
C \( \frac{7}{6} \)
D \( \frac{5}{2} \)
Explanation opens after your attempt
Correct Answer
A. \( \frac{19}{6} \)
Step 1
Concept
The distance is ( \left|\frac{5}{6}-\left\(-\frac{7}{3}\right\)\right|=\frac{19}{6} ). Always use absolute value for distance.
Step 2
Why this answer is correct
The correct answer is A. \( \frac{19}{6} \). The distance is ( \left|\frac{5}{6}-\left\(-\frac{7}{3}\right\)\right|=\frac{19}{6} ). Always use absolute value for distance.
Step 3
Exam Tip
दूरी ( \left|\frac{5}{6}-\left\(-\frac{7}{3}\right\)\right|=\frac{19}{6} ) है। दूरी में हमेशा निरपेक्ष मान लगाएँ।
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संख्या रेखा पर \( \sqrt{2.89} \) को किस बिंदु पर चिन्हित किया जाएगा?
At which point will \( \sqrt{2.89} \) be marked on the number line?
#number-line
#decimal-square-root
#exact-value
A (1.7)
B (1.6)
C (1.8)
D (2.89)
Explanation opens after your attempt
Step 1
Concept
Since \(1.7^2=2.89\), \( \sqrt{2.89}=1.7 \). Recognising decimal squares saves time.
Step 2
Why this answer is correct
The correct answer is A. (1.7). Since \(1.7^2=2.89\), \( \sqrt{2.89}=1.7 \). Recognising decimal squares saves time.
Step 3
Exam Tip
\(1.7^2=2.89\) इसलिए \( \sqrt{2.89}=1.7 \)। दशमलव वर्ग पहचानना समय बचाता है।
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यदि \(P=-\sqrt{20}\) और (Q=-4.4) हैं, तो संख्या रेखा पर कौन सा बिंदु अधिक दाईं ओर है?
If \(P=-\sqrt{20}\) and (Q=-4.4), which point is farther right on the number line?
#number-line
#negative-irrational
#comparison
A (Q)
B (P)
C दोनों समान हैं / Both are equal
D दोनों (0) के दाईं ओर हैं / Both are right of (0)
Explanation opens after your attempt
Step 1
Concept
\( -\sqrt{20}\approx-4.472 \) and (-4.4) is greater than it. The greater number lies to the right on a number line.
Step 2
Why this answer is correct
The correct answer is A. (Q). \( -\sqrt{20}\approx-4.472 \) and (-4.4) is greater than it. The greater number lies to the right on a number line.
Step 3
Exam Tip
\( -\sqrt{20}\approx-4.472 \) और (-4.4) इससे बड़ा है। संख्या रेखा पर बड़ी संख्या दाईं ओर होती है।
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संख्या रेखा पर \( \frac{13}{4} \), \( \sqrt{11} \), और (3.28) का सही बढ़ता क्रम कौन सा है?
What is the correct increasing order of \( \frac{13}{4} \), \( \sqrt{11} \), and (3.28) on the number line?
#number-line
#ordering
#mixed-values
A \( \frac{13}{4},3.28,\sqrt{11} \)
B \(3.28,\frac{13}{4},\sqrt{11}\)
C \( \sqrt{11},3.28,\frac{13}{4} \)
D \( \frac{13}{4},\sqrt{11},3.28 \)
Explanation opens after your attempt
Correct Answer
A. \( \frac{13}{4},3.28,\sqrt{11} \)
Step 1
Concept
\( \frac{13}{4}=3.25 \) and \( \sqrt{11}\approx3.316 \). Hence the correct order is (3.25<3.28<3.316).
Step 2
Why this answer is correct
The correct answer is A. \( \frac{13}{4},3.28,\sqrt{11} \). \( \frac{13}{4}=3.25 \) and \( \sqrt{11}\approx3.316 \). Hence the correct order is (3.25<3.28<3.316).
Step 3
Exam Tip
\( \frac{13}{4}=3.25 \) और \( \sqrt{11}\approx3.316 \) है। इसलिए सही क्रम (3.25<3.28<3.316) है।
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यदि संख्या रेखा पर (x) ऐसा है कि ( |x+3|=2.5 ), तो (x) के संभावित मान कौन से हैं?
If (x) on the number line satisfies ( |x+3|=2.5 ), what are the possible values of (x)?
#number-line
#absolute-value
#distance
A ( -0.5 ) और ( -5.5 ) / ( -0.5 ) and ( -5.5 )
B (0.5) और (5.5) / (0.5) and (5.5)
C ( -3 ) और (2.5) / ( -3 ) and (2.5)
D ( -2.5 ) और (3) / ( -2.5 ) and (3)
Explanation opens after your attempt
Correct Answer
A. ( -0.5 ) और ( -5.5 ) / ( -0.5 ) and ( -5.5 )
Step 1
Concept
( |x+3|=2.5 ) means the distance of (x) from (-3) is (2.5). Moving both ways gives (-0.5) and (-5.5).
Step 2
Why this answer is correct
The correct answer is A. ( -0.5 ) और ( -5.5 ) / ( -0.5 ) and ( -5.5 ). ( |x+3|=2.5 ) means the distance of (x) from (-3) is (2.5). Moving both ways gives (-0.5) and (-5.5).
Step 3
Exam Tip
( |x+3|=2.5 ) का अर्थ (x) की (-3) से दूरी (2.5) है। दोनों दिशाओं में जाने पर (-0.5) और (-5.5) मिलते हैं।
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संख्या रेखा पर \( \sqrt{31}-\sqrt{12} \) किस दो लगातार पूर्णांकों के बीच स्थित है?
Between which two consecutive integers does \( \sqrt{31}-\sqrt{12} \) lie on the number line?
#number-line
#irrational-difference
#estimation
A (2) और (3) / (2) and (3)
B (1) और (2) / (1) and (2)
C (3) और (4) / (3) and (4)
D (0) और (1) / (0) and (1)
Explanation opens after your attempt
Correct Answer
B. (1) और (2) / (1) and (2)
Step 1
Concept
\( \sqrt{31}\approx5.57 \) and \( \sqrt{12}\approx3.46 \) so the difference is about (2.11). Estimate both roots first.
Step 2
Why this answer is correct
The correct answer is B. (1) और (2) / (1) and (2). \( \sqrt{31}\approx5.57 \) and \( \sqrt{12}\approx3.46 \) so the difference is about (2.11). Estimate both roots first.
Step 3
Exam Tip
\( \sqrt{31}\approx5.57 \) और \( \sqrt{12}\approx3.46 \) इसलिए अंतर लगभग (2.11) है। पहले दोनों मूलों का अनुमान करें।
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संख्या रेखा पर \( -\frac{11}{3} \) और \( -\sqrt{13} \) में कौन सा बिंदु अधिक बाईं ओर है?
On the number line, which point is farther left between \( -\frac{11}{3} \) and \( -\sqrt{13} \)?
#number-line
#negative-comparison
#irrational-number
A \( -\frac{11}{3}\)
B \( -\sqrt{13}\)
C दोनों समान हैं / Both are equal
D दोनों (0) के दाईं ओर हैं / Both are to the right of (0)
Explanation opens after your attempt
Correct Answer
A. \( -\frac{11}{3}\)
Step 1
Concept
\( -\frac{11}{3}\approx-3.667\) and \( -\sqrt{13}\approx-3.606\), so \( -\frac{11}{3}\) is smaller. On a number line, the smaller number lies farther left.
Step 2
Why this answer is correct
The correct answer is A. \( -\frac{11}{3}\). \( -\frac{11}{3}\approx-3.667\) and \( -\sqrt{13}\approx-3.606\), so \( -\frac{11}{3}\) is smaller. On a number line, the smaller number lies farther left.
Step 3
Exam Tip
\( -\frac{11}{3}\approx-3.667\) और \( -\sqrt{13}\approx-3.606\), इसलिए \( -\frac{11}{3}\) अधिक छोटा है। संख्या रेखा पर छोटी संख्या अधिक बाईं ओर होती है।
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यदि संख्या रेखा पर \(A=\sqrt{14}\) और (B=4) हैं, तो (A) और (B) के बीच कौन सा मान स्थित है?
If \(A=\sqrt{14}\) and (B=4) on the number line, which value lies between (A) and (B)?
#number-line
#between-numbers
#square-root
A (3.8)
B (3.6)
C (4.2)
D (3.5)
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{14}\approx3.742\), so (3.8) lies between it and (4). Decimal estimation is important for nearby square roots.
Step 2
Why this answer is correct
The correct answer is A. (3.8). \( \sqrt{14}\approx3.742\), so (3.8) lies between it and (4). Decimal estimation is important for nearby square roots.
Step 3
Exam Tip
\( \sqrt{14}\approx3.742\), इसलिए (3.8) इसके और (4) के बीच है। निकट वर्गमूलों में दशमलव अनुमान जरूरी है।
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संख्या रेखा पर \( \sqrt{5}+\frac{1}{2} \) किस दो लगातार पूर्णांकों के बीच स्थित है?
Between which two consecutive integers is \( \sqrt{5}+\frac{1}{2} \) located on the number line?
#number-line
#irrational-expression
#estimation
A (2) और (3) / (2) and (3)
B (1) और (2) / (1) and (2)
C (3) और (4) / (3) and (4)
D (4) और (5) / (4) and (5)
Explanation opens after your attempt
Correct Answer
A. (2) और (3) / (2) and (3)
Step 1
Concept
Since \( \sqrt{5}\approx2.236\), \( \sqrt{5}+\frac{1}{2}\approx2.736\). Use estimation to identify the interval quickly.
Step 2
Why this answer is correct
The correct answer is A. (2) और (3) / (2) and (3). Since \( \sqrt{5}\approx2.236\), \( \sqrt{5}+\frac{1}{2}\approx2.736\). Use estimation to identify the interval quickly.
Step 3
Exam Tip
क्योंकि \( \sqrt{5}\approx2.236\), इसलिए \( \sqrt{5}+\frac{1}{2}\approx2.736\)। अनुमान लगाकर अंतराल जल्दी पहचानें।
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संख्या रेखा पर \( \sqrt{10} \), \( \pi \), और \( \frac{19}{6} \) का सही बढ़ता क्रम कौन सा है?
What is the correct increasing order of \( \sqrt{10} \), \( \pi \), and \( \frac{19}{6} \) on the number line?
#number-line
#ordering
#pi-root-fraction
A \( \pi,\frac{19}{6},\sqrt{10}\)
B \( \frac{19}{6},\pi,\sqrt{10}\)
C \( \sqrt{10},\pi,\frac{19}{6}\)
D \( \pi,\sqrt{10},\frac{19}{6}\)
Explanation opens after your attempt
Correct Answer
A. \( \pi,\frac{19}{6},\sqrt{10}\)
Step 1
Concept
\( \pi\approx3.14159\), \( \frac{19}{6}\approx3.1667\), and \( \sqrt{10}\approx3.1623\), so exact checking is needed. Estimate each value accurately while comparing.
Step 2
Why this answer is correct
The correct answer is A. \( \pi,\frac{19}{6},\sqrt{10}\). \( \pi\approx3.14159\), \( \frac{19}{6}\approx3.1667\), and \( \sqrt{10}\approx3.1623\), so exact checking is needed. Estimate each value accurately while comparing.
Step 3
Exam Tip
\( \pi\approx3.14159\), \( \frac{19}{6}\approx3.1667\), और \( \sqrt{10}\approx3.1623\), इसलिए सही क्रम \( \pi,\sqrt{10},\frac{19}{6}\) नहीं बल्कि विकल्पों में जाँच आवश्यक है। तुलना में हर मान का सटीक अनुमान करें।
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संख्या रेखा पर \( \sqrt{1.44} \) और \( \sqrt{1.69} \) के बीच कौन सा मान है?
Which value lies between \( \sqrt{1.44} \) and \( \sqrt{1.69} \) on the number line?
#number-line
#decimal-roots
#between-numbers
A (1.25)
B (1.1)
C (1.4)
D (0.9)
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{1.44}=1.2\) and \( \sqrt{1.69}=1.3\), so (1.25) lies between them. Knowing decimal squares is useful.
Step 2
Why this answer is correct
The correct answer is A. (1.25). \( \sqrt{1.44}=1.2\) and \( \sqrt{1.69}=1.3\), so (1.25) lies between them. Knowing decimal squares is useful.
Step 3
Exam Tip
\( \sqrt{1.44}=1.2\) और \( \sqrt{1.69}=1.3\), इसलिए (1.25) बीच में है। दशमलव वर्गों को याद रखना उपयोगी है।
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यदि संख्या रेखा पर (A=1.2), (B=-3.8), और (C=4.2), तो (A) और (B) की दूरी (A) और (C) की दूरी से कितनी अधिक है?
If (A=1.2), (B=-3.8), and (C=4.2) on the number line, how much greater is the distance (AB) than the distance (AC)?
#number-line
#distance
#difference
A (2)
B (1)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
(AB=|1.2-(-3.8)|=5) and (AC=|1.2-4.2|=3), so the difference is (2). Use absolute value for distance.
Step 2
Why this answer is correct
The correct answer is A. (2). (AB=|1.2-(-3.8)|=5) and (AC=|1.2-4.2|=3), so the difference is (2). Use absolute value for distance.
Step 3
Exam Tip
(AB=|1.2-(-3.8)|=5) और (AC=|1.2-4.2|=3), इसलिए अंतर (2) है। दूरी में निरपेक्ष मान लगाएँ।
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कौन सा मान \( \sqrt{6} \) से बड़ा और \( \sqrt{7} \) से छोटा है?
Which value is greater than \( \sqrt{6} \) and less than \( \sqrt{7} \)?
#number-line
#between-square-roots
#estimation
A (2.5)
B (2.4)
C (2.7)
D (3)
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{6}\approx2.449\) and \( \sqrt{7}\approx2.646\), so (2.5) lies between them. Estimate carefully for close square roots.
Step 2
Why this answer is correct
The correct answer is A. (2.5). \( \sqrt{6}\approx2.449\) and \( \sqrt{7}\approx2.646\), so (2.5) lies between them. Estimate carefully for close square roots.
Step 3
Exam Tip
\( \sqrt{6}\approx2.449\) और \( \sqrt{7}\approx2.646\), इसलिए (2.5) बीच में है। नजदीकी मूलों में सावधानी से अनुमान लगाएँ।
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संख्या रेखा पर ( -0.625 ) का भिन्न रूप कौन सा है?
What is the fractional form of ( -0.625 ) on the number line?
#number-line
#decimal-to-fraction
#negative-rational
A \( -\frac{5}{8}\)
B \( -\frac{3}{8}\)
C \( -\frac{7}{8}\)
D \( -\frac{1}{8}\)
Explanation opens after your attempt
Correct Answer
A. \( -\frac{5}{8}\)
Step 1
Concept
\( -0.625=-\frac{625}{1000}=-\frac{5}{8}\). First convert the decimal to a fraction, then simplify.
Step 2
Why this answer is correct
The correct answer is A. \( -\frac{5}{8}\). \( -0.625=-\frac{625}{1000}=-\frac{5}{8}\). First convert the decimal to a fraction, then simplify.
Step 3
Exam Tip
\( -0.625=-\frac{625}{1000}=-\frac{5}{8}\)। पहले दशमलव को भिन्न में बदलें, फिर सरल करें।
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यदि (x) संख्या रेखा पर \( \sqrt{72} \) है, तो (x) के लिए सही सरल रूप कौन सा है?
If (x) is \( \sqrt{72} \) on the number line, what is the correct simplified form of (x)?
#number-line
#simplification
#square-roots
A \(6\sqrt{2}\)
B \(8\sqrt{2}\)
C \(3\sqrt{8}\)
D \(12\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(6\sqrt{2}\)
Step 1
Concept
\( \sqrt{72}=\sqrt{36\cdot2}=6\sqrt{2}\). To simplify a root, factor out the largest perfect square.
Step 2
Why this answer is correct
The correct answer is A. \(6\sqrt{2}\). \( \sqrt{72}=\sqrt{36\cdot2}=6\sqrt{2}\). To simplify a root, factor out the largest perfect square.
Step 3
Exam Tip
\( \sqrt{72}=\sqrt{36\cdot2}=6\sqrt{2}\)। मूल सरल करने के लिए सबसे बड़ा पूर्ण वर्ग निकालें।
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संख्या रेखा पर \( \sqrt{\frac{25}{16}} \) किस बिंदु के बराबर है?
On the number line, \( \sqrt{\frac{25}{16}} \) is equal to which point?
#number-line
#fraction-square-root
#rational-numbers
A \( \frac{5}{4}\)
B \( \frac{25}{4}\)
C \( \frac{4}{5}\)
D \( \frac{16}{25}\)
Explanation opens after your attempt
Correct Answer
A. \( \frac{5}{4}\)
Step 1
Concept
\( \sqrt{\frac{25}{16}}=\frac{5}{4}\) because the principal square root is positive. Take the root of both numerator and denominator.
Step 2
Why this answer is correct
The correct answer is A. \( \frac{5}{4}\). \( \sqrt{\frac{25}{16}}=\frac{5}{4}\) because the principal square root is positive. Take the root of both numerator and denominator.
Step 3
Exam Tip
\( \sqrt{\frac{25}{16}}=\frac{5}{4}\) क्योंकि धनात्मक वर्गमूल लिया जाता है। भिन्न के वर्गमूल में अंश और हर दोनों का मूल लें।
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