medium se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.
1071 questions tagged with medium.
Which point will be to the right of \(-\sqrt{5}\) on the number line?
C. (-2)
\(-\sqrt{5}\) लगभग (-2.24) है और (-2) उससे बड़ा है। परीक्षा में दाईं ओर बड़ी संख्या होती है। / \(-\sqrt{5}\) is about (-2.24), and (-2) is greater than it. In exams, the right side has the greater number.
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Which number is less than \(\sqrt{14}\) but greater than (3) on the number line?
B. (3.5)
\(\sqrt{14}\) लगभग (3.74) है, इसलिए (3.5) (3) से बड़ा और \(\sqrt{14}\) से छोटा है। परीक्षा में वर्गमूल का मोटा अनुमान लगाएं। / \(\sqrt{14}\) is about (3.74), so (3.5) is greater than (3) and less than \(\sqrt{14}\). In exams, make a rough estimate of the square root.
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Which point can be just to the right of \(\sqrt{11}\) on the number line?
C. (3.4)
\(\sqrt{11}\) लगभग (3.32) है, इसलिए (3.4) उसके दाईं ओर है। परीक्षा में दाईं ओर वाली संख्या बड़ी होती है। / \(\sqrt{11}\) is about (3.32), so (3.4) is to its right. In exams, a point to the right is greater.
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Which point is closest to \(\sqrt{6}\) on the number line?
B. (2.4)
\(\sqrt{6}\) लगभग (2.45) है, इसलिए (2.4) सबसे निकट है। परीक्षा में अनुमान के लिए \(2.4^2\) और \(2.5^2\) सोचें। / \(\sqrt{6}\) is about (2.45), so (2.4) is closest. In exams, think of \(2.4^2\) and \(2.5^2\) for estimation.
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Which points will be the zeros of \(x^2-2x=0\) on the number line?
A. (0) और (2)(0) and (2)
(x-2-2x=x(x-2)), इसलिए शून्यक (0) और (2) हैं। परीक्षा में सामान्य गुणनखंड निकालना आसान तरीका है। / (x-2-2x=x(x-2)), so the zeros are (0) and (2). In exams, taking a common factor is an easy method.
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In what form will the zeros of \(x^2-7\) appear on the number line?
D. \(-\sqrt{7}\) और \(\sqrt{7}\)\(-\sqrt{7}\) and \(\sqrt{7}\)
\(x^2-7=0\) से \(x=\pm\sqrt{7}\) मिलता है। परीक्षा में वर्ग समीकरण में धनात्मक और ऋणात्मक दोनों वर्गमूल लें। / From \(x^2-7=0\), \(x=\pm\sqrt{7}\). In exams, take both positive and negative square roots in a square equation.
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If (s(x)=x-2-16), what are its zeros on the number line?
B. (-4) और (4)(-4) and (4)
\(x^2-16=0\) से \(x=\pm4\) मिलता है। परीक्षा में \(a^2-b^2\) के शून्यक दोनों ओर देखें। / From \(x^2-16=0\), \(x=\pm4\). In exams, check both sides for zeros of \(a^2-b^2\).
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In which interval will the zero of (r(x)=4x+6) lie on the number line?
A. (-2) और (-1)(-2) and (-1)
(4x+6=0) से \(x=-\frac{3}{2}\), जो (-2) और (-1) के बीच है। परीक्षा में ऋणात्मक भिन्न का अंतराल सावधानी से पहचानें। / From (4x+6=0), \(x=-\frac{3}{2}\), which lies between (-2) and (-1). In exams, identify the interval of a negative fraction carefully.
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Between which two integers will the zero of (q(x)=3x-7) lie on the number line?
B. (2) और (3)(2) and (3)
(3x-7=0) से \(x=\frac{7}{3}\), जो (2) और (3) के बीच है। परीक्षा में पहले शून्यक निकालें फिर स्थान तय करें। / From (3x-7=0), \(x=\frac{7}{3}\), which lies between (2) and (3). In exams, first find the zero and then locate it.
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At which point will the zero of (p(x)=2x+5) lie on the number line?
B. (-2.5)
(2x+5=0) से \(x=-\frac{5}{2}=-2.5\) मिलता है। परीक्षा में शून्यक निकालकर उसे वास्तविक संख्या की तरह रखें। / From (2x+5=0), we get \(x=-\frac{5}{2}=-2.5\). In exams, find the zero and place it like a real number.
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What is the midpoint of (2.4) and (5.6) on the number line?
B. (4)
मध्य बिंदु \(\frac{2.4+5.6}{2}=4\) है। परीक्षा में दशमलव जोड़कर औसत निकालें। / The midpoint is \(\frac{2.4+5.6}{2}=4\). In exams, add decimals and find the average.
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What is the midpoint of \(-\frac{7}{3}\) and \(\frac{2}{3}\) on the number line?
A. \(-\frac{5}{6}\)
मध्य बिंदु \(\frac{-\frac{7}{3}+\frac{2}{3}}{2}=-\frac{5}{6}\) है। परीक्षा में पहले योग फिर (2) से भाग करें। / The midpoint is \(\frac{-\frac{7}{3}+\frac{2}{3}}{2}=-\frac{5}{6}\). In exams, first add and then divide by (2).
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What is the distance between (-2.75) and (1.25) on the number line?
B. (4) इकाई(4) units
दूरी (1.25-\left\(-2.75\right\)=4) इकाई है। परीक्षा में ऋणात्मक दशमलव घटाते समय चिह्न न भूलें। / The distance is (1.25-\left\(-2.75\right\)=4) units. In exams, do not miss signs while subtracting negative decimals.
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What is the distance between \(A=-\frac{3}{2}\) and \(B=\frac{5}{2}\) on the number line?
C. (4) इकाई(4) units
दूरी (\frac{5}{2}-\left\(-\frac{3}{2}\right\)=4) इकाई है। परीक्षा में दूरी हमेशा धनात्मक लें। / The distance is (\frac{5}{2}-\left\(-\frac{3}{2}\right\)=4) units. In exams, always take distance as positive.
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To get \(1+\frac{3}{8}\) on the number line, which mark between (1) and (2) is needed?
A. (1) के बाद तीसरा निशान जब (8) बराबर भाग होंThird mark after (1) when there are (8) equal parts
\(1+\frac{3}{8}\), (1) के बाद (8) बराबर भागों में तीसरे भाग पर है। परीक्षा में पूर्णांक के बाद भिन्न भाग गिनें। / \(1+\frac{3}{8}\) is the third of (8) equal parts after (1). In exams, count the fractional parts after the integer.
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B. (6) भाग(6) parts
\(\frac{5}{6}\) में हर (6) है, इसलिए (0) से (1) तक (6) बराबर भाग होंगे। परीक्षा में हर भागों की संख्या बताता है। / The denominator of \(\frac{5}{6}\) is (6), so the segment from (0) to (1) has (6) equal parts. In exams, the denominator tells the number of parts.
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At which mixed number position will \(-\frac{17}{5}\) lie on the number line?
B. \(-3-\frac{2}{5}\)
\(-\frac{17}{5}=-3-\frac{2}{5}\), इसलिए यह (-4) और (-3) के बीच है। परीक्षा में ऋणात्मक मिश्र संख्या का चिह्न ठीक रखें। / \(-\frac{17}{5}=-3-\frac{2}{5}\), so it lies between (-4) and (-3). In exams, keep the sign of a negative mixed number correct.
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How will \(\frac{13}{4}\) be shown as a mixed number on the number line?
A. \(3+\frac{1}{4}\)
\(\frac{13}{4}=3+\frac{1}{4}\), इसलिए यह (3) के बाद एक चौथाई पर होगा। परीक्षा में विषम भिन्न को मिश्र संख्या में बदलें। / \(\frac{13}{4}=3+\frac{1}{4}\), so it lies one-fourth after (3). In exams, convert an improper fraction into a mixed number.
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Between which two integers will \(5-\sqrt{2}\) come on the number line?
B. (3) और (4)(3) and (4)
\(\sqrt{2}\) (1) और (2) के बीच है, इसलिए \(5-\sqrt{2}\) (3) और (4) के बीच होगा। परीक्षा में घटाने पर सीमा सावधानी से बदलें। / \(\sqrt{2}\) lies between (1) and (2), so \(5-\sqrt{2}\) lies between (3) and (4). In exams, change limits carefully while subtracting.
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Between which two integers will \(2+\sqrt{3}\) lie on the number line?
B. (3) और (4)(3) and (4)
\(\sqrt{3}\) (1) और (2) के बीच है, इसलिए \(2+\sqrt{3}\) (3) और (4) के बीच होगा। परीक्षा में जोड़ने पर पूरा अंतराल आगे खिसकता है। / \(\sqrt{3}\) lies between (1) and (2), so \(2+\sqrt{3}\) lies between (3) and (4). In exams, adding a number shifts the whole interval forward.
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Between which two integers will \(-\sqrt{18}\) lie on the number line?
C. (-5) और (-4)(-5) and (-4)
क्योंकि \(\sqrt{18}\) (4) और (5) के बीच है, इसलिए \(-\sqrt{18}\) (-5) और (-4) के बीच होगा। परीक्षा में ऋणात्मक वर्गमूल में दिशा उलटी हो जाती है। / Since \(\sqrt{18}\) lies between (4) and (5), \(-\sqrt{18}\) lies between (-5) and (-4). In exams, the direction reverses for negative square roots.
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Between which two integers will \(\sqrt{10}\) be correctly represented on the number line?
B. (3) और (4)(3) and (4)
क्योंकि \(3^2=9\) और \(4^2=16\), इसलिए \(\sqrt{10}\) (3) और (4) के बीच है। परीक्षा में वर्गमूल को पूर्ण वर्गों से घेरें। / Since \(3^2=9\) and \(4^2=16\), \(\sqrt{10}\) lies between (3) and (4). In exams, bracket square roots between perfect squares.
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Which statement gives the correct position of \(-\sqrt{4}\) on the number line?
B. यह (-2) पर होगाIt will be at (-2)
\(\sqrt{4}=2\), इसलिए \(-\sqrt{4}=-2\) होगा। ऋण चिह्न को वर्गमूल लेने के बाद भी याद रखें। / \(\sqrt{4}=2\), so \(-\sqrt{4}=-2\). Remember the negative sign after finding the square root.
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Between which two integers will \(-\frac{7}{4}\) lie on the number line?
A. (-2) और (-1)(-2) and (-1)
\(-\frac{7}{4}=-1.75\), इसलिए यह (-2) और (-1) के बीच होगा। ऋणात्मक भिन्न में दिशा को ध्यान से देखें। / \(-\frac{7}{4}=-1.75\), so it lies between (-2) and (-1). Be careful with direction for negative fractions.
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What are the roots of \(2x^2-7x+3=0\) by factorisation method?
A. \(x=3,\frac{1}{2}\)
(2x-2-7x+3=(2x-1)(x-3)), इसलिए (x=3) और \(x=\frac{1}{2}\) हैं। परीक्षा में रैखिक गुणनखंड को अलग-अलग हल करें। / (2x-2-7x+3=(2x-1)(x-3)), so (x=3) and \(x=\frac{1}{2}\). In exams, solve each linear factor separately.
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What are the roots of \(4x^2+3x-10=0\)?
A. \(\frac{5}{4}\) और (-2)\(\frac{5}{4}\) and (-2)
(4x-2+3x-10=(4x-5)(x+2)) है। इसलिए मूल \(\frac{5}{4}\) और (-2) हैं। / (4x-2+3x-10=(4x-5)(x+2)). Therefore the roots are \(\frac{5}{4}\) and (-2).
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What are the roots of \(3x^2+2x-8=0\)?
A. \(\frac{4}{3}\) और (-2)\(\frac{4}{3}\) and (-2)
(3x-2+2x-8=(3x-4)(x+2)) है। इसलिए मूल \(\frac{4}{3}\) और (-2) हैं। / (3x-2+2x-8=(3x-4)(x+2)). Therefore the roots are \(\frac{4}{3}\) and (-2).
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What are the roots of \(2x^2+x-6=0\)?
A. \(\frac{3}{2}\) और (-2)\(\frac{3}{2}\) and (-2)
(2x-2+x-6=(2x-3)(x+2)) है। इसलिए मूल \(\frac{3}{2}\) और (-2) हैं। / (2x-2+x-6=(2x-3)(x+2)). Therefore the roots are \(\frac{3}{2}\) and (-2).
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A right triangle has base (x), height (x+2), and area (24). Which quadratic equation is correct?
A. \(x^2+2x-48=0\)
क्षेत्रफल (\frac{1}{2}x(x+2)=24) होगा। इसलिए (x(x+2)=48) और \(x^2+2x-48=0\) मिलता है। / The area is (\frac{1}{2}x(x+2)=24). Thus (x(x+2)=48), giving \(x^2+2x-48=0\).
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Which equation will have sum of roots (0)?
A. \(x^2-36=0\)
\(x^2-36=0\) में (b=0), इसलिए मूलों का योग \(-\frac{b}{a}=0\) है। (x) पद अनुपस्थित हो तो योग (0) हो सकता है। / In \(x^2-36=0\), (b=0), so the sum of roots is \(-\frac{b}{a}=0\). If the (x) term is absent, the sum can be (0).
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