class11 se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.
1558 questions tagged with class11.
There are (10) points, no (3) of which are collinear. How many circles will be determined?
C. (120)
एक वृत्त (3) बिंदुओं से निर्धारित होता है। अतः \(\binom{10}{3}=120\) होगा। / A circle is determined by (3) points. Thus \(\binom{10}{3}=120\).
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How many straight lines can be formed from (12) points if no (3) points lie on the same line?
B. (66)
एक रेखा (2) बिंदुओं से बनती है। इसलिए \(\binom{12}{2}=66\) सही है। / A line is formed by (2) points. Hence \(\binom{12}{2}=66\) is correct.
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C. (364)
त्रिभुज के लिए (3) बिंदु चाहिए। इसलिए \(\binom{14}{3}=364\) है। / A triangle needs (3) points. Hence \(\binom{14}{3}=364\).
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B. (55)
हर मैच (2) टीमों की जोड़ी से बनता है। कुल मैच \(\binom{11}{2}=55\) होंगे। / Each match is formed by a pair of (2) teams. The total matches are \(\binom{11}{2}=55\).
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What is the maximum number of handshakes among (20) persons?
A. (190)
हर हाथ मिलाना (2) व्यक्तियों की एक जोड़ी है। इसलिए \(\binom{20}{2}=190\) होगा। / Each handshake is a pair of (2) persons. Therefore \(\binom{20}{2}=190\).
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D. (200)
तरीके \(\binom{5}{2}\binom{6}{3}=10\cdot20=200\) हैं। अलग विषयों के चयन को गुणा करें। / The ways are \(\binom{5}{2}\binom{6}{3}=10\cdot20=200\). Multiply selections from different subjects.
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In how many ways can a team of (2) doctors and (1) nurse be formed from (7) doctors and (4) nurses?
C. (84)
तरीके \(\binom{7}{2}\binom{4}{1}=21\cdot4=84\) हैं। शर्तों को अलग-अलग गिनें। / The ways are \(\binom{7}{2}\binom{4}{1}=21\cdot4=84\). Count each condition separately.
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From (8) red and (7) white flowers, in how many ways can (2) red and (2) white flowers be selected?
B. (588)
चयन \(\binom{8}{2}\binom{7}{2}=28\cdot21=588\) है। हर रंग के लिए अलग संयोजन लगाएं। / The selection is \(\binom{8}{2}\binom{7}{2}=28\cdot21=588\). Use a separate combination for each color.
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From (6) boys and (5) girls, in how many ways can (3) boys and (1) girl be selected?
A. (100)
तरीके \(\binom{6}{3}\binom{5}{1}=20\cdot5=100\) हैं। अलग वर्गों से चयन में गुणा करें। / The ways are \(\binom{6}{3}\binom{5}{1}=20\cdot5=100\). Multiply selections from different groups.
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How many ways are there to choose (6) files from (9) different files?
D. (84)
\(\binom{9}{6}=\binom{9}{3}=84\) है। पूरक चयन से गणना आसान होती है। / \(\binom{9}{6}=\binom{9}{3}=84\). Complementary selection makes calculation easier.
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How many ways can (3) chapters be selected from (13) different chapters for revision?
C. (286)
अध्यायों का केवल चयन है। इसलिए \(\binom{13}{3}=286\) सही है। / Only selection of chapters is involved. Hence \(\binom{13}{3}=286\) is correct.
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In how many ways can a duty team of (5) volunteers be selected from (10) volunteers?
B. (252)
टीम चुनना संयोजन है इसलिए \(\binom{10}{5}=252\) होगा। पद न दिए हों तो क्रम नहीं देखें। / Selecting a team is a combination, so \(\binom{10}{5}=252\). If posts are not assigned, do not consider order.
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How many ways are there to choose (2) badges from (18) different badges?
A. (153)
दो बैज चुनने के तरीके \(\binom{18}{2}=153\) हैं। चयन में क्रम नहीं गिना जाता। / The number of ways is \(\binom{18}{2}=153\). Order is not counted in selection.
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C. (46)
कुल \(\binom{8}{3}=56\) हैं और केवल लड़के \(\binom{5}{3}=10\) हैं। इसलिए (56-10=46) तरीके हैं। / Total ways are \(\binom{8}{3}=56\), and all-boy selections are \(\binom{5}{3}=10\). Therefore (56-10=46) ways.
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Selecting (9) students from (12) students is equal to not selecting how many students from (12)?
B. (3)
\(\binom{12}{9}=\binom{12}{3}\) होता है। (9) चुनना (3) न चुनने के बराबर है। / \(\binom{12}{9}=\binom{12}{3}\). Selecting (9) is the same as not selecting (3).
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In how many ways can (2) questions be left out from (11) questions?
B. (55)
छोड़ने के लिए (2) प्रश्न चुनने हैं। इसलिए \(\binom{11}{2}=55\) तरीके हैं। / We need to choose (2) questions to leave out. Hence there are \(\binom{11}{2}=55\) ways.
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How many ways are there to choose exactly (4) chapters from (7) chapters for revision?
B. (35)
अध्यायों का क्रम नहीं पूछा गया है। इसलिए \(\binom{7}{4}=35\) होगा। / The order of chapters is not asked. Therefore \(\binom{7}{4}=35\).
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What is the total number of ways to choose (0) gifts or (1) gift from (10) different gifts?
B. (11)
कुल तरीके \(\binom{10}{0}+\binom{10}{1}=1+10=11\) हैं। (0) चयन को भी शामिल करें। / Total ways are \(\binom{10}{0}+\binom{10}{1}=1+10=11\). Include the (0) selection too.
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B. (36)
स्थान तय नहीं है इसलिए केवल रंगों का चयन है। तरीके \(\binom{9}{2}=36\) हैं। / Positions are not fixed, so only colors are selected. The ways are \(\binom{9}{2}=36\).
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How many ways are there to choose exactly (2) sweets from (6) sweets?
B. (15)
ठीक (2) चुनने का अर्थ \(\binom{6}{2}\) है। इसका मान (15) है। / Choosing exactly (2) means \(\binom{6}{2}\). Its value is (15).
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C. (100)
तरीके \(\binom{5}{1}\binom{6}{3}=5\cdot20=100\) हैं। पहले शर्तों को अलग करें फिर गुणा करें। / The ways are \(\binom{5}{1}\binom{6}{3}=5\cdot20=100\). Separate the conditions first and then multiply.
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C. (30)
तरीके \(\binom{4}{2}\binom{5}{1}=6\cdot5=30\) हैं। अलग श्रेणियों का चयन गुणा से जुड़ता है। / The ways are \(\binom{4}{2}\binom{5}{1}=6\cdot5=30\). Selections from different categories are multiplied.
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A. (3)
दोनों पुस्तकें हिंदी होनी हैं इसलिए \(\binom{3}{2}=3\) तरीके हैं। शर्त पढ़कर सही समूह चुनें। / Both books must be Hindi, so there are \(\binom{3}{2}=3\) ways. Read the condition and choose the correct group.
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How many ways are there to choose (5) tickets from (8) different tickets?
B. (56)
\(\binom{8}{5}=\binom{8}{3}=56\) है। पूरक रूप से चुनना आसान है। / \(\binom{8}{5}=\binom{8}{3}=56\). Choosing by the complementary form is easier.
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In how many ways can an ice cream with (3) flavors be selected from (7) flavors?
C. (35)
तीन स्वादों का चयन \(\binom{7}{3}=35\) तरीकों से होगा। स्वादों का क्रम सामान्यतः नहीं गिना जाता। / The (3) flavors can be selected in \(\binom{7}{3}=35\) ways. The order of flavors is usually not counted.
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(2) pictures are to be selected from (6) pictures for a poster. How many selections are possible?
B. (15)
दो चित्र चुनने के तरीके \(\binom{6}{2}=15\) हैं। लगाने की जगह न दी हो तो केवल चयन मानें। / The ways to choose two pictures are \(\binom{6}{2}=15\). If positions are not given, consider only selection.
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In how many ways can (4) letters be selected from (10) letters?
C. (210)
अक्षर केवल चुने जा रहे हैं इसलिए \(\binom{10}{4}=210\) होगा। व्यवस्था न पूछी जाए तो संयोजन लगाएं। / Letters are only being selected, so \(\binom{10}{4}=210\). Use combination when arrangement is not asked.
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B. (36)
क्रम महत्वपूर्ण नहीं है इसलिए \(\binom{9}{2}=36\) है। यही संयोजन की पहचान है। / Order is not important, so \(\binom{9}{2}=36\). This is the key idea of combination.
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In how many ways can at most (1) subject be selected from (7) subjects?
B. (8)
अधिकतम (1) का अर्थ (0) या (1) चयन है। इसलिए \(\binom{7}{0}+\binom{7}{1}=1+7=8\) है। / At most (1) means selecting (0) or (1). Hence \(\binom{7}{0}+\binom{7}{1}=1+7=8\).
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In how many ways can at least (2) fruits be selected from (4) fruits?
C. (11)
तरीके \(\binom{4}{2}+\binom{4}{3}+\binom{4}{4}=6+4+1=11\) हैं। कम से कम में सभी मान जोड़ें। / The ways are \(\binom{4}{2}+\binom{4}{3}+\binom{4}{4}=6+4+1=11\). Add all possible values in at least questions.
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