यदि (5) पुस्तकों में से (2) पुस्तकें चुननी हों तो कुल कितने चयन होंगे?
If (2) books are to be selected from (5) books, how many selections are possible?
#combinations
#class11
#easy
A (8)
B (10)
C (12)
D (20)
Explanation opens after your attempt
Step 1
Concept
This is a direct use of \(\binom{5}{2}=10\). In exams, order is not counted in selection.
Step 2
Why this answer is correct
The correct answer is B. (10). This is a direct use of \(\binom{5}{2}=10\). In exams, order is not counted in selection.
Step 3
Exam Tip
यह \(\binom{5}{2}=10\) का सरल प्रयोग है। परीक्षा में चयन का क्रम नहीं गिना जाता।
Login to save your score, XP, coins and progress. Login
(6) विद्यार्थियों में से (3) विद्यार्थियों की टीम कितने तरीकों से चुनी जा सकती है?
In how many ways can a team of (3) students be selected from (6) students?
#combinations
#class11
#easy
A (18)
B (15)
C (20)
D (12)
Explanation opens after your attempt
Step 1
Concept
Order is not important while selecting a team. Hence \(\binom{6}{3}=20\) is correct.
Step 2
Why this answer is correct
The correct answer is C. (20). Order is not important while selecting a team. Hence \(\binom{6}{3}=20\) is correct.
Step 3
Exam Tip
टीम चुनने में क्रम महत्वपूर्ण नहीं होता। इसलिए \(\binom{6}{3}=20\) सही है।
Login to save your score, XP, coins and progress. Login
(7) अलग-अलग फूलों में से (2) फूल चुनने के कितने तरीके हैं?
How many ways are there to choose (2) flowers from (7) different flowers?
#combinations
#class11
#easy
A (14)
B (21)
C (35)
D (42)
Explanation opens after your attempt
Step 1
Concept
It is \(\binom{7}{2}=\frac{7\cdot6}{2}=21\). Such questions form pairs of objects.
Step 2
Why this answer is correct
The correct answer is B. (21). It is \(\binom{7}{2}=\frac{7\cdot6}{2}=21\). Such questions form pairs of objects.
Step 3
Exam Tip
यह \(\binom{7}{2}=\frac{7\cdot6}{2}=21\) है। ऐसे प्रश्नों में वस्तुओं की जोड़ी बनती है।
Login to save your score, XP, coins and progress. Login
(8) खिलाड़ियों में से (4) खिलाड़ियों का समूह कितने तरीकों से बनाया जा सकता है?
In how many ways can a group of (4) players be formed from (8) players?
#combinations
#class11
#easy
A (32)
B (56)
C (70)
D (1680)
Explanation opens after your attempt
Step 1
Concept
A group has no order, so \(\binom{8}{4}=70\). In exams, the word group usually indicates combination.
Step 2
Why this answer is correct
The correct answer is C. (70). A group has no order, so \(\binom{8}{4}=70\). In exams, the word group usually indicates combination.
Step 3
Exam Tip
समूह में क्रम नहीं होता इसलिए \(\binom{8}{4}=70\) होगा। परीक्षा में समूह शब्द दिखे तो संयोजन लगाएं।
Login to save your score, XP, coins and progress. Login
(9) प्रश्नों में से (1) प्रश्न चुनने के कितने तरीके हैं?
How many ways are there to select (1) question from (9) questions?
#combinations
#class11
#easy
A (1)
B (8)
C (9)
D (18)
Explanation opens after your attempt
Step 1
Concept
Selecting one object gives \(\binom{9}{1}=9\). Remember \(\binom{n}{1}=n\).
Step 2
Why this answer is correct
The correct answer is C. (9). Selecting one object gives \(\binom{9}{1}=9\). Remember \(\binom{n}{1}=n\).
Step 3
Exam Tip
एक वस्तु चुनने पर \(\binom{9}{1}=9\) होता है। \(\binom{n}{1}=n\) याद रखें।
Login to save your score, XP, coins and progress. Login
(10) पेन में से (0) पेन चुनने का एक ही तरीका क्यों माना जाता है?
Why is selecting (0) pens from (10) pens considered one way?
#combinations
#class11
#easy
A क्योंकि \(\binom{10}{0}=1\) / Because \(\binom{10}{0}=1\)
B क्योंकि \(\binom{10}{0}=0\) / Because \(\binom{10}{0}=0\)
C क्योंकि \(\binom{10}{0}=10\) / Because \(\binom{10}{0}=10\)
D क्योंकि \(\binom{10}{0}=100\) / Because \(\binom{10}{0}=100\)
Explanation opens after your attempt
Correct Answer
A. क्योंकि \(\binom{10}{0}=1\) / Because \(\binom{10}{0}=1\)
Step 1
Concept
Choosing nothing is also one definite selection. Therefore \(\binom{n}{0}=1\).
Step 2
Why this answer is correct
The correct answer is A. क्योंकि \(\binom{10}{0}=1\) / Because \(\binom{10}{0}=1\). Choosing nothing is also one definite selection. Therefore \(\binom{n}{0}=1\).
Step 3
Exam Tip
कुछ भी न चुनना भी एक निश्चित चयन है। इसलिए \(\binom{n}{0}=1\) होता है।
Login to save your score, XP, coins and progress. Login
(5) रंगों में से (5) रंग चुनने के कितने तरीके हैं?
How many ways are there to choose all (5) colors from (5) colors?
#combinations
#class11
#easy
A (0)
B (1)
C (5)
D (25)
Explanation opens after your attempt
Step 1
Concept
There is only one way to choose all objects. Hence \(\binom{5}{5}=1\).
Step 2
Why this answer is correct
The correct answer is B. (1). There is only one way to choose all objects. Hence \(\binom{5}{5}=1\).
Step 3
Exam Tip
सभी वस्तुएं चुनने का केवल एक तरीका होता है। इसलिए \(\binom{5}{5}=1\) है।
Login to save your score, XP, coins and progress. Login
(6) दोस्तों में से (2) दोस्तों की जोड़ी कितने तरीकों से चुनी जा सकती है?
In how many ways can a pair of friends be selected from (6) friends?
#combinations
#class11
#easy
A (12)
B (15)
C (18)
D (30)
Explanation opens after your attempt
Step 1
Concept
For a pair, \(\binom{6}{2}=15\). In a pair, first and second are not counted separately.
Step 2
Why this answer is correct
The correct answer is B. (15). For a pair, \(\binom{6}{2}=15\). In a pair, first and second are not counted separately.
Step 3
Exam Tip
जोड़ी के लिए \(\binom{6}{2}=15\) होगा। जोड़ी में पहला और दूसरा अलग नहीं गिने जाते।
Login to save your score, XP, coins and progress. Login
(4) लड़कों और (3) लड़कियों में से (1) लड़का और (1) लड़की कितने तरीकों से चुने जा सकते हैं?
From (4) boys and (3) girls, in how many ways can (1) boy and (1) girl be selected?
#combinations
#class11
#easy
A (7)
B (12)
C (24)
D (1)
Explanation opens after your attempt
Step 1
Concept
The selection is \(\binom{4}{1}\binom{3}{1}=12\). Multiply choices when selecting from different groups.
Step 2
Why this answer is correct
The correct answer is B. (12). The selection is \(\binom{4}{1}\binom{3}{1}=12\). Multiply choices when selecting from different groups.
Step 3
Exam Tip
चयन \(\binom{4}{1}\binom{3}{1}=12\) है। अलग-अलग वर्गों से चयन में गुणा करते हैं।
Login to save your score, XP, coins and progress. Login
(5) लड़कों और (4) लड़कियों में से (2) लड़के चुनने के कितने तरीके हैं?
From (5) boys and (4) girls, how many ways are there to select (2) boys?
#combinations
#class11
#easy
A (10)
B (20)
C (9)
D (30)
Explanation opens after your attempt
Step 1
Concept
Only boys are being selected, so \(\binom{5}{2}=10\). Do not get confused by extra information.
Step 2
Why this answer is correct
The correct answer is A. (10). Only boys are being selected, so \(\binom{5}{2}=10\). Do not get confused by extra information.
Step 3
Exam Tip
केवल लड़कों में से चयन है इसलिए \(\binom{5}{2}=10\) होगा। अनावश्यक सूचना से भ्रमित न हों।
Login to save your score, XP, coins and progress. Login
