Choose (a) first, then (b) from the remaining, and (c) is automatically fixed. In exams match sequential selection with factorial form.
Step 2
Why this answer is correct
The correct answer is A. (a+b+c=n). Choose (a) first, then (b) from the remaining, and (c) is automatically fixed. In exams match sequential selection with factorial form.
Step 3
Exam Tip
पहले (a) चुनें, फिर बचे में से (b), और (c) अपने आप तय होता है। परीक्षा में sequential selection को factorial form से मिलाएं।
A. चुनी गई (r) वस्तुओं के सभी क्रम/All orders of the selected (r) objects
Step 1
Concept
Combination gives only the group and (r!) adds arrangements of that group. In exams treat permutation as selection plus arrangement.
Step 2
Why this answer is correct
The correct answer is A. चुनी गई (r) वस्तुओं के सभी क्रम / All orders of the selected (r) objects. Combination gives only the group and (r!) adds arrangements of that group. In exams treat permutation as selection plus arrangement.
Step 3
Exam Tip
Combination केवल समूह देता है और (r!) उस समूह के arrangements जोड़ता है। परीक्षा में permutation को selection plus arrangement समझें।
To get unordered pairs from ordered pairs (2!) orders are removed. This connection is very useful in pair selection exams.
Step 2
Why this answer is correct
The correct answer is B. \(^{n}C_2=\frac{^{n}P_2}{2!}\). To get unordered pairs from ordered pairs (2!) orders are removed. This connection is very useful in pair selection exams.
Step 3
Exam Tip
Ordered pair से unordered pair पाने के लिए (2!) orders हटते हैं। परीक्षा में pair selection में यह connection बहुत उपयोगी है।
Once one group is chosen, the other group is fixed, so \(^{n}C_r\) is enough. In exams count only one selection when the complement is fixed.
Step 2
Why this answer is correct
The correct answer is B. \(^{n}C_r\). Once one group is chosen, the other group is fixed, so \(^{n}C_r\) is enough. In exams count only one selection when the complement is fixed.
Step 3
Exam Tip
एक group चुनते ही दूसरा group तय हो जाता है इसलिए \(^{n}C_r\) पर्याप्त है। परीक्षा में complement fixed हो तो एक ही selection गिनें।
This is an or situation so there are (5+6) choices. In exams look for the addition principle when the word or appears.
Step 2
Why this answer is correct
The correct answer is B. जोड़ सिद्धांत / Addition principle. This is an or situation so there are (5+6) choices. In exams look for the addition principle when the word or appears.
Step 3
Exam Tip
यह या वाली स्थिति है इसलिए (5+6) choices मिलते हैं। परीक्षा में or शब्द पर addition principle देखें।
Each shirt can pair with (4) pants so there are \(3\times4\) choices. In exams multiply when independent choices are needed together.
Step 2
Why this answer is correct
The correct answer is B. गुणन सिद्धांत / Multiplication principle. Each shirt can pair with (4) pants so there are \(3\times4\) choices. In exams multiply when independent choices are needed together.
Step 3
Exam Tip
हर shirt के साथ (4) pants जुड़ सकते हैं इसलिए \(3\times4\) choices हैं। परीक्षा में independent choices साथ चाहिए तो multiply करें।
A. (n) वस्तुओं से (2) का ordered pair/Ordered pair of (2) from (n) objects
Step 1
Concept
In a directed pair (AB) and (BA) are different so permutation is used. In exams choose (P) when direction or order appears.
Step 2
Why this answer is correct
The correct answer is A. (n) वस्तुओं से (2) का ordered pair / Ordered pair of (2) from (n) objects. In a directed pair (AB) and (BA) are different so permutation is used. In exams choose (P) when direction or order appears.
Step 3
Exam Tip
Directed pair में (AB) और (BA) अलग होते हैं इसलिए permutation लगता है। परीक्षा में direction या order दिखे तो (P) चुनें।
A. (n) vertices में unordered pair of vertices की संख्या/Number of unordered pairs of vertices among (n) vertices
Step 1
Concept
An edge is formed by an unordered pair of two vertices. In exams use \(^{n}C_2\) for pairs without direction.
Step 2
Why this answer is correct
The correct answer is A. (n) vertices में unordered pair of vertices की संख्या / Number of unordered pairs of vertices among (n) vertices. An edge is formed by an unordered pair of two vertices. In exams use \(^{n}C_2\) for pairs without direction.
Step 3
Exam Tip
एक edge दो vertices के unordered pair से बनता है। परीक्षा में pair without direction के लिए \(^{n}C_2\) लगाएँ।
For the (r)th position (n-r+1) choices are added as a factor. In exams identify the factor of the next position.
Step 2
Why this answer is correct
The correct answer is B. \(^{n}P_r=^{n}P_{r-1}\times(n-r+1)\). For the (r)th position (n-r+1) choices are added as a factor. In exams identify the factor of the next position.
Step 3
Exam Tip
(r)वें स्थान के लिए (n-r+1) विकल्प जुड़ते हैं। परीक्षा में next position का factor अलग पहचानें।
Two independent selections are needed together so the multiplication principle applies. In exams the word and often means multiply.
Step 2
Why this answer is correct
The correct answer is B. \(^{4}C_2\times{}^{5}C_1\). Two independent selections are needed together so the multiplication principle applies. In exams the word and often means multiply.
Step 3
Exam Tip
दो स्वतंत्र selections साथ-साथ चाहिए इसलिए गुणन सिद्धांत लगेगा। परीक्षा में and शब्द आने पर अक्सर multiply करें।
Seating in positions depends on order so permutation is used. In exams when position seat or rank appears check order.
Step 2
Why this answer is correct
The correct answer is D. \(^{6}P_3\). Seating in positions depends on order so permutation is used. In exams when position seat or rank appears check order.
Step 3
Exam Tip
पदों पर बैठाना क्रम पर निर्भर करता है इसलिए permutation लगेगा। परीक्षा में पद सीट या rank आने पर order देखें।
A. संपर्क अधिक स्थिर हो सकता है/Connection can be more stable
Step 1
Concept
In a wired network, devices are connected by cables.
Step 2
Why this answer is correct
Such connection can be stable in many cases.
Step 3
Exam Tip
Understand the difference between wired and wireless networks. चरण 1: तारयुक्त जाल में उपकरण तार से जुड़े होते हैं। चरण 2: ऐसा संपर्क कई स्थितियों में स्थिर हो सकता है। चरण 3: तारयुक्त और तार रहित जाल का अंतर समझें।
