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In how many different ways can the letters of the word ‘ARCHIVE’ be arranged? शब्द ‘ARCHIVE’ के अक्षरों को कितने भिन्न तरीकों से पुनर्व्यवस्थित किया जा सकता है? 
A) 2630
B) 5040
C) 1680
D) 3456
Correct Answer : 5040 Explanation : There are 7 unique letters in ARCHIVE which means that there are 7!=7*6*5*4*3*2*1=5040 different ways to rearrange them. 
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By using digits 1 to 9 how many 4 digit numbers can be formed which has 5 as a unit digit? Repetition of digits is are not allowed. अंक 1 से 9 तक का उपयोग करके कितनी 4 अंकीय संख्याएं बनाई जा सकती हैं जिनमें 5 एक इकाई अंक के रूप में है? अंकों की पुनरावृत्ति की अनुमति नहीं है। 
A) 336
B) 1400
C) 504
D) 251
Correct Answer : 336 Explanation : 5 at the unit place or divisible by 5. So, there is 1 way of doing it. 
In how many ways can 5 prizes be given away to 7 boys when each boy is eligible for all the prizes? 5 पारितोषकी को 7 लड़कों को कितने तरह से दिया जा सकता है जब प्रत्येक लड़का सारे पारितोषकी को पाने के लिए योग्य हैं? 
A) 5!
B) 7!
C) 5^{7}
D) 7^{5}
Correct Answer : 7^{5} Explanation : A prize can be given to any one of the 7 boys in (7/1)=7 ways 
How many different words, can be formed by rearranging the letters of the word ‘SUCCESS’? ‘SUCCESS’ शब्द के अक्षरों को पुर्नव्यस्थित करते हुए कितने भिन्न शब्द बनाये जा सकते हैं? 
A) 5040
B) 840
C) 420
D) 1680
Correct Answer : 420 Explanation : The word "SUCCESS" has total 7 elements, there two repeated elements S(thrice) and C(twice). The formula for permutations with repeated elements is as follows, When k out of n elements are indistinguishable, e.g. k copies of the same book, the number of different permutations is n!/k!. 
In how many different ways can the letters of the word ‘PUBLIC’ be arranged so that the vowels are at the two ends? शब्द ‘PUBLIC’ के अक्षरों को कितने भिन्न तरीको से पनुव्यर्वस्थित किया जा सकता है, ताकि स्वर दोनो छोरों पर रहें । 
A) 48
B) 72
C) 36
D) None of these
Correct Answer : 48 Explanation : PUBLIC has 2 vowels(UI) and 4 consonants (PBLC). All the letters are distinct. 
If ^{56}P_{r + 6} : ^{54}P_{r + 3} = 30800 : 1 then the value of r is ? यदि ^{56}P_{r + 6} : ^{54}P_{r + 3} = 30800 : 1 तो r का मान है ? 
A) 40 B) 41 C) 42 D) 43 Correct Answer : 41 Explanation : ^{56}P_{r + 6} : ^{54}P_{r + 3} = 30800 : 1 As 56! = 56*55*54! So, 
How many groups of 6 persons can be formed from 8 men and 7 women ? 8 पुरुषों और 7 महिलाओं से 6 व्यक्तियों के कितने समूह बनाए जा सकते हैं? 
A) 5000 B) 5005 C) 5050 D) 5650 Correct Answer : 5005 Explanation : Total number of person = 8 men + 7 women = 15 

If 10 persons meet at a meeting and shake hands exactly once with each other, what is the total number of handshakes? यदि 10 व्यक्ति एक बैठक में मिलते हैं और एक दूसरे से ठीक एक बार हाथ मिलाते हैं, तो हाथ मिलाने की कुल संख्या क्या है? 
A) 35
B) 35
C) 50
D) 45
Correct Answer : 45 Explanation : Combinations of n objects taken r at a time = ^{n}C_{r}= n! / [r!(nr!)] 
In a chess competition involving some boys and girls of a school, every student had to play exactly one game with every other student. It was found that in 45 games both the players were girls and in 190 games both were boys. The number of games in which one player was a boy and the other was a girl is? एक स्कूल के कुछ लड़कों और लड़कियों की शतरंज प्रतियोगिता में, प्रत्येक छात्र को हर दूसरे छात्र के साथ एक खेल खेलना था। यह पाया गया कि 45 खेलों में दोनों खिलाड़ी लड़कियां थीं और 190 खेलों में दोनों लड़के थे। उन खेलों की संख्या जिनमें एक खिलाड़ी लड़का था और दूसरा लड़की थी? 
A) 200
B) 216
C) 235
D) 256
Correct Answer : 200 Explanation : Let there were g girls and b boys. As given, total number of games in which both players were men ^{b}C_{2} = 190 Total number of games= ^{(g + b)}C_{2} => ^{30}C_{2} => (30 *29) / (2* 1) => 435 Number of games in which one player is a boy and the other is a girl = 435  45  190 = 200 
In how many different ways can the letters of the word ‘DESIGN’ be arranged so that the vowels are at the two ends? 'DESIGN' शब्द के अक्षरों को कितने अलगअलग तरीकों से व्यवस्थित किया जा सकता है ताकि दो छोरों स्वर पर हों? 
A) 56 B) 64 C) 24 D) 48 Correct Answer : 48 Explanation : DESIGN has 2 vowels(EI) and 4 consonants (DSGN). Total number of arrangements= 4!×2! = 48 