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Important Formulas

Vedic/Quicker Math

Alligation or Mixture

Area

Average

Banker's Discount

Boats and Streams

Calendar

Chain Rule

Clock

Compound Interest

Decimal Fraction

Height and Distance

Logarithm

Numbers

Odd Man Out and Series

Partnership

Percentage

Permutation & Combination

Pipes and Cistern

Probability

Problems on Ages

Problems on H.C.F & L.C.M

Problems on Numbers

Problems on Trains

Profit & Loss

Races and Games

Ratio and Proportion

Simple Interest

Simplification

Square Root and Cube Root

Stocks and Shares

Surds and Indices

Time and Distance

Time and Work

True Discount

Volume and Surface Area

Practice Questions

:- You can add tough questions into
your favourite list for second revision. Note |

Q1. | In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women ? |

A. | 63 [Correct Answer] |

B. | 90 [Wrong Answer] |

C. | 126 [Wrong Answer] |

D. | 45 [Wrong Answer] |

View Answer
Explanation:-
Answer : ADiscuss it below :Required number of ways = (^{7}C_{5} X ^{3}C_{2}) = (^{7}C_{2} X ^{3}C_{1}) = ^{7 X 6}/_{2 X 1}^{ X 3}Click here for more comments |

Q2. | How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated ? |

A. | 5 [Wrong Answer] |

B. | 10 [Wrong Answer] |

C. | 15 [Wrong Answer] |

D. | 20 [Correct Answer] |

View Answer
Explanation:-
Answer : DDiscuss it below :Since each desired number is divisible by 5, so we must have 5 at the unit place. So,
there is 1 way of doing it.Tens place can be filled by any of the remaining 5 numbers. So, there-are 5 ways of filling the tens place. The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it. So Required number of numbers = (1 x 5 x 4) = 20. Click here for more comments |

Q3. | In how many ways can 21 books on English and 19 books on Hindi be placed in a row on a shelf so that two books on Hindi may not be together ? |

A. | 3990 [Wrong Answer] |

B. | 1540 [Correct Answer] |

C. | 1995 [Wrong Answer] |

D. | 1965 [Wrong Answer] |

View Answer
Explanation:-
Answer : BDiscuss it below :In order that two books on Hindi are never together, we must place all these books
as underX E X E X E X ... X E X where E denotes the position of an English book and X that of a Hindi book. Since there are 21 books on English, the number of places marked X are therefore, 22. Now, 19 places out of 22 can be chosen in ^{22}C_{19} = ^{22}C_{3}= ^{22 x 21 x 20}/_{3 x 2 x 1}Hence, the required number of ways = 1540. Click here for more comments |

Q4. | In how many ways can the letters of the word 'LEADER' be arranged ? |

A. | 72 [Wrong Answer] |

B. | 144 [Wrong Answer] |

C. | 360 [Correct Answer] |

D. | 720 [Wrong Answer] |

View Answer
Explanation:-
Answer : CDiscuss it below :The word 'LEADER' contains 6 letters, namely 1L, 2E, 1A, 1D and 1R.
Required number of ways =
^{6!}/_{ (1 !) (2 !) (1 !) (1 !) (2 !)}Click here for more comments |

Q5. | In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together ? |

A. | 810 [Wrong Answer] |

B. | 1440 [Wrong Answer] |

C. | 2880 [Wrong Answer] |

D. | 50400 [Correct Answer] |

View Answer
Explanation:-
Answer : DDiscuss it below :In the word 'CORPORATION', we treat the vowels OOAIO as one letter. Thus,
we have CRPRTN (OOAIO).This has 7 letters of which R occurs 2 times and the rest are different. Number of ways of arranging these letters = ^{7!}/_{2!}Now, 5 vowels in which 0 occurs 3 times and the rest dre different, can be arranged in ^{5!}/_{3!}Required number of ways = (2520 X 20) = 50400. Click here for more comments |

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