Key Points
Key points: Permutations
When all the objects are distinct
- \[^nP_r\mathrm{~or~}P(n,r).\mathrm{~i.e.~}P\left(n,r\right)={}^nP_r=\frac{n!}{\left(n-r\right)!},0\leq r\leq n\]
- Repetition Allowed: nn
- Objects Together: 2(n − 1)!
- Specified Object Included: \[r\times^{(n-1)}P_{(r-1)}\]
When some objects are identical
- Identical objects (p same, rest distinct): \[\frac{n!}{p!}\]
- Multiple identical objects: \[\frac{n!}{p_{1}!p_{2}!\ldots p_{k}!}\]
Special Cases:
- \[^nP_n\] = \[\mathrm{n!}\]
- \[{}^{\mathrm{n}}\mathrm{P}_{0}=1\]
- \[^nP_1\] = n
- \[{}^{n}P_{n-1}\]= n!
- \[^nP_r\] = \[\mathrm{^{n-1}P_r+r.^{n-1}P_{r-1}}\]
Important Questions [84]
- The Parallel Sides of a Trapezium Shaped Field Are 25 M and 10 M and Non Parallel Sides Are 14 M and 13 M. What is the Area (In M2 ) of the Field?
- A Patient in a Hospital is Given Soup Daily in a Cylindrical Bowl of Diameter 7 Cm.
- Naresh Bought a Bicycle Each for His Two Sons, Each Bicycle Priced at Rs. 3500. If the First Bicycle is Sold at a Profit of 5%, How Much Should the Other Bicycle Be Sold For, to Gain
- Reshma Sells an Article to Rekha at 37.5% Profit, Rekha Sells It to Madhu at 9 1 11 % Profit. Again Madhu Sells It to Mitu at 25% Loss. If Mitu Pays Rs.342 for the Article, Then What is the Cost
- A Book Seller Sold a Box of 10 Pencils for Rs. 80 and Incurred a Loss. Had He Sold It for Rs. 98, His Gain Would Have Been Twice the Loss He Incurred Earlier. the Cost Price of the Box of Pencils Is:
- A Trader Sells Rice at a Profit of 20% and Uses Weights Which Are 10% Less than the Correct Weight. the Total Gain Earned by Him Is:
- A man earns ₹ 20 on the first day and spends ₹15 on the next day. He again earns ₹20 on the third day and spends ₹15 on the fourth day.
- The Municipality of a Town Increases Water Tax by 20% and Water Consumption Decreased by 20%. Then the Percentage of Increase Or Decrease in the Monthly Expenditure Is:
- An Employee of an Organization Invests a Total of Rs 25,400 in Two Different Schemes X and Y at a Simple Interest Rate of 18% per Annum and 10% per Annum Respectively.
- The Value of a Machine Depreciates Every Year at the Rate of 10% on Its Value at the Beginning of that Year. If the Present Value of the Machine is Rs. 729, Its Worth Three Years Ago Was:
- A Part of Monthly Hostel Charges is Fixed and the Remaining Depends on the Number of Days One Has Taken Food in the Mess.
- In a 120 Litre of Solution of Acid and Water, Acid is 75%. a Person Takes Out 20 Litres of this Solution and Added 16.2 Litres of Acid and 3.8 Litres of Water in the Remaining Solution.
- The Banker’S Discount on a Sum of Money for 18 Months is Rs. 600 and the True Discount on the Same Sum for 3 Years is Rs. 750/. the Rate Percentage Is:
- A Shop Gives 15% Discount on the Purchase of a T.V. If Paid for in Cash Immediately, a Further Discount of 12% is Given.
- If N2 = 12345678987654321, What is N?
- A Speaks Truth in 75% Cases and B in 80% of the Cases. in V1hat Percentage of Cases Are They Likely to Contradict Each Other. Narrating the Same Incident?
- A Man Buys Rs. 20 Shares Paying 9% Dividend. the Man Expects to Have an Interest of 12% on His Money.
- Two Men and Seven Boys Can Do a Work in 14 Days. Three Men and Eight Boys Can Do the Same Work in 11 Days. Further Eight Men and Six Boys Can Do Three Times the Amount of this Work In:
- A Tank is Connected to Three Pipes – Pipe A, B, and C. Pipe a Can Fill the Tank in 6 Hours, B Can Fill the Tank in 8 Hours and Pipe C Can Empty the Full Tank in 12 Hours. How Much Time
- A Can Do a Piece of Work in 8 Days and B Alone Can Do the Same Work in 10 Days. a and B Agreed to Do the Work Together for Rs. 720.
- ‘A’ and ‘B’ Complete a Work in 12 Days, ‘B’ and ‘C’ in 8 Days and ‘C’ and ‘A’ in 16 Days. ‘A’ Left After Working for 3 Days. in How Many Days More Will ‘B’ and ‘C’ Finish the Remaining Work?
- If Monday Falls on 1st of October, Which Day Will Fall Three Days After the 20th in that Month?
- A Clock Was Set Correct at 12 O’ Clock. It Loses 10 Minutes per Hour. What Will Be the Angle Between the Hour and Minute Hands of the Clock After One Hour?
- How many times from 4 pm to 10 pm, the hands of a clock are at right angles?
- The Birthday of Ms. Y Was Celebrated Six Days before Ms. X, Who Was Born on 4th October 1999.
- The Angles Between the Hands of a Clock When the Time is 4:25 Am Is:
- If 27th March, 2011 Was Sunday, What Was the Day on 27th June, 2011?
- The Traffic Lights at Three Different Signal Points Change After Every 45 Seconds, 75 Seconds and 90 Seconds Respectively.
- A Clock Gains 2 Minutes Every Hour. Then the Angle Traversed by the Second Hand in One Minute Is:
- From Morning 11 O’ Clock to Evening 7 O’ Clock, How Many Times the Hour Hand and Minutes Hand Will Overlap Each Other?
- The Smallest Number that Should Be Subtracted from 2085, So that the New Number is Completely Divisible by 23 is
- Two Consecutive Even Positive Integers, Sum of the Squares of Whichis 1060 Are
- Let X Be the Greatest Number of 4 Digits, Which When Divided by 15, 20 and 28 Leaves in Each Case the Remainder 2. the Sum of Digits of X is
- When 13511, 13903 and 14589 Are Divided by the Greatest Number ‘N’, the Remainder in Each Case is ‘M’. the Value of (N + M) is
- Abcd is a Quadrilateral in Which Measures of Angle D and Angle C Are 60 Degrees, and 100 Degrees Respectively. If the Internal Bisectors of Angle a and Angle B Meet at P, Then Measure of Angle Apb is
- The number of ‘three digit numbers’ which are multiples of 9 are:
- Directions: Examine the Following Expressions/Activities/Processes, and Arrange Them in the Most Logical Sequence 1. Design, 2. Need, 3. Launching, 4. Research, 5. Testing, 6. Identify
- What is the Sum of All the Natural Numbers from 1 to 100?
- The Sum of All the Natural Numbers from 200 to 600 (Both Inclusive) Which Are Neither Divisible by 8 Nor by 12 Is:
- What is the approximate percent increase in the number of units sold by Company E in the year 2007 from the previous year?
- Answer the Questions Based on the Information Given in the Following Table. A, B, C, D, E Denote Companies and 2006, 2007, 2008. 2009and 2010 Denote Years.
- What is the Total Number of Units Manufactured by Company Cover Me Years Together?
- What is the average number of units sold by company D over all the years together?
- What is the Respective Ratio of Total Number of Units Manufactured by Company a and B Together in the Year 2009 to Those Sold by Them 1n the Same Year?
- If the Product of Zeroes of the Polynomial Ax2 - 6x - 6 is 4, Find the Value of 'A'.
- A Grocer Mixes Coffee Powder of 2 Types, One of Which is Priced at Rs. 60 and the Other at Rs. 90. What Should Be the Ratio of Combining the Two, to Sell the Blended Mix Coffee Powder of the Two
- Praveen Has Rs. 4,662 in the Form of 2, 5 and 10 Rupee Notes. If These Notes Are in the Ratio of 3:5:8, the Number of Five Rupees Notes with Hi M Is:
- The Value of the Expression ( 1 29 36 + 4 1 8 × 1 7 11 ) ÷ ( 5 1 9 − 7 7 8 ÷ 9 9 20 ) 3 1 5 ÷ 9 2 of 5 1 3 is
- In a tournament, there are n teams, T1, T2, T3 ...., Tn, with n > 5. Each team consists of K players K > 3.
- A and B Are Inversely Proportional to Each Other and Are Positive. If a Increases by 100%, Then B Decreases by
- The Average Weight of Three Men ‘X’, ‘Y’ and ‘Z’ is 75 Kgs. Another Man ‘A’ Joins the Group and the Average Weight Now Becomes 80 Kgs.
- Choose the Most Appropriate Option: a Library Has an Average of 510 Vis1tors on Sunday and 240 on the Other Days. the Average Number of Visitors per Day in a Month of 30 Days Beginning with a Sunday
- The Age of Father 10 Years Ago Was Three Times the Age of His Son. After 10 Years, Father’S Age is Twice that of His Son. the Ratio of Their Present Ages Is:
- Kiran‘S Brother is 5 Years Older than Her. Her Father Was 30 Years Old When Kiran'S Sister Was Born, While Her Mother Was 28 Years Old When Kiran Was Born. If Kiran'S Sister Was 2 Years
- Beena Got Married 8 Years Ago. Today, Her Age is 11/4 Times Her Age at the Time of Marriage. If Her Daughter'S Age is 1/10 Times Her Age, Then Her Daughter'S Age Is:
- The Number of Children in a Camp is X and Their Average Weight is 20 Kg. If 5 Children Each Weighing 12 Kg, Join the Camp
- A Train 600 Meters Long is Running at a Speed of 90 Kms/Hr. If It Crosses a Tunnel in One Minute, Then the Length of the Tunnel Is:
- A Watch Which Gains Uniformly is 2 Minutes Slow at Noon on Monday and is 4 Minutes 48 Second Fast at 2 P.M on the Following Monday. When Was It Correct?
- If a Person Travels at a Speed of 40 Km/H He Will Reach His Destination on Time. He Covered Half the Journey in 2 3 of the Time. at What Speed (In Km/H) Should He Travel to Cove
- A Car Driver Increases the Average Speed of His Car by 3 Km/Hr Every Hour. the Total Distance Travelled in 7 Hours If the Distance Covered in First Hour Was 30 Km, is
- Along a Road Lie an Odd Number of Stones Placed at Intervals of 10 M. These Stones Have to Be Assembled Around the Middle Stone.
- In a 100 Meters Race, a Beats B by 20 Meters B Beats C by 5 Meters. in the Same Race, A Beats C By:
- Two Trains, One from Howrah to Patna and Other from Patna to Howrah Start Simultaneously. After They Meet, the Trains Reach Their Destinations After 9 Hours and 16 Hours Respectively.
- Taps ‘A’ and ‘B’ can fill a tank in 37 1/2minutes and 45 minutes respect ively. Both taps are opened and after some time tap ‘B’ is turned off. The tank is filled completely in exactly 30 minutes,
- A Train Which is Moving at an Average Speed of 40 Kmph, Reaches Its Destination on Time.
- A Train ‘X’ Leaves Station ‘A’ at 3 P.M and Reaches Station ‘B’ at 4.30 P. M., While Another Train ‘Y’ Leaves Station ‘B’ at 3.00 P.M and Reaches Station ‘A’ at 4.00 P.M.
- A Boat Travels Upstream from a to B and Back from B to a in 5 Hours. the Speed of the Boat in Still Water is 8 Km/Hour and the Speed of the Current is 4 Km/Hour. Then, the Distance from a to B Is:
- A Man Rows to a Place 45 K.Ms Distant and Back in 12 Hours. He Realises that He Can Row 5 K.Ms Downstream at the Same Time as 3 K.Ms Against the Stream. the Velocity of the Stream Is:
- What is the value of (x) in the following equation? x0.4 , 16 = 32 , x2.6
- If X = (163 + 173 + 183 + 193), Then X Divided by 70 Leaves a Remainder Of...
- The Simplified Value of (0.111)3 + (0.222)3 - (0.333)3 + (0.333)2 × (0.222)3 is :
- A Student Was Asked to Simplify the Expression: 0.1216 × 0.105 × 0.0002 0.625 × 0.08512 × 0.039 × 0.16 His Answer Was 1 65 . What is the Difference Between His Answer and the Correct Answer?
- What Are the Last Two Digits of 72008 ?
- When 2 1/2, is Added to a Number and the Sum is Multiplied by 4 1/2, and Then 3 is Added to the Product and Then the Sum is Divided by 1 1/5. the Quotient Becomes 25. What is that Number?
- A Vessel Contains a Mixture of Milk and Water in the Ratio of 5:3 Respectively. How Much of the Mixture Must Be Siphoned off and Replaced with Water,
- Gold and Copper Are as Heavy as Water by 19 and 9 Times Respectively. the Ratio in Which These Two Metals Be Mixed So that the Mixture is 17 Times as Heavy as Water Is:
- 60 Kg of an Alloy X is Mixed with 100 Kg of an Alloy Y. If Alloy X Has Lead and Tin in the Ratio of 3:2 and Alloy Y Has Tin and Copper in the Ratio of 1:4
- The Difference Between Simple Interest and Compound Interest at the Same Rate for Rupees 5,000 for Two Years is Rupees 98. the Rate of Interest Is:
- A Sum Amounts to Rs. 9680 in 2 Years and to Rs. 10648 in 3 Years Respectively at Compound Interest. What Will Be the Amount of the Same Sum is Invested
- The Difference Between Simple Interest and Compound Interest on Rs. 500 for 1 Year at 10% per Annum, Reckoned Half-yearly is
- A Circular Park, 42 M in Diameter, Has a Path 3.5 M Wide Running Around It on the Outside. Find the Cost of Gravelling the Path at Rs. 4 per M2
- The Perimeter of a Rectangle is 60 Cms. If Its Length is Twice Its Breadth, Then Its Area Is:
- A Tree Grows at the Rate of 1/5th of Its Height Annually. by How Much Height Will It Grow After 2 Years, If Its Present Height is 75 Cms?
- If a Boy is Standing at the Top of the Tower and Another Boy is at the Ground at Some Distance from the Foot of the Tower,
Concepts [20]
- Mensuration - Area and Volume (Entrance Exam)
- Profit and Loss (Entrance Exam)
- Percentage, Discount and Partnership (Entrance Exam)
- Time and Work (Entrance Exam)
- Permutations
- Concept of Probability
- Clock and Calender (Entrance Exam)
- Number System (Entrance Exam)
- HCF and LCM (Entrance Exam)
- Graph and Charts (Entrance Exam)
- Logarithm and Function (Entrance Exam)
- Ratio and Proportion (Entrance Exam)
- Average and Age
- Time, Speed and Distance (Entrance Exam)
- Simplification (Entrance Exam)
- Mixture and Allegations (Entrance Exam)
- Simple and Compound Interest (Entrance Exam)
- Quadratic and Linear Equation (Entrance Exam)
- Series and Equations (Entrance Exam)
- Miscellaneous (Entrance Exam)
