LFM Stats And Pure

jee-main 2012 Q64 Selection and Task Assignment View

The number of arrangements that can be formed from the letters $a , b , c , d , e , f$ taken 3 at a time without repetition and each arrangement containing at least one vowel, is
(1) 96
(2) 128
(3) 24
(4) 72

jee-main 2012 Q89 Forming Numbers with Digit Constraints View

The number of 3-digit numbers, with distinct digits, that can be formed using the digits $1, 2, 3, 4, 5, 6, 7$ and divisible by 3 is
(1) 80
(2) 120
(3) 40
(4) 108

jee-main 2013 Q63 Forming Numbers with Digit Constraints View

5-digit numbers are to be formed using $2,3,5,7,9$ without repeating the digits. If $p$ be the number of such numbers that exceed 20000 and $q$ be the number of those that lie between 30000 and 90000, then $p : q$ is:
(1) $6 : 5$
(2) $3 : 2$
(3) $4 : 3$
(4) $5 : 3$

jee-main 2014 Q64 Forming Numbers with Digit Constraints View

The sum of the digits in the unit's place of all the 4-digit numbers formed by using the numbers $3,4,5$ and $6$, without repetition is:
(1) 18
(2) 36
(3) 108
(4) 432

jee-main 2015 Q61 Forming Numbers with Digit Constraints View

The number of integers greater than 6,000 that can be formed, using the digits 3, 5, 6, 7 and 8, without repetition, is:
(1) 216
(2) 192
(3) 120
(4) 72

jee-main 2015 Q63 Forming Numbers with Digit Constraints View

The number of integers greater than 6000 that can be formed, using the digits $3,5,6,7$ and 8 , without repetition is
(1) 72
(2) 216
(3) 192
(4) 120

jee-main 2015 Q85 Lattice Path / Grid Route Counting View

The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices $(0, 0)$, $(0, 41)$ and $(41, 0)$, is:
(1) 820
(2) 780
(3) 901
(4) 861

jee-main 2016 Q63 Dictionary Order / Rank of a Permutation View

If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary; then the position of the word SMALL is:
(1) 46th
(2) 59th
(3) 52nd
(4) 58th

jee-main 2016 Q90 Dictionary Order / Rank of a Permutation View

If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary; then the position of the word SMALL is: (1) 46th (2) 59th (3) 52nd (4) 58th

jee-main 2017 Q63 Dictionary Order / Rank of a Permutation View

If all the words, with or without meaning, are written using the letters of the word QUEEN and are arranged as in English dictionary, then the position of the word QUEEN is:
(1) $47 ^ { t h }$
(2) $45 ^ { t h }$
(3) $46 ^ { t h }$
(4) $44 ^ { \text {th } }$

jee-main 2018 Q63 Selection and Task Assignment View

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is:
(1) At least 750 but less than 1000
(2) At least 1000
(3) Less than 500
(4) At least 500 but less than 750

jee-main 2018 Q63 Forming Numbers with Digit Constraints View

$n$ - digit numbers are formed using only three digits 2,5 and 7 . The smallest value of $n$ for which 900 such distinct numbers can be formed, is
(1) 6
(2) 8
(3) 9
(4) 7

jee-main 2018 Q64 Forming Numbers with Digit Constraints View

The number of numbers between 2,000 and 5,000 that can be formed with the digits $0,1,2,3,4$ (repetition of digits is not allowed) and are multiple of 3 is
(1) 36
(2) 30
(3) 24
(4) 48

jee-main 2018 Q64 Forming Numbers with Digit Constraints View

$n$-digit numbers are formed using only three digits 2, 5 and 7. The smallest value of $n$ for which 900 such distinct numbers can be formed is :
(1) 9
(2) 7
(3) 8
(4) 6

jee-main 2019 Q63 Handshake / Product Counting View

There are $m$ men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by 84 , then the value of $m$ is :
(1) 11
(2) 12
(3) 7
(4) 9

jee-main 2019 Q63 Word Permutations with Repeated Letters View

All possible numbers are formed using the digits $1,1,2,2,2,2,3,4,4$ taken all at a time. The number of such numbers in which the odd digits occupy even places is
(1) 175
(2) 162
(3) 180
(4) 160

jee-main 2019 Q64 Forming Numbers with Digit Constraints View

The number of natural numbers less than 7000 which can be formed by using the digits $0,1,3,7,9$ (repetition of digits allowed) is equal to:
(1) 375
(2) 250
(3) 374
(4) 372

jee-main 2019 Q64 Forming Numbers with Digit Constraints View

The number of four-digit numbers strictly greater than 4321 that can be formed using the digit $0,1,2,3,4,5$ (repetition of digits is allowed) is:
(1) 360
(2) 288
(3) 306
(4) 310

jee-main 2020 Q53 Word Permutations with Repeated Letters View

Total number of 6-digit numbers in which only and all the five digits $1, 3, 5, 7$ and 9 appears, is
(1) $\frac { 1 } { 2 } (6!)$
(2) $6!$
(3) $5 ^ { 6 }$
(4) $\frac { 5 } { 2 } (6!)$

jee-main 2020 Q53 Forming Numbers with Digit Constraints View

If the number of five digit numbers with distinct digits and 2 at the $10 ^ { \text {th} }$ place is $336 k$, then $k$ is equal to:
(1) 4
(2) 6
(3) 7
(4) 8

jee-main 2020 Q53 Linear Arrangement with Constraints View

Two families with three members each and one family with four members are to be seated in a row. In how many ways can they be seated so that the same family members are not separated ?
(1) $2 ! 3 ! 4$ !
(2) $( 3 ! ) ^ { 3 } \cdot ( 4 ! )$
(3) $( 3 ! ) 2 . ( 4 ! )$
(4) $3 ! ( 4 ! ) ^ { 3 }$

jee-main 2020 Q54 Factorial and Combinatorial Expression Simplification View

The value of $\left( 2 \cdot { } ^ { 1 } P _ { 0 } - 3 \cdot { } ^ { 2 } P _ { 1 } + 4 \cdot { } ^ { 3 } P _ { 2 } - \right.$ up to $51 ^ { \text {th} }$ term $) + ( 1 ! - 2 ! + 3 ! -$ up to $51 ^ { \text {th} }$ term) is equal to
(1) $1 - 51 ( 51 )$ !
(2) $1 + ( 51 )$ !
(3) $1 + ( 52 )$ !
(4) 1

jee-main 2021 Q63 Word Permutations with Repeated Letters View

The sum of all the 4-digit distinct numbers that can be formed with the digits $1, 2, 2$ and 3 is:
(1) 26664
(2) 122664
(3) 122234
(4) 22264

jee-main 2021 Q63 Distribution of Objects into Bins/Groups View

The total number of positive integral solutions $( x , y , z )$ such that $x y z = 24$ is :
(1) 45
(2) 30
(3) 36
(4) 24

jee-main 2021 Q65 Factorial and Combinatorial Expression Simplification View

If ${ } ^ { n } P _ { r } = { } ^ { n } P _ { r + 1 }$ and ${ } ^ { n } C _ { r } = { } ^ { n } C _ { r - 1 }$, then the value of $r$ is equal to:
(1) 1
(2) 4
(3) 2
(4) 3

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LFM Stats And Pure

Completing the square and sketching 61

Inequalities 181

Discriminant and conditions for roots 65

Solving quadratics and applications 131

Curve Sketching 228

Factor & Remainder Theorem 61

Polynomial Division & Manipulation 35

Binomial Theorem (positive integer n) 197

Function Transformations 28

Composite & Inverse Functions 211

Partial Fractions 12

Generalised Binomial Theorem 10

Complex Numbers Arithmetic 207

Complex Numbers Argand & Loci 159

Permutations & Arrangements 255

Combinations & Selection 237

Measures of Location and Spread 181

Probability Definitions 212

Tree Diagrams 18

Principle of Inclusion/Exclusion 33

Independent Events 35

Conditional Probability 167

Discrete Probability Distributions 176

Uniform Distribution 3

Binomial Distribution 101

Geometric Distribution 8

Hypergeometric Distribution 9

Negative Binomial Distribution 1

Modelling and Hypothesis Testing 22

Hypothesis test of binomial distributions 2

Data representation 21

Continuous Probability Distributions and Random Variables 322

Continuous Uniform Random Variables 3

Geometric Probability 16

Normal Distribution 87

Approximating Binomial to Normal Distribution 4

Sign Change & Interval Methods 26

Fixed Point Iteration 9

Newton-Raphson method 6