LFM Stats And Pure

jee-main 2023 Q63 Forming Numbers with Digit Constraints View

The number of numbers, strictly between 5000 and 10000 can be formed using the digits $1,3,5,7,9$ without repetition, is
(1) 6
(2) 12
(3) 120
(4) 72

jee-main 2023 Q63 Dictionary Order / Rank of a Permutation View

The letters of the word OUGHT are written in all possible ways and these words are arranged as in a dictionary, in a series. Then the serial number of the word TOUGH is : (1) 89 (2) 84 (3) 86 (4) 79

jee-main 2023 Q63 Word Permutations with Repeated Letters View

The number of seven digits odd numbers, that can be formed using all the seven digits $1, 2, 2, 2, 3, 3, 5$ is

jee-main 2023 Q63 Word Permutations with Repeated Letters View

The number of arrangements of the letters of the word "INDEPENDENCE" in which all the vowels always occur together is
(1) 16800
(2) 33600
(3) 18000
(4) 14800

jee-main 2023 Q63 Forming Numbers with Digit Constraints View

The number of five-digit numbers, greater than 40000 and divisible by 5 , which can be formed using the digits $0,1,3,5,7$ and 9 without repetition, is equal to
(1) 132
(2) 120
(3) 72
(4) 96

jee-main 2023 Q64 Selection with Group/Category Constraints View

The number of 4-letter words, with or without meaning, each consisting of 2 vowels and 2 consonants, which can be formed from the letters of the word UNIVERSE without repetition is $\_\_\_\_$.

jee-main 2023 Q64 Basic Combination Computation View

Five digit numbers are formed using the digits $1,2,3,5,7$ with repetitions and are written in descending order with serial numbers. For example, the number 77777 has serial number 1. Then the serial number of 35337 is

jee-main 2023 Q67 Factorial and Combinatorial Expression Simplification View

If ${}^{2n+1}P_{n-1} : {}^{2n-1}P_n = 11 : 21$, then $n^2 + n + 15$ is equal to $\_\_\_\_$.

jee-main 2023 Q69 Linear Arrangement with Constraints View

The number of 9-digit numbers, that can be formed using all the digits of the number 123456789, such that the even digits occupy only even places, is
(1) 2880
(2) 2520
(3) 2160
(4) 2400

jee-main 2023 Q78 Counting Functions with Composition or Mapping Constraints View

Let $A = \{1, 2, 3, 5, 8, 9\}$. Then the number of possible functions $f: A \rightarrow A$ such that $f(m \cdot n) = f(m) \cdot f(n)$ for every $m, n \in A$ with $m \cdot n \in A$ is equal to

jee-main 2023 Q81 Word Permutations with Repeated Letters View

The number of words, with or without meaning, that can be formed using all the letters of the word ASSASSINATION so that the vowels occur together, is $\_\_\_\_$.

jee-main 2023 Q81 Dictionary Order / Rank of a Permutation View

Let 5 digit numbers be constructed using the digits $0, 2, 3, 4, 7, 9$ with repetition allowed, and are arranged in ascending order with serial numbers. Then the serial number of the number 42923 is $\underline{\hspace{1cm}}$.

jee-main 2023 Q82 Linear Arrangement with Constraints View

The number of permutations, of the digits $1, 2, 3, \ldots, 7$ without repetition, which neither contain the string 153 nor the string 2467, is $\_\_\_\_$.

jee-main 2023 Q83 Forming Numbers with Digit Constraints View

Number of 4-digit numbers that are less than or equal to 2800 and either divisible by 3 or by 11, is equal to $\underline{\hspace{1cm}}$.

jee-main 2024 Q62 Distribution of Objects into Bins/Groups View

Number of ways of arranging 8 identical books into 4 identical shelves where any number of shelves may remain empty is equal to
(1) 18
(2) 16
(3) 12
(4) 15

jee-main 2024 Q62 Dictionary Order / Rank of a Permutation View

60 words can be made using all the letters of the word BHBJO, with or without meaning. If these words are written as in a dictionary, then the $50 ^ { \text {th} }$ word is :
(1) JBBOH
(2) OBBJH
(3) OBBHJ
(4) HBBJO

jee-main 2024 Q63 Dictionary Order / Rank of a Permutation View

If all the words with or without meaning made using all the letters of the word "NAGPUR" are arranged as in a dictionary, then the word at $315 ^ { \text {th} }$ position in this arrangement is:
(1) NRAGUP
(2) NRAPUG
(3) NRAPGU
(4) NRAGPU

jee-main 2024 Q69 Counting Functions with Constraints View

Let $[ t ]$ be the greatest integer less than or equal to $t$. Let $A$ be the set of all prime factors of 2310 and $f : A \rightarrow \mathbb { Z }$ be the function $f ( x ) = \left[ \log _ { 2 } \left( x ^ { 2 } + \left[ \frac { x ^ { 3 } } { 5 } \right] \right) \right]$. The number of one-to-one functions from $A$ to the range of $f$ is
(1) 25
(2) 24
(3) 20
(4) 120

jee-main 2024 Q81 Forming Numbers with Digit Constraints View

The number of 3-digit numbers, formed using the digits $2,3,4,5$ and 7, when the repetition of digits is not allowed, and which are not divisible by 3, is equal to $\_\_\_\_$

jee-main 2024 Q82 Dictionary Order / Rank of a Permutation View

All the letters of the word $G T W E N T Y$ are written in all possible ways with or without meaning and these words are written as in a dictionary. The serial number of the word $G T W E N T Y$ IS

jee-main 2024 Q87 Counting Functions or Mappings with Constraints View

Let $A = \{ ( x , y ) : 2 x + 3 y = 23 , x , y \in \mathbb { N } \}$ and $B = \{ x : ( x , y ) \in A \}$. Then the number of one-one functions from $A$ to $B$ is equal to $\_\_\_\_$

jee-main 2025 Q2 Linear Arrangement with Constraints View

In a group of 3 girls and 4 boys, there are two boys $B _ { 1 }$ and $B _ { 2 }$. The number of ways, in which these girls and boys can stand in a queue such that all the girls stand together, all the boys stand together, but $B _ { 1 }$ and $B _ { 2 }$ are not adjacent to each other, is :
(1) 96
(2) 144
(3) 120
(4) 72

jee-main 2025 Q6 Probability via Permutation Counting View

Let S be the set of all the words that can be formed by arranging all the letters of the word GARDEN. From the set S, one word is selected at random. The probability that the selected word will NOT have vowels in alphabetical order is :
(1) $\frac { 1 } { 2 }$
(2) $\frac { 1 } { 4 }$
(3) $\frac { 2 } { 3 }$
(4) $\frac { 1 } { 3 }$

jee-main 2025 Q6 Forming Numbers with Digit Constraints View

Let P be the set of seven digit numbers with sum of their digits equal to 11. If the numbers in P are formed by using the digits 1, 2 and 3 only, then the number of elements in the set $P$ is:
(1) 173
(2) 164
(3) 158
(4) 161

jee-main 2025 Q7 Dictionary Order / Rank of a Permutation View

If all the words with or without meaning made using all the letters of the word ``KANPUR'' are arranged as in a dictionary, then the word at $440 ^ { \text {th} }$ position in this arrangement, is :
(1) PRNAUK
(2) PRKANU
(3) PRKAUN
(4) PRNAKU

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LFM Stats And Pure

Completing the square and sketching 80

Inequalities 215

Discriminant and conditions for roots 106

Solving quadratics and applications 106

Curve Sketching 295

Factor & Remainder Theorem 90

Polynomial Division & Manipulation 44

Binomial Theorem (positive integer n) 244

Function Transformations 65

Composite & Inverse Functions 249

Partial Fractions 22

Generalised Binomial Theorem 16

Generalised Binomial Theorem and Partial Fractions 3

Complex Numbers Arithmetic 283

Complex Numbers Argand & Loci 135

Permutations & Arrangements 276

Combinations & Selection 268

Measures of Location and Spread 233

Probability Definitions 413

Tree Diagrams 5

Principle of Inclusion/Exclusion 23

Independent Events 51

Conditional Probability 127

Discrete Probability Distributions 210

Binomial Distribution 107

Geometric Distribution 11

Hypergeometric Distribution 10

Negative Binomial Distribution 2

Modelling and Hypothesis Testing 38

Hypothesis test of binomial distributions 12

Data representation 29

Continuous Probability Distributions and Random Variables 30

Continuous Uniform Random Variables 15

Geometric Probability 28

Normal Distribution 96

Approximating Binomial to Normal Distribution 7

Sign Change & Interval Methods 74

Fixed Point Iteration 12