LFM Stats And Pure

jee-main 2017 Q76 Probability Involving Algebraic or Number-Theoretic Conditions View

If two different numbers are taken from the set $\{ 0 , 1 , 2 , 3 , \ldots , 10 \}$; then the probability that their sum as well as absolute difference are both multiple of 4, is:
(1) $\frac { 6 } { 55 }$
(2) $\frac { 12 } { 55 }$
(3) $\frac { 14 } { 45 }$
(4) $\frac { 7 } { 55 }$

jee-main 2017 Q89 Probability Using Set/Event Algebra View

For three events $A$, $B$ and $C$, $P(\text{Exactly one of } A \text{ or } B \text{ occurs}) = P(\text{Exactly one of } B \text{ or } C \text{ occurs}) = P(\text{Exactly one of } C \text{ or } A \text{ occurs}) = \dfrac{1}{4}$ and $P(\text{All the three events occur simultaneously}) = \dfrac{1}{16}$. Then the probability that at least one of the events occurs, is:
(1) $\dfrac{7}{32}$
(2) $\dfrac{7}{16}$
(3) $\dfrac{1}{64}$
(4) $\dfrac{3}{16}$

jee-main 2017 Q89 Probability Using Set/Event Algebra View

An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is:
(1) $\frac { 127 } { 128 }$
(2) $\frac { 63 } { 64 }$
(3) $\frac { 255 } { 256 }$
(4) $\frac { 1 } { 2 }$

jee-main 2017 Q90 Probability Involving Algebraic or Number-Theoretic Conditions View

If two different numbers are taken from the set $\{0, 1, 2, 3, \ldots, 10\}$; then the probability that their sum as well as absolute difference are both multiples of 4, is:
(1) $\dfrac{6}{55}$
(2) $\dfrac{12}{55}$
(3) $\dfrac{14}{45}$
(4) $\dfrac{7}{55}$

jee-main 2018 Q90 Conditional Probability and Bayes' Theorem View

A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its color is observed and this ball along with two additional balls of the same color are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red, is:
(1) $\frac { 3 } { 4 }$
(2) $\frac { 3 } { 10 }$
(3) $\frac { 2 } { 5 }$
(4) $\frac { 1 } { 5 }$

jee-main 2019 Q89 Probability Using Set/Event Algebra View

In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC and NSS. If one of these students is selected at random, then the probability that the student selected has opted neither for NCC nor for NSS is :
(1) $\frac { 1 } { 6 }$
(2) $\frac { 5 } { 6 }$
(3) $\frac { 1 } { 3 }$
(4) $\frac { 2 } { 3 }$

jee-main 2019 Q90 Conditional Probability and Bayes' Theorem View

An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is:
(1) $\frac{21}{49}$
(2) $\frac{26}{49}$
(3) $\frac{32}{49}$
(4) $\frac{27}{49}$

jee-main 2019 Q90 Conditional Probability and Bayes' Theorem View

An unbiased coin is tossed. If the outcome is a head then a pair of unbiased dice is rolled and the sum of the numbers obtained on them is noted. If the toss of the coin results in tail then a card from a well-shuffled pack of nine cards numbered $1,2,3 , \ldots , 9$ is randomly picked and the number on the card is noted. The probability that the noted number is either 7 or 8 is
(1) $\frac { 13 } { 36 }$
(2) $\frac { 19 } { 72 }$
(3) $\frac { 15 } { 72 }$
(4) $\frac { 19 } { 36 }$

jee-main 2019 Q90 Probability Using Set/Event Algebra View

Four persons can hit a target correctly with probabilities $\frac { 1 } { 2 } , \frac { 1 } { 3 } , \frac { 1 } { 4 }$ and $\frac { 1 } { 8 }$ respectively. If all hit at the target independently, then the probability that the target would be hit, is
(1) $\frac { 25 } { 192 }$
(2) $\frac { 7 } { 32 }$
(3) $\frac { 1 } { 192 }$
(4) $\frac { 25 } { 32 }$

jee-main 2019 Q90 Probability Using Set/Event Algebra View

Two newspapers $A$ and $B$ are published in a city. It is known that $25 \%$ of the city population reads $A$ and $20 \%$ reads $B$ while $8 \%$ reads both $A$ and $B$. Further, 30\% of those who read $A$ but not $B$ look into advertisements and $40 \%$ of those who read $B$ but not $A$ also look into advertisements, while $50 \%$ of those who read both $A$ and $B$ look into advertisements. Then the percentage of the population who look into advertisements is:
(1) 13.5
(2) 12.8
(3) 13.9
(4) 13

jee-main 2021 Q80 Probability Involving Algebraic or Number-Theoretic Conditions View

Let $A$ be a set of all 4-digit natural numbers whose exactly one digit is 7. Then the probability that a randomly chosen element of $A$ leaves remainder 2 when divided by 5 is:
(1) $\frac { 1 } { 5 }$
(2) $\frac { 122 } { 297 }$
(3) $\frac { 97 } { 297 }$
(4) $\frac { 2 } { 9 }$

jee-main 2021 Q80 Conditional Probability and Bayes' Theorem View

A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade, is :
(1) $\frac { 3 } { 4 }$
(2) $\frac { 52 } { 867 }$
(3) $\frac { 39 } { 50 }$
(4) $\frac { 22 } { 425 }$

jee-main 2021 Q80 Probability Using Set/Event Algebra View

Let $A , B$ and $C$ be three events such that the probability that exactly one of $A$ and $B$ occurs is $( 1 - k )$, the probability that exactly one of $B$ and $C$ occurs is $( 1 - 2k )$, the probability that exactly one of $C$ and $A$ occurs is $( 1 - k )$ and the probability of all $A , B$ and $C$ occur simultaneously is $k ^ { 2 }$, where $0 < k < 1$. Then the probability that at least one of $A , B$ and $C$ occur is:
(1) greater than $\frac { 1 } { 8 }$ but less than $\frac { 1 } { 4 }$
(2) greater than $\frac { 1 } { 2 }$
(3) greater than $\frac { 1 } { 4 }$ but less than $\frac { 1 } { 2 }$
(4) exactly equal to $\frac { 1 } { 2 }$

jee-main 2021 Q90 Conditional Probability and Bayes' Theorem View

An electric instrument consists of two units. Each unit must function independently for the instrument to operate. The probability that the first unit functions is 0.9 and that of the second unit is 0.8 . The instrument is switched on and it fails to operate. If the probability that only the first unit failed and second unit is functioning is $p$, then $98p$ is equal to

jee-main 2022 Q70 Finite Equally-Likely Probability Computation View

The probability that a randomly chosen $2 \times 2$ matrix with all the entries from the set of first 10 primes, is singular, is equal to
(1) $\frac { 133 } { 10 ^ { 4 } }$
(2) $\frac { 19 } { 10 ^ { 3 } }$
(3) $\frac { 18 } { 10 ^ { 3 } }$
(4) $\frac { 271 } { 10 ^ { 4 } }$

jee-main 2022 Q80 Probability Using Set/Event Algebra View

Let $E _ { 1 } , E _ { 2 } , E _ { 3 }$ be three mutually exclusive events such that $P \left( E _ { 1 } \right) = \frac { 2 + 3 p } { 6 } , P \left( E _ { 2 } \right) = \frac { 2 - p } { 8 }$ and $P \left( E _ { 3 } \right) = \frac { 1 - p } { 2 }$. If the maximum and minimum values of $p$ are $p _ { 1 }$ and $p _ { 2 }$ then $\left( p _ { 1 } + p _ { 2 } \right)$ is equal to:
(1) $\frac { 2 } { 3 }$
(2) $\frac { 5 } { 3 }$
(3) $\frac { 5 } { 4 }$
(4) 1

jee-main 2022 Q80 Probability Involving Algebraic or Number-Theoretic Conditions View

Let $S$ be the sample space of all five digit numbers. If $p$ is the probability that a randomly selected number from $S$, is a multiple of 7 but not divisible by 5 , then $9 p$ is equal to
(1) 1.0146
(2) 1.2085
(3) 1.0285
(4) 1.1521

jee-main 2022 Q90 Combinatorial Counting (Non-Probability) View

Let $S = \left\{ E _ { 1 } , E _ { 2 } \ldots E _ { 8 } \right\}$ be a sample space of a random experiment such that $P \left( E _ { n } \right) = \frac { n } { 36 }$ for every $n = 1,2 \ldots 8$. Then the number of elements in the set $\left\{ A \subset S : P ( A ) \geq \frac { 4 } { 5 } \right\}$ is $\_\_\_\_$.

jee-main 2023 Q63 Set Operations View

Let $A = \{1, 2, 3, 4, 5, 6, 7\}$. Then the relation $R = \{(x, y) \in A \times A : x + y = 7\}$ is
(1) symmetric but neither reflexive nor transitive
(2) an equivalence relation
(3) reflexive but neither symmetric nor transitive
(4) transitive but neither reflexive nor symmetric

jee-main 2023 Q89 Finite Equally-Likely Probability Computation View

Let $N$ be the sum of the numbers appeared when two fair dice are rolled and let the probability that $N - 2 , \sqrt { 3 N } , N + 2$ are in geometric progression be $\frac { k } { 48 }$. Then the value of $k$ is
(1) 2
(2) 4
(3) 16
(4) 8

jee-main 2023 Q89 Finite Equally-Likely Probability Computation View

Fifteen football players of a club-team are given 15 T-shirts with their names written on the backside. If the players pick up the T-shirts randomly, then the probability that at least 3 players pick the correct T-shirt is
(1) $\frac { 5 } { 24 }$
(2) $\frac { 2 } { 15 }$
(3) $\frac { 1 } { 6 }$
(4) $\frac { 5 } { 36 }$

jee-main 2023 Q90 Probability Involving Algebraic or Number-Theoretic Conditions View

Let M be the maximum value of the product of two positive integers when their sum is 66 . Let the sample space $S = \left\{ x \in Z : x ( 66 - x ) \geq \frac { 5 } { 9 } M \right\}$ and the event $\mathrm { A } = \{ \mathrm { x } \in \mathrm { S } : \mathrm { x }$ is a multiple of $3 \}$. Then $\mathrm { P } ( \mathrm { A } )$ is equal to
(1) $\frac { 15 } { 44 }$
(2) $\frac { 1 } { 3 }$
(3) $\frac { 1 } { 5 }$
(4) $\frac { 7 } { 22 }$

jee-main 2023 Q90 Probability Distribution and Sampling View

Let $S = \left\{ w _ { 1 } , w _ { 2 } , \ldots \right\}$ be the sample space associated to a random experiment. Let $P \left( w _ { n } \right) = \frac { P \left( w _ { n - 1 } \right) } { 2 } , n \geq 2$ . Let $A = \{ 2 k + 3 l ; k , l \in \mathbb { N } \}$ and $B = \left\{ w _ { n } ; n \in A \right\}$. Then $P ( B )$ is equal to (1) $\frac { 3 } { 32 }$ (2) $\frac { 3 } { 64 }$ (3) $\frac { 1 } { 16 }$ (4) $\frac { 1 } { 32 }$

jee-main 2024 Q68 Finite Equally-Likely Probability Computation View

Let $R$ be a relation on $Z \times Z$ defined by $( a , b ) R ( c , d )$ if and only if $a d - b c$ is divisible by 5 . Then R is
(1) Reflexive and symmetric but not transitive
(2) Reflexive but neither symmetric not transitive
(3) Reflexive, symmetric and transitive
(4) Reflexive and transitive but not symmetric

jee-main 2024 Q68 Finite Equally-Likely Probability Computation View

Let $A = \{ 2,3,6,8,9,11 \}$ and $B = \{ 1,4,5,10,15 \}$. Let $R$ be a relation on $A \times B$ defined by ( $a , b$ ) $R ( c , d )$ if and only if $3 a d - 7 b c$ is an even integer. Then the relation $R$ is (1) an equivalence relation. (2) reflexive and symmetric but not transitive. (3) transitive but not symmetric. (4) reflexive but not symmetric.

1
2
3
4
5
6
7
8
9

Load questions...

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