Home
Class 12
MATHS
Statement-1 : The number of ways of dist...

Statement-1 : The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is `^9C_3` . Statement-2 : The number of ways of choosing any 3 places from 9 different places is `^9C_3` . Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1. Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1. Statement-1 is true, Statement-2 is false. Statement-1 is false, Statement-2 is true.

Text Solution

AI Generated Solution

To solve the question, we need to analyze both statements provided and determine their validity. ### Step-by-Step Solution: **Step 1: Analyze Statement 1** We need to find the number of ways to distribute 10 identical balls into 4 distinct boxes such that no box is empty. ...
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    JEE MAINS PREVIOUS YEAR|Exercise All Questions|9 Videos
  • PROBABILITY

    JEE MAINS PREVIOUS YEAR|Exercise All Questions|16 Videos

Similar Questions

Explore conceptually related problems

Statement-1: The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is ""^(9)C_(3) . Statement-2: The number of ways of choosing any 3 places from 9 different places is ""^(9)C_(3) .

Let A be a 2""xx""2 matrix Statement 1 : a d j""(a d j""A)""=""A Statement 2 : |a d j""A|""=""|A| (1) Statement1 is true, Statement2 is true, Statement2 is a correct explanation for statement1 (2) Statement1 is true, Statement2 is true; Statement2 is not a correct explanation for statement1. (3) Statement1 is true, statement2 is false. (4) Statement1 is false, Statement2 is true

Statement-1: intsin^-1xdx+intsin^-1sqrt(1-x^2)dx=pi/2x+c Statement-2: sin^-1x+cos^-1x=pi/2 (A) Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1. (C) Statement-1 is True, Statement-2 is False. (D) Statement-1 is False, Statement-2 is True.

Statement-1: The function F(x)=intsin^2xdx satisfies F(x+pi)=F(x),AAxinR ,Statement-2: sin^2(x+pi)=sin^2x (A) Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1. (C) Statement-1 is True, Statement-2 is False. (D) Statement-1 is False, Statement-2 is True.

Statement -1 (1/2)^7lt(1/3)^4 implies 7log(1/2)lt4log(1/3)implies7lt4 Statement-2 If axltay , where alt0 ,x, ygt0 , then xgty . (a) Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation for Statement-1 Statement-1 is true, Statement-2 is true, Statement-2 is not a correct explanation for Statement -1 (c) Statement -1 is true, Statement -2 is false (d) Statement -1 is false, Statement -2 is true.

If A is 2 x 2 invertible matrix such that A=adjA-A^-1 Statement-I 2A^2+I=O(null matrix) Statement-II: 2|A|=1 (i) Statement-I is true, Statement-II is true; Statement-II is a correct explanation for Statement-I (2) Statement-I is true, Statement-II is true; Statement-II is not a correct explanation for Statement-I. 3) Statement-I is true, Statement-II is false. (4) Statement-I is false, Statement-II is true.

Let f(x)={x^n sin (1/x) , x!=0; 0, x=0; and n>0 Statement-1: f(x) is continuous at x=0 and AA n>0. and Statement-2: f(x) is differentiable at x=0 AA n>0 (1) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (2) Statement-1 is True, Statement-2 is True Statement-2 is NOT a correct explanation for Statement-1. (3) Statement-1 is True, Statement-2 is False (4) Statement-1 is False, Statement-2 is True.

Statement-1: int(sinx)^x(xcotx+logsinx)dx=x(sinx)^x Statement-2: d/dx(f(x))^(g(x))=(f(x))^(g(x))d/dx[g(x)logf(x)] (A) Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1. (C) Statement-1 is True, Statement-2 is False. (D) Statement-1 is False, Statement-2 is True.

Let A and B be two symmetric matrices of order 3. Statement-1 : A(BA) and (AB)A are symmetric matrices. Statement-2 : AB is symmetric matrix if matrix multiplication of A with B is commutative. Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1. Statement-1 is true, Statement-2 is true; Statement-2 is true; Statement-2 is not a correct explanation for Statement-1. Statement-1 is true, Statement-2 is false. Statement-1 is false, Statement-2 is true.