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JEE Advanced

Hydrogen peroxide in its reaction with $KIO_{4}andNH_{2}OH$ respectively, is acting as a

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Let $P=⎣⎡ 1416 014 001 ⎦⎤ $and $I$ be the identity matrix of order $3$. If $Q=[q_{()}ij]$ is a matrix, such that $P_{50}−Q=I$, then $q_{21}q_{31}+q_{32} $ equals

The number of 5 digit numbers which are divisible by 4, with digits from the set ${1,2,3,4,5}$and the repetition of digits is allowed, is ________.

A cylindrica container is to be made from certain solid material with the following constraints: It has a fixed inner volume of $Vm_{3}$, has a 2 mm thick solid wall and is open at the top. The bottom of the container is a solid circular disc of thickness 2mm and is of radius equal to the outer radius of the container. If the volume the material used to make the container is minimum when the inner radius of the container is $10mm$. then the value of $250πV $ is

A manufacturer has three machine operators A, B and C. The first operator A produces 1% defective items, where as the other two operators B and C produce 5% and 7% defective items respectively. A is on the job for 50% of the tune, B is on the job for 30% of the time and C is on the job for 20% of the time. A defective item is produced, what is the probability that it was produced by A?

Let $f:[a,b]1,∞ $be a continuous function and let $g:RR$be defined as$g(x)={0ifxbThen$$g(x)$is continuous but not differentiable at a$g(x)$is differentiable on $R$$g(x)$is continuous but nut differentiable at $b$$g(x)$is continuous and differentiable at either $a$or $b$but not both.

Football teams T1 and T2 have to play two games against each other. It is assumed that theoutcomes of the two games are independent. The probabilities of T1 winning, drawing andlosing a game against T2 are1/ 2,and1/6,1/3respectively. Each team gets 3 points for a win,1 point for a draw and 0 point for a loss in a game. Let X and Y denote the total pointsscored by teams T1 and T2, respectively, after two gamesP $(X=Y)$ is

Let m and n be two positive integers greater than 1.If $α→0lim α_{m}e_{cosα_{n}}−e =−(2e )$ then the value of $nm $ is

The coefficients of three consecutive terms of $(1+x)_{n+5}$are in the ratio 5:10:14. Then $n=$___________.