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JEE Advanced

A student performs a titration with different burettes and finds titre values of 25.2 mL, 25.25 mL, and 25.0 mL. the number of significant figures in the average titre value is

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A rectangular sheet of fixed perimeter with sides having their lengths in the ratio $8:15$is converted into anopen rectangular box by folding after removing squares of equal area from all four corners. If the total area of removed squares is 100, the resulting box has maximum volume. Then the length of the sides of the rectangular sheet are24 (b) 32 (c) 45 (d) 60

Let $O$be the origin, and $OX,OY,OZ$be three unit vectors in the direction of the sides $QR$, $RP$, $PQ$, respectively of a triangle PQR.$∣OX×OY∣=$$s∈(P+R)$ (b) $sin2R$$(c)sin(Q+R)$(d) $sin(P+Q)˙$

For $a>b>c>0$, if the distance between $(1,1)$ and the point of intersection of the line $ax+by−c=0$ is less than $22 $ then,

For a real number $α,$ if the system $⎣⎡ 1αα_{2} α1α α_{2}α1 ⎦⎤ ⎣⎡ xyz ⎦⎤ =⎣⎡ 1−11 ⎦⎤ $ of linear equations, has infinitely many solutions, then $1+α+α_{2}=$

Let $S={xϵ(−π,π):x=0,+2π }$The sum of all distinct solutions of the equation $3 secx+cosecx+2(tanx−cotx)=0$ in the set S is equal to

A debate club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this club including the selection of a captain (from among these 4 members) for the team. If the team has to include at most one boy, then the number of ways of selecting the team is

Let PQ be a focal chord of the parabola $y_{2}=4ax$ The tangents to the parabola at P and Q meet at a point lying on the line $y=2x+a,a>0$. Length of chord PQ is

For a non-zero complex number $z$, let $arg(z)$denote theprincipal argument with $π<arg(z)≤π$Then, whichof the following statement(s) is (are) FALSE?$arg(−1,−i)=4π ,$where $i=−1 $(b) The function $f:R→(−π,π],$defined by $f(t)=arg(−1+it)$for all $t∈R$, iscontinuous at all points of $R$, where $i=−1 $(c) For any two non-zero complex numbers $z_{1}$and $z_{2}$, $arg(z_{2}z_{1} )−arg(z_{1})+arg(z_{2})$is an integer multiple of $2π$(d) For any three given distinct complex numbers $z_{1}$, $z_{2}$and $z_{3}$, the locus of the point $z$satisfying the condition $arg((z−z_{3})(z_{2}−z_{1})(z−z_{1})(z_{2}−z_{3}) )=π$, lies on a straight line