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JEE Advanced

The $K_{sp}$ of $Ag_{2}CrO_{4}$ is $1.1×10_{−2}$ at 298 K. The solubility (in mol/L) of $Ag_{2}CrO_{4}$ in a 0.1 $MAgNO_{3}$ solution is

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Let x, y and z be three vectors each of magnitude V2 tion on and the angle between each pair of them is E. If a is a let non-zero vector perpendicular to x and yx z and b is a non-zero tor perpendicular to y and z x x, then 1.

Let $f:[0,∞)→R$be a continuous function such that $f(x)=1−2x+∫_{0}e_{x−t}f(t)dt$for all $x∈[0,∞)$. Then, which of the following statement(s) is (are) TRUE?The curve $y=f(x)$passes through the point $(1,2)$(b) The curve $y=f(x)$passes through the point $(2,−1)$(c) The area of the region ${(x,y)∈[0,1]×R:f(x)≤y≤1−x_{2} }$is $4π−2 $(d) The area of the region ${(x,y)∈[0,1]×R:f(x)≤y≤1−x_{2} }$is $4π−1 $

Let a,b ,c be positive integers such that $ab $ is an integer. If a,b,c are in GP and the arithmetic mean of a,b,c, is b+2 then the value of $a+1a_{2}+a−14 $ is

Suppose that $p ,q andr$ are three non-coplanar vectors in $R_{3}$. Let the components of a vector $s$ along $p ,q andr$ be 4, 3 and 5, respectively. If the components of this vector $s$ along $(−p +q +r),(p −q +r)and(−p −q +r)$ are x, y and z, respectively, then the value of $2x+y +z$ is

The quadratic equation $p(x)=0$ with real coefficients has purely imaginary roots. Then the equation $p(p(x))=0$ has A. only purely imaginary roots B. all real roots C. two real and purely imaginary roots D. neither real nor purely imaginary roots

Let n be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that all the girls stand consecutively in the queue. Let m be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that exactly four girls stand consecutively in the queue. Then the value of m/n is

Let P be the point on parabola $y_{2}=4x$ which is at the shortest distance from the center S of the circle $x_{2}+y_{2}−4x−16y+64=0$ let Q be the point on the circle dividing the line segment SP internally. Then

Let m be the smallest positive integer such that the coefficient of $x_{2}$ in the expansion of $(1+x)_{2}+(1+x)_{3}+(1+x)_{4}+……..+(1+x)_{49}+(1+mx)_{50}$ is $(3n+1)._{51}C_{3}$ for some positive integer n. Then the value of n is