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JEE Advanced

A Tin-chloride 'P' gives following reaction (unbalanced reaction) $P+Cl_{−}→X$ [Monoanion pyramidal geometry] $P+Me_{3}N→Y$ $P+CuCl_{2}→Z+CuCl$ Then which of the following is/are correct.

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If $2x−y+1=0$ is a tangent to the hyperbola $a_{2}x_{2} −16y_{2} =1$ then which of the following CANNOT be sides of a right angled triangle? (a)$a,4,2$ (b) $a,4,1$(c)$2a,4,1$ (d) $2a,8,1$

Which of the following values of $α$satisfying the equation $∣∣ (1+α)_{2}(1+2α)_{2}(1+3α)_{2}(2+α)_{2}(2+2α)_{2}(2+3α)_{2}(3+α)_{2}(3+2α)_{2}(3+3α)_{2}∣∣ =−648α?$$−4$b. $9$c. $−9$d. $4$

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

A circle S passes through the point (0, 1) and is orthogonal to the circles $(x−1)_{2}+y_{2}=16$ and $x_{2}+y_{2}=1$. Then (A) radius of S is 8 (B) radius of S is 7 (C) center of S is (-7,1) (D) center of S is (-8,1)

Let $n≥2$be integer. Take $n$distinct points on a circle and join each pair of points by a line segment. Color the line segment joining every pair of adjacent points by blue and the rest by red. If the number of red and blue line segments are equal, then the value of $n$is

Let $f:R→R$and $g:R→R$be two non-constant differentiable functions. If $f_{prime}(x)=(e_{(f(x)−g(x))})g_{prime}(x)$for all $x∈R$, and $f(1)=g(2)=1$, then which of the following statement(s) is (are) TRUE?$f(2)<1−(g)_{e}2$(b) $f(2)>1−(g)_{e}2$(c) $g(1)>1−(g)_{e}2$(d) $g(1)<1−(g)_{e}2$

In a triangle the sum of two sides is x and the product of the same is y. If $x_{2}−c_{2}=y$ where c is the third side. Determine the ration of the in-radius and circum-radius

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 $