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JEE Advanced

$EDTA_{4−}$ is ethylenediaminetetraacetate ion. The total number of N-Co-O bond angles in $[Co(EDTA)]_{1−}$ complex ion is

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Let $f:R0,1 $ be a continuous function. Then, which of the following function (s) has (have) the value zero at some point in the interval (0,1)? $e_{x}−∫_{0}f(t)sintdt$ (b) $f(x)+∫_{0}f(t)sintdt$(c)$x−∫_{0}f(t)costdt$ (d) $x_{9}−f(x)$

Word of length 10 are formed using the letters A,B,C,D,E,F,G,H,I,J. Let $x$be the number of such words where no letter is repeated; and let $y$be the number of such words where exactly one letter is repeated twice and no other letter is repeated. The, $9xy =$

Consider two straight lines, each of which is tangent to both the circle $x_{2}+y_{2}=21 $and the parabola $y_{2}=4x$. Let these lines intersect at the point $Q$. Consider the ellipse whose center is at the origin $O(0,0)$and whose semi-major axis is $OQ$. If the length of the minor axis of this ellipse is $2 $, then which of the following statement(s) is (are) TRUE?For the ellipse, the eccentricity is $2 1 $and the length of the latus rectum is 1(b) For the ellipse, the eccentricity is $21 $and the length of the latus rectum is $21 $(c) The area of the region bounded by the ellipse between the lines $x=2 1 $and $x=1$is $42 1 (π−2)$(d) The area of the region bounded by the ellipse between the lines $x=2 1 $and $x=1$is $161 (π−2)$

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 $y(x)$ be a solution of the differential equation $(1+e_{x})y_{prime}+ye_{x}=1.$ If $y(0)=2$ , then which of the following statements is (are) true? (a)$y(−4)=0$ (b)$y(−2)=0$ (c)$y(x)$ has a critical point in the interval $(−1,0)$ (d)$y(x)$ has no critical point in the interval$(−1,0)$

Let $F(x)=∫_{x}[2cos_{2}t.dt]$ for all $x∈R$ and $f:[0,21 ]→[0,∞)$ be a continuous function.For $a∈[0,21 ]$, if F'(a)+2 is the area of the region bounded by x=0,y=0,y=f(x) and x=a, then f(0) is

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)

If $α=3sin_{−1}(116 )$and $β=3cos_{−1}(94 )$, where the inverse trigonometric functions take only the principal values, then the correct option(s) is (are)