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JEE Advanced

Hydrogen bonding plays a central role in the following phenomena:

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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

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

PARAGRAPH $X$Let $S$be the circle in the $xy$-plane defined by the equation $x_{2}+y_{2}=4.$(For Ques. No 15 and 16)Let $E_{1}E_{2}$and $F_{1}F_{2}$be the chords of $S$passing through the point $P_{0}(1,1)$and parallel to the x-axis and the y-axis, respectively. Let $G_{1}G_{2}$be the chord of $S$passing through $P_{0}$and having slope $−1$. Let the tangents to $S$at $E_{1}$and $E_{2}$meet at $E_{3}$, the tangents to $S$at $F_{1}$and $F_{2}$meet at $F_{3}$, and the tangents to $S$at $G_{1}$and $G_{2}$meet at $G_{3}$. Then, the points $E_{3},F_{3}$and $G_{3}$lie on the curve$x+y=4$(b) $(x−4)_{2}+(y−4)_{2}=16$(c) $(x−4)(y−4)=4$(d) $xy=4$

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, $9xy =$

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

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)

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

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