class 12

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JEE Advanced

The total number(s) of stable conformers with non-zero dipole moment for the following compound is (are) .

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Let $b_{1}>1$ for $i=1,2,……,101.$ Suppose $g_{e}b_{1},g_{e}b_{10}$ are in Arithmetic progression $(A.P.)$ with the common difference $g_{e}2.$ suppose $a_{1},a_{2}……….a_{101}$ are in A.P. such $a_{1}=b_{1}anda_{51}=b_{51}.$ If $t=b_{1}+b_{2}+……+b_{51}ands=a_{1}+a_{2}+……+a_{51}$ then

A vertical line passing through the point $(h,0)$ intersects the ellipse $4x_{2} +3y_{2} =1$ at the points $P$ and $Q$.Let the tangents to the ellipse at P and Q meet at $R$. If $δ(h)$ Area of triangle $δPQR$, and $δ_{1}21 ≤h≤1max δ(h)$ A further $δ_{2}21 ≤h≤1min δ(h)$ Then $5 8 δ_{1}−8δ_{2}$

Let $P$be a matrix of order $3×3$such that all the entries in $P$are from the set ${−1,0,1}$. Then, the maximum possible value of the determinant of $P$is ______.

Let $f[0,1]→R$ (the set of all real numbers be a function.Suppose the function f is twice differentiable, $f(0)=f(1)=0$,and satisfies $f_{′}(x)–2f_{′}(x)+f(x)≤e_{x},x∈[0,1]$.Which of the following is true for $0<x<1?$

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) $sin(P+Q)˙$

Football teams T1 and T2 have to play two games against each other. It is assumed that theoutcomes of the two games are independent. The probabilities of T1 winning, drawing andlosing a game against T2 are1/ 2,and1/6,1/3respectively. Each team gets 3 points for a win,1 point for a draw and 0 point for a loss in a game. Let X and Y denote the total pointsscored by teams T1 and T2, respectively, after two gamesP $(X=Y)$ is

Box 1 contains three cards bearing numbers 1, 2, 3; box 2 contains five cards bearing numbers 1, 2, 3,4, 5; and box 3 contains seven cards bearing numbers 1, 2, 3, 4, 5, 6, 7. A card is drawn from each of the boxes. Let $x_{i}$ be the number on the card drawn from the ith box, i = 1, 2, 3.The probability that $x_{1}+x_{2}+x_{3}$ is odd isThe probability that $x_{1},x_{2},x_{3}$ are in an aritmetic progression is

Let $f(x)=∣1−x∣1−x(1+∣1−x∣) cos(1−x1 )$ for $x=1.$ Then: (A)$(lim)_{n→1_{−}}f(x)$ does not exist (B)$(lim)_{n→1_{+}}f(x)$ does not exist (C)$(lim)_{n→1_{−}}f(x)=0$ (D)$(lim)_{n→1_{+}}f(x)=0$