class 12

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JEE Advanced

STATEMENT - 1 : Molecules that are not superimposable on their mirror images are chiral. because STATEMENT - 2 : All chiral molecules have chiral centres.

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Let $O$be the origin, and $OXxOY,OZ$be three unit vectors in the direction of the sides $QR$, $RP$, $PQ$, respectively of a triangle PQR.If the triangle PQR varies, then the minimum value of $cos(P+Q)+cos(Q+R)+cos(R+P)$is:$−23 $ (b) $35 $ (c) $23 $ (d) $−35 $

Circle(s) touching x-axis at a distance 3 from the origin and having an intercept of length $27 $ on y-axis is (are)

For $a>b>c>0$, if the distance between $(1,1)$ and the point of intersection of the line $ax+by−c=0$ is less than $22 $ then,

Three randomly chosen nonnegative integers $x,yandz$are found to satisfy the equation $x+y+z=10.$Then the probability that $z$is even, is:$125 $ (b) $21 $ (c) $116 $ (d) $5536 $

A rectangular sheet of fixed perimeter with sides having their lengths in the ratio $8:15$is converted into anopen rectangular box by folding after removing squares of equal area from all four corners. If the total area of removed squares is 100, the resulting box has maximum volume. Then the length of the sides of the rectangular sheet are24 (b) 32 (c) 45 (d) 60

Let $F_{1}(x_{1},0)$ and $F_{2}(x_{2},0)$, for $x_{1}<0$ and $x_{2}>0$, be the foci of the ellipse $9x_{2} +8y_{2} =1$ Suppose a parabola having vertex at the origin and focus at $F_{2}$ intersects the ellipse at point M in the first quadrant and at point N in the fourth quadrant. If the tangents to the ellipse at M and N meet at R and the normal to the parabola at M meets the x-axis at Q, then the ratio of area of the triangle MQR to area of the quadrilateral $MF_{1}NF_{2}$ is

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

For each positive integer $n$, let $y_{n}=n1 ((n+1)(n+2)n+n˙ )_{n1}$For $x∈R$let $[x]$be the greatest integer less than or equal to $x$. If $(lim)_{n→∞}y_{n}=L$, then the value of $[L]$is ______.